Coarse graining Escherichia coli chemotaxis: from multi-flagella propulsion to logarithmic sensing.

PubMed

Curk, Tine; Matthäus, Franziska; Brill-Karniely, Yifat; Dobnikar, Jure

2012-01-01

Various sensing mechanisms in nature can be described by the Weber-Fechner law stating that the response to varying stimuli is proportional to their relative rather than absolute changes. The chemotaxis of bacteria Escherichia coli is an example where such logarithmic sensing enables sensitivity over large range of concentrations. It has recently been experimentally demonstrated that under certain conditions E. coli indeed respond to relative gradients of ligands. We use numerical simulations of bacteria in food gradients to investigate the limits of validity of the logarithmic behavior. We model the chemotactic signaling pathway reactions, couple them to a multi-flagella model for propelling and take the effects of rotational diffusion into account to accurately reproduce the experimental observations of single cell swimming. Using this simulation scheme we analyze the type of response of bacteria subject to exponential ligand profiles and identify the regimes of absolute gradient sensing, relative gradient sensing, and a rotational diffusion dominated regime. We explore dependance of the swimming speed, average run time and the clockwise (CW) bias on ligand variation and derive a small set of relations that define a coarse grained model for bacterial chemotaxis. Simulations based on this coarse grained model compare well with microfluidic experiments on E. coli diffusion in linear and exponential gradients of aspartate.

Chemotaxis in Microfluidic Devices

NASA Astrophysics Data System (ADS)

Wyatt, Danica; Nadkarni, Sharvari; Song, Loling; Voeltz, Camilla; Bodenschatz, Eberhard

2004-03-01

Dictyostelium amoebae use chemical signaling to begin starvation-induced aggregation. Cells generate a complex and dynamic pattern of cyclic AMP that drives their migration toward a central point. While this phenomenon is unique to social amoebae, the signaling pathways of chemotaxis are similar in all eukaryotic cells. Dicty serves as a model organism for imaging these intracellular protein dynamics. To date, chemotaxis has been primarily studied in diffusion-generated gradients in chambers many orders of magnitude larger than a cell. To better quantify which aspects of a gradient trigger a response, we have designed a microfluidic channel that confines cells in an environment where spatiotemporal cAMP concentration can be precisely manipulated. We report results on an early event in the signaling cascade, the translocation of PH domain-containing proteins, which test current models of chemotaxis. This work was supported by the NSF Biocomplexity program and the Nanobiotechnology Center, an STC Program of the NSF under Agreement No. ECS-9876771.

Role of chemotaxis in the ecology of denitrifiers

NASA Technical Reports Server (NTRS)

Kennedy, M. J.; Lawless, J. G.

1985-01-01

It has been recognized that the process of denitrification represents a major sequence in the nitrogen cycle. It involves the anaerobic reduction of nitrate or nitrite to nitrous oxide or elemental nitrogen. This process is responsible for significant losses of nitrogen from agricultural soils. Up to now, little attention has been paid to the ecology of the organisms responsible for denitrification. It is pointed out that chemotaxis would probably offer a strong competitive mechanism for denitrifiers, since chemotaxis would allow denitrifiers to actively reach nitrate by directed motility, rather than by random movement or diffusion of nitrate. The present investigation was initiated to examine the chemotactic responses of several denitrifiers to nitrate and nitrite. Attention is given to bacterial strains, culture media and cell preparation, chemotaxis assays, and competition experiments. It was found that several denitrifiers, including P. aeruginosa, P. fluorescens, and P. Stutzeri, were strongly attracted to NO3(-) and NO2(-).

Epstein-Barr virus (EBV) provides survival factors to EBV+ diffuse large B-cell lymphoma (DLBCL) lines and modulates cytokine induced specific chemotaxis in EBV+  DLBCL.

PubMed

Wu, Liang; Ehlin-Henriksson, Barbro; Zhou, Xiaoying; Zhu, Hong; Ernberg, Ingemar; Kis, Lorand L; Klein, George

2017-12-01

Diffuse large B-cell lymphoma (DLBCL), the most common type of malignant lymphoma, accounts for 30% of adult non-Hodgkin lymphomas. Epstein-Barr virus (EBV) -positive DLBCL of the elderly is a newly recognized subtype that accounts for 8-10% of DLBCLs in Asian countries, but is less common in Western populations. Five DLBCL-derived cell lines were employed to characterize patterns of EBV latent gene expression, as well as response to cytokines and chemotaxis. Interleukin-4 and interleukin-21 modified LMP1, EBNA1 and EBNA2 expression depending on cell phenotype and type of EBV latent programme (type I, II or III). These cytokines also affected CXCR4- or CCR7-mediated chemotaxis in two of the cell lines, Farage (type III) and Val (type II). Further, we investigated the effect of EBV by using dominant-negative EBV nuclear antigen 1(dnEBNA1) to eliminate EBV genomes. This resulted in decreased chemotaxis. By employing an alternative way to eliminate EBV genomes, Roscovitine, we show an increase of apoptosis in the EBV-positive lines. These results show that EBV plays an important role in EBV-positive DLBCL lines with regard to survival and chemotactic response. Our findings provide evidence for the impact of microenvironment on EBV-carrying DLBCL cells and might have therapeutic implications. © 2017 John Wiley & Sons Ltd.

Quantifying the correlation between spatially defined oxygen gradients and cell fate in an engineered three-dimensional culture model.

PubMed

Ardakani, Amir G; Cheema, Umber; Brown, Robert A; Shipley, Rebecca J

2014-09-06

A challenge in three-dimensional tissue culture remains the lack of quantitative information linking nutrient delivery and cellular distribution. Both in vivo and in vitro, oxygen is delivered by diffusion from its source (blood vessel or the construct margins). The oxygen level at a defined distance from its source depends critically on the balance of diffusion and cellular metabolism. Cells may respond to this oxygen environment through proliferation, death and chemotaxis, resulting in spatially resolved gradients in cellular density. This study extracts novel spatially resolved and simultaneous data on tissue oxygenation, cellular proliferation, viability and chemotaxis in three-dimensional spiralled, cellular collagen constructs. Oxygen concentration gradients drove preferential cellular proliferation rates and viability in the higher oxygen zones and induced chemotaxis along the spiral of the collagen construct; an oxygen gradient of 1.03 mmHg mm(-1) in the spiral direction induced a mean migratory speed of 1015 μm day(-1). Although this movement was modest, it was effective in balancing the system to a stable cell density distribution, and provided insights into the natural cell mechanism for adapting cell number and activity to a prevailing oxygen regime.

A fixed-time diffusion analysis method determines that the three cheV genes of Helicobacter pylori differentially affect motility

PubMed Central

Lowenthal, Andrew C.; Simon, Christopher; Fair, Amber S.; Mehmood, Khalid; Terry, Karianne; Anastasia, Stephanie; Ottemann, Karen M.

2009-01-01

Helicobacter pylori is a chemotactic bacterium that has three CheV proteins in its predicted chemotaxis signal transduction system. CheV proteins contain both CheW- and response-regulator-like domains. To determine the function of these proteins, we developed a fixed-time diffusion method that would quantify bacterial direction change without needing to define particular behaviours, to deal with the many behaviours that swimming H. pylori exhibit. We then analysed mutants that had each cheV gene deleted individually and found that the behaviour of each mutant differed substantially from wild-type and the other mutants. cheV1 and cheV2 mutants displayed smooth swimming behaviour, consistent with decreased cellular CheY-P, similar to a cheW mutant. In contrast, the cheV3 mutation had the opposite effect and the mutant cells appeared to change direction frequently. Additional analysis showed that the cheV mutants displayed aberrant behaviour as compared to the wild-type in the soft-agar chemotaxis assay. The soft-agar assay phenotype was less extreme compared to that seen in the fixed-time diffusion model, suggesting that the cheV mutants are able to partially compensate for their defects under some conditions. Each cheV mutant furthermore had defects in mouse colonization that ranged from severe to modest, consistent with a role in chemotaxis. These studies thus show that the H. pylori CheV proteins each differently affect swimming behaviour. PMID:19332820

Influence of cell shape, inhomogeneities and diffusion barriers in cell polarization models

NASA Astrophysics Data System (ADS)

Giese, Wolfgang; Eigel, Martin; Westerheide, Sebastian; Engwer, Christian; Klipp, Edda

2015-12-01

In silico experiments bear the potential for further understanding of biological transport processes by allowing a systematic modification of any spatial property and providing immediate simulation results. Cell polarization and spatial reorganization of membrane proteins are fundamental for cell division, chemotaxis and morphogenesis. We chose the yeast Saccharomyces cerevisiae as an exemplary model system which entails the shuttling of small Rho GTPases such as Cdc42 and Rho, between an active membrane-bound form and an inactive cytosolic form. We used partial differential equations to describe the membrane-cytosol shuttling of proteins. In this study, a consistent extension of a class of 1D reaction-diffusion systems into higher space dimensions is suggested. The membrane is modeled as a thin layer to allow for lateral diffusion and the cytosol is modeled as an enclosed volume. Two well-known polarization mechanisms were considered. One shows the classical Turing-instability patterns, the other exhibits wave-pinning dynamics. For both models, we investigated how cell shape and diffusion barriers like septin structures or bud scars influence the formation of signaling molecule clusters and subsequent polarization. An extensive set of in silico experiments with different modeling hypotheses illustrated the dependence of cell polarization models on local membrane curvature, cell size and inhomogeneities on the membrane and in the cytosol. In particular, the results of our computer simulations suggested that for both mechanisms, local diffusion barriers on the membrane facilitate Rho GTPase aggregation, while diffusion barriers in the cytosol and cell protrusions limit spontaneous molecule aggregations of active Rho GTPase locally.

A Diffusion Approximation Based on Renewal Processes with Applications to Strongly Biased Run-Tumble Motion.

PubMed

Thygesen, Uffe Høgsbro

2016-03-01

We consider organisms which use a renewal strategy such as run-tumble when moving in space, for example to perform chemotaxis in chemical gradients. We derive a diffusion approximation for the motion, applying a central limit theorem due to Anscombe for renewal-reward processes; this theorem has not previously been applied in this context. Our results extend previous work, which has established the mean drift but not the diffusivity. For a classical model of tumble rates applied to chemotaxis, we find that the resulting chemotactic drift saturates to the swimming velocity of the organism when the chemical gradients grow increasingly steep. The dispersal becomes anisotropic in steep gradients, with larger dispersal across the gradient than along the gradient. In contrast to one-dimensional settings, strong bias increases dispersal. We next include Brownian rotation in the model and find that, in limit of high chemotactic sensitivity, the chemotactic drift is 64% of the swimming velocity, independent of the magnitude of the Brownian rotation. We finally derive characteristic timescales of the motion that can be used to assess whether the diffusion limit is justified in a given situation. The proposed technique for obtaining diffusion approximations is conceptually and computationally simple, and applicable also when statistics of the motion is obtained empirically or through Monte Carlo simulation of the motion.

Stabilization in a two-species chemotaxis system with a logistic source

NASA Astrophysics Data System (ADS)

Tello, J. I.; Winkler, M.

2012-05-01

We study a system of three partial differential equations modelling the spatio-temporal behaviour of two competitive populations of biological species both of which are attracted chemotactically by the same signal substance. More precisely, we consider the initial-boundary value problem for \\[ \\begin{equation*} \\fl\\left\\{ \\begin{array}{@{}l} u_t= d_1\\Delta u - \\chi_1 \

Chemotaxis of active, self-oscillating polymer gels in solution

NASA Astrophysics Data System (ADS)

Dayal, Pratyush; Bhattacharya, Amitabh; Kuksenok, Olga; Balazs, Anna C.

2012-02-01

Fighting, fleeing and feeding are hallmarks of all living things; all these activities require some degree of mobility. Herein, we undertake the first computational study of self-oscillating polymer gels and show that this system can ``communicate'' to undergo a biomimetic, collective response to small-scale chemical changes. In this study we harness unique properties of polymer gels that undergo oscillatory Belousov-Zhabotinsky (BZ) reaction. The activator for the reaction is generated within these BZ cilia and diffuses between the neighboring gels. In order to simulate the dynamics of the BZ gels in surrounding fluid we have developed a nonlinear hybrid 3D model which captures the elasto-dynamics of polymer gel and diffusive exchange of BZ reagents between the gel and the fluid. We illustrate that multiple BZ gels in solution exhibit a distinct form of chemotaxis, moving towards the highest activator concentration in the solution. Similar ability to sense and move in response to chemical gradients constitutes a vital function in simple organisms, enabling them to find food and flee from poisons.

Guanylyl cyclase-dependent chemotaxis of endothelial cells in response to nitric oxide gradients.

PubMed

Isenberg, Jeff S; Ridnour, Lisa A; Thomas, Douglas D; Wink, David A; Roberts, David D; Espey, Michael Graham

2006-03-15

Nitric oxide (NO) is an important regulator of angiogenesis and neovascularization. The nature of endothelial cell motility responses to NO was examined using a Boyden chamber method. NO generated via decomposition of either DEA/NO or DETA/NO produced increases in human umbilical vein endothelial cell (HUVEC) chemotaxis, which were completely abrogated by ODQ, a soluble guanylyl cyclase inhibitor. Measurements of NO either directly by chemiluminescence or its chemistry with diaminofluorescein revealed that chemotaxis was driven by subtle NO gradients between the lower and the upper wells in this system. In addition to diffusion and volatilization from the upper chambers, the data showed that HUVEC consumption of NO contributed to these sustained gradients. Comparison of DEA/NO- and DETA/NO-mediated responses suggested that the persistence of spatial NO gradients is as significant as the absolute magnitude of NO exposure per unit time. The findings suggest that subnanomolar NO gradients are sufficient to mobilize endothelial cell migration into hypoxic tissue during neovascularization events, such as in wound healing and cancer.

Highly Permeable Silicon Membranes for Shear Free Chemotaxis and Rapid Cell Labeling

PubMed Central

Chung, Henry H.; Chan, Charles K.; Khire, Tejas S.; Marsh, Graham A.; Clark, Alfred; Waugh, Richard E.; McGrath, James L.

2015-01-01

Microfluidic systems are powerful tools for cell biology studies because they enable the precise addition and removal of solutes in small volumes. However, the fluid forces inherent in the use of microfluidics for cell cultures are sometimes undesirable. An important example is chemotaxis systems where fluid flow creates well-defined and steady chemotactic gradients but also pushes cells downstream. Here we demonstrate a chemotaxis system in which two chambers are separated by a molecularly thin (15 nm), transparent, and nanoporous silicon membrane. One chamber is a microfluidic channel that carries a flow-generated gradient while the other chamber is a shear-free environment for cell observation. The molecularly thin membranes provide effectively no resistance to molecular diffusion between the two chambers, making them ideal elements for creating flow-free chambers in microfluidic systems. Analytical and computational flow models that account for membrane and chamber geometry, predict shear reduction of more than five orders of magnitude. This prediction is confirmed by observing the pure diffusion of nanoparticles in the cell-hosting chamber despite high input flow (Q = 10 µL min−1; vavg ~45 mm min−1) in the flow chamber only 15 nm away. Using total internal reflection fluorescence (TIRF) microscopy, we show that a flow-generated molecular gradient will pass through the membrane into the quiescent cell chamber. Finally we demonstrate that our device allows us to expose migrating neutrophils to a chemotactic gradient or fluorescent label without any influence from flow. PMID:24850320

Role of chemotaxis in the transport of bacteria through saturated porous media

USGS Publications Warehouse

Ford, R.M.; Harvey, R.W.

2007-01-01

Populations of chemotactic bacteria are able to sense and respond to chemical gradients in their surroundings and direct their migration toward increasing concentrations of chemicals that they perceive to be beneficial to their survival. It has been suggested that this phenomenon may facilitate bioremediation processes by bringing bacteria into closer proximity to the chemical contaminants that they degrade. To determine the significance of chemotaxis in these processes it is necessary to quantify the magnitude of the response and compare it to other groundwater processes that affect the fate and transport of bacteria. We present a systematic approach toward quantifying the chemotactic response of bacteria in laboratory scale experiments by starting with simple, well-defined systems and gradually increasing their complexity. Swimming properties of individual cells were assessed from trajectories recorded by a tracking microscope. These properties were used to calculate motility and chemotaxis coefficients of bacterial populations in bulk aqueous media which were compared to experimental results of diffusion studies. Then effective values of motility and chemotaxis coefficients in single pores, pore networks and packed columns were analyzed. These were used to estimate the magnitude of the chemotactic response in porous media and to compare with dispersion coefficients reported in the field. This represents a compilation of many studies over a number of years. While there are certainly limitations with this approach for ultimately quantifying motility and chemotaxis in granular aquifer media, it does provide insight into what order of magnitude responses are possible and which characteristics of the bacteria and media are expected to be important. ?? 2006 Elsevier Ltd. All rights reserved.

Dimensionless Analysis Applied to Bacterial Chemotaxis towards NAPL Contaminants

NASA Astrophysics Data System (ADS)

Wang, X.; GAO, B.; Zhong, W.; Kihaule, K. S.; Ford, R.

2017-12-01

The use of chemotactic bacteria in bioremediation may improve the efficiency and decrease the cost of restoration, which means it has the potential to address environmental problems caused by oil spills. However, most previous studies were focused at the laboratory-scale and there lacks a formalism that can use these laboratory-scale results as input to evaluate the relative importance of chemotaxis at the field scale. In this study, a dimensionless equation is formulated to solve this problem. First, the main influential factors were extracted based on previous researches in environmental bioremediation and then five sets of dimensionless numbers were obtained according to Buckingham theory. After collecting basic parameter values and supplementary calculations to determine the concentration gradient of the chemoattractant, all dimensionless numbers were calculated and categorized into two types, those that were sensitive to chemotaxis or those to groundwater velocity. The bacteria ratio (BR), defined as the ratio of maximum bacteria concentration to its original value, was correlated with a combination of dimensionless numbers to yield, BR=cP1-0.085P20.329P30.1P4-0.098. For a bacterial ratio greater than one, the bioremediation strategy based on chemotaxis is expected to be effective, and chemotactic bacteria are expected to accumulate around NAPL contaminant sources efficiently.

Feeding ducks, bacterial chemotaxis, and the Gini index

NASA Astrophysics Data System (ADS)

Peaudecerf, François J.; Goldstein, Raymond E.

2015-08-01

Classic experiments on the distribution of ducks around separated food sources found consistency with the "ideal free" distribution in which the local population is proportional to the local supply rate. Motivated by this experiment and others, we examine the analogous problem in the microbial world: the distribution of chemotactic bacteria around multiple nearby food sources. In contrast to the optimization of uptake rate that may hold at the level of a single cell in a spatially varying nutrient field, nutrient consumption by a population of chemotactic cells will modify the nutrient field, and the uptake rate will generally vary throughout the population. Through a simple model we study the distribution of resource uptake in the presence of chemotaxis, consumption, and diffusion of both bacteria and nutrients. Borrowing from the field of theoretical economics, we explore how the Gini index can be used as a means to quantify the inequalities of uptake. The redistributive effect of chemotaxis can lead to a phenomenon we term "chemotactic levelling," and the influence of these results on population fitness are briefly considered.

A computational model for how cells choose temporal or spatial sensing during chemotaxis.

PubMed

Tan, Rui Zhen; Chiam, Keng-Hwee

2018-03-01

Cell size is thought to play an important role in choosing between temporal and spatial sensing in chemotaxis. Large cells are thought to use spatial sensing due to large chemical difference at its ends whereas small cells are incapable of spatial sensing due to rapid homogenization of proteins within the cell. However, small cells have been found to polarize and large cells like sperm cells undergo temporal sensing. Thus, it remains an open question what exactly governs spatial versus temporal sensing. Here, we identify the factors that determines sensing choices through mathematical modeling of chemotactic circuits. Comprehensive computational search of three-node signaling circuits has identified the negative integral feedback (NFB) and incoherent feedforward (IFF) circuits as capable of adaptation, an important property for chemotaxis. Cells are modeled as one-dimensional circular system consisting of diffusible activator, inactivator and output proteins, traveling across a chemical gradient. From our simulations, we find that sensing outcomes are similar for NFB or IFF circuits. Rather than cell size, the relevant parameters are the 1) ratio of cell speed to the product of cell diameter and rate of signaling, 2) diffusivity of the output protein and 3) ratio of the diffusivities of the activator to inactivator protein. Spatial sensing is favored when all three parameters are low. This corresponds to a cell moving slower than the time it takes for signaling to propagate across the cell diameter, has an output protein that is polarizable and has a local-excitation global-inhibition system to amplify the chemical gradient. Temporal sensing is favored otherwise. We also find that temporal sensing is more robust to noise. By performing extensive literature search, we find that our prediction agrees with observation in a wide range of species and cell types ranging from E. coli to human Fibroblast cells and propose that our result is universally applicable.

A computational model for how cells choose temporal or spatial sensing during chemotaxis

PubMed Central

Tan, Rui Zhen; Chiam, Keng-Hwee

2018-01-01

Cell size is thought to play an important role in choosing between temporal and spatial sensing in chemotaxis. Large cells are thought to use spatial sensing due to large chemical difference at its ends whereas small cells are incapable of spatial sensing due to rapid homogenization of proteins within the cell. However, small cells have been found to polarize and large cells like sperm cells undergo temporal sensing. Thus, it remains an open question what exactly governs spatial versus temporal sensing. Here, we identify the factors that determines sensing choices through mathematical modeling of chemotactic circuits. Comprehensive computational search of three-node signaling circuits has identified the negative integral feedback (NFB) and incoherent feedforward (IFF) circuits as capable of adaptation, an important property for chemotaxis. Cells are modeled as one-dimensional circular system consisting of diffusible activator, inactivator and output proteins, traveling across a chemical gradient. From our simulations, we find that sensing outcomes are similar for NFB or IFF circuits. Rather than cell size, the relevant parameters are the 1) ratio of cell speed to the product of cell diameter and rate of signaling, 2) diffusivity of the output protein and 3) ratio of the diffusivities of the activator to inactivator protein. Spatial sensing is favored when all three parameters are low. This corresponds to a cell moving slower than the time it takes for signaling to propagate across the cell diameter, has an output protein that is polarizable and has a local-excitation global-inhibition system to amplify the chemical gradient. Temporal sensing is favored otherwise. We also find that temporal sensing is more robust to noise. By performing extensive literature search, we find that our prediction agrees with observation in a wide range of species and cell types ranging from E. coli to human Fibroblast cells and propose that our result is universally applicable. PMID:29505572

A new necessary condition for Turing instabilities.

PubMed

Elragig, Aiman; Townley, Stuart

2012-09-01

Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition. Specifically, we show that if the linearised reaction matrix and the diffusion matrix share a common Lyapunov function, then Turing instability is not possible. The existence of common Lyapunov functions is readily checked using semi-definite programming. We apply this result to the Gierer-Meinhardt system modelling regenerative properties of Hydra, the Oregonator, to a host-parasite-hyperparasite system with diffusion and to a reaction-diffusion-chemotaxis model for a multi-species host-parasitoid community. Copyright © 2012 Elsevier Inc. All rights reserved.

A predictive computational model of the kinetic mechanism of stimulus-induced transducer methylation and feedback regulation through CheY in archaeal phototaxis and chemotaxis.

PubMed

Streif, Stefan; Oesterhelt, Dieter; Marwan, Wolfgang

2010-03-18

Photo- and chemotaxis of the archaeon Halobacterium salinarum is based on the control of flagellar motor switching through stimulus-specific methyl-accepting transducer proteins that relay the sensory input signal to a two-component system. Certain members of the transducer family function as receptor proteins by directly sensing specific chemical or physical stimuli. Others interact with specific receptor proteins like the phototaxis photoreceptors sensory rhodopsin I and II, or require specific binding proteins as for example some chemotaxis transducers. Receptor activation by light or a change in receptor occupancy by chemical stimuli results in reversible methylation of glutamate residues of the transducer proteins. Both, methylation and demethylation reactions are involved in sensory adaptation and are modulated by the response regulator CheY. By mathematical modeling we infer the kinetic mechanisms of stimulus-induced transducer methylation and adaptation. The model (deterministic and in the form of ordinary differential equations) correctly predicts experimentally observed transducer demethylation (as detected by released methanol) in response to attractant and repellent stimuli of wildtype cells, a cheY deletion mutant, and a mutant in which the stimulated transducer species is methylation-deficient. We provide a kinetic model for signal processing in photo- and chemotaxis in the archaeon H. salinarum suggesting an essential role of receptor cooperativity, antagonistic reversible methylation, and a CheY-dependent feedback on transducer demethylation.

Lateral diffusion of proteins in the periplasm of Escherichia coli.

PubMed Central

Brass, J M; Higgins, C F; Foley, M; Rugman, P A; Birmingham, J; Garland, P B

1986-01-01

We have introduced biologically active, fluorescently labeled maltose-binding protein into the periplasmic space of Escherichia coli and measured its lateral diffusion coefficient by the fluorescence photobleaching recovery method. Diffusion of this protein in the periplasm was found to be surprisingly low (lateral diffusion coefficient, 0.9 X 10(-10) cm2 s-1), about 1,000-fold lower than would be expected for diffusion in aqueous medium and almost 100-fold lower than for an equivalent-size protein in the cytoplasm. Galactose-binding protein, myoglobin, and cytochrome c were also introduced into the periplasm and had diffusion coefficients identical to that determined for the maltose-binding protein. For all proteins nearly 100% recovery of fluorescence was obtained after photobleaching, indicating that the periplasm is a single contiguous compartment surrounding the cell. These data have considerable implications for periplasmic structure and for the role of periplasmic proteins in transport and chemotaxis. Images PMID:3005237

Generation and precise control of dynamic biochemical gradients for cellular assays

NASA Astrophysics Data System (ADS)

Saka, Yasushi; MacPherson, Murray; Giuraniuc, Claudiu V.

2017-03-01

Spatial gradients of diffusible signalling molecules play crucial roles in controlling diverse cellular behaviour such as cell differentiation, tissue patterning and chemotaxis. In this paper, we report the design and testing of a microfluidic device for diffusion-based gradient generation for cellular assays. A unique channel design of the device eliminates cross-flow between the source and sink channels, thereby stabilizing gradients by passive diffusion. The platform also enables quick and flexible control of chemical concentration that makes highly dynamic gradients in diffusion chambers. A model with the first approximation of diffusion and surface adsorption of molecules recapitulates the experimentally observed gradients. Budding yeast cells cultured in a gradient of a chemical inducer expressed a reporter fluorescence protein in a concentration-dependent manner. This microfluidic platform serves as a versatile prototype applicable to a broad range of biomedical investigations.

Modelling cell motility and chemotaxis with evolving surface finite elements

PubMed Central

Elliott, Charles M.; Stinner, Björn; Venkataraman, Chandrasekhar

2012-01-01

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction–diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/∼maskae/CV_Warwick/Chemotaxis.html. PMID:22675164

Directed transport of bacteria-based drug delivery vehicles: bacterial chemotaxis dominates particle shape.

PubMed

Sahari, Ali; Traore, Mahama A; Scharf, Birgit E; Behkam, Bahareh

2014-10-01

Several attenuated and non-pathogenic bacterial species have been demonstrated to actively target diseased sites and successfully deliver plasmid DNA, proteins and other therapeutic agents into mammalian cells. These disease-targeting bacteria can be employed for targeted delivery of therapeutic and imaging cargos in the form of a bio-hybrid system. The bio-hybrid drug delivery system constructed here is comprised of motile Escherichia coli MG1655 bacteria and elliptical disk-shaped polymeric microparticles. The transport direction for these vehicles can be controlled through biased random walk of the attached bacteria in presence of chemoattractant gradients in a process known as chemotaxis. In this work, we utilize a diffusion-based microfluidic platform to establish steady linear concentration gradients of a chemoattractant and investigate the roles of chemotaxis and geometry in transport of bio-hybrid drug delivery vehicles. Our experimental results demonstrate for the first time that bacterial chemotactic response dominates the effect of body shape in extravascular transport; thus, the non-spherical system could be more favorable for drug delivery applications owing to the known benefits of using non-spherical particles for vascular transport (e.g. relatively long circulation time).

Chemotactic droplet swimmers in complex geometries

NASA Astrophysics Data System (ADS)

Jin, Chenyu; Hokmabad, Babak V.; Baldwin, Kyle A.; Maass, Corinna C.

2018-02-01

Chemotaxis1 and auto-chemotaxis are key mechanisms in the dynamics of micro-organisms, e.g. in the acquisition of nutrients and in the communication between individuals, influencing the collective behaviour. However, chemical signalling and the natural environment of biological swimmers are generally complex, making them hard to access analytically. We present a well-controlled, tunable artificial model to study chemotaxis and autochemotaxis in complex geometries, using microfluidic assays of self-propelling oil droplets in an aqueous surfactant solution (Herminghaus et al 2014 Soft Matter 10 7008-22 Krüger et al 2016 Phys. Rev. Lett. 117). Droplets propel via interfacial Marangoni stresses powered by micellar solubilisation. Moreover, filled micelles act as a chemical repellent by diffusive phoretic gradient forces. We have studied these chemotactic effects in a series of microfluidic geometries, as published in Jin et al (2017 Proc. Natl Acad. Sci. 114 5089-94): first, droplets are guided along the shortest path through a maze by surfactant diffusing into the maze from the exit. Second, we let auto-chemotactic droplet swimmers pass through bifurcating microfluidic channels and record anticorrelations between the branch choices of consecutive droplets. We present an analytical Langevin model matching the experimental data. In a previously unpublished experiment, pillar arrays of variable sizes and shapes provide a convex wall interacting with the swimmer and, in the case of attachment, bending its trajectory and forcing it to revert to its own trail. We observe different behaviours based on the interplay of wall curvature and negative autochemotaxis, i.e. no attachment for highly curved interfaces, stable trapping at large pillars, and a narrow transition region where negative autochemotaxis makes the swimmers detach after a single orbit.

Nutrient chemotaxis suppression of a diffusive instability in bacterial colony dynamics

NASA Astrophysics Data System (ADS)

Arouh, Scott; Levine, Herbert

2000-07-01

Bacteria grown on a semisolid agar surface have been observed to form branching patterns as the colony envelope propagates outward. The fundamental cause of this instability relates to the need for limited nutrient to diffuse towards the colony. Here, we investigate the effect on this instability of allowing the bacteria to move chemotactically in response to the nutrient gradient. Our results show that this additional effect has a tendency to suppress the instability. Our calculations are done within the context of a simple ``cutoff'' model of colony dynamics, but presumably remain valid for more complex and hence more realistic approaches.

On a Parabolic-Elliptic system with chemotaxis and logistic type growth

NASA Astrophysics Data System (ADS)

Galakhov, Evgeny; Salieva, Olga; Tello, J. Ignacio

2016-10-01

We consider a nonlinear PDEs system of two equations of Parabolic-Elliptic type with chemotactic terms. The system models the movement of a biological population ;u; towards a higher concentration of a chemical agent ;w; in a bounded and regular domain Ω ⊂RN for arbitrary N ∈ N. After normalization, the system is as follows

Branching instability in expanding bacterial colonies.

PubMed

Giverso, Chiara; Verani, Marco; Ciarletta, Pasquale

2015-03-06

Self-organization in developing living organisms relies on the capability of cells to duplicate and perform a collective motion inside the surrounding environment. Chemical and mechanical interactions coordinate such a cooperative behaviour, driving the dynamical evolution of the macroscopic system. In this work, we perform an analytical and computational analysis to study pattern formation during the spreading of an initially circular bacterial colony on a Petri dish. The continuous mathematical model addresses the growth and the chemotactic migration of the living monolayer, together with the diffusion and consumption of nutrients in the agar. The governing equations contain four dimensionless parameters, accounting for the interplay among the chemotactic response, the bacteria-substrate interaction and the experimental geometry. The spreading colony is found to be always linearly unstable to perturbations of the interface, whereas branching instability arises in finite-element numerical simulations. The typical length scales of such fingers, which align in the radial direction and later undergo further branching, are controlled by the size parameters of the problem, whereas the emergence of branching is favoured if the diffusion is dominant on the chemotaxis. The model is able to predict the experimental morphologies, confirming that compact (resp. branched) patterns arise for fast (resp. slow) expanding colonies. Such results, while providing new insights into pattern selection in bacterial colonies, may finally have important applications for designing controlled patterns. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Chemotaxis migration and morphogenesis of living colonies.

PubMed

Ben Amar, Martine

2013-06-01

Development of forms in living organisms is complex and fascinating. Morphogenetic theories that investigate these shapes range from discrete to continuous models, from the variational elasticity to time-dependent fluid approach. Here a mixture model is chosen to describe the mass transport in a morphogenetic gradient: it gives a mathematical description of a mixture involving several constituents in mechanical interactions. This model, which is highly flexible can incorporate many biological processes but also complex interactions between cells as well as between cells and their environment. We use this model to derive a free-boundary problem easier to handle analytically. We solve it in the simplest geometry: an infinite linear front advancing with a constant velocity. In all the cases investigated here as the 3 D diffusion, the increase of mitotic activity at the border, nonlinear laws for the uptake of morphogens or for the mobility coefficient, a planar front exists above a critical threshold for the mobility coefficient but it becomes unstable just above the threshold at long wavelengths due to the existence of a Goldstone mode. This explains why sparsely bacteria exhibit dendritic patterns experimentally in opposition to other colonies such as biofilms and epithelia which are more compact. In the most unstable situation, where all the laws: diffusion, chemotaxis driving and chemoattractant uptake are linear, we show also that the system can recover a dynamic stability. A second threshold for the mobility exists which has a lower value as the ratio between diffusion coefficients decreases. Within the framework of this model where the biomass is treated mainly as a viscous and diffusive fluid, we show that the multiplicity of independent parameters in real biologic experimental set-up may explain varieties of observed patterns.

Chemotaxis in P. Aeruginosa Biofilm Formation

NASA Astrophysics Data System (ADS)

Bienvenu, Samuel; Strain, Shinji; Thatcher, Travis; Gordon, Vernita

2010-10-01

Pseudomonas biofilms form infections in the lungs of Cystic Fibrosis (CF) patients that damage lung tissue and lead to death. Previous work shows chemotaxis is important for Pseudomonas in CF lungs. The work studied swimming bacteria at high concentrations. In contrast, medically relevant biofilms initiate from sparse populations of surface-bound bacteria. The recent development of software techniques for automated, high-throughput bacteria tracking leaves us well-poised to quantitatively study these chemotactic conditions. We will develop experimental systems for such studies, focusing on L-Arginine (an amino acid), D-Galactose (a sugar present in lungs), and succinate and glucose (carbon sources for bacteria). This suite of chemoattractants will allow us to study how chemoattractant characteristics--size and diffusion behavior--change bacterial response; the interaction of competing chemoattractants; and, differences in bacterial behaviors, like motility modes, in response to different types of chemoattractions and varying neighbor cell density.

Low-Reynolds-number predator.

PubMed

Ebrahimian, Mehran; Yekehzare, Mohammad; Ejtehadi, Mohammad Reza

2015-12-01

To generalize simple bead-linker model of swimmers to higher dimensions and to demonstrate the chemotaxis ability of such swimmers, here we introduce a low-Reynolds predator, using a two-dimensional triangular bead-spring model. Two-state linkers as mechanochemical enzymes expand as a result of interaction with particular activator substances in the environment, causing the whole body to translate and rotate. The concentration of the chemical stimulator controls expansion versus the contraction rate of each arm and so affects the ability of the body for diffusive movements; also the variation of activator substance's concentration in the environment breaks the symmetry of linkers' preferred state, resulting in the drift of the random walker along the gradient of the density of activators. External food or danger sources may attract or repel the body by producing or consuming the chemical activators of the organism's enzymes, inducing chemotaxis behavior. Generalization of the model to three dimensions is straightforward.

Low-Reynolds-number predator

NASA Astrophysics Data System (ADS)

Ebrahimian, Mehran; Yekehzare, Mohammad; Ejtehadi, Mohammad Reza

2015-12-01

To generalize simple bead-linker model of swimmers to higher dimensions and to demonstrate the chemotaxis ability of such swimmers, here we introduce a low-Reynolds predator, using a two-dimensional triangular bead-spring model. Two-state linkers as mechanochemical enzymes expand as a result of interaction with particular activator substances in the environment, causing the whole body to translate and rotate. The concentration of the chemical stimulator controls expansion versus the contraction rate of each arm and so affects the ability of the body for diffusive movements; also the variation of activator substance's concentration in the environment breaks the symmetry of linkers' preferred state, resulting in the drift of the random walker along the gradient of the density of activators. External food or danger sources may attract or repel the body by producing or consuming the chemical activators of the organism's enzymes, inducing chemotaxis behavior. Generalization of the model to three dimensions is straightforward.

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

Bacterial chemotaxis along vapor-phase gradients of naphthalene.

PubMed

Hanzel, Joanna; Harms, Hauke; Wick, Lukas Y

2010-12-15

The role of bacterial growth and translocation for the bioremediation of organic contaminants in the vadose zone is poorly understood. Whereas air-filled pores restrict the mobility of bacteria, diffusion of volatile organic compounds in air is more efficient than in water. Past research, however, has focused on chemotactic swimming of bacteria along gradients of water-dissolved chemicals. In this study we tested if and to what extent Pseudomonas putida PpG7 (NAH7) chemotactically reacts to vapor-phase gradients forming above their swimming medium by the volatilization from a spot source of solid naphthalene. The development of an aqueous naphthalene gradient by air-water partitioning was largely suppressed by means of activated carbon in the agar. Surprisingly, strain PpG7 was repelled by vapor-phase naphthalene although the steady state gaseous concentrations were 50-100 times lower than the aqueous concentrations that result in positive chemotaxis of the same strain. It is thus assumed that the efficient gas-phase diffusion resulting in a steady, and possibly toxic, naphthalene flux to the cells controlled the chemotactic reaction rather than the concentration to which the cells were exposed. To our knowledge this is the first demonstration of apparent chemotactic behavior of bacteria in response to vapor-phase effector gradients.

Migration of Chemotactic Bacteria in Soft Agar: Role of Gel Concentration

PubMed Central

Croze, Ottavio A.; Ferguson, Gail P.; Cates, Michael E.; Poon, Wilson C.K.

2011-01-01

We study the migration of chemotactic wild-type Escherichia coli populations in semisolid (soft) agar in the concentration range C = 0.15–0.5% (w/v). For C≲0.35%, expanding bacterial colonies display characteristic chemotactic rings. At C = 0.35%, however, bacteria migrate as broad circular bands rather than sharp rings. These are growth/diffusion waves arising because of suppression of chemotaxis by the agar and have not been previously reported experimentally to our knowledge. For C = 0.4–0.5%, expanding colonies do not span the depth of the agar and develop pronounced front instabilities. The migration front speed is weakly dependent on agar concentration at C < 0.25%, but decreases sharply above this value. We discuss these observations in terms of an extended Keller-Segel model for which we derived novel transport parameter expressions accounting for perturbations of the chemotactic response by collisions with the agar. The model makes it possible to fit the observed front speed decay in the range C = 0.15–0.35%, and its solutions qualitatively reproduce the observed transition from chemotactic to growth/diffusion bands. We discuss the implications of our results for the study of bacteria in porous media and for the design of improved bacteriological chemotaxis assays. PMID:21806920

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ho, C.-L.; Lee, C.-C., E-mail: chieh.no27@gmail.com

2016-01-15

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

A model-based approach for automated in vitro cell tracking and chemotaxis analyses.

PubMed

Debeir, Olivier; Camby, Isabelle; Kiss, Robert; Van Ham, Philippe; Decaestecker, Christine

2004-07-01

Chemotaxis may be studied in two main ways: 1) counting cells passing through an insert (e.g., using Boyden chambers), and 2) directly observing cell cultures (e.g., using Dunn chambers), both in response to stationary concentration gradients. This article promotes the use of Dunn chambers and in vitro cell-tracking, achieved by video microscopy coupled with automatic image analysis software, in order to extract quantitative and qualitative measurements characterizing the response of cells to a diffusible chemical agent. Previously, we set up a videomicroscopy system coupled with image analysis software that was able to compute cell trajectories from in vitro cell cultures. In the present study, we are introducing a new software increasing the application field of this system to chemotaxis studies. This software is based on an adapted version of the active contour methodology, enabling each cell to be efficiently tracked for hours and resulting in detailed descriptions of individual cell trajectories. The major advantages of this method come from an improved robustness with respect to variability in cell morphologies between different cell lines and dynamical changes in cell shape during cell migration. Moreover, the software includes a very small number of parameters which do not require overly sensitive tuning. Finally, the running time of the software is very short, allowing improved possibilities in acquisition frequency and, consequently, improved descriptions of complex cell trajectories, i.e. trajectories including cell division and cell crossing. We validated this software on several artificial and real cell culture experiments in Dunn chambers also including comparisons with manual (human-controlled) analyses. We developed new software and data analysis tools for automated cell tracking which enable cell chemotaxis to be efficiently analyzed. Copyright 2004 Wiley-Liss, Inc.

Perspectives in flow-based microfluidic gradient generators for characterizing bacterial chemotaxis

PubMed Central

Wolfram, Christopher J.; Rubloff, Gary W.; Luo, Xiaolong

2016-01-01

Chemotaxis is a phenomenon which enables cells to sense concentrations of certain chemical species in their microenvironment and move towards chemically favorable regions. Recent advances in microbiology have engineered the chemotactic properties of bacteria to perform novel functions, but traditional methods of characterizing chemotaxis do not fully capture the associated cell motion, making it difficult to infer mechanisms that link the motion to the microbiology which induces it. Microfluidics offers a potential solution in the form of gradient generators. Many of the gradient generators studied to date for this application are flow-based, where a chemical species diffuses across the laminar flow interface between two solutions moving through a microchannel. Despite significant research efforts, flow-based gradient generators have achieved mixed success at accurately capturing the highly subtle chemotactic responses exhibited by bacteria. Here we present an analysis encompassing previously published versions of flow-based gradient generators, the theories that govern their gradient-generating properties, and new, more practical considerations that result from experimental factors. We conclude that flow-based gradient generators present a challenge inherent to their design in that the residence time and gradient decay must be finely balanced, and that this significantly narrows the window for reliable observation and quantification of chemotactic motion. This challenge is compounded by the effects of shear on an ellipsoidal bacterium that causes it to preferentially align with the direction of flow and subsequently suppresses the cross-flow chemotactic response. These problems suggest that a static, non-flowing gradient generator may be a more suitable platform for chemotaxis studies in the long run, despite posing greater difficulties in design and fabrication. PMID:27917249

Perspectives in flow-based microfluidic gradient generators for characterizing bacterial chemotaxis.

PubMed

Wolfram, Christopher J; Rubloff, Gary W; Luo, Xiaolong

2016-11-01

Chemotaxis is a phenomenon which enables cells to sense concentrations of certain chemical species in their microenvironment and move towards chemically favorable regions. Recent advances in microbiology have engineered the chemotactic properties of bacteria to perform novel functions, but traditional methods of characterizing chemotaxis do not fully capture the associated cell motion, making it difficult to infer mechanisms that link the motion to the microbiology which induces it. Microfluidics offers a potential solution in the form of gradient generators. Many of the gradient generators studied to date for this application are flow-based, where a chemical species diffuses across the laminar flow interface between two solutions moving through a microchannel. Despite significant research efforts, flow-based gradient generators have achieved mixed success at accurately capturing the highly subtle chemotactic responses exhibited by bacteria. Here we present an analysis encompassing previously published versions of flow-based gradient generators, the theories that govern their gradient-generating properties, and new, more practical considerations that result from experimental factors. We conclude that flow-based gradient generators present a challenge inherent to their design in that the residence time and gradient decay must be finely balanced, and that this significantly narrows the window for reliable observation and quantification of chemotactic motion. This challenge is compounded by the effects of shear on an ellipsoidal bacterium that causes it to preferentially align with the direction of flow and subsequently suppresses the cross-flow chemotactic response. These problems suggest that a static, non-flowing gradient generator may be a more suitable platform for chemotaxis studies in the long run, despite posing greater difficulties in design and fabrication.

Bacteria foraging in turbulent waters

NASA Astrophysics Data System (ADS)

Taylor, John; Tang, Wenbo; Stocker, Roman

2009-11-01

Marine bacteria are the Ocean's recyclers, contributing to as much as 50% of the productivity of the marine food web. Bacteria forage on patches of dissolved nutrients using chemotaxis, the ability to swim up chemical gradients. As turbulence is ubiquitous in the Ocean, it is important to understand how turbulent flow conditions affect bacterial foraging. We used three-dimensional, isotropic direct numerical simulations coupled with a bacterial transport equation to address this problem. After the flow is continuously forced until it reaches a steady state, microscale nutrient patches are injected into the turbulent flow, and stirring produces thin nutrient filaments. Two populations of bacteria compete against each other: one population is motile and chemotactic (`active'), the other is non-motile (`passive'). The distribution of both populations is initially uniform. Chemotaxis allows active bacteria to cluster near the center of the nutrient filaments, increasing their nutrient uptake relative to passive bacteria. Increasing the turbulence intensity increases the short-term chemotactic advantage by quickly producing large gradients in the nutrient concentration, but also leads to rapid mixing of the nutrient field, which makes the chemotactic advantage short-lived. The results suggest that the evolutionary advantage of chemotaxis, based on the increase in nutrient uptake relative to the energetic cost of swimming, strongly depends on the turbulence level.

Chemotaxis in cancer

PubMed Central

Roussos, Evanthia T.; Condeelis, John S.; Patsialou, Antonia

2014-01-01

Chemotaxis of tumour cells and stromal cells in the surrounding microenvironment is an essential component of tumour dissemination during progression and metastasis. This Review summarizes how chemotaxis directs the different behaviours of tumour cells and stromal cells in vivo, how molecular pathways regulate chemotaxis in tumour cells and how chemotaxis choreographs cell behaviour to shape the tumour microenvironment and to determine metastatic spread. The central importance of chemotaxis in cancer progression is highlighted by discussion of the use of chemotaxis as a prognostic marker, a treatment end point and a target of therapeutic intervention. PMID:21779009

Chemistry with spatial control using particles and streams†

PubMed Central

Kalinin, Yevgeniy V.; Murali, Adithya

2012-01-01

Spatial control of chemical reactions, with micro- and nanometer scale resolution, has important consequences for one pot synthesis, engineering complex reactions, developmental biology, cellular biochemistry and emergent behavior. We review synthetic methods to engineer this spatial control using chemical diffusion from spherical particles, shells and polyhedra. We discuss systems that enable both isotropic and anisotropic chemical release from isolated and arrayed particles to create inhomogeneous and spatially patterned chemical fields. In addition to such finite chemical sources, we also discuss spatial control enabled with laminar flow in 2D and 3D microfluidic networks. Throughout the paper, we highlight applications of spatially controlled chemistry in chemical kinetics, reaction-diffusion systems, chemotaxis and morphogenesis. PMID:23145348

E. coli chemotaxis and super-diffusion

NASA Astrophysics Data System (ADS)

Dobnikar, Jure; Matthäus, Franziska; Jagodic, Marko

2010-03-01

The bacteria E. coli actively propel by switching between clockwise and anti-clockwise rotation of the flagella attached to their cell membranes. This results in two modes of motion: tumbling and swimming. The switching between the two modes is coupled to the ligand sensing through the chemotactic signalling pathway inside the cell. We modelled the signalling pathway and performed numerical simulations of the chemotactic motion of a large number of E. coli bacteria under various external conditions. We have shown that under certain conditions the thermal noise in the level of receptor-bound CheR (an enzyme responsible for methylation of the receptor sites) leads to super-diffusive behaviour (L'evy walk) which is advantageous for the bacterial populations in environments with scarce food. Exerting external pressure we might observe evolution of the wild-type to the super-diffusive populations.

Collective chemotaxis and segregation of active bacterial colonies

NASA Astrophysics Data System (ADS)

Amar, M. Ben

2016-02-01

Still recently, bacterial fluid suspensions have motivated a lot of works, both experimental and theoretical, with the objective to understand their collective dynamics from universal and simple rules. Since some species are active, most of these works concern the strong interactions that these bacteria exert on a forced flow leading to instabilities, chaos and turbulence. Here, we investigate the self-organization of expanding bacterial colonies under chemotaxis, proliferation and eventually active-reaction. We propose a simple model to understand and quantify the physical properties of these living organisms which either give cohesion or on the contrary dispersion to the colony. Taking into account the diffusion and capture of morphogens complicates the model since it induces a bacterial density gradient coupled to bacterial density fluctuations and dynamics. Nevertheless under some specific conditions, it is possible to investigate the pattern formation as a usual viscous fingering instability. This explains the similarity and differences of patterns according to the physical bacterial suspension properties and explain the factors which favor compactness or branching.

BMP2 and BMP7 play antagonistic roles in feather induction

PubMed Central

Michon, Frédéric; Forest, Loïc; Collomb, Elodie; Demongeot, Jacques; Dhouailly, Danielle

2008-01-01

Summary During embryonic development, feathers first appear as primordia consisting of an epidermal placode associated with a dermal condensation. In most previous studies, the BMPs have been proposed to function as inhibitors of the formation of cutaneous appendages. We showed that the function of BMPs is quite nuanced: BMP-2 and BMP-7, which are expressed in both skin components, act antagonistically and yet are both involved in the dermal condensations formation. BMP-7, the first to be expressed, is implicated in chemotaxis which leads to cell recruitment to the condensation, whereas BMP-2, which is expressed later, leads to an arrest of cell migration, likely via its modulation of EIIIA Fibronectin domain and α4-Integrin expression. We also propose a mathematical model, a reaction-diffusion system, based on cell proliferation, chemotaxis and the timing of BMP-2 and BMP-7 expression, which simulates the endogenous situation and reproduces the negative effects of excess BMP-2 or BMP-7 on feather patterning. PMID:18635609

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

PubMed

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

Measuring Borrelia burgdorferi Motility and Chemotaxis.

PubMed

Zhang, Kai; Li, Chunhao

2018-01-01

Swimming plate, cell motion tracking, and capillary tube assays are very useful tools to quantitatively measure bacterial motility and chemotaxis. These methods were modified and applied to study Borrelia burgdorferi motility and chemotaxis. By using these methods, numerous motility and chemotaxis mutants have been characterized and several chemoattractants were identified. With the assistance of these tools, the role of motility and chemotaxis in the pathogenicity of B. burgdorferi has been established. In addition, these tools also facilitate the study of motility and chemotaxis in other spirochetes.

Metabolic products of soluble epoxide hydrolase are essential for monocyte chemotaxis to MCP-1 in vitro and in vivo.

PubMed

Kundu, Suman; Roome, Talat; Bhattacharjee, Ashish; Carnevale, Kevin A; Yakubenko, Valentin P; Zhang, Renliang; Hwang, Sung Hee; Hammock, Bruce D; Cathcart, Martha K

2013-02-01

Monocyte chemoattractant protein-1 (MCP-1)-induced monocyte chemotaxis is a major event in inflammatory disease. Our prior studies have demonstrated that MCP-1-dependent chemotaxis requires release of arachidonic acid (AA) by activated cytosolic phospholipase A(2) (cPLA(2)). Here we investigated the involvement of AA metabolites in chemotaxis. Neither cyclooxygenase nor lipoxygenase pathways were required, whereas pharmacologic inhibitors of both the cytochrome-P450 (CYP) and the soluble epoxide hydrolase (sEH) pathways blocked monocyte chemotaxis to MCP-1. To verify specificity, we demonstrated that the CYP and sEH products epoxyeiscosatrienoic acids (EETs) and dihydroxyeicosatrienoic acids (DHETs), respectively, restored chemotaxis in the presence of the inhibitors, indicating that sEH-derived products are essential for MCP-1-driven chemotaxis. Importantly, DHETs also rescued chemotaxis in cPLA(2)-deficient monocytes and monocytes with blocked Erk1/2 activity, because Erk controls cPLA(2) activation. The in vitro findings regarding the involvement of CYP/sEH pathways were further validated in vivo using two complementary approaches measuring MCP-1-dependent chemotaxis in mice. These observations reveal the importance of sEH in MCP-1-regulated monocyte chemotaxis and may explain the observed therapeutic value of sEH inhibitors in treatment of inflammatory diseases, cardiovascular diseases, pain, and even carcinogenesis. Their effectiveness, often attributed to increasing EET levels, is probably influenced by the impairment of DHET formation and inhibition of chemotaxis.

Collective Signal Processing in Cluster Chemotaxis: Roles of Adaptation, Amplification, and Co-attraction in Collective Guidance

PubMed Central

Camley, Brian A.; Zimmermann, Juliane; Levine, Herbert; Rappel, Wouter-Jan

2016-01-01

Single eukaryotic cells commonly sense and follow chemical gradients, performing chemotaxis. Recent experiments and theories, however, show that even when single cells do not chemotax, clusters of cells may, if their interactions are regulated by the chemoattractant. We study this general mechanism of “collective guidance” computationally with models that integrate stochastic dynamics for individual cells with biochemical reactions within the cells, and diffusion of chemical signals between the cells. We show that if clusters of cells use the well-known local excitation, global inhibition (LEGI) mechanism to sense chemoattractant gradients, the speed of the cell cluster becomes non-monotonic in the cluster’s size—clusters either larger or smaller than an optimal size will have lower speed. We argue that the cell cluster speed is a crucial readout of how the cluster processes chemotactic signals; both amplification and adaptation will alter the behavior of cluster speed as a function of size. We also show that, contrary to the assumptions of earlier theories, collective guidance does not require persistent cell-cell contacts and strong short range adhesion. If cell-cell adhesion is absent, and the cluster cohesion is instead provided by a co-attraction mechanism, e.g. chemotaxis toward a secreted molecule, collective guidance may still function. However, new behaviors, such as cluster rotation, may also appear in this case. Co-attraction and adaptation allow for collective guidance that is robust to varying chemoattractant concentrations while not requiring strong cell-cell adhesion. PMID:27367541

Cellular Automata for Spatiotemporal Pattern Formation from Reaction-Diffusion Partial Differential Equations

NASA Astrophysics Data System (ADS)

Ohmori, Shousuke; Yamazaki, Yoshihiro

2016-01-01

Ultradiscrete equations are derived from a set of reaction-diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction-diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction-diffusion equations.

Monte Carlo simulation for kinetic chemotaxis model: An application to the traveling population wave

NASA Astrophysics Data System (ADS)

Yasuda, Shugo

2017-02-01

A Monte Carlo simulation of chemotactic bacteria is developed on the basis of the kinetic model and is applied to a one-dimensional traveling population wave in a microchannel. In this simulation, the Monte Carlo method, which calculates the run-and-tumble motions of bacteria, is coupled with a finite volume method to calculate the macroscopic transport of the chemical cues in the environment. The simulation method can successfully reproduce the traveling population wave of bacteria that was observed experimentally and reveal the microscopic dynamics of bacterium coupled with the macroscopic transports of the chemical cues and bacteria population density. The results obtained by the Monte Carlo method are also compared with the asymptotic solution derived from the kinetic chemotaxis equation in the continuum limit, where the Knudsen number, which is defined by the ratio of the mean free path of bacterium to the characteristic length of the system, vanishes. The validity of the Monte Carlo method in the asymptotic behaviors for small Knudsen numbers is numerically verified.

Recent developments in microfluidics-based chemotaxis studies.

PubMed

Wu, Jiandong; Wu, Xun; Lin, Francis

2013-07-07

Microfluidic devices can better control cellular microenvironments compared to conventional cell migration assays. Over the past few years, microfluidics-based chemotaxis studies showed a rapid growth. New strategies were developed to explore cell migration in manipulated chemical gradients. In addition to expanding the use of microfluidic devices for a broader range of cell types, microfluidic devices were used to study cell migration and chemotaxis in complex environments. Furthermore, high-throughput microfluidic chemotaxis devices and integrated microfluidic chemotaxis systems were developed for medical and commercial applications. In this article, we review recent developments in microfluidics-based chemotaxis studies and discuss the new trends in this field observed over the past few years.

Statins and nitric oxide donors affect thrombospondin 1-induced chemotaxis.

PubMed

Seymour, Keri; Stein, Jeffrey; Han, Xuan; Maier, Kristopher G; Gahtan, Vivian

2014-01-01

Thrombospondin 1 (TSP-1) induces vascular smooth muscle cell (VSMC) migration and intimal hyperplasia. Statins and nitric oxide (NO) donors decrease intimal hyperplasia. We previously showed that statins (long-term exposure) and NO donors inhibit TSP-1-induced VSMC chemotaxis. (1) Pretreatment with short-term statin will inhibit TSP-1-induced VSMC chemotaxis and (2) NO donors will enhance statin inhibition of TSP-1-induced or platelet-derived growth factor (PDGF)-induced VSMC chemotaxis. We examined these treatment effects on TSP-1-induced VSMC chemotaxis: (1) long-term (20 hours) versus short-term (20 minutes) pravastatin, (2) diethylenetriamine NONOate (DETA/NO) or S-nitroso-N-acetylpenicillamine (SNAP) in combination with pravastatin, and (3) comparison of TSP-1 to PDGF as a chemoattractant. Pravastatin (long term or short term) inhibited TSP-1-induced chemotaxis. Diethylenetriamine NONOate and SNAP impeded statin inhibition of TSP-1-induced chemotaxis. Platelet-derived growth factor and TSP-1 had opposite effects on DETA/NO-pravastatin treatment. Short-term statin pretreatment inhibited TSP-1-induced VSMC chemotaxis, suggesting a pleiotropic effect. High-dose NO reversed statin inhibition of TSP-1-induced chemotaxis, suggesting NO and statin combination therapies warrant further study. © The Author(s) 2014.

Transformed Fourier and Fick equations for the control of heat and mass diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guenneau, S.; Petiteau, D.; Zerrad, M.

We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves,more » the temperature (or mass concentration) inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass) diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.« less

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in (0,2] and skewness theta (\\verttheta\\vertlemin \\{alpha ,2-alpha \\}), and the first-order time derivative with a Caputo derivative of order beta in (0,1] . The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process. We view it as a generalized diffusion process that we call fractional diffusion process, and present an integral representation of the fundamental solution. A more general approach to anomalous diffusion is however known to be provided by the master equation for a continuous time random walk (CTRW). We show how this equation reduces to our fractional diffusion equation by a properly scaled passage to the limit of compressed waiting times and jump widths. Finally, we describe a method of simulation and display (via graphics) results of a few numerical case studies.

Some Properties of the Fractional Equation of Continuity and the Fractional Diffusion Equation

NASA Astrophysics Data System (ADS)

Fukunaga, Masataka

2006-05-01

The fractional equation of continuity (FEC) and the fractional diffusion equation (FDE) show peculiar behaviors that are in the opposite sense to those expected from the equation of continuity and the diffusion equation, respectively. The behaviors are interpreted in terms of the memory effect of the fractional time derivatives included in the equations. Some examples are given by solutions of the FDE.

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

Boundedness of the solution of a higher-dimensional parabolic-ODE-parabolic chemotaxis-haptotaxis model with generalized logistic source

NASA Astrophysics Data System (ADS)

Zheng, Jiashan

2017-05-01

This paper deals with a quasilinear chemotaxis-haptotaxis system with generalized logistic source {ut=∇ṡ(ϕ(u)∇u)-∇ṡ(u∇v)-∇ṡ(u∇w)+u(1-ur-1-w),vt=Δv-v+u,wt=-vw, under homogeneous Neumann boundary conditions in a smooth bounded domain {{{R}}N}(N≥slant 3) , with parameter r  >  1, where the given function φ (u) is the nonlinear diffusion. Besides appropriate smoothness assumptions, in this paper it is only required that φ (u)≥slant {{C}φ}(u+1){{}m-1} for all u≥slant 0 with some {{C}φ}>0 and some m{>2-2N if 11+(N+2-2r)+N+2 if N+22⩾r⩾N+2N,⩾1 if r>N+22. It is shown that then for all reasonably regular initial data, a corresponding initial-boundary value problem for (0.1) possesses a unique global classical solution that is uniformly bounded in Ω × (0,∞ ) .

Diffusion Coefficients from Molecular Dynamics Simulations in Binary and Ternary Mixtures

NASA Astrophysics Data System (ADS)

Liu, Xin; Schnell, Sondre K.; Simon, Jean-Marc; Krüger, Peter; Bedeaux, Dick; Kjelstrup, Signe; Bardow, André; Vlugt, Thijs J. H.

2013-07-01

Multicomponent diffusion in liquids is ubiquitous in (bio)chemical processes. It has gained considerable and increasing interest as it is often the rate limiting step in a process. In this paper, we review methods for calculating diffusion coefficients from molecular simulation and predictive engineering models. The main achievements of our research during the past years can be summarized as follows: (1) we introduced a consistent method for computing Fick diffusion coefficients using equilibrium molecular dynamics simulations; (2) we developed a multicomponent Darken equation for the description of the concentration dependence of Maxwell-Stefan diffusivities. In the case of infinite dilution, the multicomponent Darken equation provides an expression for [InlineEquation not available: see fulltext.] which can be used to parametrize the generalized Vignes equation; and (3) a predictive model for self-diffusivities was proposed for the parametrization of the multicomponent Darken equation. This equation accurately describes the concentration dependence of self-diffusivities in weakly associating systems. With these methods, a sound framework for the prediction of mutual diffusion in liquids is achieved.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

Instability of turing patterns in reaction-diffusion-ODE systems.

PubMed

Marciniak-Czochra, Anna; Karch, Grzegorz; Suzuki, Kanako

2017-02-01

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.

Azospirillum brasilense Chemotaxis Depends on Two Signaling Pathways Regulating Distinct Motility Parameters

PubMed Central

Mukherjee, Tanmoy; Kumar, Dhivya; Burriss, Nathan; Xie, Zhihong

2016-01-01

ABSTRACT The genomes of most motile bacteria encode two or more chemotaxis (Che) systems, but their functions have been characterized in only a few model systems. Azospirillum brasilense is a motile soil alphaproteobacterium able to colonize the rhizosphere of cereals. In response to an attractant, motile A. brasilense cells transiently increase swimming speed and suppress reversals. The Che1 chemotaxis pathway was previously shown to regulate changes in the swimming speed, but it has a minor role in chemotaxis and root surface colonization. Here, we show that a second chemotaxis system, named Che4, regulates the probability of swimming reversals and is the major signaling pathway for chemotaxis and wheat root surface colonization. Experimental evidence indicates that Che1 and Che4 are functionally linked to coordinate changes in the swimming motility pattern in response to attractants. The effect of Che1 on swimming speed is shown to enhance the aerotactic response of A. brasilense in gradients, likely providing the cells with a competitive advantage in the rhizosphere. Together, the results illustrate a novel mechanism by which motile bacteria utilize two chemotaxis pathways regulating distinct motility parameters to alter movement in gradients and enhance the chemotactic advantage. IMPORTANCE Chemotaxis provides motile bacteria with a competitive advantage in the colonization of diverse niches and is a function enriched in rhizosphere bacterial communities, with most species possessing at least two chemotaxis systems. Here, we identify the mechanism by which cells may derive a significant chemotactic advantage using two chemotaxis pathways that ultimately regulate distinct motility parameters. PMID:27068592

Serum from the Human Fracture Hematoma Contains a Potent Inducer of Neutrophil Chemotaxis.

PubMed

Bastian, Okan W; Mrozek, Mikolaj H; Raaben, Marco; Leenen, Luke P H; Koenderman, Leo; Blokhuis, Taco J

2018-06-01

A controlled local inflammatory response is essential for adequate fracture healing. However, the current literature suggests that local and systemic hyper-inflammatory conditions after major trauma induce increased influx of neutrophils into the fracture hematoma (FH) and impair bone regeneration. Inhibiting neutrophil chemotaxis towards the FH without compromising the hosts' defense may therefore be a target of future therapies that prevent impairment of fracture healing after major trauma. We investigated whether chemotaxis of neutrophils towards the FH could be studied in vitro. Moreover, we determined whether chemotaxis of neutrophils towards the FH was mediated by the CXCR1, CXCR2, FPR, and C5aR receptors. Human FHs were isolated during an open reduction internal fixation (ORIF) procedure within 3 days after trauma and spun down to obtain the fracture hematoma serum. Neutrophil migration towards the FH was studied using Ibidi™ Chemotaxis 3D μ-Slides and image analysis of individual neutrophil tracks was performed. Our study showed that the human FH induces significant neutrophil chemotaxis, which was not affected by blocking CXCR1 and CXCR2. In contrast, neutrophil chemotaxis towards the FH was significantly inhibited by chemotaxis inhibitory protein of Staphylococcus aureus (CHIPS), which blocks FPR and C5aR. Blocking only C5aR with CHIPSΔ1F also significantly inhibited neutrophil chemotaxis towards the FH. Our finding that neutrophil chemotaxis towards the human FH can be blocked in vitro using CHIPS may aid the development of therapies that prevent impairment of fracture healing after major trauma.

Azospirillum brasilense Chemotaxis Depends on Two Signaling Pathways Regulating Distinct Motility Parameters.

PubMed

Mukherjee, Tanmoy; Kumar, Dhivya; Burriss, Nathan; Xie, Zhihong; Alexandre, Gladys

2016-06-15

The genomes of most motile bacteria encode two or more chemotaxis (Che) systems, but their functions have been characterized in only a few model systems. Azospirillum brasilense is a motile soil alphaproteobacterium able to colonize the rhizosphere of cereals. In response to an attractant, motile A. brasilense cells transiently increase swimming speed and suppress reversals. The Che1 chemotaxis pathway was previously shown to regulate changes in the swimming speed, but it has a minor role in chemotaxis and root surface colonization. Here, we show that a second chemotaxis system, named Che4, regulates the probability of swimming reversals and is the major signaling pathway for chemotaxis and wheat root surface colonization. Experimental evidence indicates that Che1 and Che4 are functionally linked to coordinate changes in the swimming motility pattern in response to attractants. The effect of Che1 on swimming speed is shown to enhance the aerotactic response of A. brasilense in gradients, likely providing the cells with a competitive advantage in the rhizosphere. Together, the results illustrate a novel mechanism by which motile bacteria utilize two chemotaxis pathways regulating distinct motility parameters to alter movement in gradients and enhance the chemotactic advantage. Chemotaxis provides motile bacteria with a competitive advantage in the colonization of diverse niches and is a function enriched in rhizosphere bacterial communities, with most species possessing at least two chemotaxis systems. Here, we identify the mechanism by which cells may derive a significant chemotactic advantage using two chemotaxis pathways that ultimately regulate distinct motility parameters. Copyright © 2016, American Society for Microbiology. All Rights Reserved.

Quantitative chemical biosensing by bacterial chemotaxis in microfluidic chips.

PubMed

Roggo, Clémence; Picioreanu, Cristian; Richard, Xavier; Mazza, Christian; van Lintel, Harald; van der Meer, Jan Roelof

2018-01-01

Whole-cell bacterial bioreporters are proposed as alternatives to chemical analysis of, for example, pollutants in environmental compartments. Commonly based on reporter gene induction, bioreporters produce a detectable signal within 30 min to a few hours after exposure to the chemical target, which is impractical for applications aiming at a fast response. In an attempt to attain faster readout but maintain flexibility of chemical targeting, we explored the concept for quantitative chemical sensing by bacterial chemotaxis. Chemotaxis was quantified from enrichment of cells across a 600 µm-wide chemical gradient stabilized by parallel flow in a microfluidic chip, further supported by transport and chemotaxis steady state and kinetic modelling. As proof-of-concept, we quantified Escherichia coli chemotaxis towards serine, aspartate and methylaspartate as a function of attractant concentration and exposure time. E. coli chemotaxis enrichment increased sharply between 0 and 10 µM serine, before saturating at 100 µM. The chemotaxis accumulation rate was maximal at 10 µM serine, leading to observable cell enrichment within 5 min. The potential application for biosensing of environmental toxicants was investigated by quantifying chemotaxis of Cupriavidus pinatubonensis JMP134 towards the herbicide 2,4-dichlorophenoxyacetate. Our results show that bacterial chemotaxis can be quantified on a scale of minutes and may be used for developing faster bioreporter assays. © 2017 The Authors. Environmental Microbiology published by Society for Applied Microbiology and John Wiley & Sons Ltd.

[Chemotaxis response of Erwinia carotovora on sugars and amino acids of root exudates of Panax ginseng].

PubMed

Zhang, Ai-Hua; An, Ning-Bo; Lei, Feng-Jie; Ma, Wen-Li; Chi, Kun; Zhang, Lian-Xue

2016-11-01

The chemotaxis response of Erwinia carotovora to different sugars and amino acids in four kinds of chemotactic parameters (concentration, time, temperature and pH ) was determined by capillary method. The results showed that when pH was 8, concentration was 0.025 mg•L ⁻¹, culture temperature was 25 ℃ and the duration was 60 minutes, the optimal chemotaxis rate of lysine was 2.509,when pH was 6, concentration was 0.25 mg•L ⁻¹, culture temperature was 25 ℃ and the duration was 60 minutes, the optimal chemotaxis rate of arginine was 2.218 8,when pH was 7, concentration was 0.25 mg•L ⁻¹, culture temperature was 30 ℃ and the duration was 60 minutes, the optimal chemotaxis rate of L-rhamnose was 3.091 2, when pH was 6, concentration was 0.25 mg•L ⁻¹, culture temperature was 30 ℃ and the duration was 45 minutes, the optimal chemotaxis rate of D-arabinose was 3.026 3. Sugars and amino acids had obvious chemotaxis with E. carotovora,the high concentration of carbohydrate and amino acid exited an inhibitory effect on chemotaxis response of E. carotovora, and the chemotaxis response decreased with the increase of concentration of carbohydrates and amino acids. Copyright© by the Chinese Pharmaceutical Association.

Exosome secretion promotes chemotaxis of cancer cells.

PubMed

Sung, Bong Hwan; Weaver, Alissa M

2017-03-04

Migration of cells toward chemical cues, or chemotaxis, is important for many biologic processes such as immune defense, wound healing and cancer metastasis. Although chemotaxis is thought to occur in cancer cells, it is less well characterized than chemotaxis of professional immune cells such as neutrophils. Here, we show that cancer cell chemotaxis relies on secretion of exosome-type extracellular vesicles. Migration of fibrosarcoma cells toward a gradient of exosome-depleted serum was diminished by knockdown of the exosome secretion regulator Rab27a. Rescue experiments in which chemotaxis chambers were coated with purified extracellular vesicles demonstrate that exosomes but not microvesicles affect both speed and directionality of migrating cells. Chamber coating with purified fibronectin and fibronectin-depleted exosomes demonstrates that the exosome cargo fibronectin promotes cell speed but cannot account for the role of exosomes in promoting directionality of fibrosarcoma cell movement during chemotaxis. These experiments indicate that exosomes contain multiple motility-promoting cargoes that contribute to different aspects of cell motility.

Fold-change detection and scalar symmetry of sensory input fields.

PubMed

Shoval, Oren; Goentoro, Lea; Hart, Yuval; Mayo, Avi; Sontag, Eduardo; Alon, Uri

2010-09-07

Recent studies suggest that certain cellular sensory systems display fold-change detection (FCD): a response whose entire shape, including amplitude and duration, depends only on fold changes in input and not on absolute levels. Thus, a step change in input from, for example, level 1 to 2 gives precisely the same dynamical output as a step from level 2 to 4, because the steps have the same fold change. We ask what the benefit of FCD is and show that FCD is necessary and sufficient for sensory search to be independent of multiplying the input field by a scalar. Thus, the FCD search pattern depends only on the spatial profile of the input and not on its amplitude. Such scalar symmetry occurs in a wide range of sensory inputs, such as source strength multiplying diffusing/convecting chemical fields sensed in chemotaxis, ambient light multiplying the contrast field in vision, and protein concentrations multiplying the output in cellular signaling systems. Furthermore, we show that FCD entails two features found across sensory systems, exact adaptation and Weber's law, but that these two features are not sufficient for FCD. Finally, we present a wide class of mechanisms that have FCD, including certain nonlinear feedback and feed-forward loops. We find that bacterial chemotaxis displays feedback within the present class and hence, is expected to show FCD. This can explain experiments in which chemotaxis searches are insensitive to attractant source levels. This study, thus, suggests a connection between properties of biological sensory systems and scalar symmetry stemming from physical properties of their input fields.

Background-Error Correlation Model Based on the Implicit Solution of a Diffusion Equation

DTIC Science & Technology

2010-01-01

1 Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation Matthew J. Carrier* and Hans Ngodock...4. TITLE AND SUBTITLE Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation 5a. CONTRACT NUMBER 5b. GRANT...2001), which sought to model error correlations based on the explicit solution of a generalized diffusion equation. The implicit solution is

Optogenetic Manipulation of Cyclic Di-GMP (c-di-GMP) Levels Reveals the Role of c-di-GMP in Regulating Aerotaxis Receptor Activity in Azospirillum brasilense.

PubMed

O'Neal, Lindsey; Ryu, Min-Hyung; Gomelsky, Mark; Alexandre, Gladys

2017-09-15

Bacterial chemotaxis receptors provide the sensory inputs that inform the direction of navigation in changing environments. Recently, we described the bacterial second messenger cyclic di-GMP (c-di-GMP) as a novel regulator of a subclass of chemotaxis receptors. In Azospirillum brasilense , c-di-GMP binds to a chemotaxis receptor, Tlp1, and modulates its signaling function during aerotaxis. Here, we further characterize the role of c-di-GMP in aerotaxis using a novel dichromatic optogenetic system engineered for manipulating intracellular c-di-GMP levels in real time. This system comprises a red/near-infrared-light-regulated diguanylate cyclase and a blue-light-regulated c-di-GMP phosphodiesterase. It allows the generation of transient changes in intracellular c-di-GMP concentrations within seconds of irradiation with appropriate light, which is compatible with the time scale of chemotaxis signaling. We provide experimental evidence that binding of c-di-GMP to the Tlp1 receptor activates its signaling function during aerotaxis, which supports the role of transient changes in c-di-GMP levels as a means of adjusting the response of A. brasilense to oxygen gradients. We also show that intracellular c-di-GMP levels in A. brasilense change with carbon metabolism. Our data support a model whereby c-di-GMP functions to imprint chemotaxis receptors with a record of recent metabolic experience, to adjust their contribution to the signaling output, thus allowing the cells to continually fine-tune chemotaxis sensory perception to their metabolic state. IMPORTANCE Motile bacteria use chemotaxis to change swimming direction in response to changes in environmental conditions. Chemotaxis receptors sense environmental signals and relay sensory information to the chemotaxis machinery, which ultimately controls the swimming pattern of cells. In bacteria studied to date, differential methylation has been known as a mechanism to control the activity of chemotaxis receptors and modulates their contribution to the overall chemotaxis response. Here, we used an optogenetic system to perturb intracellular concentrations of the bacterial second messenger c-di-GMP to show that in some chemotaxis receptors, c-di-GMP functions in a similar feedback loop to connect the metabolic status of the cells to the sensory activity of chemotaxis receptors. Copyright © 2017 American Society for Microbiology.

Optogenetic Manipulation of Cyclic Di-GMP (c-di-GMP) Levels Reveals the Role of c-di-GMP in Regulating Aerotaxis Receptor Activity in Azospirillum brasilense

PubMed Central

O'Neal, Lindsey; Ryu, Min-Hyung; Gomelsky, Mark

2017-01-01

ABSTRACT Bacterial chemotaxis receptors provide the sensory inputs that inform the direction of navigation in changing environments. Recently, we described the bacterial second messenger cyclic di-GMP (c-di-GMP) as a novel regulator of a subclass of chemotaxis receptors. In Azospirillum brasilense, c-di-GMP binds to a chemotaxis receptor, Tlp1, and modulates its signaling function during aerotaxis. Here, we further characterize the role of c-di-GMP in aerotaxis using a novel dichromatic optogenetic system engineered for manipulating intracellular c-di-GMP levels in real time. This system comprises a red/near-infrared-light-regulated diguanylate cyclase and a blue-light-regulated c-di-GMP phosphodiesterase. It allows the generation of transient changes in intracellular c-di-GMP concentrations within seconds of irradiation with appropriate light, which is compatible with the time scale of chemotaxis signaling. We provide experimental evidence that binding of c-di-GMP to the Tlp1 receptor activates its signaling function during aerotaxis, which supports the role of transient changes in c-di-GMP levels as a means of adjusting the response of A. brasilense to oxygen gradients. We also show that intracellular c-di-GMP levels in A. brasilense change with carbon metabolism. Our data support a model whereby c-di-GMP functions to imprint chemotaxis receptors with a record of recent metabolic experience, to adjust their contribution to the signaling output, thus allowing the cells to continually fine-tune chemotaxis sensory perception to their metabolic state. IMPORTANCE Motile bacteria use chemotaxis to change swimming direction in response to changes in environmental conditions. Chemotaxis receptors sense environmental signals and relay sensory information to the chemotaxis machinery, which ultimately controls the swimming pattern of cells. In bacteria studied to date, differential methylation has been known as a mechanism to control the activity of chemotaxis receptors and modulates their contribution to the overall chemotaxis response. Here, we used an optogenetic system to perturb intracellular concentrations of the bacterial second messenger c-di-GMP to show that in some chemotaxis receptors, c-di-GMP functions in a similar feedback loop to connect the metabolic status of the cells to the sensory activity of chemotaxis receptors. PMID:28264994

A hybrid agent-based approach for modeling microbiological systems.

PubMed

Guo, Zaiyi; Sloot, Peter M A; Tay, Joc Cing

2008-11-21

Models for systems biology commonly adopt Differential Equations or Agent-Based modeling approaches for simulating the processes as a whole. Models based on differential equations presuppose phenomenological intracellular behavioral mechanisms, while models based on Multi-Agent approach often use directly translated, and quantitatively less precise if-then logical rule constructs. We propose an extendible systems model based on a hybrid agent-based approach where biological cells are modeled as individuals (agents) while molecules are represented by quantities. This hybridization in entity representation entails a combined modeling strategy with agent-based behavioral rules and differential equations, thereby balancing the requirements of extendible model granularity with computational tractability. We demonstrate the efficacy of this approach with models of chemotaxis involving an assay of 10(3) cells and 1.2x10(6) molecules. The model produces cell migration patterns that are comparable to laboratory observations.

A Model for Direction Sensing in Dictyostelium discoideum: Ras Activity and Symmetry Breaking Driven by a Gβγ-Mediated, Gα2-Ric8 -- Dependent Signal Transduction Network

PubMed Central

Cheng, Yougan; Othmer, Hans

2016-01-01

Chemotaxis is a dynamic cellular process, comprised of direction sensing, polarization and locomotion, that leads to the directed movement of eukaryotic cells along extracellular gradients. As a primary step in the response of an individual cell to a spatial stimulus, direction sensing has attracted numerous theoretical treatments aimed at explaining experimental observations in a variety of cell types. Here we propose a new model of direction sensing based on experiments using Dictyostelium discoideum (Dicty). The model is built around a reaction-diffusion-translocation system that involves three main component processes: a signal detection step based on G-protein-coupled receptors (GPCR) for cyclic AMP (cAMP), a transduction step based on a heterotrimetic G protein Gα2βγ, and an activation step of a monomeric G-protein Ras. The model can predict the experimentally-observed response of cells treated with latrunculin A, which removes feedback from downstream processes, under a variety of stimulus protocols. We show that Gα2βγ cycling modulated by Ric8, a nonreceptor guanine exchange factor for Gα2 in Dicty, drives multiple phases of Ras activation and leads to direction sensing and signal amplification in cAMP gradients. The model predicts that both Gα2 and Gβγ are essential for direction sensing, in that membrane-localized Gα2*, the activated GTP-bearing form of Gα2, leads to asymmetrical recruitment of RasGEF and Ric8, while globally-diffusing Gβγ mediates their activation. We show that the predicted response at the level of Ras activation encodes sufficient ‘memory’ to eliminate the ‘back-of-the wave’ problem, and the effects of diffusion and cell shape on direction sensing are also investigated. In contrast with existing LEGI models of chemotaxis, the results do not require a disparity between the diffusion coefficients of the Ras activator GEF and the Ras inhibitor GAP. Since the signal pathways we study are highly conserved between Dicty and mammalian leukocytes, the model can serve as a generic one for direction sensing. PMID:27152956

Diffusion of Charged Species in Liquids

NASA Astrophysics Data System (ADS)

Del Río, J. A.; Whitaker, S.

2016-11-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids.

PubMed

Del Río, J A; Whitaker, S

2016-11-04

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids

PubMed Central

del Río, J. A.; Whitaker, S.

2016-01-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases. PMID:27811959

Chemotaxis of artificial microswimmers in active density waves

NASA Astrophysics Data System (ADS)

Geiseler, Alexander; Hänggi, Peter; Marchesoni, Fabio; Mulhern, Colm; Savel'ev, Sergey

2016-07-01

Living microorganisms are capable of a tactic response to external stimuli by swimming toward or away from the stimulus source; they do so by adapting their tactic signal transduction pathways to the environment. Their self-motility thus allows them to swim against a traveling tactic wave, whereas a simple fore-rear asymmetry argument would suggest the opposite. Their biomimetic counterpart, the artificial microswimmers, also propel themselves by harvesting kinetic energy from an active medium, but, in contrast, lack the adaptive capacity. Here we investigate the transport of artificial swimmers subject to traveling active waves and show, by means of analytical and numerical methods, that self-propelled particles can actually diffuse in either direction with respect to the wave, depending on its speed and waveform. Moreover, chiral swimmers, which move along spiraling trajectories, may diffuse preferably in a direction perpendicular to the active wave. Such a variety of tactic responses is explained by the modulation of the swimmer's diffusion inside traveling active pulses.

Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

PubMed Central

Seroussi, Inbar; Grebenkov, Denis S.; Pasternak, Ofer; Sochen, Nir

2017-01-01

In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad-hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal. PMID:28242566

Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming

2017-12-01

In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

GPCR-mediated PLCβγ/PKCβ/PKD signaling pathway regulates the cofilin phosphatase slingshot 2 in neutrophil chemotaxis

PubMed Central

Xu, Xuehua; Gera, Nidhi; Li, Hongyan; Yun, Michelle; Zhang, Liyong; Wang, Youhong; Wang, Q. Jane; Jin, Tian

2015-01-01

Chemotaxis requires precisely coordinated polymerization and depolymerization of the actin cytoskeleton at leading fronts of migrating cells. However, GPCR activation-controlled F-actin depolymerization remains largely elusive. Here, we reveal a novel signaling pathway, including Gαi, PLC, PKCβ, protein kinase D (PKD), and SSH2, in control of cofilin phosphorylation and actin cytoskeletal reorganization, which is essential for neutrophil chemotaxis. We show that PKD is essential for neutrophil chemotaxis and that GPCR-mediated PKD activation depends on PLC/PKC signaling. More importantly, we discover that GPCR activation recruits/activates PLCγ2 in a PI3K-dependent manner. We further verify that PKCβ specifically interacts with PKD1 and is required for chemotaxis. Finally, we identify slingshot 2 (SSH2), a phosphatase of cofilin (actin depolymerization factor), as a target of PKD1 that regulates cofilin phosphorylation and remodeling of the actin cytoskeleton during neutrophil chemotaxis. PMID:25568344

Prediction of stream volatilization coefficients

USGS Publications Warehouse

Rathbun, Ronald E.

1990-01-01

Equations are developed for predicting the liquid-film and gas-film reference-substance parameters for quantifying volatilization of organic solutes from streams. Molecular weight and molecular-diffusion coefficients of the solute are used as correlating parameters. Equations for predicting molecular-diffusion coefficients of organic solutes in water and air are developed, with molecular weight and molal volume as parameters. Mean absolute errors of prediction for diffusion coefficients in water are 9.97% for the molecular-weight equation, 6.45% for the molal-volume equation. The mean absolute error for the diffusion coefficient in air is 5.79% for the molal-volume equation. Molecular weight is not a satisfactory correlating parameter for diffusion in air because two equations are necessary to describe the values in the data set. The best predictive equation for the liquid-film reference-substance parameter has a mean absolute error of 5.74%, with molal volume as the correlating parameter. The best equation for the gas-film parameter has a mean absolute error of 7.80%, with molecular weight as the correlating parameter.

Causal Diffusion and the Survival of Charge Fluctuations

NASA Astrophysics Data System (ADS)

Abdel-Aziz, Mohamed; Gavin, Sean

2004-10-01

Diffusion may obliterate fluctuation signals of the QCD phase transition in nuclear collisions at SPS and RHIC energies. We propose a hyperbolic diffusion equation to study the dissipation of net charge fluctuations [1]. This equation is needed in a relativistic context, because the classic parabolic diffusion equation violates causality. We find that causality substantially limits the extent to which diffusion can dissipate these fluctuations. [1] M. Abdel-Aziz and S. Gavin, nucl-th/0404058

Threshold levels of ERK activation for chemotactic migration differ for NGF and EGF in rat pheochromocytoma PC12 cells.

PubMed

Ho, W C; Uniyal, S; Zhou, H; Morris, V L; Chan, B M C

2005-03-01

In a previous study, we show that stimulation of chemotaxis in rat pheochromocytoma PC12 cells by nerve growth factor (NGF) and epidermal growth factor (EGF) requires activation of the RAS-ERK signaling pathway. In this study, we compared the threshold levels of ERK activation required for EGF and NGF-stimulated chemotaxis in PC12 cells. The threshold ERK activity required for NGF to stimulate chemotaxis was approximately 30% lower than that for EGF. PD98059 treatment inhibited EGF stimulation of growth and chemotaxis; however, stimulation of chemotaxis required an EGF concentration approximately 10 times higher than for stimulation of PC12 cell growth. Thus, ERK-dependent cellular functions can be differentially elicited by the concentration of EGF. Also, treatment of PC12 cells with the PI3-K inhibitor LY294002 reduced ERK activation by NGF; thus, higher NGF concentrations were required to initiate chemotaxis and to achieve the same maximal chemotactic response seen in untreated PC12 cells. Therefore, the threshold NGF concentration to stimulate chemotaxis could be adjusted by the crosstalk between the ERK and PI3-K pathways, and the contributions of PI3-K and ERK to signal chemotaxis varied with the concentrations of NGF used. In comparison, LY294002 treatment had no effect on ERK activation by EGF, but the chemotactic response was reduced at all the concentrations of EGF tested indicating that NGF and EGF differed in the utilization of ERK and PI3-K to signal chemotaxis in PC12 cells.

Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane

NASA Astrophysics Data System (ADS)

Hu, Wenjie; Duan, Yueliang

2018-04-01

We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.

FRACTIONAL PEARSON DIFFUSIONS.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-07-15

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.

A nonlinear equation for ionic diffusion in a strong binary electrolyte

PubMed Central

Ghosal, Sandip; Chen, Zhen

2010-01-01

The problem of the one-dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson–Nernst–Planck (PNP) system, consists of a diffusion equation for each species augmented by transport owing to a self-consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important problems in physics, such as electron and hole diffusion across semiconductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here, we derive a more general theory by exploiting the ratio of the Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear partial differential equation that provides a better approximation than the classical linear equation for ambipolar diffusion, but reduces to it in the appropriate limit. PMID:21818176

An Ab Initio and Kinetic Monte Carlo Simulation Study of Lithium Ion Diffusion on Graphene

PubMed Central

Zhong, Kehua; Yang, Yanmin; Xu, Guigui; Zhang, Jian-Min; Huang, Zhigao

2017-01-01

The Li+ diffusion coefficients in Li+-adsorbed graphene systems were determined by combining first-principle calculations based on density functional theory with Kinetic Monte Carlo simulations. The calculated results indicate that the interactions between Li ions have a very important influence on lithium diffusion. Based on energy barriers directly obtained from first-principle calculations for single-Li+ and two-Li+ adsorbed systems, a new equation predicting energy barriers with more than two Li ions was deduced. Furthermore, it is found that the temperature dependence of Li+ diffusion coefficients fits well to the Arrhenius equation, rather than meeting the equation from electrochemical impedance spectroscopy applied to estimate experimental diffusion coefficients. Moreover, the calculated results also reveal that Li+ concentration dependence of diffusion coefficients roughly fits to the equation from electrochemical impedance spectroscopy in a low concentration region; however, it seriously deviates from the equation in a high concentration region. So, the equation from electrochemical impedance spectroscopy technique could not be simply used to estimate the Li+ diffusion coefficient for all Li+-adsorbed graphene systems with various Li+ concentrations. Our work suggests that interactions between Li ions, and among Li ion and host atoms will influence the Li+ diffusion, which determines that the Li+ intercalation dependence of Li+ diffusion coefficient should be changed and complex. PMID:28773122

Chemotaxis toward carbohydrates and peptides by mixed ruminal protozoa when fed, fasted, or incubated with polyunsaturated fatty acids.

PubMed

Diaz, H L; Karnati, S K R; Lyons, M A; Dehority, B A; Firkins, J L

2014-01-01

In contrast to the well-characterized chemotaxis and migratory behavior between the dorsal and ventral locations of the rumen by isotrichids, we hypothesized that chemotaxis toward soluble nutrients maintains entodiniomorphid protozoa in the particulate fraction. The objectives of these experiments were to compare the dose-responsive chemotaxis (1) toward different glucose concentrations when ruminal samples were harvested from fed versus fasted cows; (2) toward increasing concentrations of glucose compared with xylose when protozoa were harvested from a fed cow; (3) toward peptides of bacterial, protozoal, and soy origin; and (4) toward glucose when mixed ruminal protozoa were previously incubated for 0, 3, or 6h in the presence of emulsified polyunsaturated fatty acids (PUFA; Liposyn II, Hospira, Lake Forest, IL). In experiment 1, isotrichid protozoa decreased chemotaxis toward increasing glucose concentration when cows were fasted. Entodiniomorphids exhibited chemotaxis to similar concentrations of glucose as did isotrichids, but to a lesser magnitude of response. In experiment 2, xylose was chemotactic to both groups. Xylose might draw fibrolytic entodiniomorphid protozoa toward newly ingested feed. In contrast, even though isotrichids should not use xylose as an energy source, they were highly chemoattracted to xylose. In experiment 3, entodiniomorphids were not selectively chemoattracted toward bacterial or protozoal peptides compared with soy peptides. In experiment 4, despite isotrichid populations decreasing in abundance with increasing time of incubation in PUFA, chemotaxis to glucose remained unchanged. In contrast, entodiniomorphids recovered chemotaxis to glucose with increased time of PUFA incubation. Current results support isotrichid chemotaxis to sugars but also our hypothesis that a more moderate chemotaxis toward glucose and peptides explains how they swim in the fluid but pass from the rumen with the potentially digestible fraction of particulates. Copyright © 2014 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

A Real Time Chemotaxis Assay Unveils Unique Migratory Profiles amongst Different Primary Murine Macrophages

PubMed Central

Iqbal, Asif J.; Regan-Komito, Daniel; Christou, Ivy; White, Gemma E.; McNeill, Eileen; Kenyon, Amy; Taylor, Lewis; Kapellos, Theodore S.; Fisher, Edward A.; Channon, Keith M.; Greaves, David R.

2013-01-01

Chemotaxis assays are an invaluable tool for studying the biological activity of inflammatory mediators such as CC chemokines, which have been implicated in a wide range of chronic inflammatory diseases. Conventional chemotaxis systems such as the modified Boyden chamber are limited in terms of the data captured given that the assays are analysed at a single time-point. We report the optimisation and validation of a label-free, real-time cell migration assay based on electrical cell impedance to measure chemotaxis of different primary murine macrophage populations in response to a range of CC chemokines and other chemoattractant signalling molecules. We clearly demonstrate key differences in the migratory behavior of different murine macrophage populations and show that this dynamic system measures true macrophage chemotaxis rather than chemokinesis or fugetaxis. We highlight an absolute requirement for Gαi signaling and actin cytoskeletal rearrangement as demonstrated by Pertussis toxin and cytochalasin D inhibition. We also studied the chemotaxis of CD14+ human monocytes and demonstrate distinct chemotactic profiles amongst different monocyte donors to CCL2. This real-time chemotaxis assay will allow a detailed analysis of factors that regulate macrophage responses to chemoattractant cytokines and inflammatory mediators. PMID:23516549

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Physics of chemoreception.

PubMed Central

Berg, H C; Purcell, E M

1977-01-01

Statistical fluctuations limit the precision with which a microorganism can, in a given time T, determine the concentration of a chemoattractant in the surrounding medium. The best a cell can do is to monitor continually the state of occupation of receptors distributed over its surface. For nearly optimum performance only a small fraction of the surface need be specifically adsorbing. The probability that a molecule that has collided with the cell will find a receptor is Ns/(Ns + pi a), if N receptors, each with a binding site of radius s, are evenly distributed over a cell of radius a. There is ample room for many indenpendent systems of specific receptors. The adsorption rate for molecules of moderate size cannot be significantly enhanced by motion of the cell or by stirring of the medium by the cell. The least fractional error attainable in the determination of a concentration c is approximately (TcaD) - 1/2, where D is diffusion constant of the attractant. The number of specific receptors needed to attain such precision is about a/s. Data on bacteriophage absorption, bacterial chemotaxis, and chemotaxis in a cellular slime mold are evaluated. The chemotactic sensitivity of Escherichia coli approaches that of the cell of optimum design. PMID:911982

The exit-time problem for a Markov jump process

NASA Astrophysics Data System (ADS)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

Effects of curved midline and varying width on the description of the effective diffusivity of Brownian particles

NASA Astrophysics Data System (ADS)

Chávez, Yoshua; Chacón-Acosta, Guillermo; Dagdug, Leonardo

2018-05-01

Axial diffusion in channels and tubes of smoothly-varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with a position-dependent effective diffusion coefficient, by means of the modified Fick–Jacobs equation. In this work, we derive analytical expressions for the position-dependent effective diffusivity for two-dimensional asymmetric varying-width channels, and for three-dimensional curved midline tubes, formed by straight walls. To this end, we use a recently developed theoretical framework using the Frenet–Serret moving frame as the coordinate system (2016 J. Chem. Phys. 145 074105). For narrow tubes and channels, an effective one-dimensional description reducing the diffusion equation to a Fick–Jacobs-like equation in general coordinates is used. From this last equation, one can calculate the effective diffusion coefficient applying Neumann boundary conditions.

Mesenchymal chemotaxis requires selective inactivation of Myosin II at the leading edge via a non-canonical PLCγ/PKCα pathway

PubMed Central

Asokan, Sreeja B.; Johnson, Heath E.; Rahman, Anisur; King, Samantha J.; Rotty, Jeremy D.; Lebedeva, Irina P.; Haugh, Jason M.; Bear, James E.

2014-01-01

Summary Chemotaxis, migration towards soluble chemical cues, is critical for processes such as wound healing and immune surveillance, and is exhibited by various cell types from rapidly-migrating leukocytes to slow-moving mesenchymal cells. To interrogate the mechanisms involved in mesenchymal chemotaxis, we observed cell migration in microfluidic chambers that generate stable gradients of the chemoattractant PDGF. Surprisingly, we found that pathways implicated in amoeboid chemotaxis, such as PI3K and mTOR signaling, are dispensable for chemotaxis to PDGF. Instead, we find that local inactivation of Myosin IIA, through a non-canonical Ser1/2 phosphorylation of the regulatory light chain, is essential. This site is phosphorylated by PKCα, which is activated by an intracellular gradient of diacylglycerol generated by PLCγ. Using a combination of TIRF imaging and gradients of activators/inhibitors in the microfluidic chambers, we demonstrate that this signaling pathway and subsequent inhibition of Myosin II activity at the leading edge is required for mesenchymal chemotaxis. PMID:25482883

General PFG signal attenuation expressions for anisotropic anomalous diffusion by modified-Bloch equations

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-05-01

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) anomalous diffusion is complicated, especially in the anisotropic case where limited research has been reported. A general PFG signal attenuation expression, including the finite gradient pulse (FGPW) effect for free general anisotropic fractional diffusion { 0 < α , β ≤ 2 } based on the fractional derivative, has not been obtained, where α and β are time and space derivative orders. It is essential to derive a general PFG signal attenuation expression including the FGPW effect for PFG anisotropic anomalous diffusion research. In this paper, two recently developed modified-Bloch equations, the fractal differential modified-Bloch equation and the fractional integral modified-Bloch equation, were extended to obtain general PFG signal attenuation expressions for anisotropic anomalous diffusion. Various cases of PFG anisotropic anomalous diffusion were investigated, including coupled and uncoupled anisotropic anomalous diffusion. The continuous-time random walk (CTRW) simulation was also carried out to support the theoretical results. The theory and the CTRW simulation agree with each other. The obtained signal attenuation expressions and the three-dimensional fractional modified-Bloch equations are important for analyzing PFG anisotropic anomalous diffusion in NMR and MRI.

A parallel algorithm for nonlinear convection-diffusion equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1990-01-01

A parallel algorithm for the efficient solution of nonlinear time-dependent convection-diffusion equations with small parameter on the diffusion term is presented. The method is based on a physically motivated domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. The method is suitable for the solution of problems arising in the simulation of fluid dynamics. Experimental results for a nonlinear equation in two-dimensions are presented.

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

Computational and Theoretical Study of the Physical Constraints on Chemotaxis

NASA Astrophysics Data System (ADS)

Varennes, Julien

Cell chemotaxis is crucial to many biological functions including development, wound healing, and cancer metastasis. Chemotaxis is the process in which cells migrate in response to chemical concentration gradients. Recent experiments show that cells are capable of detecting shallow gradients as small as a 1% concentration difference, and multicellular groups can improve on this by an additional order of magnitude. Examples from morphogenesis and metastasis demonstrate collective response to gradients equivalent to a 1 molecule difference in concentration across a cell body. While the physical constraints to cell gradient sensing are well understood, how the sensory information leads to cell migration, and coherent multicellular movement in the case of collectives, remains poorly understood. Here we examine how extrinsic sensory noise leads to error in chemotactic performance. First, we study single cell chemotaxis and use both simulations and analytical models to place physical constraints on chemotactic performance. Next we turn our attention to collective chemotaxis. We examine how collective cell interactions can improve chemotactic performance. We develop a novel model for quantifying the physical limit to chemotactic precision for two stereotypical modes of collective chemotaxis. Finally, we conclude by examining the effects of intercellular communication on collective chemotaxis. We use simulations to test how well collectives can chemotax through very shallow gradients with the help of communication. By studying these computational and theoretical models of individual and collective chemotaxis, we address the gap in knowledge between chemical sensing and directed migration.

Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights

NASA Astrophysics Data System (ADS)

Chechkin, A. V.; Gonchar, V. Yu.; Gorenflo, R.; Korabel, N.; Sokolov, I. M.

2008-08-01

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order. Such equations were introduced in A. V. Chechkin, R. Gorenflo, and I. Sokolov [Phys. Rev. E 66, 046129 (2002)] for the description of the processes getting more anomalous in the course of time (decelerating subdiffusion and accelerating superdiffusion). Here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time, which we call, respectively, accelerating subdiffusion and decelerating superdiffusion. For the former process, by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time. For the latter process we demonstrate by a particular example how the power-law truncated Lévy stable distribution evolves in time to the distribution with power-law asymptotics and Gaussian shape in the central part. The special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics.

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

Heavy-tailed fractional Pearson diffusions.

PubMed

Leonenko, N N; Papić, I; Sikorskii, A; Šuvak, N

2017-11-01

We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.

Feynman-Kac equations for reaction and diffusion processes

NASA Astrophysics Data System (ADS)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Ezz-Eldien, Samer S.

2013-10-01

In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

Actin dynamics in cells on nanotopographical surfaces in competition with chemotaxis and electrotaxis

NASA Astrophysics Data System (ADS)

Schmidt, Sebastian

Directed cell migration can be guided by different types of gradients, for example chemotaxis. We use surfaces with nanotopographical ridges to examine a type of guidance called esotaxis on migration in the well-studied amoeba Dictyostelium Discoideum. In this work we compare chemotaxis with esotaxis on ridges as well as the influence of electrotaxis on the formation of the actin cytoskeleton on these nanotopographies. These esotactic surfaces have more guidance cues for cells than planar 2D cultures and can disrupt other guidance types like chemotaxis.

The exit-time problem for a Markov jump process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

2014-12-15

The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developedmore » nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.« less

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

NASA Astrophysics Data System (ADS)

Frank, T. D.

2008-02-01

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

Evaluation of bacterial motility from non-Gaussianity of finite-sample trajectories using the large deviation principle

NASA Astrophysics Data System (ADS)

Hanasaki, Itsuo; Kawano, Satoyuki

2013-11-01

Motility of bacteria is usually recognized in the trajectory data and compared with Brownian motion, but the diffusion coefficient is insufficient to evaluate it. In this paper, we propose a method based on the large deviation principle. We show that it can be used to evaluate the non-Gaussian characteristics of model Escherichia coli motions and to distinguish combinations of the mean running duration and running speed that lead to the same diffusion coefficient. Our proposed method does not require chemical stimuli to induce the chemotaxis in a specific direction, and it is applicable to various types of self-propelling motions for which no a priori information of, for example, threshold parameters for run and tumble or head/tail direction is available. We also address the issue of the finite-sample effect on the large deviation quantities, but we propose to make use of it to characterize the nature of motility.

Hydrodynamic collective effects of active protein machines in solution and lipid bilayers

PubMed Central

Mikhailov, Alexander S.; Kapral, Raymond

2015-01-01

The cytoplasm and biomembranes in biological cells contain large numbers of proteins that cyclically change their shapes. They are molecular machines that can function as molecular motors or carry out various other tasks in the cell. Many enzymes also undergo conformational changes within their turnover cycles. We analyze the advection effects that nonthermal fluctuating hydrodynamic flows induced by active proteins have on other passive molecules in solution or membranes. We show that the diffusion constants of passive particles are enhanced substantially. Furthermore, when gradients of active proteins are present, a chemotaxis-like drift of passive particles takes place. In lipid bilayers, the effects are strongly nonlocal, so that active inclusions in the entire membrane contribute to local diffusion enhancement and the drift. All active proteins in a biological cell or in a membrane contribute to such effects and all passive particles, and the proteins themselves, will be subject to them. PMID:26124140

Modification of β-Defensin-2 by Dicarbonyls Methylglyoxal and Glyoxal Inhibits Antibacterial and Chemotactic Function In Vitro.

PubMed

Kiselar, Janna G; Wang, Xiaowei; Dubyak, George R; El Sanadi, Caroline; Ghosh, Santosh K; Lundberg, Kathleen; Williams, Wesley M

2015-01-01

Beta-defensins (hBDs) provide antimicrobial and chemotactic defense against bacterial, viral and fungal infections. Human β-defensin-2 (hBD-2) acts against gram-negative bacteria and chemoattracts immature dendritic cells, thus regulating innate and adaptive immunity. Immunosuppression due to hyperglycemia underlies chronic infection in Type 2 diabetes. Hyperglycemia also elevates production of dicarbonyls methylgloxal (MGO) and glyoxal (GO). The effect of dicarbonyl on defensin peptide structure was tested by exposing recombinant hBD-2 (rhBD-2) to MGO or GO with subsequent analysis by MALDI-TOF MS and LC/MS/MS. Antimicrobial function of untreated rhBD-2 vs. rhBD-2 exposed to dicarbonyl against strains of both gram-negative and gram-positive bacteria in culture was determined by radial diffusion assay. The effect of dicarbonyl on rhBD-2 chemotactic function was determined by chemotaxis assay in CEM-SS cells. MGO or GO in vitro irreversibly adducts to the rhBD-2 peptide, and significantly reduces antimicrobial and chemotactic functions. Adducts derive from two arginine residues, Arg22 and Arg23 near the C-terminus, and the N-terminal glycine (Gly1). We show by radial diffusion testing on gram-negative E. coli and P. aeruginosa, and gram-positive S. aureus, and a chemotaxis assay for CEM-SS cells, that antimicrobial activity and chemotactic function of rhBD-2 are significantly reduced by MGO. Dicarbonyl modification of cationic antimicrobial peptides represents a potential link between hyperglycemia and the clinical manifestation of increased susceptibility to infection, protracted wound healing, and chronic inflammation in undiagnosed and uncontrolled Type 2 diabetes.

Analysis of bacterial migration. 2: Studies with multiple attractant gradients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strauss, I.; Frymier, P.D.; Hahn, C.M.

1995-02-01

Many motile bacteria exhibit chemotaxis, the ability to bias their random motion toward or away from increasing concentrations of chemical substances which benefit or inhibit their survival, respectively. Since bacteria encounter numerous chemical concentration gradients simultaneously in natural surroundings, it is necessary to know quantitatively how a bacterial population responds in the presence of more than one chemical stimulus to develop predictive mathematical models describing bacterial migration in natural systems. This work evaluates three hypothetical models describing the integration of chemical signals from multiple stimuli: high sensitivity, maximum signal, and simple additivity. An expression for the tumbling probability for individualmore » stimuli is modified according to the proposed models and incorporated into the cell balance equation for a 1-D attractant gradient. Random motility and chemotactic sensitivity coefficients, required input parameters for the model, are measured for single stimulus responses. Theoretical predictions with the three signal integration models are compared to the net chemotactic response of Escherichia coli to co- and antidirectional gradients of D-fucose and [alpha]-methylaspartate in the stopped-flow diffusion chamber assay. Results eliminate the high-sensitivity model and favor the simple additivity over the maximum signal. None of the simple models, however, accurately predict the observed behavior, suggesting a more complex model with more steps in the signal processing mechanism is required to predict responses to multiple stimuli.« less

Distinct Domains of CheA Confer Unique Functions in Chemotaxis and Cell Length in Azospirillum brasilense Sp7.

PubMed

Gullett, Jessica M; Bible, Amber; Alexandre, Gladys

2017-07-01

Chemotaxis is the movement of cells in response to gradients of diverse chemical cues. Motile bacteria utilize a conserved chemotaxis signal transduction system to bias their motility and navigate through a gradient. A central regulator of chemotaxis is the histidine kinase CheA. This cytoplasmic protein interacts with membrane-bound receptors, which assemble into large polar arrays, to propagate the signal. In the alphaproteobacterium Azospirillum brasilense , Che1 controls transient increases in swimming speed during chemotaxis, but it also biases the cell length at division. However, the exact underlying molecular mechanisms for Che1-dependent control of multiple cellular behaviors are not known. Here, we identify specific domains of the CheA1 histidine kinase implicated in modulating each of these functions. We show that CheA1 is produced in two isoforms: a membrane-anchored isoform produced as a fusion with a conserved seven-transmembrane domain of unknown function (TMX) at the N terminus and a soluble isoform similar to prototypical CheA. Site-directed and deletion mutagenesis combined with behavioral assays confirm the role of CheA1 in chemotaxis and implicate the TMX domain in mediating changes in cell length. Fluorescence microscopy further reveals that the membrane-anchored isoform is distributed around the cell surface while the soluble isoform localizes at the cell poles. Together, the data provide a mechanism for the role of Che1 in controlling multiple unrelated cellular behaviors via acquisition of a new domain in CheA1 and production of distinct functional isoforms. IMPORTANCE Chemotaxis provides a significant competitive advantage to bacteria in the environment, and this function has been transferred laterally multiple times, with evidence of functional divergence in different genomic contexts. The molecular principles that underlie functional diversification of chemotaxis in various genomic contexts are unknown. Here, we provide a molecular mechanism by which a single CheA protein controls two unrelated functions: chemotaxis and cell length. Acquisition of this multifunctionality is seemingly a recent evolutionary event. The findings illustrate a mechanism by which chemotaxis function may be co-opted to regulate additional cellular functions. Copyright © 2017 American Society for Microbiology.

Distinct Domains of CheA Confer Unique Functions in Chemotaxis and Cell Length in Azospirillum brasilense Sp7

PubMed Central

Gullett, Jessica M.

2017-01-01

ABSTRACT Chemotaxis is the movement of cells in response to gradients of diverse chemical cues. Motile bacteria utilize a conserved chemotaxis signal transduction system to bias their motility and navigate through a gradient. A central regulator of chemotaxis is the histidine kinase CheA. This cytoplasmic protein interacts with membrane-bound receptors, which assemble into large polar arrays, to propagate the signal. In the alphaproteobacterium Azospirillum brasilense, Che1 controls transient increases in swimming speed during chemotaxis, but it also biases the cell length at division. However, the exact underlying molecular mechanisms for Che1-dependent control of multiple cellular behaviors are not known. Here, we identify specific domains of the CheA1 histidine kinase implicated in modulating each of these functions. We show that CheA1 is produced in two isoforms: a membrane-anchored isoform produced as a fusion with a conserved seven-transmembrane domain of unknown function (TMX) at the N terminus and a soluble isoform similar to prototypical CheA. Site-directed and deletion mutagenesis combined with behavioral assays confirm the role of CheA1 in chemotaxis and implicate the TMX domain in mediating changes in cell length. Fluorescence microscopy further reveals that the membrane-anchored isoform is distributed around the cell surface while the soluble isoform localizes at the cell poles. Together, the data provide a mechanism for the role of Che1 in controlling multiple unrelated cellular behaviors via acquisition of a new domain in CheA1 and production of distinct functional isoforms. IMPORTANCE Chemotaxis provides a significant competitive advantage to bacteria in the environment, and this function has been transferred laterally multiple times, with evidence of functional divergence in different genomic contexts. The molecular principles that underlie functional diversification of chemotaxis in various genomic contexts are unknown. Here, we provide a molecular mechanism by which a single CheA protein controls two unrelated functions: chemotaxis and cell length. Acquisition of this multifunctionality is seemingly a recent evolutionary event. The findings illustrate a mechanism by which chemotaxis function may be co-opted to regulate additional cellular functions. PMID:28416707

The effect of stress-inducible extracellular Hsp72 on human neutrophil chemotaxis: a role during acute intense exercise.

PubMed

Ortega, Eduardo; Hinchado, M D; Martín-Cordero, L; Asea, A

2009-05-01

We studied the physiological role of the 72 kDa extracellular heat shock protein (Hsp72, a stress-inducible protein) in modulating neutrophil chemotaxis during a single bout of intense exercise performed by sedentary women, together with various cell mechanisms potentially involved in the modulation. For each volunteer, we evaluated neutrophil chemotaxis and serum Hsp72 concentration before and immediately after a single bout of exercise (1 h on a cycle ergometer at 70% VO(2) max), and 24 h later. Both parameters were found to be stimulated by the exercise, and had returned to basal values 24 h later. In vitro, there was a dose-dependent increase in chemotaxis when neutrophils were incubated both with physiological Hsp72 concentrations and with a 100 x greater concentration. The chemotaxis was greater when the neutrophils were incubated with the post-exercise Hsp72 concentration than with the basal concentration, suggesting a physiological role for this protein in the context of the stimulation of neutrophil chemotaxis by intense exercise. The 100 x Hsp72 concentration stimulated chemotaxis even more strongly. In addition, Hsp72 was found to have chemoattractant and chemokinetic effects on the neutrophils at physiological concentrations, with these effects being significantly greater with the post-exercise than with the basal Hsp72 concentration. The Hsp72-induced stimulation of neutrophil chemotaxis disappeared when the toll-like receptor 2 (TLR-2) was blocked, and phosphatidylinositol-3-kinase (PI3K), extracellular signal-regulated kinase (ERK), and nuclear transcription factor kappa B (NF-kappaB) were also found to be involved in the signaling process. No changes were observed, however, in neutrophil intracellular calcium levels in response to Hsp72. In conclusion, physiological concentrations of the stress protein Hsp72 stimulate human neutrophil chemotaxis through TLR-2 with its cofactor CD14, involving ERK, NF-kappaB, and PI3K, but not iCa(2 + ), as intracellular messengers. In addition, Hsp72 seems to participate in the stimulation of chemotaxis induced by a single bout of intense exercise performed by sedentary women.

Diffusion Influenced Adsorption Kinetics.

PubMed

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.

Chemotaxis by natural populations of coral reef bacteria.

PubMed

Tout, Jessica; Jeffries, Thomas C; Petrou, Katherina; Tyson, Gene W; Webster, Nicole S; Garren, Melissa; Stocker, Roman; Ralph, Peter J; Seymour, Justin R

2015-08-01

Corals experience intimate associations with distinct populations of marine microorganisms, but the microbial behaviours underpinning these relationships are poorly understood. There is evidence that chemotaxis is pivotal to the infection process of corals by pathogenic bacteria, but this evidence is limited to experiments using cultured isolates under laboratory conditions. We measured the chemotactic capabilities of natural populations of coral-associated bacteria towards chemicals released by corals and their symbionts, including amino acids, carbohydrates, ammonium and dimethylsulfoniopropionate (DMSP). Laboratory experiments, using a modified capillary assay, and in situ measurements, using a novel microfabricated in situ chemotaxis assay, were employed to quantify the chemotactic responses of natural microbial assemblages on the Great Barrier Reef. Both approaches showed that bacteria associated with the surface of the coral species Pocillopora damicornis and Acropora aspera exhibited significant levels of chemotaxis, particularly towards DMSP and amino acids, and that these levels of chemotaxis were significantly higher than that of bacteria inhabiting nearby, non-coral-associated waters. This pattern was supported by a significantly higher abundance of chemotaxis and motility genes in metagenomes within coral-associated water types. The phylogenetic composition of the coral-associated chemotactic microorganisms, determined using 16S rRNA amplicon pyrosequencing, differed from the community in the seawater surrounding the coral and comprised known coral associates, including potentially pathogenic Vibrio species. These findings indicate that motility and chemotaxis are prevalent phenotypes among coral-associated bacteria, and we propose that chemotaxis has an important role in the establishment and maintenance of specific coral-microbe associations, which may ultimately influence the health and stability of the coral holobiont.

Analytical solutions of the space-time fractional Telegraph and advection-diffusion equations

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Schlickeiser, Reinhard; Elhanbaly, A.

2018-02-01

The aim of this paper is to develop a fractional derivative model of energetic particle transport for both uniform and non-uniform large-scale magnetic field by studying the fractional Telegraph equation and the fractional advection-diffusion equation. Analytical solutions of the space-time fractional Telegraph equation and space-time fractional advection-diffusion equation are obtained by use of the Caputo fractional derivative and the Laplace-Fourier technique. The solutions are given in terms of Fox's H function. As an illustration they are applied to the case of solar energetic particles.

Boundary value problems for multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations

NASA Astrophysics Data System (ADS)

Lin, Zeng; Wang, Dongdong

2017-10-01

Due to the nonlocal property of the fractional derivative, the finite element analysis of fractional diffusion equation often leads to a dense and non-symmetric stiffness matrix, in contrast to the conventional finite element formulation with a particularly desirable symmetric and banded stiffness matrix structure for the typical diffusion equation. This work first proposes a finite element formulation that preserves the symmetry and banded stiffness matrix characteristics for the fractional diffusion equation. The key point of the proposed formulation is the symmetric weak form construction through introducing a fractional weight function. It turns out that the stiffness part of the present formulation is identical to its counterpart of the finite element method for the conventional diffusion equation and thus the stiffness matrix formulation becomes trivial. Meanwhile, the fractional derivative effect in the discrete formulation is completely transferred to the force vector, which is obviously much easier and efficient to compute than the dense fractional derivative stiffness matrix. Subsequently, it is further shown that for the general fractional advection-diffusion-reaction equation, the symmetric and banded structure can also be maintained for the diffusion stiffness matrix, although the total stiffness matrix is not symmetric in this case. More importantly, it is demonstrated that under certain conditions this symmetric diffusion stiffness matrix formulation is capable of producing very favorable numerical solutions in comparison with the conventional non-symmetric diffusion stiffness matrix finite element formulation. The effectiveness of the proposed methodology is illustrated through a series of numerical examples.

Diffusion coefficients in organic-water solutions and comparison with Stokes-Einstein predictions

NASA Astrophysics Data System (ADS)

Evoy, E.; Kamal, S.; Bertram, A. K.

2017-12-01

Diffusion coefficients of organic species in particles containing secondary organic material (SOM) are necessary for predicting the growth and reactivity of these particles in the atmosphere. Previously, the Stokes-Einstein equation combined with viscosity measurements have been used to predict these diffusion coefficients. However, the accuracy of the Stokes-Einstein equation for predicting diffusion coefficients in SOM-water particles has not been quantified. To test the Stokes-Einstein equation, diffusion coefficients of fluorescent organic probe molecules were measured in citric acid-water and sorbitol-water solutions. These solutions were used as proxies for SOM-water particles found in the atmosphere. Measurements were performed as a function of water activity, ranging from 0.26-0.86, and as a function of viscosity ranging from 10-3 to 103 Pa s. Diffusion coefficients were measured using fluorescence recovery after photobleaching. The measured diffusion coefficients were compared with predictions made using the Stokes-Einstein equation combined with literature viscosity data. Within the uncertainties of the measurements, the measured diffusion coefficients agreed with the predicted diffusion coefficients, in all cases.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less

S{sub 2}SA preconditioning for the S{sub n} equations with strictly non negative spatial discretization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

2013-07-01

Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S{sub n} transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use amore » linear diffusion equation has important implications for preconditioning the S{sub n} equations with a strictly non negative spatial discretization in multiple dimensions. (authors)« less

Eukaryotic Chemotaxis

PubMed Central

Rappel, Wouter-Jan; Loomis, William F.

2009-01-01

During eukaryotic chemotaxis, external chemical gradients guide the crawling motion of cells. This process plays an important role in a large variety of biological systems and has wide ranging medical implications. New experimental techniques including confocal microscopy and microfluidics have advanced our understanding of chemotaxis while numerical modeling efforts are beginning to offer critical insights. In this short review, we survey the current experimental status of the field by dividing chemotaxis into three distinct “modules”: directional sensing, polarity and motility. For each module, we attempt to point out potential new directions of research and discuss how modeling studies interact with experimental investigations. PMID:20648241

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

The Impact of Odor--Reward Memory on Chemotaxis in Larval "Drosophila"

ERIC Educational Resources Information Center

Schleyer, Michael; Reid, Samuel F.; Pamir, Evren; Saumweber, Timo; Paisios, Emmanouil; Davies, Alexander; Gerber, Bertram; Louis, Matthieu

2015-01-01

How do animals adaptively integrate innate with learned behavioral tendencies? We tackle this question using chemotaxis as a paradigm. Chemotaxis in the "Drosophila" larva largely results from a sequence of runs and oriented turns. Thus, the larvae minimally need to determine (i) how fast to run, (ii) when to initiate a turn, and (iii)…

On the anisotropic advection-diffusion equation with time dependent coefficients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

On the anisotropic advection-diffusion equation with time dependent coefficients

DOE PAGES

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

2017-02-01

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

External stimulation strength controls actin response dynamics in Dictyostelium cells

NASA Astrophysics Data System (ADS)

Hsu, Hsin-Fang; Westendorf, Christian; Tarantola, Marco; Zykov, Vladimir; Bodenschatz, Eberhard; Beta, Carsten

2015-03-01

Self-sustained oscillation and the resonance frequency of the cytoskeletal actin polymerization/depolymerization have recently been observed in Dictyostelium, a model system for studying chemotaxis. Here we report that the resonance frequency is not constant but rather varies with the strength of external stimuli. To understand the underlying mechanism, we analyzed the polymerization and depolymerization time at different levels of external stimulation. We found that polymerization time is independent of external stimuli but the depolymerization time is prolonged as the stimulation increases. These observations can be successfully reproduced in the frame work of our time delayed differential equation model.

The control of neutrophil chemotaxis by inhibitors of cathepsin G and chymotrypsin.

PubMed

Lomas, D A; Stone, S R; Llewellyn-Jones, C; Keogan, M T; Wang, Z M; Rubin, H; Carrell, R W; Stockley, R A

1995-10-06

Neutrophil chemotaxis plays an important role in the inflammatory response and when excessive or persistent may augment tissue damage. The effects of inhibitors indicated the involvement of one or more serine proteinases in human neutrophil migration and shape change in response to a chemoattractant. Monospecific antibodies, chloromethylketone inhibitors, and reactive-site mutants of alpha 1-antitrypsin and alpha 1-antichymotrypsin were used to probe the specificity of the proteinases involved in chemotaxis. Antibodies specific for cathepsin G inhibited chemotaxis. Moreover, rapid inhibitors of cathepsin G and alpha-chymotrypsin suppressed neutrophil chemotaxis to the chemoattractants N-formyl-L-methionyl-L-leucyl-L-phenylalanine (fMLP) and zymosan-activated serum in multiple blind well assays and to fMLP in migration assays under agarose. The concentrations of antichymotrypsin mutants that reduced chemotaxis by 50% would inactivate free cathepsin G with a half-life of 1.5-3 s, whereas the concentrations of chloromethylketones required to produce a similar inhibition of chemotaxis would inactivate cathepsin G with a half-life of 345 s. These data suggest different modes of action for these two classes of inhibitors. Indeed the chloromethylketone inhibitors of cathepsin G (Z-Gly-Leu-Phe-CMK) and to a lesser extent of chymotrypsin (Cbz-Gly-Gly-Phe-CMK) mediated their effect by preventing a shape change in the purified neutrophils exposed to fMLP. Antichymotrypsin did not affect shape change in response to fMLP even at concentrations that were able to reduce neutrophil chemotaxis by 50%. These results support the involvement of cell surface proteinases in the control of cell migration and show that antichymotrypsin and chloromethylketones have differing modes of action. This opens the possibility for the rational design of anti-inflammatory agents targeted at neutrophil membrane enzymes.

General pulsed-field gradient signal attenuation expression based on a fractional integral modified-Bloch equation

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal attenuation expression based on the fractional derivative has not been previously reported. Additionally, the reported modified-Bloch equations for PFG anomalous diffusion in the literature yielded different results due to their different forms. Here, a new integral type modified-Bloch equation based on the fractional derivative for PFG anomalous diffusion is proposed, which is significantly different from the conventional differential type modified-Bloch equation. The merit of the integral type modified-Bloch equation is that the original properties of the contributions from linear or nonlinear processes remain unchanged at the instant of the combination. From the modified-Bloch equation, the general solutions are derived, which includes the finite gradient pulse width (FGPW) effect. The numerical evaluation of these PFG signal attenuation expressions can be obtained either by the Adomian decomposition, or a direct integration method that is fast and practicable. The theoretical results agree with the continuous-time random walk (CTRW) simulations performed in this paper. Additionally, the relaxation effect in PFG anomalous diffusion is found to be different from that in PFG normal diffusion. The new modified-Bloch equations and their solutions provide a fundamental tool to analyze PFG anomalous diffusion in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

Neutrophil chemotaxis by Propionibacterium acnes lipase and its inhibition.

PubMed Central

Lee, W L; Shalita, A R; Suntharalingam, K; Fikrig, S M

1982-01-01

The chemoattraction of Propionibacterium acnes lipase for neutrophils and the effect of lipase inhibitor and two antibiotic agents on the chemotaxis were evaluated. Of the various fractions tested, partially purified lipase (fraction 2c) was the most active cytotaxin produced by P. acnes. Serum mediators were not required for the generation of chemotaxis by lipase in vitro. Diisopropyl phosphofluoridate at low concentration (10(-4) mM) completely inhibited lipase activity as well as polymorphonuclear leukocyte chemotaxis generated by lipase. Tetracycline hydrochloride and erythromycin base at concentrations of 10(-1) mM and 1 mM, respectively, caused 100% inhibition of PMN migration toward lipase or zymosan-activated serum. The inhibiting activity of the antibiotics was directed against cells independently of any effect on lipase. Chemotaxis by P. acnes lipase suggests a wider role for this enzyme in the inflammatory process and the pathogenesis of acne vulgaris. Images PMID:7054130

THE REGULATORY ROLE OF DIVALENT CATIONS IN HUMAN GRANULOCYTE CHEMOTAXIS

PubMed Central

Gallin, John I.; Rosenthal, Alan S.

1974-01-01

Optimal human granulocyte chemotaxis has been shown to require both calcium and magnesium. Exposure of granulocytes to three different chemotactic factors (C5a, kallikrein, and dialyzable transfer factor) yielded a rapid calcium release, depressed calcium uptake, and was associated with a shift of calcium out of the cytoplasm and into a granule fraction. Colchicine, sodium azide, and cytochalasin B, in concentrations that inhibited chemotaxis, also inhibited calcium release while low concentrations of cytochalasin B, which enhanced chemotaxis, also enhanced calcium release. Microtubule assembly was visualized both in cells suspended in C5a without a chemotactic gradient and in cells actively migrating through a Micropore filter. The data suggest microtubule assembly is regulated, at least, in part, by the level of cytoplasmic calcium. It is proposed that asymmetric assembly of microtubules may be instrumental in imparting the net vector of motion during chemotaxis. PMID:4855032

Campylobacter jejuni transducer like proteins: Chemotaxis and beyond

PubMed Central

Chandrashekhar, Kshipra; Kassem, Issmat I.; Rajashekara, Gireesh

2017-01-01

ABSTRACT Chemotaxis, a process that mediates directional motility toward or away from chemical stimuli (chemoeffectors/ligands that can be attractants or repellents) in the environment, plays an important role in the adaptation of Campylobacter jejuni to disparate niches. The chemotaxis system consists of core signal transduction proteins and methyl-accepting-domain-containing Transducer like proteins (Tlps). Ligands binding to Tlps relay a signal to chemotaxis proteins in the cytoplasm which initiate a signal transduction cascade, culminating into a directional flagellar movement. Tlps facilitate substrate-specific chemotaxis in C. jejuni, which plays an important role in the pathogen's adaptation, pathobiology and colonization of the chicken gastrointestinal tract. However, the role of Tlps in C. jejuni's host tissue specific colonization, physiology and virulence remains not completely understood. Based on recent studies, it can be predicted that Tlps might be important targets for developing strategies to control C. jejuni via vaccines and antimicrobials. PMID:28080213

Campylobacter jejuni transducer like proteins: Chemotaxis and beyond.

PubMed

Chandrashekhar, Kshipra; Kassem, Issmat I; Rajashekara, Gireesh

2017-07-04

Chemotaxis, a process that mediates directional motility toward or away from chemical stimuli (chemoeffectors/ligands that can be attractants or repellents) in the environment, plays an important role in the adaptation of Campylobacter jejuni to disparate niches. The chemotaxis system consists of core signal transduction proteins and methyl-accepting-domain-containing Transducer like proteins (Tlps). Ligands binding to Tlps relay a signal to chemotaxis proteins in the cytoplasm which initiate a signal transduction cascade, culminating into a directional flagellar movement. Tlps facilitate substrate-specific chemotaxis in C. jejuni, which plays an important role in the pathogen's adaptation, pathobiology and colonization of the chicken gastrointestinal tract. However, the role of Tlps in C. jejuni's host tissue specific colonization, physiology and virulence remains not completely understood. Based on recent studies, it can be predicted that Tlps might be important targets for developing strategies to control C. jejuni via vaccines and antimicrobials.

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C072)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C048)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

Three-dimensional stochastic modeling of radiation belts in adiabatic invariant coordinates

NASA Astrophysics Data System (ADS)

Zheng, Liheng; Chan, Anthony A.; Albert, Jay M.; Elkington, Scot R.; Koller, Josef; Horne, Richard B.; Glauert, Sarah A.; Meredith, Nigel P.

2014-09-01

A 3-D model for solving the radiation belt diffusion equation in adiabatic invariant coordinates has been developed and tested. The model, named Radbelt Electron Model, obtains a probabilistic solution by solving a set of Itô stochastic differential equations that are mathematically equivalent to the diffusion equation. This method is capable of solving diffusion equations with a full 3-D diffusion tensor, including the radial-local cross diffusion components. The correct form of the boundary condition at equatorial pitch angle α0=90° is also derived. The model is applied to a simulation of the October 2002 storm event. At α0 near 90°, our results are quantitatively consistent with GPS observations of phase space density (PSD) increases, suggesting dominance of radial diffusion; at smaller α0, the observed PSD increases are overestimated by the model, possibly due to the α0-independent radial diffusion coefficients, or to insufficient electron loss in the model, or both. Statistical analysis of the stochastic processes provides further insights into the diffusion processes, showing distinctive electron source distributions with and without local acceleration.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-01-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-06-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

A moving mesh finite difference method for equilibrium radiation diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

Blocking CXCR7-mediated adipose tissue macrophages chemotaxis attenuates insulin resistance and inflammation in obesity.

PubMed

Peng, Hongxia; Zhang, Hu; Zhu, Honglei

2016-10-28

Adipose tissue macrophages (ATMs) have been considered to have a pivotal role in the chronic inflammation development during obesity. Although chemokine-chemokine receptor interaction has been studied in ATMs infiltration, most chemokine receptors remain incompletely understood and little is known about their mechanism of actions that lead to ATMs chemotaxis and pathogenesis of insulin resistance during obesity. In this study, we reported that CXCR7 expression is upregulated in adipose tissue, and specifically in ATMs during obesity. In addition, CXCL11 or CXCL12-induced ATMs chemotaxis is mediated by CXCR7 in obesity but not leanness, whereas CXCR3 and CXCR4 are not involved. Additional mechanism study shows that NF-κB activation is essential in ATMs chemotaxis, and manipulates chemotaxis of ATMs via CXCR7 expression regulation in obesity. Most importantly, CXCR7 neutralizing therapy dose dependently leads to less infiltration of macrophages into adipose tissue and thus reduces inflammation and improves insulin sensitivity in obesity. In conclusion, these findings demonstrated that blocking CXCR7-mediated ATMs chemotaxis ameliorates insulin resistance and inflammation in obesity. Copyright © 2016 Elsevier Inc. All rights reserved.

The equilibrium-diffusion limit for radiation hydrodynamics

DOE PAGES

Ferguson, J. M.; Morel, J. E.; Lowrie, R.

2017-07-27

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy.more » Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting O(β 2) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.« less

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

PubMed Central

Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing

2012-01-01

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849

Inferring the Chemotactic Strategy of P. putida and E. coli Using Modified Kramers-Moyal Coefficients

PubMed Central

Hintsche, Marius; Beta, Carsten; Stark, Holger

2017-01-01

Many bacteria perform a run-and-tumble random walk to explore their surrounding and to perform chemotaxis. In this article we present a novel method to infer the relevant parameters of bacterial motion from experimental trajectories including the tumbling events. We introduce a stochastic model for the orientation angle, where a shot-noise process initiates tumbles, and analytically calculate conditional moments, reminiscent of Kramers-Moyal coefficients. Matching them with the moments calculated from experimental trajectories of the bacteria E. coli and Pseudomonas putida, we are able to infer their respective tumble rates, the rotational diffusion constants, and the distributions of tumble angles in good agreement with results from conventional tumble recognizers. We also define a novel tumble recognizer, which explicitly quantifies the error in recognizing tumbles. In the presence of a chemical gradient we condition the moments on the bacterial direction of motion and thereby explore the chemotaxis strategy. For both bacteria we recover and quantify the classical chemotactic strategy, where the tumble rate is smallest along the chemical gradient. In addition, for E. coli we detect some cells, which bias their mean tumble angle towards smaller values. Our findings are supported by a scaling analysis of appropriate ratios of conditional moments, which are directly calculated from experimental data. PMID:28114420

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

NASA Technical Reports Server (NTRS)

Li, Jianzhong; Ning, C. Z.; Biegel, Bryan A. (Technical Monitor)

2001-01-01

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

Solution of the nonlinear Poisson-Boltzmann equation: Application to ionic diffusion in cementitious materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arnold, J.; Kosson, D.S., E-mail: david.s.kosson@vanderbilt.edu; Garrabrants, A.

2013-02-15

A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com

2015-08-15

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalousmore » diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.« less

Bacterial Chemotaxis to Naphthalene and Nitroarene Compounds

DTIC Science & Technology

2008-07-31

Qualitative capillary assays showing chemotaxis of succinate-grown 17 (uninduced) and induced (succinate plus salicylate -grown) Acidovorax sp. JS42...succinate plus 2NT- or succinate plus salicylate -grown) wild-type Acidovorax sp. JS42 cells List of Tables Table 1. Summary of chemotaxis...mM salicylate , or naphthalene crystals. Noble agar (1.8%; Difco) was used to solidify MSB medium for plates. For plasmid selection and maintenance

Projecting diffusion along the normal bundle of a plane curve

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valero-Valdés, Carlos; Herrera-Guzmán, Rafael

2014-05-15

The purpose of this paper is to provide new formulas for the effective diffusion coefficient of a generalized Fick-Jacob's equation obtained by projecting the two-dimensional diffusion equation along the normal directions of an arbitrary curve on the plane.

NUMERICAL ANALYSES FOR TREATING DIFFUSION IN SINGLE-, TWO-, AND THREE-PHASE BINARY ALLOY SYSTEMS

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1994-01-01

This package consists of a series of three computer programs for treating one-dimensional transient diffusion problems in single and multiple phase binary alloy systems. An accurate understanding of the diffusion process is important in the development and production of binary alloys. Previous solutions of the diffusion equations were highly restricted in their scope and application. The finite-difference solutions developed for this package are applicable for planar, cylindrical, and spherical geometries with any diffusion-zone size and any continuous variation of the diffusion coefficient with concentration. Special techniques were included to account for differences in modal volumes, initiation and growth of an intermediate phase, disappearance of a phase, and the presence of an initial composition profile in the specimen. In each analysis, an effort was made to achieve good accuracy while minimizing computation time. The solutions to the diffusion equations for single-, two-, and threephase binary alloy systems are numerically calculated by the three programs NAD1, NAD2, and NAD3. NAD1 treats the diffusion between pure metals which belong to a single-phase system. Diffusion in this system is described by a one-dimensional Fick's second law and will result in a continuous composition variation. For computational purposes, Fick's second law is expressed as an explicit second-order finite difference equation. Finite difference calculations are made by choosing the grid spacing small enough to give convergent solutions of acceptable accuracy. NAD2 treats diffusion between pure metals which form a two-phase system. Diffusion in the twophase system is described by two partial differential equations (a Fick's second law for each phase) and an interface-flux-balance equation which describes the location of the interface. Actual interface motion is obtained by a mass conservation procedure. To account for changes in the thicknesses of the two phases as diffusion progresses, a variable grid technique developed by Murray and Landis is employed. These equations are expressed in finite difference form and solved numerically. Program NAD3 treats diffusion between pure metals which form a two-phase system with an intermediate third phase. Diffusion in the three-phase system is described by three partial differential expressions of Fick's second law and two interface-flux-balance equations. As with the two-phase case, a variable grid finite difference is used to numerically solve the diffusion equations. Computation time is minimized without sacrificing solution accuracy by treating the three-phase problem as a two-phase problem when the thickness of the intermediate phase is less than a preset value. Comparisons between these programs and other solutions have shown excellent agreement. The programs are written in FORTRAN IV for batch execution on the CDC 6600 with a central memory requirement of approximately 51K (octal) 60 bit words.

Modeling of 2D diffusion processes based on microscopy data: parameter estimation and practical identifiability analysis.

PubMed

Hock, Sabrina; Hasenauer, Jan; Theis, Fabian J

2013-01-01

Diffusion is a key component of many biological processes such as chemotaxis, developmental differentiation and tissue morphogenesis. Since recently, the spatial gradients caused by diffusion can be assessed in-vitro and in-vivo using microscopy based imaging techniques. The resulting time-series of two dimensional, high-resolutions images in combination with mechanistic models enable the quantitative analysis of the underlying mechanisms. However, such a model-based analysis is still challenging due to measurement noise and sparse observations, which result in uncertainties of the model parameters. We introduce a likelihood function for image-based measurements with log-normal distributed noise. Based upon this likelihood function we formulate the maximum likelihood estimation problem, which is solved using PDE-constrained optimization methods. To assess the uncertainty and practical identifiability of the parameters we introduce profile likelihoods for diffusion processes. As proof of concept, we model certain aspects of the guidance of dendritic cells towards lymphatic vessels, an example for haptotaxis. Using a realistic set of artificial measurement data, we estimate the five kinetic parameters of this model and compute profile likelihoods. Our novel approach for the estimation of model parameters from image data as well as the proposed identifiability analysis approach is widely applicable to diffusion processes. The profile likelihood based method provides more rigorous uncertainty bounds in contrast to local approximation methods.

Fractional diffusion on bounded domains

DOE PAGES

Defterli, Ozlem; D'Elia, Marta; Du, Qiang; ...

2015-03-13

We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

EXPERIMENTAL STUDIES ON INFLAMMATION : I. THE INFLUENCE OF CHEMICALS UPON THE CHEMOTAXIS OF LEUCOCYTES IN VITRO.

PubMed

Wolf, E P

1921-09-30

1. Wright's method for the study of chemotaxis of leucocytes in vitro, slightly modified, has been found to be most satisfactory in the estimation of the degree of chemotaxis of various substances, because it is possible to make an exact quantitative determination of the leucocytes that have migrated from the blood clot and adhere to the surfaces containing the tested substance. 2. The calcium ion is the only inorganic ion per se which is found to be positively chemotactic under the conditions of these experiments. It is markedly chemotactic in all concentrations and in all combinations, except the citrate. Here the negative chemotaxis of the citrate ion neutralizes the positive chemotaxis of the calcium ion, and neutrality of chemotactic effect results. 3. The sodium and magnesium ions themselves are neutral. Magnesium and sodium salts are dependent upon the negative ion with which the magnesium or sodium is combined for such positive or negative chemotaxis as is exhibited. All the phosphates of sodium, whether tri-, di-, or monobasic salts, are markedly positively chemotactic, and when combined with other reagents which are themselves neutral or negatively chemotactic, produce marked positive chemotaxis. The blood of a person who has taken phosphates either by mouth or intravenously shows a great increase in chemotaxis with sodium phosphate, with calcium chloride, and even with sodium chloride which is ordinarily neutral. 4. All potassium salts are negatively chemotactic. 5. Many substances act synergistically as regards chemotaxis; e.g., when strontium and magnesium salts are mixed there is a marked increase in chemotaxis. Sodium phosphate acts synergistically with calcium chloride. 6. Mercury salts fix the leucocytes in this method so that their influence on chemotaxis cannot be determined. 7. Morphine and morphine salts are positively chemotactic; this is contrary to the results obtained by others with different methods. 8. Substances which produce a very acute inflammation, such as cantharidin, histamine, or turpentine, are found to be positively chemotactic by this method, but substances, such as mustard gas, which produce a marked necrotizing effect are found to be negatively chemotactic, or neutral, though physiologically they would appear to be positively chemotactic. 9. All amino-acids and amines are positively chemotactic to a certain extent. It seems that the longer the carbon chain, the greater the degree of chemotaxis, though this is not absolute. Tyramine is one exception to this, for it causes a peculiar clumping of the cells, so that it is impossible to count the number adhering, and thus determine whether or not tyramine is positively chemotactic. 10. The time that the blood of animals is examined after eating makes a marked difference in the number of cells adhering, for shortly after eating, within 30 minutes, very many more cells will adhere to the agar than at a later time. 11. The blood of different species of animals reacts differently towards different reagents. The chemical composition of these agents seems to have nothing to do with this difference in reaction as far as we could determine. 12. With frozen serial sections it has been found that the depth of penetration of the leucocytes into the agar is proportional to the positive chemotaxis produced by the substance combined with the agar, as demonstrated by the number of leucocytes adherent to the walls of the test chambers.

Mathematics of thermal diffusion in an exponential temperature field

NASA Astrophysics Data System (ADS)

Zhang, Yaqi; Bai, Wenyu; Diebold, Gerald J.

2018-04-01

The Ludwig-Soret effect, also known as thermal diffusion, refers to the separation of gas, liquid, or solid mixtures in a temperature gradient. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fractions. Here solutions to the nonlinear differential equation for a binary mixture are discussed for an externally imposed, exponential temperature field. The equation of motion for the separation without the effects of mass diffusion is reduced to a Hamiltonian pair from which spatial distributions of the components of the mixture are found. Analytical calculations with boundary effects included show shock formation. The results of numerical calculations of the equation of motion that include both thermal and mass diffusion are given.

Double diffusivity model under stochastic forcing

NASA Astrophysics Data System (ADS)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real-life fluctuating environments.

A model for cell migration in non-isotropic fibrin networks with an application to pancreatic tumor islets.

PubMed

Chen, Jiao; Weihs, Daphne; Vermolen, Fred J

2018-04-01

Cell migration, known as an orchestrated movement of cells, is crucially important for wound healing, tumor growth, immune response as well as other biomedical processes. This paper presents a cell-based model to describe cell migration in non-isotropic fibrin networks around pancreatic tumor islets. This migration is determined by the mechanical strain energy density as well as cytokines-driven chemotaxis. Cell displacement is modeled by solving a large system of ordinary stochastic differential equations where the stochastic parts result from random walk. The stochastic differential equations are solved by the use of the classical Euler-Maruyama method. In this paper, the influence of anisotropic stromal extracellular matrix in pancreatic tumor islets on T-lymphocytes migration in different immune systems is investigated. As a result, tumor peripheral stromal extracellular matrix impedes the immune response of T-lymphocytes through changing direction of their migration.

Adverse effects of metal exposure on chemotaxis towards water-soluble attractants regulated mainly by ASE sensory neuron in nematode Caenorhabditis elegans.

PubMed

Xing, Xiaojuan; Du, Min; Zhang, Yanfen; Wang, Dayong

2009-01-01

Chemotaxis to water-soluble attractants is mainly controlled by ASE sensory neuron whose specification is regulated by che-1 in Caenorhabditis elegans. Our data suggested that exposure to high concentrations of metals, such as Pb, Cu, Ag, and Cr, would result in severe defects of chemotaxis to water-soluble attractants of NaCl, cAMP, and biotin. Moreover, the morphology of ASE neuron structures as observed by relative fluorescent intensities and relative size of fluorescent puncta of cell bodies, relative lengths of sensory endings in ASE neurons, and the expression patterns of che-1 were obviously altered in metal exposed animals when they meanwhile exhibited obvious chemotaxis defects to water-soluble attractants. In addition, the dendrite morphology could be noticeably changed in animals exposed to 150 micromol/L of Pb, Cu, and Ag. Furthermore, we observed significant decreases of chemotaxis to water-soluble attractants in Pb exposed che-1 mutant at concentrations more than 2.5 micromol/L, and in Cu, Ag, and Cr exposed che-1 mutant at concentrations more than 50 micromol/L. Therefore, impairment of the ASE neuron structures and functions may largely contribute to the appearance of chemotaxis defects to water-soluble attractants in metal exposed nematodes.

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki

2010-11-01

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

Numerical applications of the advective-diffusive codes for the inner magnetosphere

NASA Astrophysics Data System (ADS)

Aseev, N. A.; Shprits, Y. Y.; Drozdov, A. Y.; Kellerman, A. C.

2016-11-01

In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.

Fractional-calculus diffusion equation

PubMed Central

2010-01-01

Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

A dual-docking microfluidic cell migration assay (D2-Chip) for testing neutrophil chemotaxis and the memory effect.

PubMed

Yang, Ke; Wu, Jiandong; Xu, Guoqing; Xie, Dongxue; Peretz-Soroka, Hagit; Santos, Susy; Alexander, Murray; Zhu, Ling; Zhang, Michael; Liu, Yong; Lin, Francis

2017-04-18

Chemotaxis is a classic mechanism for guiding cell migration and an important topic in both fundamental cell biology and health sciences. Neutrophils are a widely used model to study eukaryotic cell migration and neutrophil chemotaxis itself can lead to protective or harmful immune actions to the body. While much has been learnt from past research about how neutrophils effectively navigate through a chemoattractant gradient, many interesting questions remain unclear. For example, while it is tempting to model neutrophil chemotaxis using the well-established biased random walk theory, the experimental proof was challenged by the cell's highly persistent migrating nature. A special experimental design is required to test the key predictions from the random walk model. Another question that has interested the cell migration community for decades concerns the existence of chemotactic memory and its underlying mechanism. Although chemotactic memory has been suggested in various studies, a clear quantitative experimental demonstration will improve our understanding of the migratory memory effect. Motivated by these questions, we developed a microfluidic cell migration assay (so-called dual-docking chip or D 2 -Chip) that can test both the biased random walk model and the memory effect for neutrophil chemotaxis on a single chip enabled by multi-region gradient generation and dual-region cell alignment. Our results provide experimental support for the biased random walk model and chemotactic memory for neutrophil chemotaxis. Quantitative data analyses provide new insights into neutrophil chemotaxis and memory by making connections to entropic disorder, cell morphology and oscillating migratory response.

Analysis of bacterial migration; 1: Numerical solution of balance equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frymier, P.D.; Ford, R.M.; Cummings, P.T.

1994-04-01

Chemotaxis describes the ability of motile bacteria to bias their motion in the direction of increasing gradients of chemicals, usually energy sources, known as attractants. In experimental studies of the migration of chemotactic bacteria, 1-D phenomenological cell balance equations have been used to quantitatively analyze experimental observations. While attractive for their simplicity and the ease of solution, they are limited in the strict mathematical sense to the situation in which individual bacteria are confined to motion in one dimension and respond to attractant gradients in one dimension only. Recently, Ford and Cummings (1992) reduced the general 3-D cell balance equationmore » of Alt (1980) to obtain an equation describing the migration of a bacterial population in response to a 1-D attractant gradient. Solutions of this equation for single gradients of attractants are compared to those of 1-D balance equations, results from cellular dynamics simulations, and experimental data from the authors' laboratory for E. coli responding to [alpha]-methylaspartate. The authors also investigate two aspects of the experimentally derived expression for the tumbling probability: the effect of different models for the down-gradient swimming behavior of the bacteria and the validity of ignoring the temporal derivative of the attractant concentration.« less

Stochastic switching in biology: from genotype to phenotype

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.

2017-03-01

There has been a resurgence of interest in non-equilibrium stochastic processes in recent years, driven in part by the observation that the number of molecules (genes, mRNA, proteins) involved in gene expression are often of order 1-1000. This means that deterministic mass-action kinetics tends to break down, and one needs to take into account the discrete, stochastic nature of biochemical reactions. One of the major consequences of molecular noise is the occurrence of stochastic biological switching at both the genotypic and phenotypic levels. For example, individual gene regulatory networks can switch between graded and binary responses, exhibit translational/transcriptional bursting, and support metastability (noise-induced switching between states that are stable in the deterministic limit). If random switching persists at the phenotypic level then this can confer certain advantages to cell populations growing in a changing environment, as exemplified by bacterial persistence in response to antibiotics. Gene expression at the single-cell level can also be regulated by changes in cell density at the population level, a process known as quorum sensing. In contrast to noise-driven phenotypic switching, the switching mechanism in quorum sensing is stimulus-driven and thus noise tends to have a detrimental effect. A common approach to modeling stochastic gene expression is to assume a large but finite system and to approximate the discrete processes by continuous processes using a system-size expansion. However, there is a growing need to have some familiarity with the theory of stochastic processes that goes beyond the standard topics of chemical master equations, the system-size expansion, Langevin equations and the Fokker-Planck equation. Examples include stochastic hybrid systems (piecewise deterministic Markov processes), large deviations and the Wentzel-Kramers-Brillouin (WKB) method, adiabatic reductions, and queuing/renewal theory. The major aim of this review is to provide a self-contained survey of these mathematical methods, mainly within the context of biological switching processes at both the genotypic and phenotypic levels. However, applications to other examples of biological switching are also discussed, including stochastic ion channels, diffusion in randomly switching environments, bacterial chemotaxis, and stochastic neural networks.

An asymptotic induced numerical method for the convection-diffusion-reaction equation

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.; Sorensen, Danny C.

1988-01-01

A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.

A new Eulerian model for viscous and heat conducting compressible flows

NASA Astrophysics Data System (ADS)

Svärd, Magnus

2018-09-01

In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, is presented. We show that these inconsistencies are consequences of the Lagrangian derivation that models viscous stresses rather than diffusion. A new model for compressible and diffusive (viscous and heat conducting) flows of an ideal gas, is derived in a purely Eulerian framework. We propose that these equations supersede the Navier-Stokes equations. A few numerical experiments demonstrate some differences and similarities between the new system and the Navier-Stokes equations.

Analytical solution of the nonlinear diffusion equation

NASA Astrophysics Data System (ADS)

Shanker Dubey, Ravi; Goswami, Pranay

2018-05-01

In the present paper, we derive the solution of the nonlinear fractional partial differential equations using an efficient approach based on the q -homotopy analysis transform method ( q -HATM). The fractional diffusion equations derivatives are considered in Caputo sense. The derived results are graphically demonstrated as well.

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form ismore » based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.« less

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

DOE PAGES

Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick; ...

2017-02-21

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form ismore » based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.« less

The effective boundary conditions and their lifespan of the logistic diffusion equation on a coated body

NASA Astrophysics Data System (ADS)

Li, Huicong; Wang, Xuefeng; Wu, Yanxia

2014-11-01

We consider the logistic diffusion equation on a bounded domain, which has two components with a thin coating surrounding a body. The diffusion tensor is isotropic on the body, and anisotropic on the coating. The size of the diffusion tensor on these components may be very different; within the coating, the diffusion rates in the normal and tangent directions may be in different scales. We find effective boundary conditions (EBCs) that are approximately satisfied by the solution of the diffusion equation on the boundary of the body. We also prove that the lifespan of each EBC, which measures how long the EBC remains effective, is infinite. The EBCs enable us to see clearly the effect of the coating and ease the difficult task of solving the PDE in a thin region with a small diffusion tensor. The motivation of the mathematics includes a nature reserve surrounded by a buffer zone.

Worst case prediction of additives migration from polystyrene for food safety purposes: a model update.

PubMed

Martínez-López, Brais; Gontard, Nathalie; Peyron, Stéphane

2018-03-01

A reliable prediction of migration levels of plastic additives into food requires a robust estimation of diffusivity. Predictive modelling of diffusivity as recommended by the EU commission is carried out using a semi-empirical equation that relies on two polymer-dependent parameters. These parameters were determined for the polymers most used by packaging industry (LLDPE, HDPE, PP, PET, PS, HIPS) from the diffusivity data available at that time. In the specific case of general purpose polystyrene, the diffusivity data published since then shows that the use of the equation with the original parameters results in systematic underestimation of diffusivity. The goal of this study was therefore, to propose an update of the aforementioned parameters for PS on the basis of up to date diffusivity data, so the equation can be used for a reasoned overestimation of diffusivity.

Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods

DTIC Science & Technology

2002-05-06

reaction- diffusion equation is a difficult problem in analysis that will not be addressed here. Errors will also arise from numerically approx solutions to...the ODEs. When comparing the approximate solution to actual reaction- diffusion systems found in nature, we must also take into account errors that...

Bacterial Chemotaxis: The Early Years of Molecular Studies

PubMed Central

Hazelbauer, Gerald L.

2014-01-01

This review focuses on the early years of molecular studies of bacterial chemotaxis and motility, beginning in the 1960s with Julius Adler's pioneering work. It describes key observations that established the field and made bacterial chemotaxis a paradigm for the molecular understanding of biological signaling. Consideration of those early years includes aspects of science seldom described in journals: the accidental findings, personal interactions, and scientific culture that often drive scientific progress. PMID:22994495

[Experimental study of the effects of impulse-electric discharge on chemotaxis and cytoadhesion of urinary infection pathogens].

PubMed

Kuderinov, S K; Azizov, I S; Turgunov, E M; Shambilova, N A

2006-01-01

The aim of the experimental study was to evaluate effects of impulse-electric discharge in liquid on chemotaxis and cytoadhesion of urinary infection pathogens. Chemotaxis was determined in respect to the lung, liver, spleen, kidney, ureter, urinary bladder, urethra of white mice by S. Likholetov's modified method. Cytoadhesion was assessed by V. Brilis. The experiments show that the impulse-electric discharge holds promise for urological practice.

Exact Solutions of Coupled Multispecies Linear Reaction–Diffusion Equations on a Uniformly Growing Domain

PubMed Central

Simpson, Matthew J.; Sharp, Jesse A.; Morrow, Liam C.; Baker, Ruth E.

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit. PMID:26407013

Exact Solutions of Coupled Multispecies Linear Reaction-Diffusion Equations on a Uniformly Growing Domain.

PubMed

Simpson, Matthew J; Sharp, Jesse A; Morrow, Liam C; Baker, Ruth E

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

An accurate computational method for the diffusion regime verification

NASA Astrophysics Data System (ADS)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-04-01

The diffusion regime (sub-diffusive, standard, or super-diffusive) is defined by the order of the derivative in the corresponding transport equation. We develop an accurate computational method for the direct estimation of the diffusion regime. The method is based on the derivative order estimation using the asymptotic analytic solutions of the diffusion equation with the integer order and the time-fractional derivatives. The robustness and the computational cheapness of the proposed method are verified using the experimental methane and methyl alcohol transport kinetics through the catalyst pellet.

Chemotactic-based adaptive self-organization during colonial development

NASA Astrophysics Data System (ADS)

Cohen, Inon; Czirók, Andras; Ben-Jacob, Eshel

1996-02-01

Bacterial colonies have developed sophisticated modes of cooperative behavior which enable them to respond to adverse growth conditions. It has been shown that such behavior can be manifested in the development of complex colonial patterns. Certain bacterial species exhibit formation of branching patterns during colony development. Here we present a generic model to describe such patterning of swimming (tumbling) bacteria on agar surfaces. The model incorporates: (1) food diffusion, (2) reproduction and sporulation of the cells, (3) movement of the bacterial cells within a self-produced wetting fluid and (4) chemotactic signaling. As a plausible explanation for transitions between different branching morphologies, we propose an interplay between chemotaxis towards food, self-produced short range chemoattractant and long range chemorepellent.

Control of reaction-diffusion equations on time-evolving manifolds.

PubMed

Rossi, Francesco; Duteil, Nastassia Pouradier; Yakoby, Nir; Piccoli, Benedetto

2016-12-01

Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such signal. Meanwhile, the diffusion of the signal is itself affected by the changes in shape and size of the organism. In other words, there is a complete coupling between the diffusion of the signal and the change of the shapes. In this paper, we introduce a mathematical model to investigate such coupling. The shape is given by a manifold, that varies in time as the result of a deformation given by a transport equation. The signal is represented by a density, diffusing on the manifold via a diffusion equation. We show the non-commutativity of the transport and diffusion evolution by introducing a new concept of Lie bracket between the diffusion and the transport operator. We also provide numerical simulations showing this phenomenon.

A mathematical model for mesenchymal and chemosensitive cell dynamics.

PubMed

Häcker, Anita

2012-01-01

The structure of an underlying tissue network has a strong impact on cell dynamics. If, in addition, cells alter the network by mechanical and chemical interactions, their movement is called mesenchymal. Important examples for mesenchymal movement include fibroblasts in wound healing and metastatic tumour cells. This paper is focused on the latter. Based on the anisotropic biphasic theory of Barocas and Tranquillo, which models a fibre network and interstitial solution as two-component fluid, a mathematical model for the interactions of cells with a fibre network is developed. A new description for fibre reorientation is given and orientation-dependent proteolysis is added to the model. With respect to cell dynamics, the equation, based on anisotropic diffusion, is extended by haptotaxis and chemotaxis. The chemoattractants are the solute network fragments, emerging from proteolysis, and the epidermal growth factor which may guide the cells to a blood vessel. Moreover the cell migration is impeded at either high or low network density. This new model enables us to study chemotactic cell migration in a complex fibre network and the consequential network deformation. Numerical simulations for the cell migration and network deformation are carried out in two space dimensions. Simulations of cell migration in underlying tissue networks visualise the impact of the network structure on cell dynamics. In a scenario for fibre reorientation between cell clusters good qualitative agreement with experimental results is achieved. The invasion speeds of cells in an aligned and an isotropic fibre network are compared. © Springer-Verlag 2011

Fractional Number Operator and Associated Fractional Diffusion Equations

NASA Astrophysics Data System (ADS)

Rguigui, Hafedh

2018-03-01

In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.

Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities

PubMed Central

Vázquez, J. L.

2010-01-01

The goal of this paper is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It relies on the identification of the optimal constants in some related Hardy–Poincaré inequalities and concludes a long series of papers devoted to generalized entropies, functional inequalities, and rates for nonlinear diffusion equations. PMID:20823259

Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou Tao, E-mail: tzhou@lsec.cc.ac.c; Tang Tao, E-mail: ttang@hkbu.edu.h

2010-11-01

In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266-281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question.

General solution of a fractional Parker diffusion-convection equation describing the superdiffusive transport of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Elhanbaly, A.; Schlickeiser, Reinhard

2018-06-01

Anomalous diffusion models of energetic particles in space plasmas are developed by introducing the fractional Parker diffusion-convection equation. Analytical solution of the space-time fractional equation is obtained by use of the Caputo and Riesz-Feller fractional derivatives with the Laplace-Fourier transforms. The solution is given in terms of the Fox H-function. Profiles of particle densities are illustrated for different values of the space fractional order and the so-called skewness parameter.

Stress, deformation and diffusion interactions in solids - A simulation study

NASA Astrophysics Data System (ADS)

Fischer, F. D.; Svoboda, J.

2015-05-01

Equations of diffusion treated in the frame of Manning's concept, are completed by equations for generation/annihilation of vacancies at non-ideal sources and sinks, by conservation laws, by equations for generation of an eigenstrain state and by a strain-stress analysis. The stress-deformation-diffusion interactions are demonstrated on the evolution of a diffusion couple consisting of two thin layers of different chemical composition forming a free-standing plate without external loading. The equations are solved for different material parameters represented by the values of diffusion coefficients of individual components and by the intensity of sources and sinks for vacancies. The results of simulations indicate that for low intensity of sources and sinks for vacancies a significant eigenstress state can develop and the interdiffusion process is slowed down. For high intensity of sources and sinks for vacancies a significant eigenstrain state can develop and the eigenstress state quickly relaxes. If the difference in the diffusion coefficients of individual components is high, then the intensity of sources and sinks for vacancies influences the interdiffusion process considerably. For such systems their description only by diffusion coefficients is insufficient and must be completed by a microstructure characterization.

Quantitative analysis of eosinophil chemotaxis tracked using a novel optical device -- TAXIScan.

PubMed

Nitta, Nao; Tsuchiya, Tomoko; Yamauchi, Akira; Tamatani, Takuya; Kanegasaki, Shiro

2007-03-30

We have reported previously the development of an optically accessible, horizontal chemotaxis apparatus, in which migration of cells in the channel from a start line can be traced with time-lapse intervals using a CCD camera (JIM 282, 1-11, 2003). To obtain statistical data of migrating cells, we have developed quantitative methods to calculate various parameters in the process of chemotaxis, employing human eosinophil and CXCL12 as a model cell and a model chemoattractant, respectively. Median values of velocity and directionality of each cell within an experimental period could be calculated from the migratory pathway data obtained from time-lapse images and the data were expressed as Velocity-Directionality (VD) plot. This plot is useful for quantitatively analyzing multiple migrating cells exposed to a certain chemoattractant, and can distinguish chemotaxis from random migration. Moreover precise observation of cell migration revealed that each cell had a different lag period before starting chemotaxis, indicating variation in cell sensitivity to the chemoattractant. Thus lag time of each cell before migration, and time course of increment of the migrating cell ratio at the early stages could be calculated. We also graphed decrement of still moving cell ratio at the later stages by calculating the duration time of cell migration of each cell. These graphs could distinguish different motion patterns of chemotaxis of eosinophils, in response to a range of chemoattractants; PGD(2), fMLP, CCL3, CCL5 and CXCL12. Finally, we compared parameters of eosinophils from normal volunteers, allergy patients and asthma patients and found significant difference in response to PGD(2). The quantitative methods described here could be applicable to image data obtained with any combination of cells and chemoattractants and useful not only for basic studies of chemotaxis but also for diagnosis and for drug screening.

Evaluation of peripheral neutrophil functions in aggressive periodontitis patients and their family members in Indian population: An assessment of neutrophil chemotaxis, phagocytosis, and microbicidal activity

PubMed Central

Bhansali, Rahul Suresh; Yeltiwar, Ramreddy Krishnarao; Bhat, Kishore

2017-01-01

Background: Association of neutrophil function abnormalities with localized aggressive periodontitis (LAP) has been reported in Indian population. There are no published studies on the familial aggregation of aggressive periodontitis (AP) and neutrophil function abnormalities associated with it in Indian population. The present study aimed to assess neutrophil chemotaxis, phagocytosis, and microbicidal activity in AP patients and their family members of Indian origin, who may or may not be suffering from AP. Materials and Methods: Eighteen families with a total of 51 individuals (18 probands, 33 family members) were included. Neutrophil chemotaxis was evaluated against an alkali-soluble casein solution using Wilkinson's method. Phagocytosis and microbicidal activity assay were performed using Candida albicans as an indicator organism. Statistical Analysis Used: The magnitude of association between the presence of defective neutrophil function and LAP or GAP was calculated using odds ratio and relative risk. Total incidence of AP, and in particular, LAP in the families attributable to the presence of defective neutrophil function was calculated by attributable risk. Results: The association between depressed neutrophil chemotaxis and presence of AP and LAP or GAP in all the family members (n = 51) was found to be significant (P < 0.05) while that for phagocytic and microbicidal activity were observed to be nonsignificant. Conclusion: The results of the present study suggest high incidence of AP (LAP and GAP) within families was associated with depressed neutrophil chemotaxis. High prevalence of depressed neutrophil chemotaxis in the family members (61%) of LAP probands exhibiting depressed chemotaxis suggests that the observed abnormalities in neutrophil functions may also be inherited by the family members. PMID:29551862

Neutrophil chemotaxis in cord blood of term and preterm neonates is reduced in preterm neonates and influenced by the mode of delivery and anaesthesia.

PubMed

Birle, Alexandra; Nebe, C Thomas; Hill, Sandra; Hartmann, Karin; Poeschl, Johannes; Koch, Lutz

2015-01-01

Bacterial infections, even without any perinatal risk factors, are common in newborns, especially in preterm neonates. The aim of this study was to evaluate possible impairment of neutrophil chemotaxis in term and preterm neonates compared with adults as well as neonates with different modes of delivery and anaesthesia. We analysed the expression of the adhesion molecule L-Selectin as well as shape change, spontaneous and N-formyl-methionyl-leucyl-phenylalanine (fMLP)-induced transmigration of neutrophils in a flow cytometric assay of chemotaxis after spontaneous delivery with Cesarian Section (CS) under spinal anaesthesia (mepivacaine, sufentanil), epidural anaesthesia (ropivacaine or bupivacaine, sufentanil) or general anaesthesia (ketamine, thiopental, succinylcholine). Chemokinesis was higher (p=0.008) in cord blood neutrophils than in the adult ones, whereas those could be more stimulated by fMLP (p=0.02). After vaginal delivery neutrophils showed a higher spontaneous and fMLP-stimulated chemotactic response compared to neonates after CS without labor. Comparing different types of anaesthesia for CS, spinal anaesthesia resulted in less impairment on chemotaxis than general anaesthesia or epidural anaesthesia. The new flow cytometric assay of neutrophil chemotaxis is an appropriate and objective method to analyse functional differences even in very small volumes of blood, essential in neonatology. Term neonates do not show reduced chemotaxis compared to adults. Preterm neonates present with reduced chemotaxis and chemokinesis, confirming the well known deficits in their neutrophil function. The side effects of maternal drugs on the neonatal immune system have to be considered especially when the immune response is already impaired, as in preterm infants.

Global boundedness of solutions to a two-species chemotaxis system

NASA Astrophysics Data System (ADS)

Zhang, Qingshan; Li, Yuxiang

2015-02-01

In this paper, we consider the chemotaxis system of two species which are attracted by the same signal substance under homogeneous Neumann boundary conditions in a smooth bounded domain . We prove that if the nonnegative initial data and for some r > n, the system possesses a unique global uniformly bounded solution under some conditions on the chemotaxis sensitivity functions χ 1( w), χ 2( w) and the logistic growth coefficients μ 1, μ 2.

N-WASP and cortactin are involved in invadopodium-dependent chemotaxis to EGF in breast tumor cells

PubMed Central

DesMarais, Vera; Yamaguchi, Hideki; Oser, Matthew; Soon, Lilian; Mouneimne, Ghassan; Sarmiento, Corina; Eddy, Robert; Condeelis, John

2009-01-01

Metastatic mammary carcinoma cells, which have previously been observed to form mature, matrix degrading invadopodia on a thick ECM matrix, are able to form invadopodia with similar characteristics on glass without previously applied matrix. They form in response to EGF, and contain the usual invadopodium core proteins N-WASP, Arp2/3, cortactin, cofilin, and F-actin. The study of invadopodia on glass allows for higher resolution analysis including the use of total internal reflection microscopy and analysis of their relationship to other cell motility events, in particular, lamellipodium extension and chemotaxis toward an EGF gradient. Invadopodium formation on glass requires N-WASP and cortactin but not microtubules. In a gradient of EGF more invadopodia form on the side of the cells facing the source of EGF. In addition, depletion of N-WASP or cortactin, which blocks invadopodium fromation, inhibits chemotaxis of cells towards EGF. This appears to be a localized defect in chemotaxis since depletion of N-WASP or cortactin via siRNA had no effect on lamellipodium protrusion or barbed end generation at the lamellipodium's leading edge. Since chemotaxis to EGF by breast tumor cells is involved in metastasis, inhibiting N-WASP activity in breast tumor cells might prevent metastasis of tumor cells while not affecting chemotaxis-dependent innate immunity which depends on WASp function in macrophages. PMID:19373774

A double medium model for diffusion in fluid-bearing rock

NASA Astrophysics Data System (ADS)

Wang, H. F.

1993-09-01

The concept of a double porosity medium to model fluid flow in fractured rock has been applied to model diffusion in rock containing a small amount of a continuous fluid phase that surrounds small volume elements of the solid matrix. The model quantifies the relative role of diffusion in the fluid and solid phases of the rock. The fluid is the fast diffusion path, but the solid contains the volumetrically significant amount of the diffusing species. The double medium model consists of two coupled differential equations. One equation is the diffusion equation for the fluid concentration; it contains a source term for change in the average concentration of the diffusing species in the solid matrix. The second equation represents the assumption that the change in average concentration in a solid element is proportional to the difference between the average concentration in the solid and the concentration in the fluid times the solid-fluid partition coefficient. The double medium model is shown to apply to laboratory data on iron diffusion in fluid-bearing dunite and to measured oxygen isotope ratios at marble-metagranite contacts. In both examples, concentration profiles are calculated for diffusion taking place at constant temperature, where a boundary value changes suddenly and is subsequently held constant. Knowledge of solid diffusivities can set a lower bound to the length of time over which diffusion occurs, but only the product of effective fluid diffusivity and time is constrained for times longer than the characteristic solid diffusion time. The double medium results approach a local, grain-scale equilibrium model for times that are large relative to the time constant for solid diffusion.

Diffusion in the special theory of relativity.

PubMed

Herrmann, Joachim

2009-11-01

The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.

Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane

NASA Astrophysics Data System (ADS)

Abd-El-Malek, Mina B.; Kassem, Magda M.; Meky, Mohammed L. M.

2002-03-01

The transformation group theoretic approach is applied to study the diffusion process of a drug through a skin-like membrane which tends to partially absorb the drug. Two cases are considered for the diffusion coefficient. The application of one parameter group reduces the number of independent variables by one, and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions. The obtained differential equation is solved numerically using the shooting method, and the results are illustrated graphically and in tables.

Ionic conduction and self-diffusion near infinitesimal concentration in lithium salt-organic solvent electrolytes

NASA Astrophysics Data System (ADS)

Aihara, Yuichi; Sugimoto, Kyoko; Price, William S.; Hayamizu, Kikuko

2000-08-01

The Debye-Hückel-Onsager and Nernst-Einstein equations, which are based on two different conceptual approaches, constitute the most widely used equations for relating ionic conduction to ionic mobility. However, both of these classical (simple) equations are predictive of ionic conductivity only at very low salt concentrations. In the present work the ionic conductivity of four organic solvent-lithium salt-based electrolytes were measured. These experimental conductivity values were then contrasted with theoretical values calculated using the translational diffusion (also known as self-diffusion or intradiffusion) coefficients of all of the species present obtained using pulsed-gradient spin-echo (1H, 19F and 7Li) nuclear magnetic resonance self-diffusion measurements. The experimental results verified the applicability of both theoretical approaches at very low salt concentrations for these particular systems as well as helping to clarify the reasons for the divergence between theory and experiment. In particular, it was found that the correspondence between the Debye-Hückel-Onsager equation and experimental values could be improved by using the measured solvent self-diffusion values to correct for salt-induced changes in the solution viscosity. The concentration dependence of the self-diffusion coefficients is discussed in terms of the Jones-Dole equation.

Sperm chemotaxis promotes individual fertilization success in sea urchins.

PubMed

Hussain, Yasmeen H; Guasto, Jeffrey S; Zimmer, Richard K; Stocker, Roman; Riffell, Jeffrey A

2016-05-15

Reproductive success fundamentally shapes an organism's ecology and evolution, and gamete traits mediate fertilization, which is a critical juncture in reproduction. Individual male fertilization success is dependent on the ability of sperm from one male to outcompete the sperm of other males when searching for a conspecific egg. Sperm chemotaxis, the ability of sperm to navigate towards eggs using chemical signals, has been studied for over a century, but such studies have long assumed that this phenomenon improves individual male fitness without explicit evidence to support this claim. Here, we assessed fertilization changes in the presence of a chemoattractant-digesting peptidase and used a microfluidic device coupled with a fertilization assay to determine the effect of sperm chemotaxis on individual male fertilization success in the sea urchin Lytechinus pictus We show that removing chemoattractant from the gametic environment decreases fertilization success. We further found that individual male differences in chemotaxis to a well-defined gradient of attractant correlate with individual male differences in fertilization success. These results demonstrate that sperm chemotaxis is an important contributor to individual reproductive success. © 2016. Published by The Company of Biologists Ltd.

Defective granulocyte chemotaxis in the Chediak-Higashi syndrome

PubMed Central

Clark, Robert A.; Kimball, Harry R.

1971-01-01

In vivo and in vitro studies of granulocyte chemotaxis were performed in three patients with the Chediak-Higashi syndrome. Rebuck skin windows showed a decreased accumulation of leukocytes at an inflammatory site. Studies in Boyden chambers documented a cellular defect in granulocyte chemotaxis. The chemotactic response of Chediak-Higashi cells by this technique averaged approximately 40% of normal and was consistently reduced using several different chemotactic stimuli. This deficit was magnified by shortening the chamber incubation time or by decreasing the pore size of the micropore filter and was independent of granulocytopenia. No abnormalities of passive motility, adhesiveness, viability, or pH optimum for migration were found in these cells. Chediak-Higashi serum contained no inhibitors of chemotaxis and was capable of generating normal amounts of chemotactic factors with the exception of one patient with the accelerated phase of the disease. Heterozygotes for the Chediak-Higashi trait had normal chemotactic function. This cellular defect in chemotaxis may contribute to the marked susceptibility to pyogenic infections which is so characteristic of patients with the Chediak-Higashi syndrome. Images PMID:4942966

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

Obstructions to Existence in Fast-Diffusion Equations

NASA Astrophysics Data System (ADS)

Rodriguez, Ana; Vazquez, Juan L.

The study of nonlinear diffusion equations produces a number of peculiar phenomena not present in the standard linear theory. Thus, in the sub-field of very fast diffusion it is known that the Cauchy problem can be ill-posed, either because of non-uniqueness, or because of non-existence of solutions with small data. The equations we consider take the general form ut=( D( u, ux) ux) x or its several-dimension analogue. Fast diffusion means that D→∞ at some values of the arguments, typically as u→0 or ux→0. Here, we describe two different types of non-existence phenomena. Some fast-diffusion equations with very singular D do not allow for solutions with sign changes, while other equations admit only monotone solutions, no oscillations being allowed. The examples we give for both types of anomaly are closely related. The most typical examples are vt=( vx/∣ v∣) x and ut= uxx/∣ ux∣. For these equations, we investigate what happens to the Cauchy problem when we take incompatible initial data and perform a standard regularization. It is shown that the limit gives rise to an initial layer where the data become admissible (positive or monotone, respectively), followed by a standard evolution for all t>0, once the obstruction has been removed.

Multi-Component Diffusion with Application To Computational Aerothermodynamics

NASA Technical Reports Server (NTRS)

Sutton, Kenneth; Gnoffo, Peter A.

1998-01-01

The accuracy and complexity of solving multicomponent gaseous diffusion using the detailed multicomponent equations, the Stefan-Maxwell equations, and two commonly used approximate equations have been examined in a two part study. Part I examined the equations in a basic study with specified inputs in which the results are applicable for many applications. Part II addressed the application of the equations in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) computational code for high-speed entries in Earth's atmosphere. The results showed that the presented iterative scheme for solving the Stefan-Maxwell equations is an accurate and effective method as compared with solutions of the detailed equations. In general, good accuracy with the approximate equations cannot be guaranteed for a species or all species in a multi-component mixture. 'Corrected' forms of the approximate equations that ensured the diffusion mass fluxes sum to zero, as required, were more accurate than the uncorrected forms. Good accuracy, as compared with the Stefan- Maxwell results, were obtained with the 'corrected' approximate equations in defining the heating rates for the three Earth entries considered in Part II.

A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics

ERIC Educational Resources Information Center

Spayd, Kimberly; Puckett, James

2016-01-01

This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical…

A third-order computational method for numerical fluxes to guarantee nonnegative difference coefficients for advection-diffusion equations in a semi-conservative form

NASA Astrophysics Data System (ADS)

Sakai, K.; Watabe, D.; Minamidani, T.; Zhang, G. S.

2012-10-01

According to Godunov theorem for numerical calculations of advection equations, there exist no higher-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. We propose a third-order computational scheme for numerical fluxes to guarantee the non-negative difference coefficients of resulting finite difference equations for advection-diffusion equations in a semi-conservative form, in which there exist two kinds of numerical fluxes at a cell surface and these two fluxes are not always coincident in non-uniform velocity fields. The present scheme is optimized so as to minimize truncation errors for the numerical fluxes while fulfilling the positivity condition of the difference coefficients which are variable depending on the local Courant number and diffusion number. The feature of the present optimized scheme consists in keeping the third-order accuracy anywhere without any numerical flux limiter. We extend the present method into multi-dimensional equations. Numerical experiments for advection-diffusion equations showed nonoscillatory solutions.

EXPERIMENTAL STUDIES ON INFLAMMATION

PubMed Central

Wolf, Elizabeth Pauline

1921-01-01

1. Wright's method for the study of chemotaxis of leucocytes in vitro, slightly modified, has been found to be most satisfactory in the estimation of the degree of chemotaxis of various substances, because it is possible to make an exact quantitative determination of the leucocytes that have migrated from the blood clot and adhere to the surfaces containing the tested substance. 2. The calcium ion is the only inorganic ion per se which is found to be positively chemotactic under the conditions of these experiments. It is markedly chemotactic in all concentrations and in all combinations, except the citrate. Here the negative chemotaxis of the citrate ion neutralizes the positive chemotaxis of the calcium ion, and neutrality of chemotactic effect results. 3. The sodium and magnesium ions themselves are neutral. Magnesium and sodium salts are dependent upon the negative ion with which the magnesium or sodium is combined for such positive or negative chemotaxis as is exhibited. All the phosphates of sodium, whether tri-, di-, or monobasic salts, are markedly positively chemotactic, and when combined with other reagents which are themselves neutral or negatively chemotactic, produce marked positive chemotaxis. The blood of a person who has taken phosphates either by mouth or intravenously shows a great increase in chemotaxis with sodium phosphate, with calcium chloride, and even with sodium chloride which is ordinarily neutral. 4. All potassium salts are negatively chemotactic. 5. Many substances act synergistically as regards chemotaxis; e.g., when strontium and magnesium salts are mixed there is a marked increase in chemotaxis. Sodium phosphate acts synergistically with calcium chloride. 6. Mercury salts fix the leucocytes in this method so that their influence on chemotaxis cannot be determined. 7. Morphine and morphine salts are positively chemotactic; this is contrary to the results obtained by others with different methods. 8. Substances which produce a very acute inflammation, such as cantharidin, histamine, or turpentine, are found to be positively chemotactic by this method, but substances, such as mustard gas, which produce a marked necrotizing effect are found to be negatively chemotactic, or neutral, though physiologically they would appear to be positively chemotactic. 9. All amino-acids and amines are positively chemotactic to a certain extent. It seems that the longer the carbon chain, the greater the degree of chemotaxis, though this is not absolute. Tyramine is one exception to this, for it causes a peculiar clumping of the cells, so that it is impossible to count the number adhering, and thus determine whether or not tyramine is positively chemotactic. 10. The time that the blood of animals is examined after eating makes a marked difference in the number of cells adhering, for shortly after eating, within 30 minutes, very many more cells will adhere to the agar than at a later time. 11. The blood of different species of animals reacts differently towards different reagents. The chemical composition of these agents seems to have nothing to do with this difference in reaction as far as we could determine. 12. With frozen serial sections it has been found that the depth of penetration of the leucocytes into the agar is proportional to the positive chemotaxis produced by the substance combined with the agar, as demonstrated by the number of leucocytes adherent to the walls of the test chambers. PMID:19868564

Global Regularity and Time Decay for the 2D Magnetohydrodynamic Equations with Fractional Dissipation and Partial Magnetic Diffusion

NASA Astrophysics Data System (ADS)

Dong, Bo-Qing; Jia, Yan; Li, Jingna; Wu, Jiahong

2018-05-01

This paper focuses on a system of the 2D magnetohydrodynamic (MHD) equations with the kinematic dissipation given by the fractional operator (-Δ )^α and the magnetic diffusion by partial Laplacian. We are able to show that this system with any α >0 always possesses a unique global smooth solution when the initial data is sufficiently smooth. In addition, we make a detailed study on the large-time behavior of these smooth solutions and obtain optimal large-time decay rates. Since the magnetic diffusion is only partial here, some classical tools such as the maximal regularity property for the 2D heat operator can no longer be applied. A key observation on the structure of the MHD equations allows us to get around the difficulties due to the lack of full Laplacian magnetic diffusion. The results presented here are the sharpest on the global regularity problem for the 2D MHD equations with only partial magnetic diffusion.

A cheZ-Like Gene in Azorhizobium caulinodans Is a Key Gene in the Control of Chemotaxis and Colonization of the Host Plant.

PubMed

Liu, Xiaolin; Liu, Wei; Sun, Yu; Xia, Chunlei; Elmerich, Claudine; Xie, Zhihong

2018-02-01

Chemotaxis can provide bacteria with competitive advantages for survival in complex environments. The CheZ chemotaxis protein is a phosphatase, affecting the flagellar motor in Escherichia coli by dephosphorylating the response regulator phosphorylated CheY protein (CheY∼P) responsible for clockwise rotation. A cheZ gene has been found in Azorhizobium caulinodans ORS571, in contrast to other rhizobial species studied so far. The CheZ protein in strain ORS571 has a conserved motif similar to that corresponding to the phosphatase active site in E. coli The construction of a cheZ deletion mutant strain and of cheZ mutant strains carrying a mutation in residues of the putative phosphatase active site showed that strain ORS571 participates in chemotaxis and motility, causing a hyperreversal behavior. In addition, the properties of the cheZ deletion mutant revealed that ORS571 CheZ is involved in other physiological processes, since it displayed increased flocculation, biofilm formation, exopolysaccharide (EPS) production, and host root colonization. In particular, it was observed that the expression of several exp genes, involved in EPS synthesis, was upregulated in the cheZ mutant compared to that in the wild type, suggesting that CheZ negatively controls exp gene expression through an unknown mechanism. It is proposed that CheZ influences the Azorhizobium -plant association by negatively regulating early colonization via the regulation of EPS production. This report established that CheZ in A. caulinodans plays roles in chemotaxis and the symbiotic association with the host plant. IMPORTANCE Chemotaxis allows bacteria to swim toward plant roots and is beneficial to the establishment of various plant-microbe associations. The level of CheY phosphorylation (CheY∼P) is central to the chemotaxis signal transduction. The mechanism of the signal termination of CheY∼P remains poorly characterized among Alphaproteobacteria , except for Sinorhizobium meliloti , which does not contain CheZ but which controls CheY∼P dephosphorylation through a phosphate sink mechanism. Azorhizobium caulinodans ORS571, a microsymbiont of Sesbania rostrata , has an orphan cheZ gene besides two cheY genes similar to those in S. meliloti In addition to controlling the chemotaxis response, the CheZ-like protein in strain ORS571 is playing a role by decreasing bacterial adhesion to the host plant, in contrast to the general situation where chemotaxis-associated proteins promote adhesion. In this study, we identified a CheZ-like protein among Alphaproteobacteria functioning in chemotaxis and the A. caulinodans - S. rostrata symbiosis. Copyright © 2018 American Society for Microbiology.

Neutrophil chemotaxis in sickle cell anaemia, sickle cell beta zero thalassaemia, and after splenectomy.

PubMed Central

Donadi, E A; Falcão, R P

1987-01-01

Neutrophil chemotaxis was evaluated in 28 patients with sickle cell anaemia, 10 patient with sickle cell beta zero thalassaemia, 25 patients who had undergone splenectomy, and 38 controls. The mean distance migrated by patients' neutrophils was not significantly different from that of neutrophils from controls. Although several immunological variables have been reported to be changed after loss of splenic function, we were unable to show a defect in neutrophil chemotaxis that could account for the increased susceptibility to infection. PMID:3611395

Fisher equation for anisotropic diffusion: simulating South American human dispersals.

PubMed

Martino, Luis A; Osella, Ana; Dorso, Claudio; Lanata, José L

2007-09-01

The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal.

Viscous regularization of the full set of nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations

DOE PAGES

Delchini, Marc O.; Ragusa, Jean C.; Ferguson, Jim

2017-02-17

A viscous regularization technique, based on the local entropy residual, was proposed by Delchini et al. (2015) to stabilize the nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations using an artificial viscosity technique. This viscous regularization is modulated by the local entropy production and is consistent with the entropy minimum principle. However, Delchini et al. (2015) only based their work on the hyperbolic parts of the Grey Radiation-Hydrodynamic equations and thus omitted the relaxation and diffusion terms present in the material energy and radiation energy equations. Here in this paper, we extend the theoretical grounds for the method and derive an entropy minimum principlemore » for the full set of nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations. This further strengthens the applicability of the entropy viscosity method as a stabilization technique for radiation-hydrodynamic shock simulations. Radiative shock calculations using constant and temperature-dependent opacities are compared against semi-analytical reference solutions, and we present a procedure to perform spatial convergence studies of such simulations.« less

Localization and Ballistic Diffusion for the Tempered Fractional Brownian-Langevin Motion

NASA Astrophysics Data System (ADS)

Chen, Yao; Wang, Xudong; Deng, Weihua

2017-10-01

This paper discusses the tempered fractional Brownian motion (tfBm), its ergodicity, and the derivation of the corresponding Fokker-Planck equation. Then we introduce the generalized Langevin equation with the tempered fractional Gaussian noise for a free particle, called tempered fractional Langevin equation (tfLe). While the tfBm displays localization diffusion for the long time limit and for the short time its mean squared displacement (MSD) has the asymptotic form t^{2H}, we show that the asymptotic form of the MSD of the tfLe transits from t^2 (ballistic diffusion for short time) to t^{2-2H}, and then to t^2 (again ballistic diffusion for long time). On the other hand, the overdamped tfLe has the transition of the diffusion type from t^{2-2H} to t^2 (ballistic diffusion). The tfLe with harmonic potential is also considered.

A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal

NASA Astrophysics Data System (ADS)

Zhou, Zhenyu; Guo, Zhichang; Zhang, Dazhi; Wu, Boying

2018-04-01

Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona-Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.

Nature of self-diffusion in two-dimensional fluids

NASA Astrophysics Data System (ADS)

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; Talkner, Peter; Kidera, Akinori; Lee, Eok Kyun

2017-12-01

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(t\\sqrt{{ln}t}), however with a rescaled time.

Dimensional reduction of a general advection–diffusion equation in 2D channels

NASA Astrophysics Data System (ADS)

Kalinay, Pavol; Slanina, František

2018-06-01

Diffusion of point-like particles in a two-dimensional channel of varying width is studied. The particles are driven by an arbitrary space dependent force. We construct a general recurrence procedure mapping the corresponding two-dimensional advection-diffusion equation onto the longitudinal coordinate x. Unlike the previous specific cases, the presented procedure enables us to find the one-dimensional description of the confined diffusion even for non-conservative (vortex) forces, e.g. caused by flowing solvent dragging the particles. We show that the result is again the generalized Fick–Jacobs equation. Despite of non existing scalar potential in the case of vortex forces, the effective one-dimensional scalar potential, as well as the corresponding quasi-equilibrium and the effective diffusion coefficient can be always found.

Diffusion of liquid polystyrene into glassy poly(phenylene oxide) characterized by DSC

NASA Astrophysics Data System (ADS)

Li, Linling; Wang, Xiaoliang; Zhou, Dongshan; Xue, Gi

2013-03-01

We report a diffusion study on the polystyrene/poly(phenylene oxide) (PS/PPO) mixture consisted by the PS and PPO nanoparticles. Diffusion of liquid PS into glassy PPO (l-PS/g-PPO) is promoted by annealing the PS/PPO mixture at several temperatures below Tg of the PPO. By tracing the Tgs of the PS-rich domain behind the diffusion front using DSC, we get the relationships of PS weight fractions and diffusion front advances with the elapsed diffusion times at different diffusion temperatures using the Gordon-Taylor equation and core-shell model. We find that the plots of weight fraction of PS vs. elapsed diffusion times at different temperatures can be converted to a master curve by Time-Temperature superposition, and the shift factors obey the Arrhenius equation. Besides, the diffusion front advances of l-PS into g-PPO show an excellent agreement with the t1/2 scaling law at the beginning of the diffusion process, and the diffusion coefficients of different diffusion temperatures also obey the Arrhenius equation. We believe the diffusion mechanism for l-PS/g-PPO should be the Fickean law rather than the Case II, though there are departures of original linearity at longer diffusion times due to the limited liquid supply system. Diffusion of liquid polystyrene into glassy poly(phenylene oxide) characterized by DSC

Vapor Transport Within the Thermal Diffusion Cloud Chamber

NASA Technical Reports Server (NTRS)

Ferguson, Frank T.; Heist, Richard H.; Nuth, Joseph A., III

2000-01-01

A review of the equations used to determine the 1-D vapor transport in the thermal diffusion cloud chamber (TDCC) is presented. These equations closely follow those of the classical Stefan tube problem in which there is transport of a volatile species through a noncondensible, carrier gas. In both cases, the very plausible assumption is made that the background gas is stagnant. Unfortunately, this assumption results in a convective flux which is inconsistent with the momentum and continuity equations for both systems. The approximation permits derivation of an analytical solution for the concentration profile in the Stefan tube, but there is no computational advantage in the case of the TDCC. Furthermore, the degree of supersaturation is a sensitive function of the concentration profile in the TD CC and the stagnant background gas approximation can make a dramatic difference in the calculated supersaturation. In this work, the equations typically used with a TDCC are compared with very general transport equations describing the 1-D diffusion of the volatile species. Whereas no pressure dependence is predicted with the typical equations, a strong pressure dependence is present with the more general equations given in this work. The predicted behavior is consistent with observations in diffusion cloud experiments. It appears that the new equations may account for much of the pressure dependence noted in TDCC experiments, but a comparison between the new equations and previously obtained experimental data are needed for verification.

A novel Ras-interacting protein required for chemotaxis and cyclic adenosine monophosphate signal relay in Dictyostelium.

PubMed

Lee, S; Parent, C A; Insall, R; Firtel, R A

1999-09-01

We have identified a novel Ras-interacting protein from Dictyostelium, RIP3, whose function is required for both chemotaxis and the synthesis and relay of the cyclic AMP (cAMP) chemoattractant signal. rip3 null cells are unable to aggregate and lack receptor activation of adenylyl cyclase but are able, in response to cAMP, to induce aggregation-stage, postaggregative, and cell-type-specific gene expression in suspension culture. In addition, rip3 null cells are unable to properly polarize in a cAMP gradient and chemotaxis is highly impaired. We demonstrate that cAMP stimulation of guanylyl cyclase, which is required for chemotaxis, is reduced approximately 60% in rip3 null cells. This reduced activation of guanylyl cyclase may account, in part, for the defect in chemotaxis. When cells are pulsed with cAMP for 5 h to mimic the endogenous cAMP oscillations that occur in wild-type strains, the cells will form aggregates, most of which, however, arrest at the mound stage. Unlike the response seen in wild-type strains, the rip3 null cell aggregates that form under these experimental conditions are very small, which is probably due to the rip3 null cell chemotaxis defect. Many of the phenotypes of the rip3 null cell, including the inability to activate adenylyl cyclase in response to cAMP and defects in chemotaxis, are very similar to those of strains carrying a disruption of the gene encoding the putative Ras exchange factor AleA. We demonstrate that aleA null cells also exhibit a defect in cAMP-mediated activation of guanylyl cyclase similar to that of rip3 null cells. A double-knockout mutant (rip3/aleA null cells) exhibits a further reduction in receptor activation of guanylyl cyclase, and these cells display almost no cell polarization or movement in cAMP gradients. As RIP3 preferentially interacts with an activated form of the Dictyostelium Ras protein RasG, which itself is important for cell movement, we propose that RIP3 and AleA are components of a Ras-regulated pathway involved in integrating chemotaxis and signal relay pathways that are essential for aggregation.

Suppression of Chemotaxis by SSeCKS via Scaffolding of Phosphoinositol Phosphates and the Recruitment of the Cdc42 GEF, Frabin, to the Leading Edge

PubMed Central

Ko, Hyun-Kyung; Guo, Li-wu; Su, Bing; Gao, Lingqiu; Gelman, Irwin H.

2014-01-01

Chemotaxis is controlled by interactions between receptors, Rho-family GTPases, phosphatidylinositol 3-kinases, and cytoskeleton remodeling proteins. We investigated how the metastasis suppressor, SSeCKS, attenuates chemotaxis. Chemotaxis activity inversely correlated with SSeCKS levels in mouse embryo fibroblasts (MEF), DU145 and MDA-MB-231 cancer cells. SSeCKS loss induced chemotactic velocity and linear directionality, correlating with replacement of leading edge lamellipodia with fascin-enriched filopodia-like extensions, the formation of thickened longitudinal F-actin stress fibers reaching to filopodial tips, relative enrichments at the leading edge of phosphatidylinositol (3,4,5)P3 (PIP3), Akt, PKC-ζ, Cdc42-GTP and active Src (SrcpoY416), and a loss of Rac1. Leading edge lamellipodia and chemotaxis inhibition in SSeCKS-null MEF could be restored by full-length SSeCKS or SSeCKS deleted of its Src-binding domain (ΔSrc), but not by SSeCKS deleted of its three MARCKS (myristylated alanine-rich C kinase substrate) polybasic domains (ΔPBD), which bind PIP2 and PIP3. The enrichment of activated Cdc42 in SSeCKS-null leading edge filopodia correlated with recruitment of the Cdc42-specific guanine nucleotide exchange factor, Frabin, likely recruited via multiple PIP2/3-binding domains. Frabin knockdown in SSeCKS-null MEF restores leading edge lamellipodia and chemotaxis inhibition. However, SSeCKS failed to co-immunoprecipitate with Rac1, Cdc42 or Frabin. Consistent with the notion that chemotaxis is controlled by SSeCKS-PIP (vs. -Src) scaffolding activity, constitutively-active phosphatidylinositol 3-kinase could override the ability of the Src inhibitor, SKI-606, to suppress chemotaxis and filopodial enrichment of Frabin in SSeCKS-null MEF. Our data suggest a role for SSeCKS in controlling Rac1 vs. Cdc42-induced cellular dynamics at the leading chemotactic edge through the scaffolding of phospholipids and signal mediators, and through the reorganization of the actin cytoskeleton controlling directional movement. PMID:25356636

Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

DOE PAGES

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

2016-07-26

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Ionic Channels as Natural Nanodevices

DTIC Science & Technology

2006-05-01

introduce the numerical techniques required to simulate charge transport in ion channels. [1] Using Poisson- Nernst -Planck-type (PNP) equations ...Eisenberg. 2003. Ionic diffusion through protein channels: from molecular description to continuum equations . Nanotech 2003, 3: 439-442. 4...Nadler, B., Schuss, Z., Singer, A., and R. S. Eisenberg. 2004. Ionic diffusion through confined geometries: from Langevin equations to partial

Feynman-Kac equation for anomalous processes with space- and time-dependent forces

NASA Astrophysics Data System (ADS)

Cairoli, Andrea; Baule, Adrian

2017-04-01

Functionals of a stochastic process Y(t) model many physical time-extensive observables, for instance particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are obtained as the solution of the celebrated Feynman-Kac equation. This equation provides the crucial link between the expected values of diffusion processes and the solutions of deterministic second-order partial differential equations. When Y(t) is non-Brownian, e.g. an anomalous diffusive process, generalizations of the Feynman-Kac equation that incorporate power-law or more general waiting time distributions of the underlying random walk have recently been derived. A general representation of such waiting times is provided in terms of a Lévy process whose Laplace exponent is directly related to the memory kernel appearing in the generalized Feynman-Kac equation. The corresponding anomalous processes have been shown to capture nonlinear mean square displacements exhibiting crossovers between different scaling regimes, which have been observed in numerous experiments on biological systems like migrating cells or diffusing macromolecules in intracellular environments. However, the case where both space- and time-dependent forces drive the dynamics of the generalized anomalous process has not been solved yet. Here, we present the missing derivation of the Feynman-Kac equation in such general case by using the subordination technique. Furthermore, we discuss its extension to functionals explicitly depending on time, which are of particular relevance for the stochastic thermodynamics of anomalous diffusive systems. Exact results on the work fluctuations of a simple non-equilibrium model are obtained. An additional aim of this paper is to provide a pedagogical introduction to Lévy processes, semimartingales and their associated stochastic calculus, which underlie the mathematical formulation of anomalous diffusion as a subordinated process.

Novel Selective Detection Method of Tumor Angiogenesis Factors Using Living Nano-Robots.

PubMed

Al-Fandi, Mohamed; Alshraiedeh, Nida; Owies, Rami; Alshdaifat, Hala; Al-Mahaseneh, Omamah; Al-Tall, Khadijah; Alawneh, Rawan

2017-07-14

This paper reports a novel self-detection method for tumor cells using living nano-robots. These living robots are a nonpathogenic strain of E. coli bacteria equipped with naturally synthesized bio-nano-sensory systems that have an affinity to VEGF, an angiogenic factor overly-expressed by cancer cells. The VEGF-affinity/chemotaxis was assessed using several assays including the capillary chemotaxis assay, chemotaxis assay on soft agar, and chemotaxis assay on solid agar. In addition, a microfluidic device was developed to possibly discover tumor cells through the overexpressed vascular endothelial growth factor (VEGF). Various experiments to study the sensing characteristic of the nano-robots presented a strong response toward the VEGF. Thus, a new paradigm of selective targeting therapies for cancer can be advanced using swimming E. coli as self-navigator miniaturized robots as well as drug-delivery vehicles.

Coupled effects of chemotaxis and growth on traveling bacterial waves.

PubMed

Yan, Zhifeng; Bouwer, Edward J; Hilpert, Markus

2014-08-01

Traveling bacterial waves are capable of improving contaminant remediation in the subsurface. It is fairly well understood how bacterial chemotaxis and growth separately affect the formation and propagation of such waves. However, their interaction is not well understood. We therefore perform a modeling study to investigate the coupled effects of chemotaxis and growth on bacterial migration, and examine their effects on contaminant remediation. We study the waves by using different initial electron acceptor concentrations for different bacteria and substrate systems. Three types of traveling waves can occur: a chemotactic wave due to the biased movement of chemotactic bacteria resulting from metabolism-generated substrate concentration gradients; a growth/decay/motility wave due to a dynamic equilibrium between bacterial growth, decay and random motility; and an integrated wave due to the interaction between bacterial chemotaxis and growth. Chemotaxis hardly enhances the bacterial propagation if it is too weak to form a chemotactic wave or its wave speed is less than half of the growth/decay/motility wave speed. However, chemotaxis significantly accelerates bacterial propagation once its wave speed exceeds the growth/decay/motility wave speed. When convection occurs, it speeds up the growth/decay/motility wave but slows down or even eliminates the chemotactic wave due to the dispersion. Bacterial survival proves particularly important for bacterial propagation. Therefore we develop a conceptual model to estimate the speed of growth/decay/motility waves. Copyright © 2014 Elsevier B.V. All rights reserved.

A Worldwide Competition to Compare the Speed and Chemotactic Accuracy of Neutrophil-Like Cells

PubMed Central

Wong, Elisabeth; Hamza, Bashar; Bae, Albert; Martel, Joseph; Kataria, Rama; Keizer-Gunnink, Ineke; Kortholt, Arjan; Van Haastert, Peter J. M.; Charras, Guillaume; Janetopoulos, Christopher; Irimia, Daniel

2016-01-01

Chemotaxis is the ability to migrate towards the source of chemical gradients. It underlies the ability of neutrophils and other immune cells to hone in on their targets and defend against invading pathogens. Given the importance of neutrophil migration to health and disease, it is crucial to understand the basic mechanisms controlling chemotaxis so that strategies can be developed to modulate cell migration in clinical settings. Because of the complexity of human genetics, Dictyostelium and HL60 cells have long served as models system for studying chemotaxis. Since many of our current insights into chemotaxis have been gained from these two model systems, we decided to compare them side by side in a set of winner-take-all races, the Dicty World Races. These worldwide competitions challenge researchers to genetically engineer and pharmacologically enhance the model systems to compete in microfluidic racecourses. These races bring together technological innovations in genetic engineering and precision measurement of cell motility. Fourteen teams participated in the inaugural Dicty World Race 2014 and contributed cell lines, which they tuned for enhanced speed and chemotactic accuracy. The race enabled large-scale analyses of chemotaxis in complex environments and revealed an intriguing balance of speed and accuracy of the model cell lines. The successes of the first race validated the concept of using fun-spirited competition to gain insights into the complex mechanisms controlling chemotaxis, while the challenges of the first race will guide further technological development and planning of future events. PMID:27332963

FDM study of ion exchange diffusion equation in glass

NASA Astrophysics Data System (ADS)

Zhou, Zigang; Yang, Yongjia; Wang, Qiang; Sun, Guangchun

2009-05-01

Ion-exchange technique in glass was developed to fabricate gradient refractive index optical devices. In this paper, the Finite Difference Method(FDM), which is used for the solution of ion-diffusion equation, is reported. This method transforms continual diffusion equation to separate difference equation. It unitizes the matrix of MATLAB program to solve the iteration process. The collation results under square boundary condition show that it gets a more accurate numerical solution. Compared to experiment data, the relative error is less than 0.2%. Furthermore, it has simply operation and kinds of output solutions. This method can provide better results for border-proliferation of the hexagonal and the channel devices too.

Gas-induced friction and diffusion of rigid rotors

NASA Astrophysics Data System (ADS)

Martinetz, Lukas; Hornberger, Klaus; Stickler, Benjamin A.

2018-05-01

We derive the Boltzmann equation for the rotranslational dynamics of an arbitrary convex rigid body in a rarefied gas. It yields as a limiting case the Fokker-Planck equation accounting for friction, diffusion, and nonconservative drift forces and torques. We provide the rotranslational friction and diffusion tensors for specular and diffuse reflection off particles with spherical, cylindrical, and cuboidal shape, and show that the theory describes thermalization, photophoresis, and the inverse Magnus effect in the free molecular regime.

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

NASA Astrophysics Data System (ADS)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

Microbial community structure and functioning in marine sediments associated with diffuse hydrothermal venting assessed by integrated meta-omics.

PubMed

Urich, Tim; Lanzén, Anders; Stokke, Runar; Pedersen, Rolf B; Bayer, Christoph; Thorseth, Ingunn H; Schleper, Christa; Steen, Ida H; Ovreas, Lise

2014-09-01

Deep-sea hydrothermal vents are unique environments on Earth, as they host chemosynthetic ecosystems fuelled by geochemical energy with chemolithoautotrophic microorganisms at the basis of the food webs. Whereas discrete high-temperature venting systems have been studied extensively, the microbiotas associated with low-temperature diffuse venting are not well understood. We analysed the structure and functioning of microbial communities in two diffuse venting sediments from the Jan Mayen vent fields in the Norwegian-Greenland Sea, applying an integrated 'omics' approach combining metatranscriptomics, metaproteomics and metagenomics. Polymerase chain reaction-independent three-domain community profiling showed that the two sediments hosted highly similar communities dominated by Epsilonproteobacteria, Deltaproteobacteria and Gammaproteobacteria, besides ciliates, nematodes and various archaeal taxa. Active metabolic pathways were identified through transcripts and peptides, with genes of sulphur and methane oxidation, and carbon fixation pathways highly expressed, in addition to genes of aerobic and anaerobic (nitrate and sulphate) respiratory chains. High expression of chemotaxis and flagella genes reflected a lifestyle in a dynamic habitat rich in physico-chemical gradients. The major metabolic pathways could be assigned to distinct taxonomic groups, thus enabling hypotheses about the function of the different prokaryotic and eukaryotic taxa. This study advances our understanding of the functioning of microbial communities in diffuse hydrothermal venting sediments. © 2013 Society for Applied Microbiology and John Wiley & Sons Ltd.

A Simple, Analytical Model of Collisionless Magnetic Reconnection in a Pair Plasma

NASA Technical Reports Server (NTRS)

Hesse, Michael; Zenitani, Seiji; Kuznetova, Masha; Klimas, Alex

2011-01-01

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region, and to impart thermal energy to the plasma by means of quasi-viscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative, procedure. The solutions show expected features such as dominance of enthalpy flux in the reconnection outflow, as well as combination of adiabatic and quasi-viscous heating. Furthermore, the model predicts a maximum reconnection electric field of E(sup *)=0.4, normalized to the parameters at the inflow edge of the diffusion region.

A simple, analytical model of collisionless magnetic reconnection in a pair plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hesse, Michael; Zenitani, Seiji; Kuznetsova, Masha

2009-10-15

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region and to impart thermal energy to the plasma by means of quasiviscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative procedure. The solutions show expected features such as dominance of enthalpymore » flux in the reconnection outflow, as well as combination of adiabatic and quasiviscous heating. Furthermore, the model predicts a maximum reconnection electric field of E{sup *}=0.4, normalized to the parameters at the inflow edge of the diffusion region.« less

Comparison of fluid neutral models for one-dimensional plasma edge modeling with a finite volume solution of the Boltzmann equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horsten, N., E-mail: niels.horsten@kuleuven.be; Baelmans, M.; Dekeyser, W.

2016-01-15

We derive fluid neutral approximations for a simplified 1D edge plasma model, suitable to study the neutral behavior close to the target of a nuclear fusion divertor, and compare its solutions to the solution of the corresponding kinetic Boltzmann equation. The plasma is considered as a fixed background extracted from a detached 2D simulation. We show that the Maxwellian equilibrium distribution is already obtained very close to the target, justifying the use of a fluid approximation. We compare three fluid neutral models: (i) a diffusion model; (ii) a pressure-diffusion model (i.e., a combination of a continuity and momentum equation) assumingmore » equal neutral and ion temperatures; and (iii) the pressure-diffusion model coupled to a neutral energy equation taking into account temperature differences between neutrals and ions. Partial reflection of neutrals reaching the boundaries is included in both the kinetic and fluid models. We propose two methods to obtain an incident neutral flux boundary condition for the fluid models: one based on a diffusion approximation and the other assuming a truncated Chapman-Enskog distribution. The pressure-diffusion model predicts the plasma sources very well. The diffusion boundary condition gives slightly better results overall. Although including an energy equation still improves the results, the assumption of equal ion and neutral temperature already gives a very good approximation.« less

Regulation of Pseudomonas aeruginosa chemotaxis by the nitrogen source.

PubMed Central

Craven, R; Montie, T C

1985-01-01

The regulation of amino acid chemotaxis by nitrogen was investigated in the gram-negative bacterium Pseudomonas aeruginosa. The quantitative capillary tube technique was used to measure chemotactic responses of bacteria to spatial gradients of amino acids and other attractants. Chemotaxis toward serine, arginine, and alpha-aminoisobutyrate was sharply dependent on the form in which nitrogen was presented to the bacteria. Bacteria grown on mineral salts-succinate with potassium nitrate gave responses to amino acids that were 2 to 3 times those of cells grown on ammonium sulfate and 10 to 20 times those of cells grown in mineral salts-succinate with Casamino Acids as the nitrogen source. A combination of ammonium sulfate and glutamate was as effective as Casamino Acids in depressing serine taxis. The threshold concentration for alpha-aminoisobutyrate taxis was consistently lower in nitrate-grown bacteria than in ammonia-grown bacteria. Responsiveness to sodium succinate, however, was not subject to regulation by nitrogen, and glucose chemotaxis was inhibited, rather than enhanced, in nitrate-grown bacteria. These results indicate that chemotaxis of P. aeruginosa toward amino acids is subject to regulation by nitrogen and that this regulation probably is expressed at the level of the chemoreceptors or transducers. PMID:3932326

Chemotaxis and flagellar genes of Chromobacterium violaceum.

PubMed

Pereira, Maristela; Parente, Juliana Alves; Bataus, Luiz Artur Mendes; Cardoso, Divina das Dores de Paula; Soares, Renata Bastos Ascenço; Soares, Célia Maria de Almeida

2004-03-31

The availability of the complete genome of the Gram-negative beta-proteobacterium Chromobacterium violaceum has increasingly impacted our understanding of this microorganism. This review focuses on the genomic organization and structural analysis of the deduced proteins of the chemosensory adaptation system of C. violaceum. C. violaceum has multiple homologues of most chemotaxis genes, organized mostly in clusters in the bacterial genome. We found at least 67 genes, distributed in 10 gene clusters, involved in the chemotaxis of C. violaceum. A close examination of the chemoreceptors methyl-accepting chemotaxis proteins (MCPs), and the deduced sequences of the members of the two-component signaling system revealed canonical motifs, described as essential for the function of the deduced proteins. The chemoreceptors found in C. violaceum include the complete repertoire of such genes described in bacteria, designated as tsr, tar, trg, and tap; 41 MCP loci were found in the C. violaceum genome. Also, the C. violaceum genome includes a large repertoire of the proteins of the chemosensory transducer system. Multiple homologues of bacterial chemotaxis genes, including CheA, CheB, CheD, CheR, CheV, CheY, CheZ, and CheW, were found in the C. violaceum genome.

Signal-activated phospholipase regulation of leukocyte chemotaxis.

PubMed

Cathcart, Martha K

2009-04-01

Signal-activated phospholipases are a recent focus of the rapidly growing field of lipid signaling. The extent of their impact on the pathways regulating diverse cell functions is beginning to be appreciated. A critical step in inflammation is the attraction of leukocytes to injured or diseased tissue. Chemotaxis of leukocytes, a requisite process for monocyte and neutrophil extravasation from the blood into tissues, is a critical step for initiating and maintaining inflammation in both acute and chronic settings. Recent studies have identified new important and required roles for two signal-activated phospholipases A2 (PLA2) in regulating chemotaxis. The two intracellular phospholipases, cPLA2alpha (Group IVA) and iPLA2beta (Group VIA), act in parallel to provide distinct lipid mediators at different intracellular sites that are both required for leukocytes to migrate toward the chemokine monocyte chemoattractant protein-1. This review will summarize the separate roles of these phospholipases as well as what is currently known about the influence of two other classes of intracellular signal-activated phospholipases, phospholipase C and phospholipase D, in regulating chemotaxis in eukaryotic cells, but particularly in human monocytes. The contributions of these phospholipases to chemotaxis both in vitro and in vivo will be highlighted.

Gas/liquid sensing via chemotaxis of Euglena cells confined in an isolated micro-aquarium.

PubMed

Ozasa, Kazunari; Lee, Jeesoo; Song, Simon; Hara, Masahiko; Maeda, Mizuo

2013-10-21

We demonstrate on-chip gas/liquid sensing by using the chemotaxis of live bacteria (Euglena gracilis) confined in an isolated micro-aquarium, and gas/liquid permeation through porous polydimethylsiloxane (PDMS). The sensing chip consisted of one closed micro-aquarium and two separated bypass microchannels along the perimeter of the micro-aquarium. Test gas/liquid and reference samples were introduced into the two individual microchannels separately, and the gas/liquid permeated through the PDMS walls and dissolved in the micro-aquarium water, resulting in a chemical concentration gradient in the micro-aquarium. By employing the closed micro-aquarium isolated from sample flows, we succeeded in measuring the chemotaxis of Euglena for a gas substance quantitatively, which cannot be achieved with the conventional flow-type or hydro-gel-type microfluidic devices. We found positive (negative) chemotaxis for CO2 concentrations below (above) 15%, with 64 ppm as the minimum concentration affecting the cells. We also observed chemotaxis for ethanol and H2O2. By supplying culture medium via the microchannels, the Euglena culture remained alive for more than 2 months. The sensing chip is thus useful for culturing cells and using them for environmental toxicity/nutrition studies by monitoring their motion.

Tumour related inhibition of macrophage chemotaxis in patients with colon cancer.

PubMed Central

Hermanowicz, A; Gibson, P R; Jewell, D P

1987-01-01

The chemotactic migration in vitro of peripheral blood, intestinal mucosal, and mesenteric lymph node mononuclear cells has been assessed in patients with colorectal carcinoma. Peripheral blood mononuclear cells of patients exhibited normal chemotaxis. For control patients with non-malignant, non-inflammatory intestinal disease, the chemotaxis of mucosal mononuclear cells was similar to that of autologous peripheral blood mononuclear cells. The chemotactic migration of mucosal mononuclear cells, however, isolated distant from a colon cancer was less than that of autologous peripheral blood mononuclear cells. Chemotactic migration was progressively impaired with increasing closeness to the tumour itself. Chemotaxis of mucosal mononuclear cell was independent of the site of tumour and the Dukes' grading. Mononuclear cells from mesenteric lymph nodes, however, exhibited impaired migration only in patients with Dukes' C tumours. Supernatants of the collagenase digestion of either tumour or adjacent mucosa contained macrophage directed inhibitors of chemotaxis and these inhibitors were not produced by tumour mononuclear cells. The presence of such inhibitors in the digestion supernatants and the demonstration that proximity to the tumour was associated with impaired mononuclear cell motility suggest that the production of macrophage directed chemotactic inhibitors is by colon cancer cells and that this may be occurring in vivo. PMID:3583069

Dispatch. Dictyostelium chemotaxis: fascism through the back door?

PubMed

Insall, Robert

2003-04-29

Aggregating Dictyostelium cells secrete cyclic AMP to attract their neighbours by chemotaxis. It has now been shown that adenylyl cyclase is enriched in the rear of cells, and this localisation is required for normal aggregation.

Symmetry Reductions of Fourth-Order Nonlinear Diffusion Equations: Lubrication Model and Some Generalizations

NASA Astrophysics Data System (ADS)

Gandarias, M. L.; Medina, E.

Fourth-order nonlinear diffusion equations appear frequently in the description of physical processes, among these, the lubrication equation ut = (unuxxxx)x or the corresponding modified version ut = unuxxxx play an important role in the study of the interface movements. In this work we analyze the generalizations of the above equations given by ut = (f(u)uxxxx)x, ut = (f(u)uxxxx, and we find that if f(u) = un or f(u) = e-u the equations admit extra classical symmetries. The corresponding reductions are performed and some solutions are characterized.

Wave and pseudo-diffusion equations from squeezed states

NASA Technical Reports Server (NTRS)

Daboul, Jamil

1993-01-01

We show that the probability distributions P(sub n)(q,p;y) := the absolute value squared of (n(p,q;y), which are obtained from squeezed states, obey an interesting partial differential equation, to which we give two intuitive interpretations: as a wave equation in one space dimension; and as a pseudo-diffusion equation. We also study the corresponding Wehrl entropies S(sub n)(y), and we show that they have minima at zero squeezing, y = 0.

Gravitational instability of filamentary molecular clouds, including ambipolar diffusion; non-isothermal filament

NASA Astrophysics Data System (ADS)

Hosseinirad, Mohammad; Abbassi, Shahram; Roshan, Mahmood; Naficy, Kazem

2018-04-01

Recent observations of the filamentary molecular clouds show that their properties deviate from the isothermal equation of state. Theoretical investigations proposed that the logatropic and the polytropic equations of state with negative indexes can provide a better description for these filamentary structures. Here, we aim to compare the effects of these softer non-isothermal equations of state with their isothermal counterpart on the global gravitational instability of a filamentary molecular cloud. By incorporating the ambipolar diffusion, we use the non-ideal magnetohydrodynamics framework for a filament that is threaded by a uniform axial magnetic field. We perturb the fluid and obtain the dispersion relation both for the logatropic and polytropic equations of state by taking the effects of magnetic field and ambipolar diffusion into account. Our results suggest that, in absence of the magnetic field, a softer equation of state makes the system more prone to gravitational instability. We also observed that a moderate magnetic field is able to enhance the stability of the filament in a way that is sensitive to the equation of state in general. However, when the magnetic field is strong, this effect is suppressed and all the equations of state have almost the same stability properties. Moreover, we find that for all the considered equations of state, the ambipolar diffusion has destabilizing effects on the filament.

Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

NASA Technical Reports Server (NTRS)

Wood, William A.

1997-01-01

The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

Strongly anomalous diffusion in sheared magnetic configurations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vanden Eijnden, E.; Balescu, R.

1996-03-01

The statistical behavior of magnetic lines in a sheared magnetic configuration with reference surface {ital x}=0 is investigated within the framework of the kinetic theory. A Liouville equation is associated with the equations of motion of the stochastic magnetic lines. After averaging over an ensemble of realizations, it yields a convection-diffusion equation within the quasilinear approximation. The diffusion coefficients are space dependent and peaked around the reference surface {ital x}=0. Due to the shear, the diffusion of lines away from the reference surface is slowed down. The behavior of the lines is asymptotically strongly non-Gaussian. The reference surface acts likemore » an attractor around which the magnetic lines spread with an effective subdiffusive behavior. Comparison is also made with more usual treatments based on the study of the first two moments equations. For sheared systems, it is explicitly shown that the Corrsin approximation assumed in the latter approach is no longer valid. It is also concluded that the diffusion coefficients cannot be derived from the mean square displacement of the magnetic lines in an inhomogeneous medium. {copyright} {ital 1996 American Institute of Physics.}« less

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes.

PubMed

Chatterjee, Abhijit; Vlachos, Dionisios G

2007-07-21

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.

Finite Difference Formulation for Prediction of Water Pollution

NASA Astrophysics Data System (ADS)

Johari, Hanani; Rusli, Nursalasawati; Yahya, Zainab

2018-03-01

Water is an important component of the earth. Human being and living organisms are demand for the quality of water. Human activity is one of the causes of the water pollution. The pollution happened give bad effect to the physical and characteristic of water contents. It is not practical to monitor all aspects of water flow and transport distribution. So, in order to help people to access to the polluted area, a prediction of water pollution concentration must be modelled. This study proposed a one-dimensional advection diffusion equation for predicting the water pollution concentration transport. The numerical modelling will be produced in order to predict the transportation of water pollution concentration. In order to approximate the advection diffusion equation, the implicit Crank Nicolson is used. For the purpose of the simulation, the boundary condition and initial condition, the spatial steps and time steps as well as the approximations of the advection diffusion equation have been encoded. The results of one dimensional advection diffusion equation have successfully been used to predict the transportation of water pollution concentration by manipulating the velocity and diffusion parameters.

Mathematical analysis of thermal diffusion shock waves

NASA Astrophysics Data System (ADS)

Gusev, Vitalyi; Craig, Walter; Livoti, Roberto; Danworaphong, Sorasak; Diebold, Gerald J.

2005-10-01

Thermal diffusion, also known as the Ludwig-Soret effect, refers to the separation of mixtures in a temperature gradient. For a binary mixture the time dependence of the change in concentration of each species is governed by a nonlinear partial differential equation in space and time. Here, an exact solution of the Ludwig-Soret equation without mass diffusion for a sinusoidal temperature field is given. The solution shows that counterpropagating shock waves are produced which slow and eventually come to a halt. Expressions are found for the shock time for two limiting values of the starting density fraction. The effects of diffusion on the development of the concentration profile in time and space are found by numerical integration of the nonlinear differential equation.

Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

NASA Astrophysics Data System (ADS)

Remizov, I. D.

2012-07-01

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.

Novel Selective Detection Method of Tumor Angiogenesis Factors Using Living Nano-Robots

PubMed Central

Alshraiedeh, Nida; Owies, Rami; Alshdaifat, Hala; Al-Mahaseneh, Omamah; Al-Tall, Khadijah; Alawneh, Rawan

2017-01-01

This paper reports a novel self-detection method for tumor cells using living nano-robots. These living robots are a nonpathogenic strain of E. coli bacteria equipped with naturally synthesized bio-nano-sensory systems that have an affinity to VEGF, an angiogenic factor overly-expressed by cancer cells. The VEGF-affinity/chemotaxis was assessed using several assays including the capillary chemotaxis assay, chemotaxis assay on soft agar, and chemotaxis assay on solid agar. In addition, a microfluidic device was developed to possibly discover tumor cells through the overexpressed vascular endothelial growth factor (VEGF). Various experiments to study the sensing characteristic of the nano-robots presented a strong response toward the VEGF. Thus, a new paradigm of selective targeting therapies for cancer can be advanced using swimming E. coli as self-navigator miniaturized robots as well as drug-delivery vehicles. PMID:28708066

Decreased numbers of chemotactic factor receptors in chronic neutropenia with defective chemotaxis: spontaneous recovery from the neutrophil abnormalities during early childhood

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yasui, K.; Yamazaki, M.; Miyagawa, Y.

Childhood chronic neutropenia with decreased numbers of chemotactic factor receptors as well as defective chemotaxis was first demonstrated in an 8-month-old girl. Chemotactic factor receptors on neutrophils were assayed using tritiated N-formyl-methionyl-leucyl-phenylalanine (/sup 3/H-FMLP). The patient's neutrophils had decreased numbers of the receptors: numbers of the receptors were 20,000 (less than 3 SD) as compared with those of control cells of 52,000 +/- 6000 (mean +/- SD) (n = 10). The neutropenia disappeared spontaneously by 28 months of age parallel with the improvement of chemotaxis and increase in numbers of chemotactic factor receptors. These results demonstrate a transient decrease ofmore » neutrophil chemotactic factor receptors as one of the pathophysiological bases of a transient defect of neutrophil chemotaxis in this disorder.« less

Relation between chemotaxis and consumption of amino acids in bacteria

PubMed Central

Yang, Yiling; M. Pollard, Abiola; Höfler, Carolin; Poschet, Gernot; Wirtz, Markus; Hell, Rüdiger

2015-01-01

Summary Chemotaxis enables bacteria to navigate chemical gradients in their environment, accumulating toward high concentrations of attractants and avoiding high concentrations of repellents. Although finding nutrients is likely to be an important function of bacterial chemotaxis, not all characterized attractants are nutrients. Moreover, even for potential nutrients, the exact relation between the metabolic value of chemicals and their efficiency as chemoattractants has not been systematically explored. Here we compare the chemotactic response of amino acids with their use by bacteria for two well‐established models of chemotactic behavior, E scherichia coli and B acillus subtilis. We demonstrate that in E . coli chemotaxis toward amino acids indeed strongly correlates with their utilization. However, no such correlation is observed for B . subtilis, suggesting that in this case, the amino acids are not followed because of their nutritional value but rather as environmental cues. PMID:25807888

Modeling boundary measurements of scattered light using the corrected diffusion approximation

PubMed Central

Lehtikangas, Ossi; Tarvainen, Tanja; Kim, Arnold D.

2012-01-01

We study the modeling and simulation of steady-state measurements of light scattered by a turbid medium taken at the boundary. In particular, we implement the recently introduced corrected diffusion approximation in two spatial dimensions to model these boundary measurements. This implementation uses expansions in plane wave solutions to compute boundary conditions and the additive boundary layer correction, and a finite element method to solve the diffusion equation. We show that this corrected diffusion approximation models boundary measurements substantially better than the standard diffusion approximation in comparison to numerical solutions of the radiative transport equation. PMID:22435102

Optical Oversampled Analog-to-Digital Conversion

DTIC Science & Technology

1992-06-29

hologram weights and interconnects in the digital image halftoning configuration. First, no temporal error diffusion occurs in the digital image... halftoning error diffusion ar- chitecture as demonstrated by Equation (6.1). Equation (6.2) ensures that the hologram weights sum to one so that the exact...optimum halftone image should be faster. Similarly, decreased convergence time suggests that an error diffusion filter with larger spatial dimensions

Modelling the radiotherapy effect in the reaction-diffusion equation.

PubMed

Borasi, Giovanni; Nahum, Alan

2016-09-01

In recent years, the reaction-diffusion (Fisher-Kolmogorov) equation has received much attention from the oncology research community due to its ability to describe the infiltrating nature of glioblastoma multiforme and its extraordinary resistance to any type of therapy. However, in a number of previous papers in the literature on applications of this equation, the term (R) expressing the 'External Radiotherapy effect' was incorrectly derived. In this note we derive an analytical expression for this term in the correct form to be included in the reaction-diffusion equation. The R term has been derived starting from the Linear-Quadratic theory of cell killing by ionizing radiation. The correct definition of R was adopted and the basic principles of differential calculus applied. The compatibility of the R term derived here with the reaction-diffusion equation was demonstrated. Referring to a typical glioblastoma tumour, we have compared the results obtained using our expression for the R term with the 'incorrect' expression proposed by other authors. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

PubMed

Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q

2013-03-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION

PubMed Central

Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.

2013-01-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian. PMID:23772179

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Traveling wave solutions to a reaction-diffusion equation

NASA Astrophysics Data System (ADS)

Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.

2009-07-01

In this paper, we restrict our attention to traveling wave solutions of a reaction-diffusion equation. Firstly we apply the Divisor Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to find a quasi-polynomial first integral of an explicit form to an equivalent autonomous system. Then through this first integral, we reduce the reaction-diffusion equation to a first-order integrable ordinary differential equation, and a class of traveling wave solutions is obtained accordingly. Comparisons with the existing results in the literature are also provided, which indicates that some analytical results in the literature contain errors. We clarify the errors and instead give a refined result in a simple and straightforward manner.

Nature of self-diffusion in two-dimensional fluids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Nature of self-diffusion in two-dimensional fluids

DOE PAGES

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; ...

2017-12-18

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

NASA Astrophysics Data System (ADS)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

Borrelia burgdorferi CheY2 Is Dispensable for Chemotaxis or Motility but Crucial for the Infectious Life Cycle of the Spirochete.

PubMed

Xu, Hui; Sultan, Syed; Yerke, Aaron; Moon, Ki Hwan; Wooten, R Mark; Motaleb, M A

2017-01-01

The requirements for bacterial chemotaxis and motility range from dispensable to crucial for host colonization. Even though more than 50% of all sequenced prokaryotic genomes possess at least one chemotaxis signaling system, many of those genomes contain multiple copies of a chemotaxis gene. However, the functions of most of those additional genes are unknown. Most motile bacteria possess at least one CheY response regulator that is typically dedicated to the control of motility and which is usually essential for virulence. Borrelia burgdorferi appears to be notably different, in that it has three cheY genes, and our current studies on cheY2 suggests that it has varied effects on different aspects of the natural infection cycle. Mutants deficient in this protein exhibit normal motility and chemotaxis in vitro but show reduced virulence in mice. Specifically, the cheY2 mutants were severely attenuated in murine infection and dissemination to distant tissues after needle inoculation. Moreover, while ΔcheY2 spirochetes are able to survive normally in the Ixodes ticks, mice fed upon by the ΔcheY2-infected ticks did not develop a persistent infection in the murine host. Our data suggest that CheY2, despite resembling a typical response regulator, functions distinctively from most other chemotaxis CheY proteins. We propose that CheY2 serves as a regulator for a B. burgdorferi virulence determinant that is required for productive infection within vertebrate, but not tick, hosts. Copyright © 2016 American Society for Microbiology.

Borrelia burgdorferi CheY2 Is Dispensable for Chemotaxis or Motility but Crucial for the Infectious Life Cycle of the Spirochete

PubMed Central

Xu, Hui; Sultan, Syed; Yerke, Aaron; Moon, Ki Hwan; Wooten, R. Mark

2016-01-01

ABSTRACT The requirements for bacterial chemotaxis and motility range from dispensable to crucial for host colonization. Even though more than 50% of all sequenced prokaryotic genomes possess at least one chemotaxis signaling system, many of those genomes contain multiple copies of a chemotaxis gene. However, the functions of most of those additional genes are unknown. Most motile bacteria possess at least one CheY response regulator that is typically dedicated to the control of motility and which is usually essential for virulence. Borrelia burgdorferi appears to be notably different, in that it has three cheY genes, and our current studies on cheY2 suggests that it has varied effects on different aspects of the natural infection cycle. Mutants deficient in this protein exhibit normal motility and chemotaxis in vitro but show reduced virulence in mice. Specifically, the cheY2 mutants were severely attenuated in murine infection and dissemination to distant tissues after needle inoculation. Moreover, while ΔcheY2 spirochetes are able to survive normally in the Ixodes ticks, mice fed upon by the ΔcheY2-infected ticks did not develop a persistent infection in the murine host. Our data suggest that CheY2, despite resembling a typical response regulator, functions distinctively from most other chemotaxis CheY proteins. We propose that CheY2 serves as a regulator for a B. burgdorferi virulence determinant that is required for productive infection within vertebrate, but not tick, hosts. PMID:27799336

Minimal Network Topologies for Signal Processing during Collective Cell Chemotaxis.

PubMed

Yue, Haicen; Camley, Brian A; Rappel, Wouter-Jan

2018-06-19

Cell-cell communication plays an important role in collective cell migration. However, it remains unclear how cells in a group cooperatively process external signals to determine the group's direction of motion. Although the topology of signaling pathways is vitally important in single-cell chemotaxis, the signaling topology for collective chemotaxis has not been systematically studied. Here, we combine mathematical analysis and simulations to find minimal network topologies for multicellular signal processing in collective chemotaxis. We focus on border cell cluster chemotaxis in the Drosophila egg chamber, in which responses to several experimental perturbations of the signaling network are known. Our minimal signaling network includes only four elements: a chemoattractant, the protein Rac (indicating cell activation), cell protrusion, and a hypothesized global factor responsible for cell-cell interaction. Experimental data on cell protrusion statistics allows us to systematically narrow the number of possible topologies from more than 40,000,000 to only six minimal topologies with six interactions between the four elements. This analysis does not require a specific functional form of the interactions, and only qualitative features are needed; it is thus robust to many modeling choices. Simulations of a stochastic biochemical model of border cell chemotaxis show that the qualitative selection procedure accurately determines which topologies are consistent with the experiment. We fit our model for all six proposed topologies; each produces results that are consistent with all experimentally available data. Finally, we suggest experiments to further discriminate possible pathway topologies. Copyright © 2018 Biophysical Society. Published by Elsevier Inc. All rights reserved.

A Novel Ras-interacting Protein Required for Chemotaxis and Cyclic Adenosine Monophosphate Signal Relay in Dictyostelium

PubMed Central

Lee, Susan; Parent, Carole A.; Insall, Robert; Firtel, Richard A.

1999-01-01

We have identified a novel Ras-interacting protein from Dictyostelium, RIP3, whose function is required for both chemotaxis and the synthesis and relay of the cyclic AMP (cAMP) chemoattractant signal. rip3 null cells are unable to aggregate and lack receptor activation of adenylyl cyclase but are able, in response to cAMP, to induce aggregation-stage, postaggregative, and cell-type-specific gene expression in suspension culture. In addition, rip3 null cells are unable to properly polarize in a cAMP gradient and chemotaxis is highly impaired. We demonstrate that cAMP stimulation of guanylyl cyclase, which is required for chemotaxis, is reduced ∼60% in rip3 null cells. This reduced activation of guanylyl cyclase may account, in part, for the defect in chemotaxis. When cells are pulsed with cAMP for 5 h to mimic the endogenous cAMP oscillations that occur in wild-type strains, the cells will form aggregates, most of which, however, arrest at the mound stage. Unlike the response seen in wild-type strains, the rip3 null cell aggregates that form under these experimental conditions are very small, which is probably due to the rip3 null cell chemotaxis defect. Many of the phenotypes of the rip3 null cell, including the inability to activate adenylyl cyclase in response to cAMP and defects in chemotaxis, are very similar to those of strains carrying a disruption of the gene encoding the putative Ras exchange factor AleA. We demonstrate that aleA null cells also exhibit a defect in cAMP-mediated activation of guanylyl cyclase similar to that of rip3 null cells. A double-knockout mutant (rip3/aleA null cells) exhibits a further reduction in receptor activation of guanylyl cyclase, and these cells display almost no cell polarization or movement in cAMP gradients. As RIP3 preferentially interacts with an activated form of the Dictyostelium Ras protein RasG, which itself is important for cell movement, we propose that RIP3 and AleA are components of a Ras-regulated pathway involved in integrating chemotaxis and signal relay pathways that are essential for aggregation. PMID:10473630

Diffuse reflectance relations based on diffusion dipole theory for large absorption and reduced scattering

NASA Astrophysics Data System (ADS)

Bremmer, Rolf H.; van Gemert, Martin J. C.; Faber, Dirk J.; van Leeuwen, Ton G.; Aalders, Maurice C. G.

2013-08-01

Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20 m at reduced scattering coefficients of 1 and 11.5 mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], derived as an approximation to one of the diffusion dipole equations of Farrell et al. [Med. Phys. 19, 879-888 (1992)]. However, two parameters were fitted to all phantom experiments, including strongly absorbing samples, implying that the reflectance equation differs from diffusion theory. Yet, the exact diffusion dipole approximation at high reduced scattering and absorption also showed agreement with the phantom measurements. The mathematical structure of the diffuse reflectance relation used, derived by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], explains this observation. In conclusion, diffuse reflectance relations derived as an approximation to the diffusion dipole theory of Farrell et al. can analyze reflectance ratios accurately, even for much larger absorption than reduced scattering coefficients. This allows calibration of fiber-probe set-ups so that the object's diffuse reflectance can be related to its absorption even when large. These findings will greatly expand the application of diffuse reflection spectroscopy. In medicine, it may allow the use of blue/green wavelengths and measurements on whole blood, and in forensic science, it may allow inclusion of objects such as blood stains and cloth at crime scenes.

Diffusion in random networks: Asymptotic properties, and numerical and engineering approximations

NASA Astrophysics Data System (ADS)

Padrino, Juan C.; Zhang, Duan Z.

2016-11-01

The ensemble phase averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of a set of pockets connected by tortuous channels. Inside a channel, we assume that fluid transport is governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pores mass density. The so-called dual porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem, we consider the one-dimensional mass diffusion in a semi-infinite domain, whose solution is sought numerically. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt- 1 / 4 rather than xt- 1 / 2 as in the traditional theory. This early time sub-diffusive similarity can be explained by random walk theory through the network. In addition, by applying concepts of fractional calculus, we show that, for small time, the governing equation reduces to a fractional diffusion equation with known solution. We recast this solution in terms of special functions easier to compute. Comparison of the numerical and exact solutions shows excellent agreement.

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

Is the kinetic equation for turbulent gas-particle flows ill posed?

PubMed

Reeks, M; Swailes, D C; Bragg, A D

2018-02-01

This paper is about the kinetic equation for gas-particle flows, in particular its well-posedness and realizability and its relationship to the generalized Langevin model (GLM) probability density function (PDF) equation. Previous analyses, e.g. [J.-P. Minier and C. Profeta, Phys. Rev. E 92, 053020 (2015)PLEEE81539-375510.1103/PhysRevE.92.053020], have concluded that this kinetic equation is ill posed, that in particular it has the properties of a backward heat equation, and as a consequence, its solution will in the course of time exhibit finite-time singularities. We show that this conclusion is fundamentally flawed because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra positive diffusion that always outweighs the negative diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these positive and negative contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing, we have drawn attention to the limitations of the GLM approach, which these studies have ignored or not properly considered, to give a more balanced appraisal of the benefits of both PDF approaches.

Void Formation during Diffusion - Two-Dimensional Approach

NASA Astrophysics Data System (ADS)

Wierzba, Bartek

2016-06-01

The final set of equations defining the interdiffusion process in solid state is presented. The model is supplemented by vacancy evolution equation. The competition between the Kirkendall shift, backstress effect and vacancy migration is considered. The proper diffusion flux based on the Nernst-Planck formula is proposed. As a result, the comparison of the experimental and calculated evolution of the void formation in the Fe-Pd diffusion couple is shown.

New Solution of Diffusion-Advection Equation for Cosmic-Ray Transport Using Ultradistributions

NASA Astrophysics Data System (ADS)

Rocca, M. C.; Plastino, A. R.; Plastino, A.; Ferri, G. L.; de Paoli, A.

2015-11-01

In this paper we exactly solve the diffusion-advection equation (DAE) for cosmic-ray transport. For such a purpose we use the Theory of Ultradistributions of J. Sebastiao e Silva, to give a general solution for the DAE. From the ensuing solution, we obtain several approximations as limiting cases of various situations of physical and astrophysical interest. One of them involves Solar cosmic-rays' diffusion.

Activated protein C promotes breast cancer cell migration through interactions with EPCR and PAR-1

PubMed Central

Beaulieu, Lea M.; Church, Frank C.

2014-01-01

Activated protein C (APC) is a serine protease that regulates thrombin (IIa) production through inactivation of blood coagulation factors Va and VIIIa. APC also has non-hemostatic functions related to inflammation, proliferation, and apoptosis through various mechanisms. Using two breast cancer cell lines, MDA-MB-231 and MDA-MB-435, we investigated the role of APC in cell chemotaxis and invasion. Treatment of cells with increasing APC concentrations (1–50 μg/ml) increased invasion and chemotaxis in a concentration-dependent manner. Only the active form of APC increased invasion and chemotaxis of the MDA-MB-231 cells when compared to 3 inactive APC derivatives. Using a modified “checkerboard” analysis, APC was shown to only affect migration when plated with the cells; therefore, APC is not a chemoattractant. Blocking antibodies to endothelial protein C receptor (EPCR) and protease-activated receptor-1 (PAR-1) attenuated the effects of APC on chemotaxis in the MDA-MB-231 cells. Finally, treatment of the MDA-MB-231 cells with the proliferation inhibitor, Na butyrate, showed that APC did not increase migration by increasing cell number. Therefore, APC increases invasion and chemotaxis of cells by binding to the cell surface and activating specific signaling pathways through EPCR and PAR-1. PMID:17254565

Chemotaxis Increases the Residence Time Distribution of Bacteria in Granular Media Containing Distributed Contaminant Sources

NASA Astrophysics Data System (ADS)

Adadevoh, J.; Triolo, S.; Ramsburg, C. A.; Ford, R.

2015-12-01

The use of chemotactic bacteria in bioremediation has the potential to increase access to, and biotransformation of, contaminant mass within the subsurface environment. This laboratory-scale study aimed to understand and quantify the influence of chemotaxis on residence times of pollutant-degrading bacteria within homogeneous treatment zones. Focus was placed on a continuous flow sand-packed column system in which a uniform distribution of naphthalene crystals created distributed sources of dissolved phase contaminant. A 10 mL pulse of Pseudomonas putida G7, which is chemotactic to naphthalene, and Pseudomonas putida G7 Y1, a non-chemotactic mutant strain, were simultaneously introduced into the sand-packed column at equal concentrations. Breakthrough curves obtained for the bacteria from column experiments conducted with and without naphthalene were used to quantify the effect of chemotaxis on transport parameters. In the presence of the chemoattractant, longitudinal dispersivity of PpG7 increased by a factor of 3 and percent recovery decreased from 21% to 12%. The results imply that pore-scale chemotaxis responses are evident at an interstitial fluid velocity of 1.7 m/d, which is within the range of typical groundwater flow. Within the context of bioremediation, chemotaxis may work to enhance bacterial residence times in zones of contamination thereby improving treatment.

Delayed hypersensitivity and neutrophil chemotaxis: effect of trauma.

PubMed

Meakins, J L; McLean, A P; Kelly, R; Bubenik, O; Pietsch, J B; MacLean, L D

1978-04-01

To investigate alterations in host defense produced by trauma, skin testing with five standard recall antigens was done on admission and weekly on 53 patients with blunt trauma and seven with penetrating missile injuries, who then were classified as normal (N), 2 or more positive responses; relatively anergic (RA), one positive response; or anergic (A), no response. Neutrophil chemotaxis was tested 145 times in 32 patients. Degree of injury was assessed by assigning one point to pelvic fracture, long-bone fracture, head, chest, or abdominal injury, to a maximum of five. The A and RA patients had greater trauma, 3 vs. 1.6 for N, and a significantly increased rate of sepsis (p less than 0.005) and mortality (p less than 0.05). Incidence of anergy depended upon age and extent of trauma. Neutrophil chemotaxis in A and RA patients was significantly (p less than 0.001) worse at 96.7 +/- 2.4 mu and 99.8 +/- 1.7 mu compared to N, 113.2 +/- 1.7 mu, and controls 121 +/- 4 mu. With recovery, chemotaxis returned to normal. It is concluded that failure of delayed hypersensitivity responses follows trauma, is related to the severity of injury and age of patient, and is associated with an abnormality of neutrophil chemotaxis and increased rate of sepsis.

A Least-Squares Transport Equation Compatible with Voids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hansen, Jon; Peterson, Jacob; Morel, Jim

Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transportmore » equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares S n formulation represents an excellent alternative to existing second-order S n transport formulations« less

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

A new nonlinear diffusion formalism in a magnetized plasma - Application to space physics and astrophysics

NASA Technical Reports Server (NTRS)

Karimbadi, H.; Krauss-Varban, D.

1992-01-01

A novel diffusion formalism that takes into account the finite width of resonances is presented. The resonance diagram technique is shown to reproduce the details of the particle orbits very accurately, and can be used to determine the acceleration/scattering in the presence of a given wave spectrum. Ways in which the nonlinear orbits can be incorporated into the diffusion equation are shown. The resulting diffusion equation is an extension of the Q-L theory to cases where the waves have large amplitudes and/or are coherent. This new equation does not have a gap at 90 deg in cases where the individual orbits can cross the gap. The conditions under which the resonance gap at 90-deg pitch angle exits are also examined.

Finite-volume scheme for anisotropic diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Es, Bram van, E-mail: bramiozo@gmail.com; FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands"1; Koren, Barry

In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

NASA Astrophysics Data System (ADS)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

Solutions for the diurnally forced advection-diffusion equation to estimate bulk fluid velocity and diffusivity in streambeds from temperature time series

NASA Astrophysics Data System (ADS)

Luce, C.; Tonina, D.; Gariglio, F. P.; Applebee, R.

2012-12-01

Differences in the diurnal variations of temperature at different depths in streambed sediments are commonly used for estimating vertical fluxes of water in the streambed. We applied spatial and temporal rescaling of the advection-diffusion equation to derive two new relationships that greatly extend the kinds of information that can be derived from streambed temperature measurements. The first equation provides a direct estimate of the Peclet number from the amplitude decay and phase delay information. The analytical equation is explicit (e.g. no numerical root-finding is necessary), and invertable. The thermal front velocity can be estimated from the Peclet number when the thermal diffusivity is known. The second equation allows for an independent estimate of the thermal diffusivity directly from the amplitude decay and phase delay information. Several improvements are available with the new information. The first equation uses a ratio of the amplitude decay and phase delay information; thus Peclet number calculations are independent of depth. The explicit form also makes it somewhat faster and easier to calculate estimates from a large number of sensors or multiple positions along one sensor. Where current practice requires a priori estimation of streambed thermal diffusivity, the new approach allows an independent calculation, improving precision of estimates. Furthermore, when many measurements are made over space and time, expectations of the spatial correlation and temporal invariance of thermal diffusivity are valuable for validation of measurements. Finally, the closed-form explicit solution allows for direct calculation of propagation of uncertainties in error measurements and parameter estimates, providing insight about error expectations for sensors placed at different depths in different environments as a function of surface temperature variation amplitudes. The improvements are expected to increase the utility of temperature measurement methods for studying groundwater-surface water interactions across space and time scales. We discuss the theoretical implications of the new solutions supported by examples with data for illustration and validation.

The dynamics of oceanic fronts. I - The Gulf Stream

NASA Technical Reports Server (NTRS)

Kao, T. W.

1980-01-01

The establishment and maintenance of the mean hydrographic properties of large-scale density fronts in the upper ocean is considered. The dynamics is studied by posing an initial value problem starting with a near-surface discharge of buoyant water with a prescribed density deficit into an ambient stationary fluid of uniform density; full time dependent diffusion and Navier-Stokes equations are then used with constant eddy diffusion and viscosity coefficients, together with a constant Coriolis parameter. Scaling analysis reveals three independent scales of the problem including the radius of deformation of the inertial length, buoyancy length, and diffusive length scales. The governing equations are then suitably scaled and the resulting normalized equations are shown to depend on the Ekman number alone for problems of oceanic interest. It is concluded that the mean Gulf Stream dynamics can be interpreted in terms of a solution of the Navier-Stokes and diffusion equations, with the cross-stream circulation responsible for the maintenance of the front; this mechanism is suggested for the maintenance of the Gulf Stream dynamics.

Research and Development of Methods for Estimating Physicochemical Properties of Organic Compounds of Environmental Concern

DTIC Science & Technology

1979-02-01

coefficient (at equilibrium) when hysteresis is apparent. 6. Coefficient n in Freundlich equation for 1/n soil or sediment adsorption isotherms ýX - KC . 7...Biodegradation Chemical structures cal clasaes (e.g., Diffusion Correlations phenols). General Diffusion coefficients Equations terms for organic...OF THE FATE AND TRANSPORT OF ORGANIC CHEMICALS Adsorption coefficients: K, n* from Freundlich equation + Desorption coefficients: K’*, n’* from

Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations.

PubMed

Sánchez-Garduño, Faustino; Pérez-Velázquez, Judith

This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D (0) = 0) and advection-degenerate (at h '(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h ( u ): (1)   h '( u ) is constant k , (2)   h '( u ) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE.

Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations

PubMed Central

Sánchez-Garduño, Faustino

2016-01-01

This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D(0) = 0) and advection-degenerate (at h′(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h(u): (1)  h′(u) is constant k, (2)  h′(u) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE. PMID:27689131

A mathematical model of atherogenesis as an inflammatory response.

PubMed

Ibragimov, A I; McNeal, C J; Ritter, L R; Walton, J R

2005-12-01

We construct a mathematical model of the early formation of an atherosclerotic lesion based on a simplification of Russell Ross' paradigm of atherosclerosis as a chronic inflammatory response. Atherosclerosis is a disease characterized by the accumulation of lipid-laden cells in the arterial wall. This disease results in lesions within the artery that may grow into the lumen restricting blood flow and, in critical cases, can rupture causing complete, sudden occlusion of the artery resulting in heart attack, stroke and possibly death. It is now understood that when chemically modified low-density lipoproteins (LDL cholesterol) enter into the wall of the human artery, they can trigger an immune response mediated by biochemical signals sent and received by immune and other cells indigenous to the vasculature. The presence of modified LDL can also corrupt the normal immune function triggering further immune response and ultimately chronic inflammation. In the construction of our mathematical model, we focus on the inflammatory component of the pathogenesis of cardiovascular disease (CVD). Because this study centres on the interplay between chemical and cellular species in the human artery and bloodstream, we employ a model of chemotaxis first given by E. F. Keller and Lee Segel in 1970 and present our model as a coupled system of non-linear reaction diffusion equations describing the state of the various species involved in the disease process. We perform numerical simulations demonstrating that our model captures certain observed features of CVD such as the localization of immune cells, the build-up of lipids and debris and the isolation of a lesion by smooth muscle cells.

Nonlocal electrical diffusion equation

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.

2016-07-01

In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

Two-Relaxation-Time Lattice Boltzmann Method and its Application to Advective-Diffusive-Reactive Transport

DOE PAGES

Yan, Zhifeng; Yang, Xiaofan; Li, Siliang; ...

2017-09-05

The lattice Boltzmann method (LBM) based on single-relaxation-time (SRT) or multiple-relaxation-time (MRT) collision operators is widely used in simulating flow and transport phenomena. The LBM based on two-relaxation-time (TRT) collision operators possesses strengths from the SRT and MRT LBMs, such as its simple implementation and good numerical stability, although tedious mathematical derivations and presentations of the TRT LBM hinder its application to a broad range of flow and transport phenomena. This paper describes the TRT LBM clearly and provides a pseudocode for easy implementation. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in subsurface environments.more » These phenomena include advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform flow, and bacterial chemotaxis in porous media. Finally, the TRT LBM demonstrated good numerical performance in terms of accuracy and stability in predicting these transport phenomena. Therefore, the TRT LBM is a powerful tool to simulate various geophysical and biogeochemical processes in subsurface environments.« less

Two-relaxation-time lattice Boltzmann method and its application to advective-diffusive-reactive transport

NASA Astrophysics Data System (ADS)

Yan, Zhifeng; Yang, Xiaofan; Li, Siliang; Hilpert, Markus

2017-11-01

The lattice Boltzmann method (LBM) based on single-relaxation-time (SRT) or multiple-relaxation-time (MRT) collision operators is widely used in simulating flow and transport phenomena. The LBM based on two-relaxation-time (TRT) collision operators possesses strengths from the SRT and MRT LBMs, such as its simple implementation and good numerical stability, although tedious mathematical derivations and presentations of the TRT LBM hinder its application to a broad range of flow and transport phenomena. This paper describes the TRT LBM clearly and provides a pseudocode for easy implementation. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in subsurface environments. These phenomena include advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform flow, and bacterial chemotaxis in porous media. The TRT LBM demonstrated good numerical performance in terms of accuracy and stability in predicting these transport phenomena. Therefore, the TRT LBM is a powerful tool to simulate various geophysical and biogeochemical processes in subsurface environments.

A novel growth mode of Physarum polycephalum during starvation

NASA Astrophysics Data System (ADS)

Lee, Jonghyun; Oettmeier, Christina; Döbereiner, Hans-Günther

2018-06-01

Organisms are constantly looking to forage and respond to various environmental queues to maximize their chance of survival. This is reflected in the unicellular organism Physarum polycephalum, which is known to grow as an optimized network. Here, we describe a new growth pattern of Physarum mesoplasmodium, where sheet-like motile bodies termed ‘satellites’ are formed. This non-network pattern formation is induced only when nutrients are scarce, suggesting that it is a type of emergency response. Our goal is to construct a model to describe the behaviour of satellites based on negative chemotaxis. We conjecture a diffusion-based model which implements detection of a signal molecule above a threshold concentration. Then we calculate how far the satellites must travel until the concentration signal falls below the threshold. These calculated distances are in good agreement with the distances where satellites stop. Based on the Akaike weight analysis, our threshold model is at least 2.3 times more likely to be the better model than the others we have considered. Based on the model, we estimate the diffusion coefficient of this molecule, which corresponds to typical signalling molecules.

Two-Relaxation-Time Lattice Boltzmann Method and its Application to Advective-Diffusive-Reactive Transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yan, Zhifeng; Yang, Xiaofan; Li, Siliang

The lattice Boltzmann method (LBM) based on single-relaxation-time (SRT) or multiple-relaxation-time (MRT) collision operators is widely used in simulating flow and transport phenomena. The LBM based on two-relaxation-time (TRT) collision operators possesses strengths from the SRT and MRT LBMs, such as its simple implementation and good numerical stability, although tedious mathematical derivations and presentations of the TRT LBM hinder its application to a broad range of flow and transport phenomena. This paper describes the TRT LBM clearly and provides a pseudocode for easy implementation. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in subsurface environments.more » These phenomena include advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform flow, and bacterial chemotaxis in porous media. Finally, the TRT LBM demonstrated good numerical performance in terms of accuracy and stability in predicting these transport phenomena. Therefore, the TRT LBM is a powerful tool to simulate various geophysical and biogeochemical processes in subsurface environments.« less

Modelling of Dictyostelium discoideum movement in a linear gradient of chemoattractant.

PubMed

Eidi, Zahra; Mohammad-Rafiee, Farshid; Khorrami, Mohammad; Gholami, Azam

2017-11-15

Chemotaxis is a ubiquitous biological phenomenon in which cells detect a spatial gradient of chemoattractant, and then move towards the source. Here we present a position-dependent advection-diffusion model that quantitatively describes the statistical features of the chemotactic motion of the social amoeba Dictyostelium discoideum in a linear gradient of cAMP (cyclic adenosine monophosphate). We fit the model to experimental trajectories that are recorded in a microfluidic setup with stationary cAMP gradients and extract the diffusion and drift coefficients in the gradient direction. Our analysis shows that for the majority of gradients, both coefficients decrease over time and become negative as the cells crawl up the gradient. The extracted model parameters also show that besides the expected drift in the direction of the chemoattractant gradient, we observe a nonlinear dependency of the corresponding variance on time, which can be explained by the model. Furthermore, the results of the model show that the non-linear term in the mean squared displacement of the cell trajectories can dominate the linear term on large time scales.

A Temporal Model of Cofilin Regulation and the Early Peak of Actin Barbed Ends in Invasive Tumor Cells

PubMed Central

Tania, Nessy; Prosk, Erin; Condeelis, John; Edelstein-Keshet, Leah

2011-01-01

Cofilin is an important regulator of actin polymerization, cell migration, and chemotaxis. Recent experimental data on mammary carcinoma cells reveal that stimulation by epidermal growth factor (EGF) generates a pool of active cofilin that results in a peak of actin filament barbed ends on the timescale of 1 min. Here, we present results of a mathematical model for the dynamics of cofilin and its transition between several pools in response to EGF stimulation. We describe the interactions of phospholipase C, membrane lipids (PIP2), and cofilin bound to PIP2 and to F-actin, as well as diffusible cofilin in active G-actin-monomer-bound or phosphorylated states. We consider a simplified representation in which the thin cell edge (lamellipod) and the cell interior are represented by two compartments that are linked by diffusion. We demonstrate that a high basal level of active cofilin stored by binding to PIP2, as well as the highly enriched local milieu of F-actin at the cell edge, is essential to capture the EGF-induced barbed-end amplification observed experimentally. PMID:21504724

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography.

PubMed

Biswas, Samir Kumar; Kanhirodan, Rajan; Vasu, Ram Mohan; Roy, Debasish

2011-08-01

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.

The diffusion approximation. An application to radiative transfer in clouds

NASA Technical Reports Server (NTRS)

Arduini, R. F.; Barkstrom, B. R.

1976-01-01

It is shown how the radiative transfer equation reduces to the diffusion equation. To keep the mathematics as simple as possible, the approximation is applied to a cylindrical cloud of radius R and height h. The diffusion equation separates in cylindrical coordinates and, in a sample calculation, the solution is evaluated for a range of cloud radii with cloud heights of 0.5 km and 1.0 km. The simplicity of the method and the speed with which solutions are obtained give it potential as a tool with which to study the effects of finite-sized clouds on the albedo of the earth-atmosphere system.

CXCR3 chemokine receptor-induced chemotaxis in human airway epithelial cells: role of p38 MAPK and PI3K signaling pathways.

PubMed

Shahabuddin, Syed; Ji, Rong; Wang, Ping; Brailoiu, Eugene; Dun, Na; Yang, Yi; Aksoy, Mark O; Kelsen, Steven G

2006-07-01

Human airway epithelial cells (HAEC) constitutively express the CXC chemokine receptor CXCR3, which regulates epithelial cell movement. In diseases such as chronic obstructive pulmonary disease and asthma, characterized by denudation of the epithelial lining, epithelial cell migration may contribute to airway repair and reconstitution. This study compared the potency and efficacy of three CXCR3 ligands, I-TAC/CXCL11, IP-10/CXCL10, and Mig/CXCL9, as inducers of chemotaxis in HAEC and examined the underlying signaling pathways involved. Studies were performed in cultured HAEC from normal subjects and the 16-HBE cell line. In normal HAEC, the efficacy of I-TAC-induced chemotaxis was 349 +/- 88% (mean +/- SE) of the medium control and approximately one-half the response to epidermal growth factor, a highly potent chemoattractant. In normal HAEC, Mig, IP-10, and I-TAC induced chemotaxis with similar potency and a rank order of efficacy of I-TAC = IP-10 > Mig. Preincubation with pertussis toxin completely blocked CXCR3-induced migration. Of interest, intracellular [Ca(2+)] did not rise in response to I-TAC, IP-10, or Mig. I-TAC induced a rapid phosphorylation (5-10 min) of two of the three MAPKs, i.e., p38 and ERK1/2. Pretreatment of HAEC with the p38 inhibitor SB 20358 or the PI3K inhibitor wortmannin dose-dependently inhibited the chemotactic response to I-TAC. In contrast, the ERK1/2 inhibitor U0126 had no effect on chemotaxis. These data indicate that in HAEC, CXCR3-mediated chemotaxis involves a G protein, which activates both the p38 MAPK and PI3K pathways in a calcium-independent fashion.

Cross-talk between Tetraspanin CD9 and Transmembrane Adaptor Protein Non-T Cell Activation Linker (NTAL) in Mast Cell Activation and Chemotaxis*

PubMed Central

Hálová, Ivana; Dráberová, Lubica; Bambousková, Monika; Machyna, Martin; Stegurová, Lucie; Smrž, Daniel; Dráber, Petr

2013-01-01

Chemotaxis, a process leading to movement of cells toward increasing concentrations of chemoattractants, is essential, among others, for recruitment of mast cells within target tissues where they play an important role in innate and adaptive immunity. Chemotaxis is driven by chemoattractants, produced by various cell types, as well as by intrinsic cellular regulators, which are poorly understood. In this study we prepared a new mAb specific for the tetraspanin CD9. Binding of the antibody to bone marrow-derived mast cells triggered activation events that included cell degranulation, Ca2+ response, dephosphorylation of ezrin/radixin/moesin (ERM) family proteins, and potent tyrosine phosphorylation of the non-T cell activation linker (NTAL) but only weak phosphorylation of the linker for activation of T cells (LAT). Phosphorylation of the NTAL was observed with whole antibody but not with its F(ab)2 or Fab fragments. This indicated involvement of the Fcγ receptors. As documented by electron microscopy of isolated plasma membrane sheets, CD9 colocalized with the high-affinity IgE receptor (FcϵRI) and NTAL but not with LAT. Further tests showed that both anti-CD9 antibody and its F(ab)2 fragment inhibited mast cell chemotaxis toward antigen. Experiments with bone marrow-derived mast cells deficient in NTAL and/or LAT revealed different roles of these two adaptors in antigen-driven chemotaxis. The combined data indicate that chemotaxis toward antigen is controlled in mast cells by a cross-talk among FcϵRI, tetraspanin CD9, transmembrane adaptor proteins NTAL and LAT, and cytoskeleton-regulatory proteins of the ERM family. PMID:23443658

Sinorhizobium meliloti Chemoreceptor McpU Mediates Chemotaxis toward Host Plant Exudates through Direct Proline Sensing

PubMed Central

Webb, Benjamin A.; Hildreth, Sherry; Helm, Richard F.

2014-01-01

Bacterial chemotaxis is an important attribute that aids in establishing symbiosis between rhizobia and their legume hosts. Plant roots and seeds exude a spectrum of molecules into the soil to attract their bacterial symbionts. The alfalfa symbiont Sinorhizobium meliloti possesses eight chemoreceptors to sense its environment and mediate chemotaxis toward its host. The methyl accepting chemotaxis protein McpU is one of the more abundant S. meliloti chemoreceptors and an important sensor for the potent attractant proline. We established a dominant role of McpU in sensing molecules exuded by alfalfa seeds. Mass spectrometry analysis determined that a single germinating seed exudes 3.72 nmol of proline, producing a millimolar concentration near the seed surface which can be detected by the chemosensory system of S. meliloti. Complementation analysis of the mcpU deletion strain verified McpU as the key proline sensor. A structure-based homology search identified tandem Cache (calcium channels and chemotaxis receptors) domains in the periplasmic region of McpU. Conserved residues Asp-155 and Asp-182 of the N-terminal Cache domain were determined to be important for proline sensing by evaluating mutant strains in capillary and swim plate assays. Differential scanning fluorimetry revealed interaction of the isolated periplasmic region of McpU (McpU40-284) with proline and the importance of Asp-182 in this interaction. Using isothermal titration calorimetry, we determined that proline binds with a Kd (dissociation constant) of 104 μM to McpU40-284, while binding was abolished when Asp-182 was substituted by Glu. Our results show that McpU is mediating chemotaxis toward host plants by direct proline sensing. PMID:24657863

Simvastatin Inhibits IL-5-Induced Chemotaxis and CCR3 Expression of HL-60-Derived and Human Primary Eosinophils.

PubMed

Fu, Chia-Hsiang; Tsai, Wan-Chun; Lee, Ta-Jen; Huang, Chi-Che; Chang, Po-Hung; Su Pang, Jong-Hwei

2016-01-01

IL-5-induced chemotaxis of eosinophils is an important feature of allergic airway inflammatory diseases. Simvastatin, a lipid lowering agent, has been shown to exhibit anti-inflammatory and anti-allergic effects. Our aim was to investigate the effect of simvastatin on IL-5-induced eosinophil chemotaxis and its regulatory mechanisms. Eosinophils were derived by treating HL-60 clone 15 (HC15) cells with butyric acid (BA) in an alkaline condition or through direct isolation from human peripheral blood. The expressions of CC chemokine receptor 3 (CCR3) and interleukin (IL)-5 receptors (IL5Rα and β) were analyzed using RT/real-time PCR. The granular proteins were stained using fast green. Eotaxin-induced chemotaxis was measured using a transwell migration assay. CCR3 protein expression was revealed by immunocytochemistry. An animal model of allergic rhinitis was established by challenging Sprague-Dawley® rats repeatedly with ovalbumin. Butyric acid significantly increased the expression of IL5Rα and IL5Rβ, CCR3 and granular proteins in HC15 cells, indicating the maturation of eosinophils (BA-E cells). IL-5 further enhanced the CCR3 expression at both the mRNA and protein levels and the eotaxin-induced chemotaxis of BA-E cells. Simvastatin inhibited the effects of IL-5 on BA-E cells, but not in the presence of mevalonate. Similar results were also exhibited in human primary eosinophils. In vivo animal studies further confirmed that oral simvastatin could significantly suppress the infiltration of eosinophils into turbinate tissues of allergic rats. Therefore, simvastatin was demonstrated to inhibit IL-5-induced CCR3 expression and chemotaxis of eosinophils mediated via the mevalonate pathway. We confirmed that simvastatin also reduced eosinophilic infiltration in allergic rhinitis.

On Entropy Production in the Madelung Fluid and the Role of Bohm's Potential in Classical Diffusion

NASA Astrophysics Data System (ADS)

Heifetz, Eyal; Tsekov, Roumen; Cohen, Eliahu; Nussinov, Zohar

2016-07-01

The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow (or decrease) due to an expansion (or compression) of the Madelung fluid. These effects result from the interference between solutions of the Schrödinger equation. Growth of the Shannon entropy due to expansion is common in diffusive processes. However, in the latter the process is irreversible while the processes in the Madelung fluid are always reversible. The relations between interference, compressibility and variation of the Shannon entropy are then examined in several simple examples. Furthermore, we demonstrate that for classical diffusive processes, the "force" accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. Expressing then the diffusion coefficient in terms of the Planck constant reveals the lower bound given by the Heisenberg uncertainty principle in terms of the product between the gas mean free path and the Brownian momentum.

Building 1D resonance broadened quasilinear (RBQ) code for fast ions Alfvénic relaxations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Berk, Herbert

2016-10-01

The performance of the burning plasma is limited by the confinement of superalfvenic fusion products, e.g. alpha particles, which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using a resonance line broadened diffusion coefficient. The interaction of fast ions and AEs is captured for cases where there are either isolated or overlapping modes. A new code RBQ1D is being built which constructs diffusion coefficients based on realistic eigenfunctions that are determined by the ideal MHD code NOVA. The wave particle interaction can be reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. Hence to a good approximation the Quasi-Linear (QL) diffusion equation only contains derivatives in the angular momentum. The diffusion equation is then one dimensional that is efficiently solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The evolution of fast ion constants of motion is governed by the QL diffusion equations which are adapted to find the ion distribution function.

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

NASA Astrophysics Data System (ADS)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

Applicability of the Fokker-Planck equation to the description of diffusion effects on nucleation

NASA Astrophysics Data System (ADS)

Sorokin, M. V.; Dubinko, V. I.; Borodin, V. A.

2017-01-01

The nucleation of islands in a supersaturated solution of surface adatoms is considered taking into account the possibility of diffusion profile formation in the island vicinity. It is shown that the treatment of diffusion-controlled cluster growth in terms of the Fokker-Planck equation is justified only provided certain restrictions are satisfied. First of all, the standard requirement that diffusion profiles of adatoms quickly adjust themselves to the actual island sizes (adiabatic principle) can be realized only for sufficiently high island concentration. The adiabatic principle is essential for the probabilities of adatom attachment to and detachment from island edges to be independent of the adatom diffusion profile establishment kinetics, justifying the island nucleation treatment as the Markovian stochastic process. Second, it is shown that the commonly used definition of the "diffusion" coefficient in the Fokker-Planck equation in terms of adatom attachment and detachment rates is justified only provided the attachment and detachment are statistically independent, which is generally not the case for the diffusion-limited growth of islands. We suggest a particular way to define the attachment and detachment rates that allows us to satisfy this requirement as well. When applied to the problem of surface island nucleation, our treatment predicts the steady-state nucleation barrier, which coincides with the conventional thermodynamic expression, even though no thermodynamic equilibrium is assumed and the adatom diffusion is treated explicitly. The effect of adatom diffusional profiles on the nucleation rate preexponential factor is also discussed. Monte Carlo simulation is employed to analyze the applicability domain of the Fokker-Planck equation and the diffusion effect beyond it. It is demonstrated that a diffusional cloud is slowing down the nucleation process for a given monomer interaction with the nucleus edge.

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Diffusion Processes Satisfying a Conservation Law Constraint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bakosi, J.; Ristorcelli, J. R.

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

A model for shrinkage strain in photo polymerization of dental composites.

PubMed

Petrovic, Ljubomir M; Atanackovic, Teodor M

2008-04-01

We formulate a new model for the shrinkage strain developed during photo polymerization in dental composites. The model is based on the diffusion type fractional order equation, since it has been proved that polymerization reaction is diffusion controlled (Atai M, Watts DC. A new kinetic model for the photo polymerization shrinkage-strain of dental composites and resin-monomers. Dent Mater 2006;22:785-91). Our model strongly confirms the observation by Atai and Watts (see reference details above) and their experimental results. The shrinkage strain is modeled by a nonlinear differential equation in (see reference details above) and that equation must be solved numerically. In our approach, we use the linear fractional order differential equation to describe the strain rate due to photo polymerization. This equation is solved exactly. As shrinkage is a consequence of the polymerization reaction and polymerization reaction is diffusion controlled, we postulate that shrinkage strain rate is described by a diffusion type equation. We find explicit form of solution to this equation and determine the strain in the resin monomers. Also by using equations of linear viscoelasticity, we determine stresses in the polymer due to the shrinkage. The time evolution of stresses implies that the maximal stresses are developed at the very beginning of the polymerization process. The stress in a dental composite that is light treated has the largest value short time after the treatment starts. The strain settles at the constant value in the time of about 100s (for the cases treated in Atai and Watts). From the model developed here, the shrinkage strain of dental composites and resin monomers is analytically determined. The maximal value of stresses is important, since this value must be smaller than the adhesive bond strength at cavo-restoration interface. The maximum stress determined here depends on the diffusivity coefficient. Since diffusivity coefficient increases as polymerization proceeds, it follows that the periods of light treatments should be shorter at the beginning of the treatment and longer at the end of the treatment, with dark interval between the initial low intensity and following high intensity curing. This is because at the end of polymerization the stress relaxation cannot take place.

Adaptability of non-genetic diversity in bacterial chemotaxis

PubMed Central

Frankel, Nicholas W; Pontius, William; Dufour, Yann S; Long, Junjiajia; Hernandez-Nunez, Luis; Emonet, Thierry

2014-01-01

Bacterial chemotaxis systems are as diverse as the environments that bacteria inhabit, but how much environmental variation can cells tolerate with a single system? Diversification of a single chemotaxis system could serve as an alternative, or even evolutionary stepping-stone, to switching between multiple systems. We hypothesized that mutations in gene regulation could lead to heritable control of chemotactic diversity. By simulating foraging and colonization of E. coli using a single-cell chemotaxis model, we found that different environments selected for different behaviors. The resulting trade-offs show that populations facing diverse environments would ideally diversify behaviors when time for navigation is limited. We show that advantageous diversity can arise from changes in the distribution of protein levels among individuals, which could occur through mutations in gene regulation. We propose experiments to test our prediction that chemotactic diversity in a clonal population could be a selectable trait that enables adaptation to environmental variability. DOI: http://dx.doi.org/10.7554/eLife.03526.001 PMID:25279698

Combined Phytochemistry and Chemotaxis Assays for Identification and Mechanistic Analysis of Anti-Inflammatory Phytochemicals in Fallopia japonica

PubMed Central

Shen, Ming-Yi; Liu, Yan-Jun; Don, Ming-Jaw; Liu, Hsien-Yueh; Chen, Zeng-Weng; Mettling, Clément; Corbeau, Pierre; Chiang, Chih-Kang; Jang, Yu-Song; Li, Tzu-Hsuan; Young, Paul; Chang, Cicero L. T.; Lin, Yea-Lih; Yang, Wen-Chin

2011-01-01

Plants provide a rich source of lead compounds for a variety of diseases. A novel approach combining phytochemistry and chemotaxis assays was developed and used to identify and study the mechanisms of action of the active compounds in F. japonica, a medicinal herb traditionally used to treat inflammation. Based on a bioactivity-guided purification strategy, two anthranoids, emodin and physcion, were identified from F. japonica. Spectroscopic techniques were used to characterize its crude extract, fractions and phytochemicals. The crude extract, chloroform fraction, and anthranoids of F. japonica significantly inhibited CXCR4-mediated chemotaxis. Mechanistic studies showed that emodin and physcion inhibited chemotaxis via inactivating the MEK/ERK pathway. Moreover, the crude extract and emodin could prevent or treat type 1 diabetes in non-obese diabetic (NOD) mice. This study illustrates the applicability of a combinational approach for the study of anti-inflammatory medicine and shows the potential of F. japonica and its anthranoids for anti-inflammatory therapy. PMID:22087325

Connecting G protein signaling to chemoattractant-mediated cell polarity and cytoskeletal reorganization.

PubMed

Liu, Youtao; Lacal, Jesus; Firtel, Richard A; Kortholt, Arjan

2018-07-04

The directional movement toward extracellular chemical gradients, a process called chemotaxis, is an important property of cells. Central to eukaryotic chemotaxis is the molecular mechanism by which chemoattractant-mediated activation of G-protein coupled receptors (GPCRs) induces symmetry breaking in the activated downstream signaling pathways. Studies with mainly Dictyostelium and mammalian neutrophils as experimental systems have shown that chemotaxis is mediated by a complex network of signaling pathways. Recently, several labs have used extensive and efficient proteomic approaches to further unravel this dynamic signaling network. Together these studies showed the critical role of the interplay between heterotrimeric G-protein subunits and monomeric G proteins in regulating cytoskeletal rearrangements during chemotaxis. Here we highlight how these proteomic studies have provided greater insight into the mechanisms by which the heterotrimeric G protein cycle is regulated, how heterotrimeric G proteins-induced symmetry breaking is mediated through small G protein signaling, and how symmetry breaking in G protein signaling subsequently induces cytoskeleton rearrangements and cell migration.

Calaxin drives sperm chemotaxis by Ca2+-mediated direct modulation of a dynein motor

PubMed Central

Mizuno, Katsutoshi; Shiba, Kogiku; Okai, Masahiko; Takahashi, Yusuke; Shitaka, Yuji; Oiwa, Kazuhiro; Tanokura, Masaru; Inaba, Kazuo

2012-01-01

Sperm chemotaxis occurs widely in animals and plants and plays an important role in the success of fertilization. Several studies have recently demonstrated that Ca2+ influx through specific Ca2+ channels is a prerequisite for sperm chemotactic movement. However, the regulator that modulates flagellar movement in response to Ca2+ is unknown. Here we show that a neuronal calcium sensor, calaxin, directly acts on outer-arm dynein and regulates specific flagellar movement during sperm chemotaxis. Calaxin inhibition resulted in significant loss of sperm chemotactic movement, despite normal increases in intracellular calcium concentration. Using a demembranated sperm model, we demonstrate that calaxin is essential for generation and propagation of Ca2+-induced asymmetric flagellar bending. An in vitro motility assay revealed that calaxin directly suppressed the velocity of microtubule sliding by outer-arm dynein at high Ca2+ concentrations. This study describes the missing link between chemoattractant-mediated Ca2+ signaling and motor-driven microtubule sliding during sperm chemotaxis. PMID:23169663

Technical report series on global modeling and data assimilation. Volume 2: Direct solution of the implicit formulation of fourth order horizontal diffusion for gridpoint models on the sphere

NASA Technical Reports Server (NTRS)

Li, Yong; Moorthi, S.; Bates, J. Ray; Suarez, Max J.

1994-01-01

High order horizontal diffusion of the form K Delta(exp 2m) is widely used in spectral models as a means of preventing energy accumulation at the shortest resolved scales. In the spectral context, an implicit formation of such diffusion is trivial to implement. The present note describes an efficient method of implementing implicit high order diffusion in global finite difference models. The method expresses the high order diffusion equation as a sequence of equations involving Delta(exp 2). The solution is obtained by combining fast Fourier transforms in longitude with a finite difference solver for the second order ordinary differential equation in latitude. The implicit diffusion routine is suitable for use in any finite difference global model that uses a regular latitude/longitude grid. The absence of a restriction on the timestep makes it particularly suitable for use in semi-Lagrangian models. The scale selectivity of the high order diffusion gives it an advantage over the uncentering method that has been used to control computational noise in two-time-level semi-Lagrangian models.

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

PubMed

Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

2011-03-21

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

Cross-Diffusion Induced Turing Instability and Amplitude Equation for a Toxic-Phytoplankton-Zooplankton Model with Nonmonotonic Functional Response

NASA Astrophysics Data System (ADS)

Han, Renji; Dai, Binxiang

2017-06-01

The spatiotemporal pattern induced by cross-diffusion of a toxic-phytoplankton-zooplankton model with nonmonotonic functional response is investigated in this paper. The linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes in the framework of a weakly nonlinear theory, and the stability analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, we illustrate the theoretical results via numerical simulations. It is shown that the spatiotemporal distribution of the plankton is homogeneous in the absence of cross-diffusion. However, when the cross-diffusivity is greater than the critical value, the spatiotemporal distribution of all the plankton species becomes inhomogeneous in spaces and results in different kinds of patterns: spot, stripe, and the mixture of spot and stripe patterns depending on the cross-diffusivity. Simultaneously, the impact of toxin-producing rate of toxic-phytoplankton (TPP) species and natural death rate of zooplankton species on pattern selection is also explored.

Bessel Fourier orientation reconstruction: an analytical EAP reconstruction using multiple shell acquisitions in diffusion MRI.

PubMed

Hosseinbor, Ameer Pasha; Chung, Moo K; Wu, Yu-Chien; Alexander, Andrew L

2011-01-01

The estimation of the ensemble average propagator (EAP) directly from q-space DWI signals is an open problem in diffusion MRI. Diffusion spectrum imaging (DSI) is one common technique to compute the EAP directly from the diffusion signal, but it is burdened by the large sampling required. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed. One, in particular, is Diffusion Propagator Imaging (DPI) which is based on the Laplace's equation estimation of diffusion signal for each shell acquisition. Viewed intuitively in terms of the heat equation, the DPI solution is obtained when the heat distribution between temperatuere measurements at each shell is at steady state. We propose a generalized extension of DPI, Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition. That is, the heat distribution between shell measurements is no longer at steady state. In addition to being analytical, the BFOR solution also includes an intrinsic exponential smootheing term. We illustrate the effectiveness of the proposed method by showing results on both synthetic and real MR datasets.

Cusping, transport and variance of solutions to generalized Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Carnaffan, Sean; Kawai, Reiichiro

2017-06-01

We study properties of solutions to generalized Fokker-Planck equations through the lens of the probability density functions of anomalous diffusion processes. In particular, we examine solutions in terms of their cusping, travelling wave behaviours, and variance, within the framework of stochastic representations of generalized Fokker-Planck equations. We give our analysis in the cases of anomalous diffusion driven by the inverses of the stable, tempered stable and gamma subordinators, demonstrating the impact of changing the distribution of waiting times in the underlying anomalous diffusion model. We also analyse the cases where the underlying anomalous diffusion contains a Lévy jump component in the parent process, and when a diffusion process is time changed by an uninverted Lévy subordinator. On the whole, we present a combination of four criteria which serve as a theoretical basis for model selection, statistical inference and predictions for physical experiments on anomalously diffusing systems. We discuss possible applications in physical experiments, including, with reference to specific examples, the potential for model misclassification and how combinations of our four criteria may be used to overcome this issue.

Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Litvinenko, Yuri E.; Fichtner, Horst; Walter, Dominik

2017-05-20

We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmic-ray distributions in the vicinity of heliospheric and astrophysical shocks imply that anomalous, superdiffusive transport plays a role in the evolution of the energetic particles. Several authors have quantitatively described the anomalous diffusion scalings, implied by the data, by solutions of a formal transport equation with fractional derivatives. Yet the physical basis of the fractional diffusion model remains uncertain. We explore an alternative model of the cosmic-ray transport: a nonlinear diffusion equation that follows from a self-consistent treatmentmore » of the resonantly interacting cosmic-ray particles and their self-generated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a power-law dependence of the particle density on the distance upstream of the shock. Although the results do not refute the use of a fractional advection–diffusion equation, they indicate a viable alternative to explain the anomalous diffusion scalings of cosmic-ray particles.« less

Some Fundamental Issues of Mathematical Simulation in Biology

NASA Astrophysics Data System (ADS)

Razzhevaikin, V. N.

2018-02-01

Some directions of simulation in biology leading to original formulations of mathematical problems are overviewed. Two of them are discussed in detail: the correct solvability of first-order linear equations with unbounded coefficients and the construction of a reaction-diffusion equation with nonlinear diffusion for a model of genetic wave propagation.

Numerical study of centrifugal compressor stage vaneless diffusers

NASA Astrophysics Data System (ADS)

Galerkin, Y.; Soldatova, K.; Solovieva, O.

2015-08-01

The authors analyzed CFD calculations of flow in vaneless diffusers with relative width in range from 0.014 to 0.100 at inlet flow angles in range from 100 to 450 with different inlet velocity coefficients, Reynolds numbers and surface roughness. The aim is to simulate calculated performances by simple algebraic equations. The friction coefficient that represents head losses as friction losses is proposed for simulation. The friction coefficient and loss coefficient are directly connected by simple equation. The advantage is that friction coefficient changes comparatively little in range of studied parameters. Simple equations for this coefficient are proposed by the authors. The simulation accuracy is sufficient for practical calculations. To create the complete algebraic model of the vaneless diffuser the authors plan to widen this method of modeling to diffusers with different relative length and for wider range of Reynolds numbers.

Integral approximations to classical diffusion and smoothed particle hydrodynamics

DOE PAGES

Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

2014-12-31

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.more » The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.« less

Chemotaxis of cancer cells in three-dimensional environment monitored label-free by quantitative phase digital holographic microscopy

NASA Astrophysics Data System (ADS)

Kemper, Björn; Schnekenburger, Jürgen; Ketelhut, Steffi

2017-02-01

We investigated the capabilities of digital holographic microscopy (DHM) for label-free quantification of the response of living single cells to chemical stimuli in 3D assays. Fibro sarcoma cells were observed in a collagen matrix inside 3D chemotaxis chambers with a Mach-Zehnder interferometer-based DHM setup. From the obtained series of quantitative phase images, the migration trajectories of single cells were retrieved by automated cell tracking and subsequently analyzed for maximum migration distance and motility. Our results demonstrate DHM as a highly reliable and efficient tool for label-free quantification of chemotaxis in 2D and 3D environments.

Defective neutrophil chemotaxis in juvenile periodontitis.

PubMed Central

Clark, R A; Page, R C; Wilde, G

1977-01-01

Neutrophil chemotaxis was evaluated in nine patients with juvenile periodontitis, with normal subjects and patients with the adult form of periodontitis as controls. Defective chemotactic responses were observed in neutrophils from seven of nine juvenile patients, and a reduced level of complement-derived chemotactic activity was demonstrated in serum from four patients. These determinations were normal in all the patients with adult periodontitis. Serum from five of the juvenile patients contained a heat-stable, non-dialyzable factor that markedly inhibited the chemotaxis of normal neutrophils. Thus the characteristic tissue destruction seen in juvenile periodontitis may be, at least in part, a consequence of a failure of host defense mechanisms. PMID:591063

A Gastric Pathogen Moves Chemotaxis in a New Direction

PubMed Central

Sweeney, Emily Goers; Guillemin, Karen

2011-01-01

Abstract For almost 50 years, Escherichia coli has been the model for understanding how bacteria orient their movement in response to chemical cues, but recent studies of chemotaxis in other bacteria have revealed interesting variations from prevailing paradigms. Investigating the human pathogen Helicobacter pylori, Amieva and colleagues [mBio 2(4):e00098-11, 2011] discovered a new chemotaxis regulator, ChePep, which modulates swimming behavior through the canonical histidine-aspartate phosphorelay system. Functionally conserved among the epsilonproteobacteria, ChePep is essential for H. pylori to navigate deep into the stomach’s gastric glands and may be an attractive target for novel antibiotics. PMID:21933915

Spin diffusion and torques in disordered antiferromagnets

NASA Astrophysics Data System (ADS)

Manchon, Aurelien

2017-03-01

We have developed a drift-diffusion equation of spin transport in collinear bipartite metallic antiferromagnets. Starting from a model tight-binding Hamiltonian, we obtain the quantum kinetic equation within Keldysh formalism and expand it to the lowest order in spatial gradient using Wigner expansion method. In the diffusive limit, these equations track the spatio-temporal evolution of the spin accumulations and spin currents on each sublattice of the antiferromagnet. We use these equations to address the nature of the spin transfer torque in (i) a spin-valve composed of a ferromagnet and an antiferromagnet, (ii) a metallic bilayer consisting of an antiferromagnet adjacent to a heavy metal possessing spin Hall effect, and in (iii) a single antiferromagnet possessing spin Hall effect. We show that the latter can experience a self-torque thanks to the non-vanishing spin Hall effect in the antiferromagnet.

Myxobacteria Fruiting Body Formation

NASA Astrophysics Data System (ADS)

Jiang, Yi

2006-03-01

Myxobacteria are social bacteria that swarm and glide on surfaces, and feed cooperatively. When starved, tens of thousands of cells change their movement pattern from outward spreading to inward concentration; they form aggregates that become fruiting bodies, inside which cells differentiate into nonmotile, environmentally resistant spores. Traditionally, cell aggregation has been considered to imply chemotaxis, a long-range cell interaction mediated by diffusing chemicals. However, myxobacteria aggregation is the consequence of direct cell-contact interactions. I will review our recent efforts in modeling the fruiting body formation of Myxobacteria, using lattice gas cellular automata models that are based on local cell-cell contact signaling. These models have reproduced the individual phases in Myxobacteria development such as the rippling, streaming, early aggregation and the final sporulation; the models can be unified to simulate the whole developmental process of Myxobacteria.

Breakdown of the reaction-diffusion master equation with nonelementary rates

NASA Astrophysics Data System (ADS)

Smith, Stephen; Grima, Ramon

2016-05-01

The chemical master equation (CME) is the exact mathematical formulation of chemical reactions occurring in a dilute and well-mixed volume. The reaction-diffusion master equation (RDME) is a stochastic description of reaction-diffusion processes on a spatial lattice, assuming well mixing only on the length scale of the lattice. It is clear that, for the sake of consistency, the solution of the RDME of a chemical system should converge to the solution of the CME of the same system in the limit of fast diffusion: Indeed, this has been tacitly assumed in most literature concerning the RDME. We show that, in the limit of fast diffusion, the RDME indeed converges to a master equation but not necessarily the CME. We introduce a class of propensity functions, such that if the RDME has propensities exclusively of this class, then the RDME converges to the CME of the same system, whereas if the RDME has propensities not in this class, then convergence is not guaranteed. These are revealed to be elementary and nonelementary propensities, respectively. We also show that independent of the type of propensity, the RDME converges to the CME in the simultaneous limit of fast diffusion and large volumes. We illustrate our results with some simple example systems and argue that the RDME cannot generally be an accurate description of systems with nonelementary rates.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

NASA Astrophysics Data System (ADS)

Broche, Rita de Cássia D. S.; de Oliveira, Luiz Augusto F.

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem.

In vitro chemotaxis and tissue remodeling assays quantitatively characterize foreign body reaction.

PubMed

Jannasch, Maren; Weigel, Tobias; Engelhardt, Lisa; Wiezoreck, Judith; Gaetzner, Sabine; Walles, Heike; Schmitz, Tobias; Hansmann, Jan

2017-01-01

Surgical implantation of a biomaterial triggers foreign-body-induced fibrous encapsulation. Two major mechanisms of this complex physiological process are (I) chemotaxis of fibroblasts from surrounding tissue to the implant region, followed by (II) tissue remodeling. As an alternative to animal studies, we here propose a process-aligned in vitro test platform to investigate the material dependency of fibroblast chemotaxis and tissue remodeling mediated by material-resident macrophages. Embedded in a biomimetic three-dimensional collagen hydrogel, chemotaxis of fibroblasts in the direction of macrophage-material-conditioned cell culture supernatant was analyzed by live cell imaging. A combination of statistical analysis with a complementary parameterized random walk model allowed quantitative and qualitative characterization of the cellular walk process. We thereby identified an increasing macrophage-mediated chemotactic potential ranking of biomaterials from glass over polytetrafluorethylene to titanium. To address long-term effects of bio-material-resident macrophages on fibroblasts in a three-dimensional microenvironment, we further studied tissue remodeling by applying macrophage-material-conditioned medium on fibrous in vitro tissue models. A high correlation of the in vitro tissue model to state of the art in vivo study data was found. Titanium exhibited a significantly lower tissue remodeling capacity compared to polytetrafluorethylene. With this approach, we identified a material dependency of both chemotaxis and tissue remodeling processes, strengthening knowledge on their specific contribution to the foreign body reaction.

Analytical modeling and experimental characterization of chemotaxis in Serratia marcescens

NASA Astrophysics Data System (ADS)

Zhuang, Jiang; Wei, Guopeng; Wright Carlsen, Rika; Edwards, Matthew R.; Marculescu, Radu; Bogdan, Paul; Sitti, Metin

2014-05-01

This paper presents a modeling and experimental framework to characterize the chemotaxis of Serratia marcescens (S. marcescens) relying on two-dimensional and three-dimensional tracking of individual bacteria. Previous studies mainly characterized bacterial chemotaxis based on population density analysis. Instead, this study focuses on single-cell tracking and measuring the chemotactic drift velocity VC from the biased tumble rate of individual bacteria on exposure to a concentration gradient of l-aspartate. The chemotactic response of S. marcescens is quantified over a range of concentration gradients (10-3 to 5 mM/mm) and average concentrations (0.5×10-3 to 2.5 mM). Through the analysis of a large number of bacterial swimming trajectories, the tumble rate is found to have a significant bias with respect to the swimming direction. We also verify the relative gradient sensing mechanism in the chemotaxis of S. marcescens by measuring the change of VC with the average concentration and the gradient. The applied full pathway model with fitted parameters matches the experimental data. Finally, we show that our measurements based on individual bacteria lead to the determination of the motility coefficient μ (7.25×10-6 cm2/s) of a population. The experimental characterization and simulation results for the chemotaxis of this bacterial species contribute towards using S. marcescens in chemically controlled biohybrid systems.

Fick's second law transformed: one path to cloaking in mass diffusion.

PubMed

Guenneau, S; Puvirajesinghe, T M

2013-06-06

Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional, time-dependent, anisotropic heterogeneous Fick's equation is considered, which is a parabolic partial differential equation also applicable to heat diffusion, when convection occurs, for example, in fluids. This theory is illustrated with finite-element computations for a liposome particle surrounded by a cylindrical multi-layered cloak in a water-based environment, and for a spherical multi-layered cloak consisting of layers of fluid with an isotropic homogeneous diffusivity, deduced from an effective medium approach. Initial potential applications could be sought in bioengineering.

Stefan-Maxwell Relations and Heat Flux with Anisotropic Transport Coefficients for Ionized Gases in a Magnetic Field with Application to the Problem of Ambipolar Diffusion

NASA Astrophysics Data System (ADS)

Kolesnichenko, A. V.; Marov, M. Ya.

2018-01-01

The defining relations for the thermodynamic diffusion and heat fluxes in a multicomponent, partially ionized gas mixture in an external electromagnetic field have been obtained by the methods of the kinetic theory. Generalized Stefan-Maxwell relations and algebraic equations for anisotropic transport coefficients (the multicomponent diffusion, thermal diffusion, electric and thermoelectric conductivity coefficients as well as the thermal diffusion ratios) associated with diffusion-thermal processes have been derived. The defining second-order equations are derived by the Chapman-Enskog procedure using Sonine polynomial expansions. The modified Stefan-Maxwell relations are used for the description of ambipolar diffusion in the Earth's ionospheric plasma (in the F region) composed of electrons, ions of many species, and neutral particles in a strong electromagnetic field.

From quantum stochastic differential equations to Gisin-Percival state diffusion

NASA Astrophysics Data System (ADS)

Parthasarathy, K. R.; Usha Devi, A. R.

2017-08-01

Starting from the quantum stochastic differential equations of Hudson and Parthasarathy [Commun. Math. Phys. 93, 301 (1984)] and exploiting the Wiener-Itô-Segal isomorphism between the boson Fock reservoir space Γ (L2(R+ ) ⊗(Cn⊕Cn ) ) and the Hilbert space L2(μ ) , where μ is the Wiener probability measure of a complex n-dimensional vector-valued standard Brownian motion {B (t ) ,t ≥0 } , we derive a non-linear stochastic Schrödinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion B. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation [N. Gisin and J. Percival, J. Phys. A 167, 315 (1992)]. This approach also yields an explicit solution of the Gisin-Percival equation, in terms of the Hudson-Parthasarathy unitary process and a randomized Weyl displacement process. Irreversible dynamics of system density operators described by the well-known Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories.

Recursion equations in predicting band width under gradient elution.

PubMed

Liang, Heng; Liu, Ying

2004-06-18

The evolution of solute zone under gradient elution is a typical problem of non-linear continuity equation since the local diffusion coefficient and local migration velocity of the mass cells of solute zones are the functions of position and time due to space- and time-variable mobile phase composition. In this paper, based on the mesoscopic approaches (Lagrangian description, the continuity theory and the local equilibrium assumption), the evolution of solute zones in space- and time-dependent fields is described by the iterative addition of local probability density of the mass cells of solute zones. Furthermore, on macroscopic levels, the recursion equations have been proposed to simulate zone migration and spreading in reversed-phase high-performance liquid chromatography (RP-HPLC) through directly relating local retention factor and local diffusion coefficient to local mobile phase concentration. This new approach differs entirely from the traditional theories on plate concept with Eulerian description, since band width recursion equation is actually the accumulation of local diffusion coefficients of solute zones to discrete-time slices. Recursion equations and literature equations were used in dealing with same experimental data in RP-HPLC, and the comparison results show that the recursion equations can accurately predict band width under gradient elution.

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

PubMed

Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar

2002-05-01

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Theory of diffusion of active particles that move at constant speed in two dimensions.

PubMed

Sevilla, Francisco J; Gómez Nava, Luis A

2014-08-01

Starting from a Langevin description of active particles that move with constant speed in infinite two-dimensional space and its corresponding Fokker-Planck equation, we develop a systematic method that allows us to obtain the coarse-grained probability density of finding a particle at a given location and at a given time in arbitrary short-time regimes. By going beyond the diffusive limit, we derive a generalization of the telegrapher equation. Such generalization preserves the hyperbolic structure of the equation and incorporates memory effects in the diffusive term. While no difference is observed for the mean-square displacement computed from the two-dimensional telegrapher equation and from our generalization, the kurtosis results in a sensible parameter that discriminates between both approximations. We carry out a comparative analysis in Fourier space that sheds light on why the standard telegrapher equation is not an appropriate model to describe the propagation of particles with constant speed in dispersive media.

On the Role of Built-in Electric Fields on the Ignition of Oxide Coated NanoAluminum: Ion Mobility versus Fickian Diffusion

DTIC Science & Technology

2010-01-01

on Al ion diffu- sion can be computed using the Nernst –Planck equation . The Nernst –Plank equation is given in Eq. 4,22 J = − D dC dx − zFDC RT d dx...The use of the bulk diffusion equation is reason- able since during the time scales considered the movement of only the atoms initially on the surface

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Flow regimes for fluid injection into a confined porous medium

DOE PAGES

Zheng, Zhong; Guo, Bo; Christov, Ivan C.; ...

2015-02-24

We report theoretical and numerical studies of the flow behaviour when a fluid is injected into a confined porous medium saturated with another fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the fluid–fluid interface. In the early time period, the fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the fluid flow is mainly driven by the injection, and the governingmore » equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the injected fluid is more viscous than the displaced fluid, whereas a rarefaction wave solution is found when the injected fluid is less viscous. In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an injected fluid with a viscosity higher than or equal to that of the displaced fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are performed; the various analytical solutions are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions.

PubMed

Péraud, Jean-Philippe; Nonaka, Andrew J; Bell, John B; Donev, Aleksandar; Garcia, Alejandro L

2017-10-10

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson-Nernst-Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation-anion diffusion coefficient. Specifically, we predict a nonzero cation-anion Maxwell-Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced "giant" velocity fluctuations and reduced fluctuations of salt concentration.

Fluctuation-enhanced electric conductivity in electrolyte solutions

PubMed Central

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; Donev, Aleksandar; Garcia, Alejandro L.

2017-01-01

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell–Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration. PMID:28973890

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes.

PubMed

Barrenechea, Gabriel R; Burman, Erik; Karakatsani, Fotini

2017-01-01

For the case of approximation of convection-diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.

Fractal Model of Fission Product Release in Nuclear Fuel

NASA Astrophysics Data System (ADS)

Stankunas, Gediminas

2012-09-01

A model of fission gas migration in nuclear fuel pellet is proposed. Diffusion process of fission gas in granular structure of nuclear fuel with presence of inter-granular bubbles in the fuel matrix is simulated by fractional diffusion model. The Grunwald-Letnikov derivative parameter characterizes the influence of porous fuel matrix on the diffusion process of fission gas. A finite-difference method for solving fractional diffusion equations is considered. Numerical solution of diffusion equation shows correlation of fission gas release and Grunwald-Letnikov derivative parameter. Calculated profile of fission gas concentration distribution is similar to that obtained in the experimental studies. Diffusion of fission gas is modeled for real RBMK-1500 fuel operation conditions. A functional dependence of Grunwald-Letnikov derivative parameter with fuel burn-up is established.

Thermodynamics of viscoelastic rate-type fluids with stress diffusion

NASA Astrophysics Data System (ADS)

Málek, Josef; Průša, Vít; Skřivan, Tomáš; Süli, Endre

2018-02-01

We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution equation for the extra stress tensor. It is shown that the stress diffusion term can be interpreted either as a consequence of a nonlocal energy storage mechanism or as a consequence of a nonlocal entropy production mechanism, while different interpretations of the stress diffusion mechanism lead to different evolution equations for the temperature. The benefits of the knowledge of the thermodynamical background of the derived models are documented in the study of nonlinear stability of equilibrium rest states. The derived models open up the possibility to study fully coupled thermomechanical problems involving viscoelastic rate-type fluids with stress diffusion.

Dusty Pair Plasma—Wave Propagation and Diffusive Transition of Oscillations

NASA Astrophysics Data System (ADS)

Atamaniuk, Barbara; Turski, Andrzej J.

2011-11-01

The crucial point of the paper is the relation between equilibrium distributions of plasma species and the type of propagation or diffusive transition of plasma response to a disturbance. The paper contains a unified treatment of disturbance propagation (transport) in the linearized Vlasov electron-positron and fullerene pair plasmas containing charged dust impurities, based on the space-time convolution integral equations. Electron-positron-dust/ion (e-p-d/i) plasmas are rather widespread in nature. Space-time responses of multi-component linearized Vlasov plasmas on the basis of multiple integral equations are invoked. An initial-value problem for Vlasov-Poisson/Ampère equations is reduced to the one multiple integral equation and the solution is expressed in terms of forcing function and its space-time convolution with the resolvent kernel. The forcing function is responsible for the initial disturbance and the resolvent is responsible for the equilibrium velocity distributions of plasma species. By use of resolvent equations, time-reversibility, space-reflexivity and the other symmetries are revealed. The symmetries carry on physical properties of Vlasov pair plasmas, e.g., conservation laws. Properly choosing equilibrium distributions for dusty pair plasmas, we can reduce the resolvent equation to: (i) the undamped dispersive wave equations, (ii) and diffusive transport equations of oscillations.

A GENERALIZED MATHEMATICAL SCHEME TO ANALYTICALLY SOLVE THE ATMOSPHERIC DIFFUSION EQUATION WITH DRY DEPOSITION. (R825689C072)

EPA Science Inventory

Abstract

A generalized mathematical scheme is developed to simulate the turbulent dispersion of pollutants which are adsorbed or deposit to the ground. The scheme is an analytical (exact) solution of the atmospheric diffusion equation with height-dependent wind speed a...

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-03-01

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

Liquefaction of Saturated Soil and the Diffusion Equation

NASA Astrophysics Data System (ADS)

Sawicki, Andrzej; Sławińska, Justyna

2015-06-01

The paper deals with the diffusion equation for pore water pressures with the source term, which is widely promoted in the marine engineering literature. It is shown that such an equation cannot be derived in a consistent way from the mass balance and the Darcy law. The shortcomings of the artificial source term are pointed out, including inconsistencies with experimental data. It is concluded that liquefaction and the preceding process of pore pressure generation and the weakening of the soil skeleton should be described by constitutive equations within the well-known framework of applied mechanics. Relevant references are provided

Transport mechanisms of contaminants released from fine sediment in rivers

NASA Astrophysics Data System (ADS)

Cheng, Pengda; Zhu, Hongwei; Zhong, Baochang; Wang, Daozeng

2015-12-01

Contaminants released from sediment into rivers are one of the main problems to study in environmental hydrodynamics. For contaminants released into the overlying water under different hydrodynamic conditions, the mechanical mechanisms involved can be roughly divided into convective diffusion, molecular diffusion, and adsorption/desorption. Because of the obvious environmental influence of fine sediment (D_{90}= 0.06 mm), non-cohesive fine sediment, and cohesive fine sediment are researched in this paper, and phosphorus is chosen for a typical adsorption of a contaminant. Through theoretical analysis of the contaminant release process, according to different hydraulic conditions, the contaminant release coupling mathematical model can be established by the N-S equation, the Darcy equation, the solute transport equation, and the adsorption/desorption equation. Then, the experiments are completed in an open water flume. The simulation results and experimental results show that convective diffusion dominates the contaminant release both in non-cohesive and cohesive fine sediment after their suspension, and that they contribute more than 90 % of the total release. Molecular diffusion and desorption have more of a contribution for contaminant release from unsuspended sediment. In unsuspension sediment, convective diffusion is about 10-50 times larger than molecular diffusion during the initial stages under high velocity; it is close to molecular diffusion in the later stages. Convective diffusion is about 6 times larger than molecular diffusion during the initial stages under low velocity, it is about a quarter of molecular diffusion in later stages, and has a similar level with desorption/adsorption. In unsuspended sediment, a seepage boundary layer exists below the water-sediment interface, and various release mechanisms in that layer mostly dominate the contaminant release process. In non-cohesive fine sediment, the depth of that layer increases linearly with shear stress. In cohesive fine sediment, the range seepage boundary is different from that in non-cohesive sediment, and that phenomenon is more obvious under a lower shear stress.

Linear response theory and transient fluctuation relations for diffusion processes: a backward point of view

NASA Astrophysics Data System (ADS)

Liu, Fei; Tong, Huan; Ma, Rui; Ou-Yang, Zhong-can

2010-12-01

A formal apparatus is developed to unify derivations of the linear response theory and a variety of transient fluctuation relations for continuous diffusion processes from a backward point of view. The basis is a perturbed Kolmogorov backward equation and the path integral representation of its solution. We find that these exact transient relations could be interpreted as a consequence of a generalized Chapman-Kolmogorov equation, which intrinsically arises from the Markovian characteristic of diffusion processes.

New explicit equations for the accurate calculation of the growth and evaporation of hydrometeors by the diffusion of water vapor

NASA Technical Reports Server (NTRS)

Srivastava, R. C.; Coen, J. L.

1992-01-01

The traditional explicit growth equation has been widely used to calculate the growth and evaporation of hydrometeors by the diffusion of water vapor. This paper reexamines the assumptions underlying the traditional equation and shows that large errors (10-30 percent in some cases) result if it is used carelessly. More accurate explicit equations are derived by approximating the saturation vapor-density difference as a quadratic rather than a linear function of the temperature difference between the particle and ambient air. These new equations, which reduce the error to less than a few percent, merit inclusion in a broad range of atmospheric models.

A Simple Mathematical Model Inspired by the Purkinje Cells: From Delayed Travelling Waves to Fractional Diffusion.

PubMed

Dipierro, Serena; Valdinoci, Enrico

2018-07-01

Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of "smoothing" the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

Birth-jump processes and application to forest fire spotting.

PubMed

Hillen, T; Greese, B; Martin, J; de Vries, G

2015-01-01

Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction-diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of forest fire spread through spotting. We show that spotting increases the invasion speed of a forest fire front.

Reexamination of relaxation of spins due to a magnetic field gradient: Identity of the Redfield and Torrey theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golub, R.; Rohm, Ryan M.; Swank, C. M.

2011-02-15

There is an extensive literature on magnetic-gradient-induced spin relaxation. Cates, Schaefer, and Happer, in a seminal publication, have solved the problem in the regime where diffusion theory (the Torrey equation) is applicable using an expansion of the density matrix in diffusion equation eigenfunctions and angular momentum tensors. McGregor has solved the problem in the same regime using a slightly more general formulation using the Redfield theory formulated in terms of the autocorrelation function of the fluctuating field seen by the spins and calculating the correlation functions using the diffusion-theory Green's function. The results of both calculations were shown to agreemore » for a special case. In the present work, we show that the eigenfunction expansion of the Torrey equation yields the expansion of the Green's function for the diffusion equation, thus showing the identity of this approach with that of the Redfield theory. The general solution can also be obtained directly from the Torrey equation for the density matrix. Thus, the physical content of the Redfield and Torrey approaches are identical. We then introduce a more general expression for the position autocorrelation function of particles moving in a closed cell, extending the range of applicability of the theory.« less

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

NASA Astrophysics Data System (ADS)

Gyrya, V.; Lipnikov, K.

2017-11-01

We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE PAGES

Gyrya, V.; Lipnikov, K.

2017-07-18

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gyrya, V.; Lipnikov, K.

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

Maximum Path Information and Fokker Planck Equation

NASA Astrophysics Data System (ADS)

Li, Wei; Wang A., Q.; LeMehaute, A.

2008-04-01

We present a rigorous method to derive the nonlinear Fokker-Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang [Chaos, Solitons & Fractals 23 (2005) 1253] for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q (the index of Tsallis entropy [J. Stat. Phys. 52 (1988) 479] and the time t.

Molecular dynamics on diffusive time scales from the phase-field-crystal equation.

PubMed

Chan, Pak Yuen; Goldenfeld, Nigel; Dantzig, Jon

2009-03-01

We extend the phase-field-crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of them. By solving the dynamical equation of the model, which is a partial differential equation, we are essentially performing molecular dynamics simulations on diffusive time scales. To illustrate this approach, we calculate the two-point correlation function of a fluid.

Non-Markovian Effects in Turbulent Diffusion in Magnetized Plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zagorodny, Anatoly; Weiland, Jan

2009-10-08

The derivation of the kinetic equations for inhomogeneous plasma in an external magnetic field is presented. The Fokker-Planck-type equations with the non-Markovian kinetic coefficients are proposed. In the time-local limit (small correlation times with respect to the distribution function relaxation time) the relations obtained recover the results known from the appropriate quasilinear theory and the Dupree-Weinstock theory of plasma turbulence. The equations proposed are used to describe zonal flow generation and to estimate the diffusion coefficient for saturated turbulence.

Lattice Boltzmann scheme for mixture modeling: analysis of the continuum diffusion regimes recovering Maxwell-Stefan model and incompressible Navier-Stokes equations.

PubMed

Asinari, Pietro

2009-11-01

A finite difference lattice Boltzmann scheme for homogeneous mixture modeling, which recovers Maxwell-Stefan diffusion model in the continuum limit, without the restriction of the mixture-averaged diffusion approximation, was recently proposed [P. Asinari, Phys. Rev. E 77, 056706 (2008)]. The theoretical basis is the Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [P. Andries, K. Aoki, and B. Perthame, J. Stat. Phys. 106, 993 (2002)]. In the present paper, the recovered macroscopic equations in the continuum limit are systematically investigated by varying the ratio between the characteristic diffusion speed and the characteristic barycentric speed. It comes out that the diffusion speed must be at least one order of magnitude (in terms of Knudsen number) smaller than the barycentric speed, in order to recover the Navier-Stokes equations for mixtures in the incompressible limit. Some further numerical tests are also reported. In particular, (1) the solvent and dilute test cases are considered, because they are limiting cases in which the Maxwell-Stefan model reduces automatically to Fickian cases. Moreover, (2) some tests based on the Stefan diffusion tube are reported for proving the complete capabilities of the proposed scheme in solving Maxwell-Stefan diffusion problems. The proposed scheme agrees well with the expected theoretical results.

A cross-diffusion system derived from a Fokker-Planck equation with partial averaging

NASA Astrophysics Data System (ADS)

Jüngel, Ansgar; Zamponi, Nicola

2017-02-01

A cross-diffusion system for two components with a Laplacian structure is analyzed on the multi-dimensional torus. This system, which was recently suggested by P.-L. Lions, is formally derived from a Fokker-Planck equation for the probability density associated with a multi-dimensional Itō process, assuming that the diffusion coefficients depend on partial averages of the probability density with exponential weights. A main feature is that the diffusion matrix of the limiting cross-diffusion system is generally neither symmetric nor positive definite, but its structure allows for the use of entropy methods. The global-in-time existence of positive weak solutions is proved and, under a simplifying assumption, the large-time asymptotics is investigated.

A nonlinear Fokker-Planck equation approach for interacting systems: Anomalous diffusion and Tsallis statistics

NASA Astrophysics Data System (ADS)

Marin, D.; Ribeiro, M. A.; Ribeiro, H. V.; Lenzi, E. K.

2018-07-01

We investigate the solutions for a set of coupled nonlinear Fokker-Planck equations coupled by the diffusion coefficient in presence of external forces. The coupling by the diffusion coefficient implies that the diffusion of each species is influenced by the other and vice versa due to this term, which represents an interaction among them. The solutions for the stationary case are given in terms of the Tsallis distributions, when arbitrary external forces are considered. We also use the Tsallis distributions to obtain a time dependent solution for a linear external force. The results obtained from this analysis show a rich class of behavior related to anomalous diffusion, which can be characterized by compact or long-tailed distributions.

The chemotaxis regulator pilG of Xylella fastidiosa is required for virulence in Vitis vinifera grapevines

USDA-ARS?s Scientific Manuscript database

Type IV pili of X. fastidiosa are regulated by pilG, a response regulator protein putatively involved in chemotaxis-like operon sensing stimuli through signal transduction pathways. To elucidate roles of pilG in pathogenicity of X. fastidiosa, the pilG-deletion mutant and complementary strain contai...

Central Synaptic Mechanisms Underlie Short-Term Olfactory Habituation in "Drosophila" Larvae

ERIC Educational Resources Information Center

Larkin, Aoife; Karak, Somdatta; Priya, Rashi; Das, Abhijit; Ayyub, Champakali; Ito, Kei; Rodrigues, Veronica; Ramaswami, Mani

2010-01-01

Naive "Drosophila" larvae show vigorous chemotaxis toward many odorants including ethyl acetate (EA). Chemotaxis toward EA is substantially reduced after a 5-min pre-exposure to the odorant and recovers with a half-time of [image omitted]20 min. An analogous behavioral decrement can be induced without odorant-receptor activation through…

cDNA-AFLP analysis of differential gene expression related to cell chemotactic and encystment of Azospirillum brasilense.

PubMed

Li, Huamin; Cui, Yanhua; Wu, Lixian; Tu, Ran; Chen, Sanfeng

2011-12-20

Our previous study indicated org35 was involved in chemotaxis and interacted with nitrogen fixation transcriptional activator NifA via PAS domain. In order to reveal the role of org35 in nitrogen regulation, the downstream target genes of org35 were identified. We here report differentially expressed genes in org35 mutants comparing with wild type Sp7 by means of cDNA-AFLP. Four up-regulated transcript-derived fragments (TDFs) homologues of chemotaxis transduction proteins were found, including CheW, methyl-accepting chemotaxis protein and response regulator CheY-like receiver. Three distinct TDFs (AB46, AB58 and AB63) were similar to PHB de-polymerase C-terminus, cell shape-determining protein and flagellin domain protein. And 11 TDFs showed similarities with signal transduction proteins, including homologous protein of the nitrogen regulation protein NtrY and nitrate/nitrite response regulator protein NarL. These data suggested that the Azospirillum brasilense org35 was a multi-effecter and involved in chemotaxis, cyst development and regulation of nitrogen fixation. Copyright © 2010 Elsevier GmbH. All rights reserved.

Chemotaxis study using optical tweezers to observe the strength and directionality of forces of Leishmania amazonensis

NASA Astrophysics Data System (ADS)

Pozzo, Liliana d. Y.; Fontes, Adriana; de Thomaz, André A.; Barbosa, Luiz C.; Ayres, Diana C.; Giorgio, Selma; Cesar, Carlos L.

2006-08-01

The displacements of a dielectric microspheres trapped by an optical tweezers (OT) can be used as a force transducer for mechanical measurements in life sciences. This system can measure forces on the 50 femto Newtons to 200 pico Newtons range, of the same order of magnitude of a typical forces induced by flagellar motion. The process in which living microorganisms search for food and run away from poison chemicals is known is chemotaxy. Optical tweezers can be used to obtain a better understanding of chemotaxy by observing the force response of the microorganism when placed in a gradient of attractors and or repelling chemicals. This report shows such observations for the protozoa Leishmania amazomenzis, responsible for the leishmaniasis, a serious tropical disease. We used a quadrant detector to monitor the movement of the protozoa for different chemicals gradient. This way we have been able to observe both the force strength and its directionality. The characterization of the chemotaxis of these parasites can help to understand the infection mechanics and improve the diagnosis and the treatments employed for this disease.

Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

NASA Astrophysics Data System (ADS)

Collier, N.; Knepley, M.

2015-12-01

The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

Asymptotic Analysis of Time-Dependent Neutron Transport Coupled with Isotopic Depletion and Radioactive Decay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brantley, P S

2006-09-27

We describe an asymptotic analysis of the coupled nonlinear system of equations describing time-dependent three-dimensional monoenergetic neutron transport and isotopic depletion and radioactive decay. The classic asymptotic diffusion scaling of Larsen and Keller [1], along with a consistent small scaling of the terms describing the radioactive decay of isotopes, is applied to this coupled nonlinear system of equations in a medium of specified initial isotopic composition. The analysis demonstrates that to leading order the neutron transport equation limits to the standard time-dependent neutron diffusion equation with macroscopic cross sections whose number densities are determined by the standard system of ordinarymore » differential equations, the so-called Bateman equations, describing the temporal evolution of the nuclide number densities.« less

Interface- and discontinuity-aware numerical schemes for plasma 3-T radiation diffusion in two and three dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dai, William W., E-mail: dai@lanl.gov; Scannapieco, Anthony J.

2015-11-01

A set of numerical schemes is developed for two- and three-dimensional time-dependent 3-T radiation diffusion equations in systems involving multi-materials. To resolve sub-cell structure, interface reconstruction is implemented within any cell that has more than one material. Therefore, the system of 3-T radiation diffusion equations is solved on two- and three-dimensional polyhedral meshes. The focus of the development is on the fully coupling between radiation and material, the treatment of nonlinearity in the equations, i.e., in the diffusion terms and source terms, treatment of the discontinuity across cell interfaces in material properties, the formulations for both transient and steady states,more » the property for large time steps, and second order accuracy in both space and time. The discontinuity of material properties between different materials is correctly treated based on the governing physics principle for general polyhedral meshes and full nonlinearity. The treatment is exact for arbitrarily strong discontinuity. The scheme is fully nonlinear for the full nonlinearity in the 3-T diffusion equations. Three temperatures are fully coupled and are updated simultaneously. The scheme is general in two and three dimensions on general polyhedral meshes. The features of the scheme are demonstrated through numerical examples for transient problems and steady states. The effects of some simplifications of numerical schemes are also shown through numerical examples, such as linearization, simple average of diffusion coefficient, and approximate treatment for the coupling between radiation and material.« less

A numerical solution for the diffusion equation in hydrogeologic systems

USGS Publications Warehouse

Ishii, A.L.; Healy, R.W.; Striegl, Robert G.

1989-01-01

The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)

A Behavioral and Genetic Dissection of Two Forms of Olfactory Plasticity in Caenorhabditis elegans: Adaptation and Habituation

PubMed Central

Bernhard, Nirit; van der Kooy, Derek

2000-01-01

Continuous presentation of an olfactory stimulus causes a decrement of the chemotaxis response in the nematode Caenorhabditis elegans. However, the differences between the learning process of habituation (a readily reversible decrease in behavioral response) and other types of olfactory plasticity such as adaptation (a decrement in response due to sensory fatigue, which cannot be dishabituated) have not been addressed. The volatile odorant diacetyl (DA) was used within a single paradigm to assess the distinct processes of olfactory adaptation and habituation. Preexposing and testing worms to 100% DA vapors caused a chemotaxis decrement that was not reversible despite the presentation of potentially dishabituating stimuli. This DA adaptation was abolished in worms with an odr-10 mutation (encoding a high-affinity DA receptor on the AWA neuron), even though naive chemotaxis remained unaffected. Conversely, DA adaptation remained intact in odr-1 mutants (defective in AWC neuron-mediated olfactory behavior), even though naive chemotaxis to DA decreased. Surprisingly, exposure to vapors of intermediate concentrations of DA (0.01% and 25%) did not cause worms to exhibit any response decrement. In contrast to preexposure to high DA concentrations, preexposure to low DA concentrations (0.001%) produced habituation of the chemotaxis response (a dishabituating stimulus could reverse the response decrement back to baseline levels). The distinct behavioral effects produced by DA preexposure highlight a concentration-dependent dissociation between two decremental olfactory processes: adaptation at high DA concentrations versus habituation at low DA concentrations. PMID:10940320

Functional asymmetry in Caenorhabditis elegans taste neurons and its computational role in chemotaxis.

PubMed

Suzuki, Hiroshi; Thiele, Tod R; Faumont, Serge; Ezcurra, Marina; Lockery, Shawn R; Schafer, William R

2008-07-03

Chemotaxis in Caenorhabditis elegans, like chemotaxis in bacteria, involves a random walk biased by the time derivative of attractant concentration, but how the derivative is computed is unknown. Laser ablations have shown that the strongest deficits in chemotaxis to salts are obtained when the ASE chemosensory neurons (ASEL and ASER) are ablated, indicating that this pair has a dominant role. Although these neurons are left-right homologues anatomically, they exhibit marked asymmetries in gene expression and ion preference. Here, using optical recordings of calcium concentration in ASE neurons in intact animals, we demonstrate an additional asymmetry: ASEL is an ON-cell, stimulated by increases in NaCl concentration, whereas ASER is an OFF-cell, stimulated by decreases in NaCl concentration. Both responses are reliable yet transient, indicating that ASE neurons report changes in concentration rather than absolute levels. Recordings from synaptic and sensory transduction mutants show that the ON-OFF asymmetry is the result of intrinsic differences between ASE neurons. Unilateral activation experiments indicate that the asymmetry extends to the level of behavioural output: ASEL lengthens bouts of forward locomotion (runs) whereas ASER promotes direction changes (turns). Notably, the input and output asymmetries of ASE neurons are precisely those of a simple yet novel neuronal motif for computing the time derivative of chemosensory information, which is the fundamental computation of C. elegans chemotaxis. Evidence for ON and OFF cells in other chemosensory networks suggests that this motif may be common in animals that navigate by taste and smell.

Chemorepulsion from the Quorum Signal Autoinducer-2 Promotes Helicobacter pylori Biofilm Dispersal

PubMed Central

Anderson, Jeneva K.; Huang, Julie Y.; Wreden, Christopher; Sweeney, Emily Goers; Goers, John; Remington, S. James

2015-01-01

ABSTRACT The gastric pathogen Helicobacter pylori forms biofilms on abiotic and biotic surfaces. We have shown previously that H. pylori perceives the quorum signal autoinducer-2 (AI-2) as a chemorepellent. We report here that H. pylori chemorepulsion from endogenous AI-2 influences the proportions and spatial organization of cells within biofilms. Strains that fail to produce AI-2 (∆luxS strains) or are defective for chemotaxis (∆cheA strains) formed more spatially homogenous biofilms with a greater proportion of adherent versus planktonic cells than wild-type biofilms. Reciprocally, a strain that overproduced AI-2 (luxSOP) formed biofilms with proportionally fewer adherent cells. Along with the known AI-2 chemoreceptor, TlpB, we identified AibA and AibB, two novel periplasmic binding proteins that are required for the AI-2 chemorepulsion response. Disruptions in any of the proteins required for AI-2 chemotaxis recapitulated the biofilm adherence and spatial organization phenotype of the ∆luxS mutant. Furthermore, exogenous administration of AI-2 was sufficient to decrease the proportion of adherent cells in biofilms and promote dispersal of cells from biofilms in a chemotaxis-dependent manner. Finally, we found that disruption of AI-2 production or AI-2 chemotaxis resulted in increased clustering of cells in microcolonies on cultured epithelial cells. We conclude that chemotaxis from AI-2 is a determinant of H. pylori biofilm spatial organization and dispersal. PMID:26152582

Dual acylation and lipid raft association of Src-family protein tyrosine kinases are required for SDF-1/CXCL12-mediated chemotaxis in the Jurkat human T cell lymphoma cell line.

PubMed

Zaman, Sabiha N; Resek, Mary E; Robbins, Stephen M

2008-10-01

Chemokines play pivotal roles in regulating a wide variety of biological processes by modulating cell migration and recruitment. Deregulation of chemokine signaling can alter cell recruitment, contributing to the pathogenic states associated with autoimmune disease, inflammatory disorders, and sepsis. During chemotaxis, lipid rafts and their resident signaling molecules have been demonstrated to partition to different parts of the cell. Herein, we investigated the role of lipid raft resident Src-family kinases (SFK) in stromal cell-derived factor 1/CXCL12-mediated chemotaxis. We have shown that Lck-deficient J.CaM 1.6 cells are defective in CXCL12-mediated chemotaxis in contrast to their parental counterpart, Jurkat cells. Ectopic expression of the SFK hematopoietic cell kinase (Hck) in J.CaM 1.6 cells reconstituted CXCL12 responsiveness. The requirement of lipid raft association of SFK was assessed using both isoforms of Hck: the dually acylated p59(Hck) isoform that is targeted to lipid rafts and the monoacylated p61(Hck) isoform that is nonraft-associated. We have shown using several gain and loss of acylation alleles that dual acylation of Hck was required for CXCL12-mediated chemotaxis in J.CaM 1.6 cells. These results highlight the importance of the unique microenvironment provided by lipid rafts and their specific contribution in providing specificity to CXCL12 signaling.

Reprint of: Quantitative proteomic analysis reveals that chemotaxis is involved in chlortetracycline resistance of Aeromonas hydrophila.

PubMed

Li, Wanxin; Ali, Farman; Cai, Qilan; Yao, Zujie; Sun, Lina; Lin, Wenxiong; Lin, Xiangmin

2018-05-30

In recent years, Aeromonas hydrophila, which has been classified as a food borne pathogen, has presented with increased levels of antibiotic resistance, with the mechanisms of this resistance being poorly understood. In this study, iTRAQ coupled mass spectrometry was employed to compare differentially expressed proteins in chlortetracycline (CTC) resistant A. hydrophila relative to a control strain. Result showed that a total of 234 differential proteins including 151 down-regulated and 83 up-regulated were identified in chlortetracycline resistance strain. Bioinformatics analysis showed that chemotaxis related proteins, such as CheA-2, CheR-3, CheW-2, EnvZ, PolA, FliS and FliG were down-regulated in addition to previously reported tricarboxylic acid cycle (TCA) related proteins also being down-regulated. A subset of identified differentially expressed proteins was then further validated via Western blotting. Exogenous metabolite combined with CTC further enhanced the bacterial susceptibilities to CTC in A. hydrophila. Furthermore, a bacterial survival capability assay showed that several chemotaxis related mutants, such as ΔcheR-3 and ΔAHA_0305, may affect the antimicrobial susceptibility of A. hydrophila. Overall, these findings contribute to a further understanding of the mechanism of CTC resistance in A. hydrophila and may contribute to the development of more effective future treatments. A. hydrophila is a well-known fish pathogenic bacterium and has presented with increasing levels of antibiotic resistance, with the mechanisms of this resistance being poorly understood. Our current study compared the differentially expression proteins between chlortetracycline (CTC) resistant and control stains via an iTARQ-based quantitative proteomics method. Chemotaxis related proteins were down-regulated in CTC resistant strain but exogenous metabolite addition increased bacterial susceptibility in A.hydrophila. Significantly, chemotaxis related genes depletion affected antimicrobial susceptibilities of A.hydrophila indicating the role of chemotaxis process in antibiotics resistance. Copyright © 2018 Elsevier B.V. All rights reserved.

On the Maxwell-Stefan approach to diffusion: a general resolution in the transient regime for one-dimensional systems.

PubMed

Leonardi, Erminia; Angeli, Celestino

2010-01-14

The diffusion process in a multicomponent system can be formulated in a general form by the generalized Maxwell-Stefan equations. This formulation is able to describe the diffusion process in different systems, such as, for instance, bulk diffusion (in the gas, liquid, and solid phase) and diffusion in microporous materials (membranes, zeolites, nanotubes, etc.). The Maxwell-Stefan equations can be solved analytically (only in special cases) or by numerical approaches. Different numerical strategies have been previously presented, but the number of diffusing species is normally restricted, with only few exceptions, to three in bulk diffusion and to two in microporous systems, unless simplifications of the Maxwell-Stefan equations are considered. In the literature, a large effort has been devoted to the derivation of the analytic expression of the elements of the Fick-like diffusion matrix and therefore to the symbolic inversion of a square matrix with dimensions n x n (n being the number of independent components). This step, which can be easily performed for n = 2 and remains reasonable for n = 3, becomes rapidly very complex in problems with a large number of components. This paper addresses the problem of the numerical resolution of the Maxwell-Stefan equations in the transient regime for a one-dimensional system with a generic number of components, avoiding the definition of the analytic expression of the elements of the Fick-like diffusion matrix. To this aim, two approaches have been implemented in a computational code; the first is the simple finite difference second-order accurate in time Crank-Nicolson scheme for which the full mathematical derivation and the relevant final equations are reported. The second is based on the more accurate backward differentiation formulas, BDF, or Gear's method (Shampine, L. F. ; Gear, C. W. SIAM Rev. 1979, 21, 1.), as implemented in the Livermore solver for ordinary differential equations, LSODE (Hindmarsh, A. C. Serial Fortran Solvers for ODE Initial Value Problems, Technical Report; https://computation.llnl.gov/casc/odepack/odepack_ home.html (2006).). Both methods have been applied to a series of specific problems, such as bulk diffusion of acetone and methanol through stagnant air, uptake of two components on a microporous material in a model system, and permeation across a microporous membrane in model systems, both with the aim to validate the method and to add new information to the comprehension of the peculiar behavior of these systems. The approach is validated by comparison with different published results and with analytic expressions for the steady-state concentration profiles or fluxes in particular systems. The possibility to treat a generic number of components (the limitation being essentially the computational power) is also tested, and results are reported on the permeation of a five component mixture through a membrane in a model system. It is worth noticing that the algorithm here reported can be applied also to the Fick formulation of the diffusion problem with concentration-dependent diffusion coefficients.

Predicting Ga and Cu Profiles in Co-Evaporated Cu(In,Ga)Se 2 Using Modified Diffusion Equations and a Spreadsheet

DOE PAGES

Repins, Ingrid L.; Harvey, Steve; Bowers, Karen; ...

2017-05-15

Cu(In,Ga)Se 2(CIGS) photovoltaic absorbers frequently develop Ga gradients during growth. These gradients vary as a function of growth recipe, and are important to device performance. Prediction of Ga profiles using classic diffusion equations is not possible because In and Ga atoms occupy the same lattice sites and thus diffuse interdependently, and there is not yet a detailed experimental knowledge of the chemical potential as a function of composition that describes this interaction. Here, we show how diffusion equations can be modified to account for site sharing between In and Ga atoms. The analysis has been implemented in an Excel spreadsheet,more » and outputs predicted Cu, In, and Ga profiles for entered deposition recipes. A single set of diffusion coefficients and activation energies are chosen, such that simulated elemental profiles track with published data and those from this study. Extent and limits of agreement between elemental profiles predicted from the growth recipes and the spreadsheet tool are demonstrated.« less

Theory and Simulation of Self- and Mutual-Diffusion of Carrier Density and Temperature in Semiconductor Lasers

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Cheung, Samson H.; Ning, C. Z.

2001-01-01

Carrier diffusion and thermal conduction play a fundamental role in the operation of high-power, broad-area semiconductor lasers. Restricted geometry, high pumping level and dynamic instability lead to inhomogeneous spatial distribution of plasma density, temperature, as well as light field, due to strong light-matter interaction. Thus, modeling and simulation of such optoelectronic devices rely on detailed descriptions of carrier dynamics and energy transport in the system. A self-consistent description of lasing and heating in large-aperture, inhomogeneous edge- or surface-emitting lasers (VCSELs) require coupled diffusion equations for carrier density and temperature. In this paper, we derive such equations from the Boltzmann transport equation for the carrier distributions. The derived self- and mutual-diffusion coefficients are in general nonlinear functions of carrier density and temperature including many-body interactions. We study the effects of many-body interactions on these coefficients, as well as the nonlinearity of these coefficients for large-area VCSELs. The effects of mutual diffusions on carrier and temperature distributions in gain-guided VCSELs will be also presented.

Predicting Ga and Cu Profiles in Co-Evaporated Cu(In,Ga)Se 2 Using Modified Diffusion Equations and a Spreadsheet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Repins, Ingrid L.; Harvey, Steve; Bowers, Karen

Cu(In,Ga)Se 2(CIGS) photovoltaic absorbers frequently develop Ga gradients during growth. These gradients vary as a function of growth recipe, and are important to device performance. Prediction of Ga profiles using classic diffusion equations is not possible because In and Ga atoms occupy the same lattice sites and thus diffuse interdependently, and there is not yet a detailed experimental knowledge of the chemical potential as a function of composition that describes this interaction. Here, we show how diffusion equations can be modified to account for site sharing between In and Ga atoms. The analysis has been implemented in an Excel spreadsheet,more » and outputs predicted Cu, In, and Ga profiles for entered deposition recipes. A single set of diffusion coefficients and activation energies are chosen, such that simulated elemental profiles track with published data and those from this study. Extent and limits of agreement between elemental profiles predicted from the growth recipes and the spreadsheet tool are demonstrated.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions

DOE PAGES

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; ...

2017-09-26

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

Viscosity and diffusivity in melts: from unary to multicomponent systems

NASA Astrophysics Data System (ADS)

Chen, Weimin; Zhang, Lijun; Du, Yong; Huang, Baiyun

2014-05-01

Viscosity and diffusivity, two important transport coefficients, are systematically investigated from unary melt to binary to multicomponent melts in the present work. By coupling with Kaptay's viscosity equation of pure liquid metals and effective radii of diffusion species, the Sutherland equation is modified by taking the size effect into account, and further derived into an Arrhenius formula for the convenient usage. Its reliability for predicting self-diffusivity and impurity diffusivity in unary liquids is then validated by comparing the calculated self-diffusivities and impurity diffusivities in liquid Al- and Fe-based alloys with the experimental and the assessed data. Moreover, the Kozlov model was chosen among various viscosity models as the most reliable one to reproduce the experimental viscosities in binary and multicomponent melts. Based on the reliable viscosities calculated from the Kozlov model, the modified Sutherland equation is utilized to predict the tracer diffusivities in binary and multicomponent melts, and validated in Al-Cu, Al-Ni and Al-Ce-Ni melts. Comprehensive comparisons between the calculated results and the literature data indicate that the experimental tracer diffusivities and the theoretical ones can be well reproduced by the present calculations. In addition, the vacancy-wind factor in binary liquid Al-Ni alloys with the increasing temperature is also discussed. What's more, the calculated inter-diffusivities in liquid Al-Cu, Al-Ni and Al-Ag-Cu alloys are also in excellent agreement with the measured and theoretical data. Comparisons between the simulated concentration profiles and the measured ones in Al-Cu, Al-Ce-Ni and Al-Ag-Cu melts are further used to validate the present calculation method.

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

The chemotaxis regulator pilG of Xylella fastidiosa is required for virulence in Vitis vinifera grapevines

USDA-ARS?s Scientific Manuscript database

Xylella fastidiosa is a Gram-negative, xylem-limited pathogenic bacterium that causes Pierce’s disease of grapevines. Type IV pili of X. fastidiosa are regulated by pilG, a chemotaxis regulator in Pil-Chp operon involving signal transduction pathways. To elucidate the role of pilG in twitching motil...

Hysteresis and Phase Transitions in a Lattice Regularization of an Ill-Posed Forward-Backward Diffusion Equation

NASA Astrophysics Data System (ADS)

Helmers, Michael; Herrmann, Michael

2018-03-01

We consider a lattice regularization for an ill-posed diffusion equation with a trilinear constitutive law and study the dynamics of phase interfaces in the parabolic scaling limit. Our main result guarantees for a certain class of single-interface initial data that the lattice solutions satisfy asymptotically a free boundary problem with a hysteretic Stefan condition. The key challenge in the proof is to control the microscopic fluctuations that are inevitably produced by the backward diffusion when a particle passes the spinodal region.

Nonequilibrium diffusive gas dynamics: Poiseuille microflow

NASA Astrophysics Data System (ADS)

Abramov, Rafail V.; Otto, Jasmine T.

2018-05-01

We test the recently developed hierarchy of diffusive moment closures for gas dynamics together with the near-wall viscosity scaling on the Poiseuille flow of argon and nitrogen in a one micrometer wide channel, and compare it against the corresponding Direct Simulation Monte Carlo computations. We find that the diffusive regularized Grad equations with viscosity scaling provide the most accurate approximation to the benchmark DSMC results. At the same time, the conventional Navier-Stokes equations without the near-wall viscosity scaling are found to be the least accurate among the tested closures.

A Comparison of Some Difference Schemes for a Parabolic Problem of Zero-Coupon Bond Pricing

NASA Astrophysics Data System (ADS)

Chernogorova, Tatiana; Vulkov, Lubin

2009-11-01

This paper describes a comparison of some numerical methods for solving a convection-diffusion equation subjected by dynamical boundary conditions which arises in the zero-coupon bond pricing. The one-dimensional convection-diffusion equation is solved by using difference schemes with weights including standard difference schemes as the monotone Samarskii's scheme, FTCS and Crank-Nicolson methods. The schemes are free of spurious oscillations and satisfy the positivity and maximum principle as demanded for the financial and diffusive solution. Numerical results are compared with analytical solutions.

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

The general relativistic thin disc evolution equation

NASA Astrophysics Data System (ADS)

Balbus, Steven A.

2017-11-01

In the classical theory of thin disc accretion discs, the constraints of mass and angular momentum conservation lead to a diffusion-like equation for the turbulent evolution of the surface density. Here, we revisit this problem, extending the Newtonian analysis to the regime of Kerr geometry relevant to black holes. A diffusion-like equation once again emerges, but now with a singularity at the radius at which the effective angular momentum gradient passes through zero. The equation may be analysed using a combination of Wentzel-Kramers-Brillouin techniques, local techniques and matched asymptotic expansions. It is shown that imposing the boundary condition of a vanishing stress tensor (more precisely the radial-azimuthal component thereof) allows smooth stable modes to exist external to the angular momentum singularity, the innermost stable circular orbit, while smoothly vanishing inside this location. The extension of the disc diffusion equation to the domain of general relativity introduces a new tool for numerical and phenomenological studies of accretion discs, and may prove to be a useful technique for understanding black hole X-ray transients.

A 2D multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements

NASA Astrophysics Data System (ADS)

Qin, Shanlin; Liu, Fawang; Turner, Ian W.

2018-03-01

The consideration of diffusion processes in magnetic resonance imaging (MRI) signal attenuation is classically described by the Bloch-Torrey equation. However, many recent works highlight the distinct deviation in MRI signal decay due to anomalous diffusion, which motivates the fractional order generalization of the Bloch-Torrey equation. In this work, we study the two-dimensional multi-term time and space fractional diffusion equation generalized from the time and space fractional Bloch-Torrey equation. By using the Galerkin finite element method with a structured mesh consisting of rectangular elements to discretize in space and the L1 approximation of the Caputo fractional derivative in time, a fully discrete numerical scheme is derived. A rigorous analysis of stability and error estimation is provided. Numerical experiments in the square and L-shaped domains are performed to give an insight into the efficiency and reliability of our method. Then the scheme is applied to solve the multi-term time and space fractional Bloch-Torrey equation, which shows that the extra time derivative terms impact the relaxation process.

Evaluation of the telegrapher's equation and multiple-flux theories for calculating the transmittance and reflectance of a diffuse absorbing slab.

PubMed

Kong, Steven H; Shore, Joel D

2007-03-01

We study the propagation of light through a medium containing isotropic scattering and absorption centers. With a Monte Carlo simulation serving as the benchmark solution to the radiative transfer problem of light propagating through a turbid slab, we compare the transmission and reflection density computed from the telegrapher's equation, the diffusion equation, and multiple-flux theories such as the Kubelka-Munk and four-flux theories. Results are presented for both normally incident light and diffusely incident light. We find that we can always obtain very good results from the telegrapher's equation provided that two parameters that appear in the solution are set appropriately. We also find an interesting connection between certain solutions of the telegrapher's equation and solutions of the Kubelka-Munk and four-flux theories with a small modification to how the phenomenological parameters in those theories are traditionally related to the optical scattering and absorption coefficients of the slab. Finally, we briefly explore how well the theories can be extended to the case of anisotropic scattering by multiplying the scattering coefficient by a simple correction factor.

Boundedness for a 3D chemotaxis-Stokes system with porous medium diffusion and tensor-valued chemotactic sensitivity

NASA Astrophysics Data System (ADS)

Wang, Yilong; Li, Xie

2017-04-01

This paper deals with the following chemotaxis-Stokes system n_t+u\\cdot nabla n=Δ n^m-nabla \\cdot (nS(x,n,c)\\cdot nabla c), &{}quad xin Ω , t>0, c_t+u\\cdot nabla c=Δ c-nf(c),&{}quad xin Ω , t>0, u_t=Δ u+nabla P+nnabla φ ,&quad xin Ω , t>0,\\ nabla \\cdot u=0,&{}quad xin Ω , t>0. under no-flux boundary conditions in a bounded domain Ω subset R3 with smooth boundary, where m≥ 1, φ in W^{1,∞}(Ω ), f and S are given functions with values in [0, ∞) and R^{3× 3}, respectively. Here S satisfies |S(x,n,c)|7/6, which insures the global existence of bounded weak solution. Our result covers completely and improves the recent result by Wang and Cao (Discrete Contin Dyn Syst Ser B 20:3235-3254, 2015) which asserts, just in the case m=1, the global existence of solutions, but without boundedness, and that by Winkler (Calc Var Partial Differ Equ 54:3789-3828, 2015) which only involves the case of α =0 and requires the convexity of the domain.

The organized melee: Emergence of collective behavior in concentrated suspensions of swimming bacteria and associated phenomena

NASA Astrophysics Data System (ADS)

Cisneros Salerno, Luis

Suspensions of the aerobic bacteria Bacilus subtilis develop patterns and flows from the interplay of motility, chemotaxis and buoyancy. In sessile drops, such bioconvectively driven flows carry plumes down the slanted meniscus and concentrate cells at the drop edge, while in pendant drops such self-concentration occurs at the bottom. These dynamics are explained quantitatively by a mathematical model consisting of oxygen diffusion and consumption, chemotaxis, and viscous fluid dynamics. Concentrated regions in both geometries comprise nearly close-packed populations, forming the collective "Zooming BioNematic" (ZBN) phase. This state exhibits large-scale orientational coherence, analogous to the molecular alignment of nematic liquid crystals, coupled with remarkable spatial and temporal correlations of velocity and vorticity, as measured by both novel and standard applications of particle imaging velocimetry. To probe mechanisms leading to this phase, response of individual cells to steric stress was explored, finding that they can reverse swimming direction at spatial constrictions without turning the cell body. The consequences of this propensity to flip the flagella are quantified, showing that "forwards" and "backwards" motion are dynamically and morphologically indistinguishable. Finally, experiments and mathematical modeling show that complex flows driven by previously unknown bipolar flagellar arrangements are induced when B. subtilis are confined in a thin layer of fluid, between asymmetric boundaries. The resulting driven flow circulates around the cell body ranging over several cell diameters, in contrast to the more localized flows surrounding free swimmers. This discovery extends our knowledge of the dynamic geometry of bacteria and their flagella, and reveals new mechanisms for motility-associated molecular transport and intercellular communication.

Conformable derivative approach to anomalous diffusion

NASA Astrophysics Data System (ADS)

Zhou, H. W.; Yang, S.; Zhang, S. Q.

2018-02-01

By using a new derivative with fractional order, referred to conformable derivative, an alternative representation of the diffusion equation is proposed to improve the modeling of anomalous diffusion. The analytical solutions of the conformable derivative model in terms of Gauss kernel and Error function are presented. The power law of the mean square displacement for the conformable diffusion model is studied invoking the time-dependent Gauss kernel. The parameters related to the conformable derivative model are determined by Levenberg-Marquardt method on the basis of the experimental data of chloride ions transportation in reinforced concrete. The data fitting results showed that the conformable derivative model agrees better with the experimental data than the normal diffusion equation. Furthermore, the potential application of the proposed conformable derivative model of water flow in low-permeability media is discussed.

Ionic channels: natural nanotubes described by the drift diffusion equations

NASA Astrophysics Data System (ADS)

Eisenberg, Bob

2000-05-01

Ionic channels are a large class of proteins with holes down their middle that control a wide range of cellular functions important in health and disease. Ionic channels can be analysed using a combination of the Poisson and drift diffusion equations familiar from computational electronics because their behavior is dominated by the electrical properties of their simple structure.

Analysis of pulse thermography using similarities between wave and diffusion propagation

NASA Astrophysics Data System (ADS)

Gershenson, M.

2017-05-01

Pulse thermography or thermal wave imaging are commonly used as nondestructive evaluation (NDE) method. While the technical aspect has evolve with time, theoretical interpretation is lagging. Interpretation is still using curved fitting on a log log scale. A new approach based directly on the governing differential equation is introduced. By using relationships between wave propagation and the diffusive propagation of thermal excitation, it is shown that one can transform from solutions in one type of propagation to the other. The method is based on the similarities between the Laplace transforms of the diffusion equation and the wave equation. For diffusive propagation we have the Laplace variable s to the first power, while for the wave propagation similar equations occur with s2. For discrete time the transformation between the domains is performed by multiplying the temperature data vector by a matrix. The transform is local. The performance of the techniques is tested on synthetic data. The application of common back projection techniques used in the processing of wave data is also demonstrated. The combined use of the transform and back projection makes it possible to improve both depth and lateral resolution of transient thermography.

Reaction rates for a generalized reaction-diffusion master equation

DOE PAGES

Hellander, Stefan; Petzold, Linda

2016-01-19

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show inmore » two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules.« less

Reaction rates for a generalized reaction-diffusion master equation

PubMed Central

Hellander, Stefan; Petzold, Linda

2016-01-01

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules. PMID:26871190

Differential equation of exospheric lateral transport and its application to terrestrial hydrogen

NASA Technical Reports Server (NTRS)

Hodges, R. R., Jr.

1973-01-01

The differential equation description of exospheric lateral transport of Hodges and Johnson is reformulated to extend its utility to light gases. Accuracy of the revised equation is established by applying it to terrestrial hydrogen. The resulting global distributions for several static exobase models are shown to be essentially the same as those that have been computed by Quessette using an integral equation approach. The present theory is subsequently used to elucidate the effects of nonzero lateral flow, exobase rotation, and diurnal tidal winds on the hydrogen distribution. Finally it is shown that the differential equation of exospheric transport is analogous to a diffusion equation. Hence it is practical to consider exospheric transport as a continuation of thermospheric diffusion, a concept that alleviates the need for an artificial exobase dividing thermosphere and exosphere.

Species and Scale Dependence of Bacterial Motion Dynamics

NASA Astrophysics Data System (ADS)

Sund, N. L.; Yang, X.; Parashar, R.; Plymale, A.; Hu, D.; Kelly, R.; Scheibe, T. D.

2017-12-01

Many metal reducing bacteria are motile with their motion characteristics described by run-and-tumble behavior exhibiting series of flights (jumps) and waiting (residence) time spanning a wide range of values. Accurate models of motility allow for improved design and evaluation of in-situ bioremediation in the subsurface. While many bioremediation models neglect the motion of the bacteria, others treat motility using an advection dispersion equation, which assumes that the motion of the bacteria is Brownian.The assumption of Brownian motion to describe motility has enormous implications on predictive capabilities of bioremediation models, yet experimental evidence of this assumption is mixed [1][2][3]. We hypothesize that this is due to the species and scale dependence of the motion dynamics. We test our hypothesis by analyzing videos of motile bacteria of five different species in open domains. Trajectories of individual cells ranging from several seconds to few minutes in duration are extracted in neutral conditions (in the absence of any chemical gradient). The density of the bacteria is kept low so that the interaction between the bacteria is minimal. Preliminary results show a transition from Fickian (Brownian) to non-Fickian behavior for one species of bacteria (Pelosinus) and persistent Fickian behavior of another species (Geobacter).Figure: Video frames of motile bacteria with the last 10 seconds of their trajectories drawn in red. (left) Pelosinus and (right) Geobacter.[1] Ariel, Gil, et al. "Swarming bacteria migrate by Lévy Walk." Nature Communications 6 (2015).[2] Saragosti, Jonathan, Pascal Silberzan, and Axel Buguin. "Modeling E. coli tumbles by rotational diffusion. Implications for chemotaxis." PloS one 7.4 (2012): e35412.[3] Wu, Mingming, et al. "Collective bacterial dynamics revealed using a three-dimensional population-scale defocused particle tracking technique." Applied and Environmental Microbiology 72.7 (2006): 4987-4994.

Extracting surface diffusion coefficients from batch adsorption measurement data: application of the classic Langmuir kinetics model.

PubMed

Chu, Khim Hoong

2017-11-09

Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6  cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.

Turbo fluid machinery and diffusers

NASA Technical Reports Server (NTRS)

Sakurai, T.

1984-01-01

The general theory behind turbo devices and diffusers is explained. Problems and the state of research on basic equations of flow and experimental and measuring methods are discussed. Conventional centrifugation-type compressor and fan diffusers are considered in detail.

Patterns induced by super cross-diffusion in a predator-prey system with Michaelis-Menten type harvesting.

PubMed

Liu, Biao; Wu, Ranchao; Chen, Liping

2018-04-01

Turing instability and pattern formation in a super cross-diffusion predator-prey system with Michaelis-Menten type predator harvesting are investigated. Stability of equilibrium points is first explored with or without super cross-diffusion. It is found that cross-diffusion could induce instability of equilibria. To further derive the conditions of Turing instability, the linear stability analysis is carried out. From theoretical analysis, note that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes by means of weakly nonlinear theory. Dynamical analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, the theoretical results are illustrated via numerical simulations. Copyright © 2018. Published by Elsevier Inc.

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

NASA Technical Reports Server (NTRS)

May, C. E.; Kautz, Harold E.

1978-01-01

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 X 10 to the minus 7th power squared cm per sec + or - 30 percent in 45 percent potassium hydroxide and 1.4 x 10 to the minus 7 squared cm per sec + or - 25 percent in 40 percent sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite size chambers. Details and discussion of the experimental method are also given.

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

NASA Technical Reports Server (NTRS)

May, C. E.; Kautz, H. E.

1978-01-01

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 x 10 to the -7th power sq cm/sec + or - 30% in 45% potassium hydroxide and 1.4 x 10 to the -7th power sq cm/sec + or - 25% in 40% sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half-cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite-size chambers. Details and discussion of the experimental method are also given.

Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory.

PubMed

Contini, D; Martelli, F; Zaccanti, G

1997-07-01

The diffusion approximation of the radiative transfer equation is a model used widely to describe photon migration in highly diffusing media and is an important matter in biological tissue optics. An analysis of the time-dependent diffusion equation together with its solutions for the slab geometry and for a semi-infinite diffusing medium are reported. These solutions, presented for both the time-dependent and the continuous wave source, account for the refractive index mismatch between the turbid medium and the surrounding medium. The results have been compared with those obtained when different boundary conditions were assumed. The comparison has shown that the effect of the refractive index mismatch cannot be disregarded. This effect is particularly important for the transmittance. The discussion of results also provides an analysis of the role of the absorption coefficient in the expression of the diffusion coefficient.

Nonparametric estimates of drift and diffusion profiles via Fokker-Planck algebra.

PubMed

Lund, Steven P; Hubbard, Joseph B; Halter, Michael

2014-11-06

Diffusion processes superimposed upon deterministic motion play a key role in understanding and controlling the transport of matter, energy, momentum, and even information in physics, chemistry, material science, biology, and communications technology. Given functions defining these random and deterministic components, the Fokker-Planck (FP) equation is often used to model these diffusive systems. Many methods exist for estimating the drift and diffusion profiles from one or more identifiable diffusive trajectories; however, when many identical entities diffuse simultaneously, it may not be possible to identify individual trajectories. Here we present a method capable of simultaneously providing nonparametric estimates for both drift and diffusion profiles from evolving density profiles, requiring only the validity of Langevin/FP dynamics. This algebraic FP manipulation provides a flexible and robust framework for estimating stationary drift and diffusion coefficient profiles, is not based on fluctuation theory or solved diffusion equations, and may facilitate predictions for many experimental systems. We illustrate this approach on experimental data obtained from a model lipid bilayer system exhibiting free diffusion and electric field induced drift. The wide range over which this approach provides accurate estimates for drift and diffusion profiles is demonstrated through simulation.

Droplet swimmers in complex geometries: Autochemotaxis and trapping at pillars.

NASA Astrophysics Data System (ADS)

Maass, Corinna; Jin, Chenyu; Krueger, Carsten; Vajdi Hokmabad, Babak

Autochemotaxis is a key feature of communication between microorganisms, via their emission of a slowly diffusing chemoattractant or repellent. We present a well-controlled, tunable artificial model to study autochemotaxis in complex geometries, using microfluidic assays of self-propelling liquid crystal droplets in an aqueous surfactant solution. Droplets gain propulsion energy by micellar solubilisation, with filled micelles acting as a chemical repellent by diffusive phoretic gradient forces. We can tune the key parameters swimmer size, velocity and persistence length. If a swimming droplet approaches a wall, it will provide a boundary to both the hydrodynamic flow field and the spread of phoretic gradients, determining the interaction between swimmer and wall. Pillar arrays of variable sizes and shapes provide a convex wall interacting with the swimmer and in the case of attachment bending its trajectory and forcing it to revert to its own trail. We observe different behavior based on the interplay of wall curvature and negative auto-chemotaxis, i. e., no attachment for highly curved interfaces, stable trapping at large pillars, and a narrow transition region where negative autochemotaxis makes the swimmers detach after a single orbit. Work funded by the DFG SPP 1726 ''Microswimmers''.

A temporal model of cofilin regulation and the early peak of actin barbed ends in invasive tumor cells.

PubMed

Tania, Nessy; Prosk, Erin; Condeelis, John; Edelstein-Keshet, Leah

2011-04-20

Cofilin is an important regulator of actin polymerization, cell migration, and chemotaxis. Recent experimental data on mammary carcinoma cells reveal that stimulation by epidermal growth factor (EGF) generates a pool of active cofilin that results in a peak of actin filament barbed ends on the timescale of 1 min. Here, we present results of a mathematical model for the dynamics of cofilin and its transition between several pools in response to EGF stimulation. We describe the interactions of phospholipase C, membrane lipids (PIP(2)), and cofilin bound to PIP(2) and to F-actin, as well as diffusible cofilin in active G-actin-monomer-bound or phosphorylated states. We consider a simplified representation in which the thin cell edge (lamellipod) and the cell interior are represented by two compartments that are linked by diffusion. We demonstrate that a high basal level of active cofilin stored by binding to PIP(2), as well as the highly enriched local milieu of F-actin at the cell edge, is essential to capture the EGF-induced barbed-end amplification observed experimentally. Copyright © 2011 Biophysical Society. Published by Elsevier Inc. All rights reserved.

FROM THE HISTORY OF PHYSICS: Mysteries of diffusion and labyrinths of destiny

NASA Astrophysics Data System (ADS)

Bakunin, Oleg G.

2003-03-01

The role of prominent Soviet physicist B I Davydov in the development of our understanding of diffusion is briefly reviewed, with emphasis on the ideas he put forward in the 1930s: introducing additional partial derivatives into diffusion equations and extending diffusion concepts to phase space.

Some basic mathematical methods of diffusion theory. [emphasis on atmospheric applications

NASA Technical Reports Server (NTRS)

Giere, A. C.

1977-01-01

An introductory treatment of the fundamentals of diffusion theory is presented, starting with molecular diffusion and leading up to the statistical methods of turbulent diffusion. A multilayer diffusion model, designed to permit concentration and dosage calculations downwind of toxic clouds from rocket vehicles, is described. The concepts and equations of diffusion are developed on an elementary level, with emphasis on atmospheric applications.

Diffuse-Interface Capturing Methods for Compressible Two-Phase Flows

NASA Astrophysics Data System (ADS)

Saurel, Richard; Pantano, Carlos

2018-01-01

Simulation of compressible flows became a routine activity with the appearance of shock-/contact-capturing methods. These methods can determine all waves, particularly discontinuous ones. However, additional difficulties may appear in two-phase and multimaterial flows due to the abrupt variation of thermodynamic properties across the interfacial region, with discontinuous thermodynamical representations at the interfaces. To overcome this difficulty, researchers have developed augmented systems of governing equations to extend the capturing strategy. These extended systems, reviewed here, are termed diffuse-interface models, because they are designed to compute flow variables correctly in numerically diffused zones surrounding interfaces. In particular, they facilitate coupling the dynamics on both sides of the (diffuse) interfaces and tend to the proper pure fluid-governing equations far from the interfaces. This strategy has become efficient for contact interfaces separating fluids that are governed by different equations of state, in the presence or absence of capillary effects, and with phase change. More sophisticated materials than fluids (e.g., elastic-plastic materials) have been considered as well.

The Azospirillum brasilense Che1 chemotaxis pathway controls swimming velocity, which affects transient cell-to-cell clumping.

PubMed

Bible, Amber; Russell, Matthew H; Alexandre, Gladys

2012-07-01

The Che1 chemotaxis-like pathway of Azospirillum brasilense contributes to chemotaxis and aerotaxis, and it has also been found to contribute to regulating changes in cell surface adhesive properties that affect the propensity of cells to clump and to flocculate. The exact contribution of Che1 to the control of chemotaxis and flocculation in A. brasilense remains poorly understood. Here, we show that Che1 affects reversible cell-to-cell clumping, a cellular behavior in which motile cells transiently interact by adhering to one another at their nonflagellated poles before swimming apart. Clumping precedes and is required for flocculation, and both processes appear to be independently regulated. The phenotypes of a ΔaerC receptor mutant and of mutant strains lacking cheA1, cheY1, cheB1, or cheR1 (alone or in combination) or with che1 deleted show that Che1 directly mediates changes in the flagellar swimming velocity and that this behavior directly modulates the transient nature of clumping. Our results also suggest that an additional receptor(s) and signaling pathway(s) are implicated in mediating other Che1-independent changes in clumping identified in the present study. Transient clumping precedes the transition to stable clump formation, which involves the production of specific extracellular polysaccharides (EPS); however, production of these clumping-specific EPS is not directly controlled by Che1 activity. Che1-dependent clumping may antagonize motility and prevent chemotaxis, thereby maintaining cells in a metabolically favorable niche.

Computer-Aided Resolution of an Experimental Paradox in Bacterial Chemotaxis

PubMed Central

Abouhamad, Walid N.; Bray, Dennis; Schuster, Martin; Boesch, Kristin C.; Silversmith, Ruth E.; Bourret, Robert B.

1998-01-01

Escherichia coli responds to its environment by means of a network of intracellular reactions which process signals from membrane-bound receptors and relay them to the flagellar motors. Although characterization of the reactions in the chemotaxis signaling pathway is sufficiently complete to construct computer simulations that predict the phenotypes of mutant strains with a high degree of accuracy, two previous experimental investigations of the activity remaining upon genetic deletion of multiple signaling components yielded several contradictory results (M. P. Conley, A. J. Wolfe, D. F. Blair, and H. C. Berg, J. Bacteriol. 171:5190–5193, 1989; J. D. Liu and J. S. Parkinson, Proc. Natl. Acad. Sci. USA 86:8703–8707, 1989). For example, “building up” the pathway by adding back CheA and CheY to a gutted strain lacking chemotaxis genes resulted in counterclockwise flagellar rotation whereas “breaking down” the pathway by deleting chemotaxis genes except cheA and cheY resulted in alternating episodes of clockwise and counterclockwise flagellar rotation. Our computer simulation predicts that trace amounts of CheZ expressed in the gutted strain could account for this difference. We tested this explanation experimentally by constructing a mutant containing a new deletion of the che genes that cannot express CheZ and verified that the behavior of strains built up from the new deletion does in fact conform to both the phenotypes observed for breakdown strains and computer-generated predictions. Our findings consolidate the present view of the chemotaxis signaling pathway and highlight the utility of molecularly based computer models in the analysis of complex biochemical networks. PMID:9683468

Integration of the Second Messenger c-di-GMP into the Chemotactic Signaling Pathway

PubMed Central

Russell, Matthew H.; Bible, Amber N.; Fang, Xin; Gooding, Jessica R.; Campagna, Shawn R.; Gomelsky, Mark; Alexandre, Gladys

2013-01-01

ABSTRACT Elevated intracellular levels of the bacterial second messenger c-di-GMP are known to suppress motility and promote sessility. Bacterial chemotaxis guides motile cells in gradients of attractants and repellents over broad concentration ranges, thus allowing bacteria to quickly adapt to changes in their surroundings. Here, we describe a chemotaxis receptor that enhances, as opposed to suppresses, motility in response to temporary increases in intracellular c-di-GMP. Azospirillum brasilense’s preferred metabolism is adapted to microaerophily, and these motile cells quickly navigate to zones of low oxygen concentration by aerotaxis. We observed that changes in oxygen concentration result in rapid changes in intracellular c-di-GMP levels. The aerotaxis and chemotaxis receptor, Tlp1, binds c-di-GMP via its C-terminal PilZ domain and promotes persistent motility by increasing swimming velocity and decreasing swimming reversal frequency, which helps A. brasilense reach low-oxygen zones. If c-di-GMP levels remain high for extended periods, A. brasilense forms nonmotile clumps or biofilms on abiotic surfaces. These results suggest that association of increased c-di-GMP levels with sessility is correct on a long-term scale, while in the short-term c-di-GMP may actually promote, as opposed to suppress, motility. Our data suggest that sensing c-di-GMP by Tlp1 functions similar to methylation-based adaptation. Numerous chemotaxis receptors contain C-terminal PilZ domains or other sensory domains, suggesting that intracellular c-di-GMP as well as additional stimuli can be used to modulate adaptation of bacterial chemotaxis receptors. PMID:23512960

Systemic Adenosine Triphosphate Impairs Neutrophil Chemotaxis and Host Defense in Sepsis.

PubMed

Li, Xiaoou; Kondo, Yutaka; Bao, Yi; Staudenmaier, Laura; Lee, Albert; Zhang, Jingping; Ledderose, Carola; Junger, Wolfgang G

2017-01-01

Sepsis remains an unresolved clinical problem. Therapeutic strategies focusing on inhibition of neutrophils (polymorphonuclear neutrophils) have failed, which indicates that a more detailed understanding of the underlying pathophysiology of sepsis is required. Polymorphonuclear neutrophil activation and chemotaxis require cellular adenosine triphosphate release via pannexin-1 channels that fuel autocrine feedback via purinergic receptors. In the current study, we examined the roles of endogenous and systemic adenosine triphosphate on polymorphonuclear neutrophil activation and host defense in sepsis. Prospective randomized animal investigation and in vitro studies. Preclinical academic research laboratory. Wild-type C57BL/6 mice, pannexin-1 knockout mice, and healthy human subjects used to obtain polymorphonuclear neutrophils for in vitro studies. Wild-type and pannexin-1 knockout mice were treated with suramin or apyrase to block the endogenous or systemic effects of adenosine triphosphate. Mice were subjected to cecal ligation and puncture and polymorphonuclear neutrophil activation (CD11b integrin expression), organ (liver) injury (plasma aspartate aminotransferase), bacterial spread, and survival were monitored. Human polymorphonuclear neutrophils were used to study the effect of systemic adenosine triphosphate and apyrase on chemotaxis. Inhibiting endogenous adenosine triphosphate reduced polymorphonuclear neutrophil activation and organ injury, but increased the spread of bacteria and mortality in sepsis. By contrast, removal of systemic adenosine triphosphate improved bacterial clearance and survival in sepsis by improving polymorphonuclear neutrophil chemotaxis. Systemic adenosine triphosphate impairs polymorphonuclear neutrophil functions by disrupting the endogenous purinergic signaling mechanisms that regulate cell activation and chemotaxis. Removal of systemic adenosine triphosphate improves polymorphonuclear neutrophil function and host defenses, making this a promising new treatment strategy for sepsis.

Evolutionary genomics suggests that CheV is an additional adaptor for accommodating specific chemoreceptors within the chemotaxis signaling complex

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ortega, Davi R.; Zhulin, Igor B.; Punta, Marco

Escherichia coli and Salmonella enterica are models for many experiments in molecular biology including chemotaxis, and most of the results obtained with one organism have been generalized to another. While most components of the chemotaxis pathway are strongly conserved between the two species, Salmonella genomes contain some chemoreceptors and an additional protein, CheV, that are not found in E. coli. The role of CheV was examined in distantly related species Bacillus subtilis and Helicobacter pylori, but its role in bacterial chemotaxis is still not well understood. We tested a hypothesis that in enterobacteria CheV functions as an additional adaptor linkingmore » the CheA kinase to certain types of chemoreceptors that cannot be effectively accommodated by the universal adaptor CheW. Phylogenetic profiling, genomic context and comparative protein sequence analyses suggested that CheV interacts with specific domains of CheA and chemoreceptors from an orthologous group exemplified by the Salmonella McpC protein. Structural consideration of the conservation patterns suggests that CheV and CheW share the same binding spot on the chemoreceptor structure, but have some affinity bias towards chemoreceptors from different orthologous groups. Finally, published experimental results and data newly obtained via comparative genomics support the idea that CheV functions as a "phosphate sink" possibly to off-set the over-stimulation of the kinase by certain types of chemoreceptors. Altogether, our results strongly suggest that CheV is an additional adaptor for accommodating specific chemoreceptors within the chemotaxis signaling complex.« less

The Azospirillum brasilense Che1 Chemotaxis Pathway Controls Swimming Velocity, Which Affects Transient Cell-to-Cell Clumping

PubMed Central

Bible, Amber; Russell, Matthew H.

2012-01-01

The Che1 chemotaxis-like pathway of Azospirillum brasilense contributes to chemotaxis and aerotaxis, and it has also been found to contribute to regulating changes in cell surface adhesive properties that affect the propensity of cells to clump and to flocculate. The exact contribution of Che1 to the control of chemotaxis and flocculation in A. brasilense remains poorly understood. Here, we show that Che1 affects reversible cell-to-cell clumping, a cellular behavior in which motile cells transiently interact by adhering to one another at their nonflagellated poles before swimming apart. Clumping precedes and is required for flocculation, and both processes appear to be independently regulated. The phenotypes of a ΔaerC receptor mutant and of mutant strains lacking cheA1, cheY1, cheB1, or cheR1 (alone or in combination) or with che1 deleted show that Che1 directly mediates changes in the flagellar swimming velocity and that this behavior directly modulates the transient nature of clumping. Our results also suggest that an additional receptor(s) and signaling pathway(s) are implicated in mediating other Che1-independent changes in clumping identified in the present study. Transient clumping precedes the transition to stable clump formation, which involves the production of specific extracellular polysaccharides (EPS); however, production of these clumping-specific EPS is not directly controlled by Che1 activity. Che1-dependent clumping may antagonize motility and prevent chemotaxis, thereby maintaining cells in a metabolically favorable niche. PMID:22522896

Assessing the chemotaxis behavior of Physarum polycephalum to a range of simple volatile organic chemicals.

PubMed

de Lacy Costello, Ben P J; Adamatzky, Andrew I

2013-09-01

The chemotaxis behavior of the plasmodial stage of the true slime mold Physarum Polycephalum was assessed when given a binary choice between two volatile organic chemicals (VOCs) placed in its environment. All possible binary combinations were tested between 19 separate VOCs selected due to their prevalence and biological activity in common plant and insect species. The slime mold exhibited positive chemotaxis toward a number of VOCs with the following order of preference:   Farnesene > β-myrcene > tridecane > limonene > p-cymene > 3-octanone > β-pinene > m-cresol > benzylacetate > cis-3-hexenylacetate. For the remaining compounds, no positive chemotaxis was observed in any of the experiments, and for most compounds there was an inhibitory effect on the growth of the slime mold. By assessing this lack of growth or failure to propagate, it was possible to produce a list of compounds ranked in terms of their inhibitory effect: nonanal > benzaldehyde > methylbenzoate > linalool > methyl-p-benzoquinone > eugenol > benzyl alcohol > geraniol > 2-phenylethanol. This analysis shows a distinct preference of the slime mold for non-oxygenated terpene and terpene-like compounds (farnesene, β-myrcene, limonene, p-cymene and β-pinene). In contrast, terpene-based alcohols such as geraniol and linalool were found to have a strong inhibitory effect on the slime mold. Both the aldehydes utilized in this study had the strongest inhibitory effect on the slime mold of all the 19 VOCs tested. Interestingly, 3-octanone, which has a strong association with a "fungal odor," was the only compound with an oxygenated functionality where Physarum Polycephalum exhibits distinct positive chemotaxis.

Assessing the chemotaxis behavior of Physarum polycephalum to a range of simple volatile organic chemicals

PubMed Central

de Lacy Costello, Ben P.J.; Adamatzky, Andrew I.

2013-01-01

The chemotaxis behavior of the plasmodial stage of the true slime mold Physarum Polycephalum was assessed when given a binary choice between two volatile organic chemicals (VOCs) placed in its environment. All possible binary combinations were tested between 19 separate VOCs selected due to their prevalence and biological activity in common plant and insect species. The slime mold exhibited positive chemotaxis toward a number of VOCs with the following order of preference:   Farnesene > β-myrcene > tridecane > limonene > p-cymene > 3-octanone > β-pinene > m-cresol > benzylacetate > cis-3-hexenylacetate. For the remaining compounds, no positive chemotaxis was observed in any of the experiments, and for most compounds there was an inhibitory effect on the growth of the slime mold. By assessing this lack of growth or failure to propagate, it was possible to produce a list of compounds ranked in terms of their inhibitory effect: nonanal > benzaldehyde > methylbenzoate > linalool > methyl-p-benzoquinone > eugenol > benzyl alcohol > geraniol > 2-phenylethanol. This analysis shows a distinct preference of the slime mold for non-oxygenated terpene and terpene-like compounds (farnesene, β-myrcene, limonene, p-cymene and β-pinene). In contrast, terpene-based alcohols such as geraniol and linalool were found to have a strong inhibitory effect on the slime mold. Both the aldehydes utilized in this study had the strongest inhibitory effect on the slime mold of all the 19 VOCs tested. Interestingly, 3-octanone, which has a strong association with a “fungal odor,” was the only compound with an oxygenated functionality where Physarum Polycephalum exhibits distinct positive chemotaxis. PMID:24265848

Evolutionary genomics suggests that CheV is an additional adaptor for accommodating specific chemoreceptors within the chemotaxis signaling complex

DOE PAGES

Ortega, Davi R.; Zhulin, Igor B.; Punta, Marco

2016-02-04

Escherichia coli and Salmonella enterica are models for many experiments in molecular biology including chemotaxis, and most of the results obtained with one organism have been generalized to another. While most components of the chemotaxis pathway are strongly conserved between the two species, Salmonella genomes contain some chemoreceptors and an additional protein, CheV, that are not found in E. coli. The role of CheV was examined in distantly related species Bacillus subtilis and Helicobacter pylori, but its role in bacterial chemotaxis is still not well understood. We tested a hypothesis that in enterobacteria CheV functions as an additional adaptor linkingmore » the CheA kinase to certain types of chemoreceptors that cannot be effectively accommodated by the universal adaptor CheW. Phylogenetic profiling, genomic context and comparative protein sequence analyses suggested that CheV interacts with specific domains of CheA and chemoreceptors from an orthologous group exemplified by the Salmonella McpC protein. Structural consideration of the conservation patterns suggests that CheV and CheW share the same binding spot on the chemoreceptor structure, but have some affinity bias towards chemoreceptors from different orthologous groups. Finally, published experimental results and data newly obtained via comparative genomics support the idea that CheV functions as a "phosphate sink" possibly to off-set the over-stimulation of the kinase by certain types of chemoreceptors. Altogether, our results strongly suggest that CheV is an additional adaptor for accommodating specific chemoreceptors within the chemotaxis signaling complex.« less

A novel finite volume discretization method for advection-diffusion systems on stretched meshes

NASA Astrophysics Data System (ADS)

Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.

2018-06-01

This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.

Numerical simulation of double‐diffusive finger convection

USGS Publications Warehouse

Hughes, Joseph D.; Sanford, Ward E.; Vacher, H. Leonard

2005-01-01

A hybrid finite element, integrated finite difference numerical model is developed for the simulation of double‐diffusive and multicomponent flow in two and three dimensions. The model is based on a multidimensional, density‐dependent, saturated‐unsaturated transport model (SUTRA), which uses one governing equation for fluid flow and another for solute transport. The solute‐transport equation is applied sequentially to each simulated species. Density coupling of the flow and solute‐transport equations is accounted for and handled using a sequential implicit Picard iterative scheme. High‐resolution data from a double‐diffusive Hele‐Shaw experiment, initially in a density‐stable configuration, is used to verify the numerical model. The temporal and spatial evolution of simulated double‐diffusive convection is in good agreement with experimental results. Numerical results are very sensitive to discretization and correspond closest to experimental results when element sizes adequately define the spatial resolution of observed fingering. Numerical results also indicate that differences in the molecular diffusivity of sodium chloride and the dye used to visualize experimental sodium chloride concentrations are significant and cause inaccurate mapping of sodium chloride concentrations by the dye, especially at late times. As a result of reduced diffusion, simulated dye fingers are better defined than simulated sodium chloride fingers and exhibit more vertical mass transfer.

New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis.

PubMed

Ingo, Carson; Magin, Richard L; Parrish, Todd B

2014-11-01

Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag-Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.

Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.

PubMed

Henry, B I; Langlands, T A M; Wearne, S L

2006-09-01

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term. Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term. We have also developed further extensions of the CTRW model to include more general reaction dynamics.

Anomalous diffusion and scaling in coupled stochastic processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bel, Golan; Nemenman, Ilya

2009-01-01

Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin processes with the friction coefficient depending on the state of a similar, unobserved, process. Integrating out the latter, we derive the Pocker-Planck the friction coefficient of the first depends on the state of the second. Integrating out the latter, we derive the Focker-Planck equation for the probability distribution of the former. This has the fonn of diffusion equation with time-dependent diffusion coefficient, resulting in an anomalous diffusion. The diffusion exponent can not be predicted using a simple scaling argument, and anomalous scaling appears as well. Themore » diffusion exponent of the Weiss-Havlin comb model is derived as a special case, and the same exponent holds even for weakly coupled processes. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems with unobserved dynamical degrees of freedom by means of standandard, diffusive Langevin descritpion.« less

A low diffusive Lagrange-remap scheme for the simulation of violent air-water free-surface flows

NASA Astrophysics Data System (ADS)

Bernard-Champmartin, Aude; De Vuyst, Florian

2014-10-01

In 2002, Després and Lagoutière [17] proposed a low-diffusive advection scheme for pure transport equation problems, which is particularly accurate for step-shaped solutions, and thus suited for interface tracking procedure by a color function. This has been extended by Kokh and Lagoutière [28] in the context of compressible multifluid flows using a five-equation model. In this paper, we explore a simplified variant approach for gas-liquid three-equation models. The Eulerian numerical scheme has two ingredients: a robust remapped Lagrange solver for the solution of the volume-averaged equations, and a low diffusive compressive scheme for the advection of the gas mass fraction. Numerical experiments show the performance of the computational approach on various flow reference problems: dam break, sloshing of a tank filled with water, water-water impact and finally a case of Rayleigh-Taylor instability. One of the advantages of the present interface capturing solver is its natural implementation on parallel processors or computers.

A computer program for the simulation of heat and moisture flow in soils

NASA Technical Reports Server (NTRS)

Camillo, P.; Schmugge, T. J.

1981-01-01

A computer program that simulates the flow of heat and moisture in soils is described. The space-time dependence of temperature and moisture content is described by a set of diffusion-type partial differential equations. The simulator uses a predictor/corrector to numerically integrate them, giving wetness and temperature profiles as a function of time. The simulator was used to generate solutions to diffusion-type partial differential equations for which analytical solutions are known. These equations include both constant and variable diffusivities, and both flux and constant concentration boundary conditions. In all cases, the simulated and analytic solutions agreed to within the error bounds which were imposed on the integrator. Simulations of heat and moisture flow under actual field conditions were also performed. Ground truth data were used for the boundary conditions and soil transport properties. The qualitative agreement between simulated and measured profiles is an indication that the model equations are reasonably accurate representations of the physical processes involved.

Automated Chemotactic Sorting and Single-cell Cultivation of Microbes using Droplet Microfluidics

NASA Astrophysics Data System (ADS)

Dong, Libing; Chen, Dong-Wei; Liu, Shuang-Jiang; Du, Wenbin

2016-04-01

We report a microfluidic device for automated sorting and cultivation of chemotactic microbes from pure cultures or mixtures. The device consists of two parts: in the first part, a concentration gradient of the chemoeffector was built across the channel for inducing chemotaxis of motile cells; in the second part, chemotactic cells from the sample were separated, and mixed with culture media to form nanoliter droplets for encapsulation, cultivation, enumeration, and recovery of single cells. Chemotactic responses were assessed by imaging and statistical analysis of droplets based on Poisson distribution. An automated procedure was developed for rapid enumeration of droplets with cell growth, following with scale-up cultivation on agar plates. The performance of the device was evaluated by the chemotaxis assays of Escherichia coli (E. coli) RP437 and E. coli RP1616. Moreover, enrichment and isolation of non-labelled Comamonas testosteroni CNB-1 from its 1:10 mixture with E. coli RP437 was demonstrated. The enrichment factor reached 36.7 for CNB-1, based on its distinctive chemotaxis toward 4-hydroxybenzoic acid. We believe that this device can be widely used in chemotaxis studies without necessarily relying on fluorescent labelling, and isolation of functional microbial species from various environments.

Automated Chemotactic Sorting and Single-cell Cultivation of Microbes using Droplet Microfluidics.

PubMed

Dong, Libing; Chen, Dong-Wei; Liu, Shuang-Jiang; Du, Wenbin

2016-04-14

We report a microfluidic device for automated sorting and cultivation of chemotactic microbes from pure cultures or mixtures. The device consists of two parts: in the first part, a concentration gradient of the chemoeffector was built across the channel for inducing chemotaxis of motile cells; in the second part, chemotactic cells from the sample were separated, and mixed with culture media to form nanoliter droplets for encapsulation, cultivation, enumeration, and recovery of single cells. Chemotactic responses were assessed by imaging and statistical analysis of droplets based on Poisson distribution. An automated procedure was developed for rapid enumeration of droplets with cell growth, following with scale-up cultivation on agar plates. The performance of the device was evaluated by the chemotaxis assays of Escherichia coli (E. coli) RP437 and E. coli RP1616. Moreover, enrichment and isolation of non-labelled Comamonas testosteroni CNB-1 from its 1:10 mixture with E. coli RP437 was demonstrated. The enrichment factor reached 36.7 for CNB-1, based on its distinctive chemotaxis toward 4-hydroxybenzoic acid. We believe that this device can be widely used in chemotaxis studies without necessarily relying on fluorescent labelling, and isolation of functional microbial species from various environments.

Effect of a 2.45-GHz radiofrequency electromagnetic field on neutrophil chemotaxis and phagocytosis in differentiated human HL-60 cells.

PubMed

Koyama, Shin; Narita, Eijiro; Suzuki, Yoshihisa; Taki, Masao; Shinohara, Naoki; Miyakoshi, Junji

2015-01-01

The potential public health risks of radiofrequency (RF) fields have been discussed at length, especially with the use of mobile phones spreading extensively throughout the world. In order to investigate the properties of RF fields, we examined the effect of 2.45-GHz RF fields at the specific absorption rate (SAR) of 2 and 10 W/kg for 4 and 24 h on neutrophil chemotaxis and phagocytosis in differentiated human HL-60 cells. Neutrophil chemotaxis was not affected by RF-field exposure, and subsequent phagocytosis was not affected either compared with that under sham exposure conditions. These studies demonstrated an initial immune response in the human body exposed to 2.45-GHz RF fields at the SAR of 2 W/kg, which is the maximum value recommended by the International Commission for Non-Ionizing Radiation Protection (ICNIRP) guidelines. The results of our experiments for RF-field exposure at an SAR under 10 W/kg showed very little or no effects on either chemotaxis or phagocytosis in neutrophil-like human HL-60 cells. © The Author 2014. Published by Oxford University Press on behalf of The Japan Radiation Research Society and Japanese Society for Radiation Oncology.

Chemotaxis of C. elegans in 3D media: a model for navigation of undulatory microswimmers

NASA Astrophysics Data System (ADS)

Patel, Amar; Bilbao, Alejandro; Rahman, Mizanur; Vanapalli, Siva; Blawzdziewicz, Jerzy

2017-11-01

While the natural environment of C. elegans consists of complex 3D media (e.g., decomposing organic matter and water), most studies of chemotactic behavior of this nematode are limited to 2D. We present a 3D chemotaxis model that combines a realistic geometrical representation of body movements associated with 3D maneuvers, an analysis of mechanical interactions of the nematode body with the surrounding medium to determine nematode trajectories, and a simple memory-function description of chemosensory apparatus that controls the frequency, magnitude, and timing of turning maneuvers. We show that two main chemotaxis strategies of C. elegans moving in 2D, i.e., the biased random walk and gradual turn, are effective also in 3D, provided that 2D turns are supplemented by the roll maneuvers that enable 3D reorientation. Optimal choices of chemosensing and gait-control parameters are discussed; we show that the nematode can maintain efficient chemotaxis in burrowing and swimming by adjusting the undulation frequency alone, without changing the chemotactic component of the body control. Understanding how C. elegans efficiently navigates in 3D media may help in developing self-navigating artificial microswimmers. Supported by NSF Grant No. CBET 1603627.

Impact of motility and chemotaxis features of the rhizobacterium Pseudomonas chlororaphis PCL1606 on its biocontrol of avocado white root rot.

PubMed

Polonio, Álvaro; Vida, Carmen; de Vicente, Antonio; Cazorla, Francisco M

2017-06-01

The biocontrol rhizobacterium Pseudomonas chlororaphis PCL1606 has the ability to protect avocado plants against white root rot produced by the phytopathogenic fungus Rosellinia necatrix. Moreover, PCL1606 displayed direct interactions with avocado roots and the pathogenic fungus. Thus, nonmotile (flgK mutant) and non-chemotactic (cheA mutant) derivatives of PCL1606 were constructed to emphasize the importance of motility and chemotaxis in the biological behaviour of PCL1606 during the biocontrol interaction. Plate chemotaxis assay showed that PCL1606 was attracted to the single compounds tested, such as glucose, glutamate, succinate, aspartate and malate, but no chemotaxis was observed to avocado or R. necatrix exudates. Using the more sensitive capillary assay, it was reported that smaller concentrations (1 mM) of single compounds elicited high chemotactic responses, and strong attraction was confirmed to avocado and R. necatrix exudates. Finally, biocontrol experiments revealed that the cheA and fglK derivative mutants reduced root protection against R. necatrix, suggesting an important role for these biological traits in biocontrol by P. chlororaphis PCL1606. [Int Microbiol 20(2):94-104 (2017)]. Copyright© by the Spanish Society for Microbiology and Institute for Catalan Studies.

Onset of nonlinearity in a stochastic model for auto-chemotactic advancing epithelia

NASA Astrophysics Data System (ADS)

Ben Amar, Martine; Bianca, Carlo

2016-09-01

We investigate the role of auto-chemotaxis in the growth and motility of an epithelium advancing on a solid substrate. In this process, cells create their own chemoattractant allowing communications among neighbours, thus leading to a signaling pathway. As known, chemotaxis provokes the onset of cellular density gradients and spatial inhomogeneities mostly at the front, a phenomenon able to predict some features revealed in in vitro experiments. A continuous model is proposed where the coupling between the cellular proliferation, the friction on the substrate and chemotaxis is investigated. According to our results, the friction and proliferation stabilize the front whereas auto-chemotaxis is a factor of destabilization. This antagonist role induces a fingering pattern with a selected wavenumber k0. However, in the planar front case, the translational invariance of the experimental set-up gives also a mode at k = 0 and the coupling between these two modes in the nonlinear regime is responsible for the onset of a Hopf-bifurcation. The time-dependent oscillations of patterns observed experimentally can be predicted simply in this continuous non-linear approach. Finally the effects of noise are also investigated below the instability threshold.

Extremal equilibria for reaction-diffusion equations in bounded domains and applications

NASA Astrophysics Data System (ADS)

Rodríguez-Bernal, Aníbal; Vidal-López, Alejandro

We show the existence of two special equilibria, the extremal ones, for a wide class of reaction-diffusion equations in bounded domains with several boundary conditions, including non-linear ones. They give bounds for the asymptotic dynamics and so for the attractor. Some results on the existence and/or uniqueness of positive solutions are also obtained. As a consequence, several well-known results on the existence and/or uniqueness of solutions for elliptic equations are revisited in a unified way obtaining, in addition, information on the dynamics of the associated parabolic problem. Finally, we ilustrate the use of the general results by applying them to the case of logistic equations. In fact, we obtain a detailed picture of the positive dynamics depending on the parameters appearing in the equation.

Determination of transport wind speed in the gaussian plume diffusion equation for low-lying point sources

NASA Astrophysics Data System (ADS)

Wang, I. T.

A general method for determining the effective transport wind speed, overlineu, in the Gaussian plume equation is discussed. Physical arguments are given for using the generalized overlineu instead of the often adopted release-level wind speed with the plume diffusion equation. Simple analytical expressions for overlineu applicable to low-level point releases and a wide range of atmospheric conditions are developed. A non-linear plume kinematic equation is derived using these expressions. Crosswind-integrated SF 6 concentration data from the 1983 PNL tracer experiment are used to evaluate the proposed analytical procedures along with the usual approach of using the release-level wind speed. Results of the evaluation are briefly discussed.

Reduced equations of motion for quantum systems driven by diffusive Markov processes.

PubMed

Sarovar, Mohan; Grace, Matthew D

2012-09-28

The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned Förster resonance transfer in Rydberg atoms with nonperturbative position fluctuations.

Grid adaption based on modified anisotropic diffusion equations formulated in the parametic domain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hagmeijer, R.

1994-11-01

A new grid-adaption algorithm for problems in computational fluid dynamics is presented. The basic equations are derived from a variational problem formulated in the parametric domain of the mapping that defines the existing grid. Modification of the basic equations provides desirable properties in boundary layers. The resulting modified anisotropic diffusion equations are solved for the computational coordinates as functions of the parametric coordinates and these functions are numerically inverted. Numerical examples show that the algorithm is robust, that shocks and boundary layers are well-resolved on the adapted grid, and that the flow solution becomes a globally smooth function of themore » computational coordinates.« less

A numerical study of the steady scalar convective diffusion equation for small viscosity

NASA Technical Reports Server (NTRS)

Giles, M. B.; Rose, M. E.

1983-01-01

A time-independent convection diffusion equation is studied by means of a compact finite difference scheme and numerical solutions are compared to the analytic inviscid solutions. The correct internal and external boundary layer behavior is observed, due to an inherent feature of the scheme which automatically produces upwind differencing in inviscid regions and the correct viscous behavior in viscous regions.

O the Derivation of the Schroedinger Equation from Stochastic Mechanics.

NASA Astrophysics Data System (ADS)

Wallstrom, Timothy Clarke

The thesis is divided into four largely independent chapters. The first three chapters treat mathematical problems in the theory of stochastic mechanics. The fourth chapter deals with stochastic mechanisms as a physical theory and shows that the Schrodinger equation cannot be derived from existing formulations of stochastic mechanics, as had previously been believed. Since the drift coefficients of stochastic mechanical diffusions are undefined on the nodes, or zeros of the density, an important problem has been to show that the sample paths stay away from the nodes. In Chapter 1, it is shown that for a smooth wavefunction, the closest approach to the nodes can be bounded solely in terms of the time -integrated energy. The ergodic properties of stochastic mechanical diffusions are greatly complicated by the tendency of the particles to avoid the nodes. In Chapter 2, it is shown that a sufficient condition for a stationary process to be ergodic is that there exist positive t and c such that for all x and y, p^{t} (x,y) > cp(y), and this result is applied to show that the set of spin-1over2 diffusions is uniformly ergodic. In stochastic mechanics, the Bopp-Haag-Dankel diffusions on IR^3times SO(3) are used to represent particles with spin. Nelson has conjectured that in the limit as the particle's moment of inertia I goes to zero, the projections of the Bopp -Haag-Dankel diffusions onto IR^3 converge to a Markovian limit process. This conjecture is proved for the spin-1over2 case in Chapter 3, and the limit process identified as the diffusion naturally associated with the solution to the regular Pauli equation. In Chapter 4 it is shown that the general solution of the stochastic Newton equation does not correspond to a solution of the Schrodinger equation, and that there are solutions to the Schrodinger equation which do not satisfy the Guerra-Morato Lagrangian variational principle. These observations are shown to apply equally to other existing formulations of stochastic mechanics, and it is argued that these difficulties represent fundamental inadequacies in the physical foundation of stochastic mechanics.

Nonlinear optical susceptibilities in the diffusion modified AlxGa1-xN/GaN single quantum well

NASA Astrophysics Data System (ADS)

Das, T.; Panda, S.; Panda, B. K.

2018-05-01

Under thermal treatment of the post growth AlGaN/GaN single quantum well, the diffusion of Al and Ga atoms across the interface is expected to form the diffusion modified quantum well with diffusion length as a quantitative parameter for diffusion. The modification of confining potential and position-dependent effective mass in the quantum well due to diffusion is calculated taking the Fick's law. The built-in electric field which arises from spontaneous and piezoelectric polarizations in the wurtzite structure is included in the effective mass equation. The electronic states are calculated from the effective mass equation using the finite difference method for several diffusion lengths. Since the effective well width decreases with increasing diffusion length, the energy levels increase with it. The intersubband energy spacing in the conduction band decreases with diffusion length due to built-in electric field and reduction of effective well width. The linear susceptibility for first-order and the nonlinear second-order and third-order susceptibilities are calculated using the compact density matrix approach taking only two levels. The calculated susceptibilities are red shifted with increase in diffusion lengths due to decrease in intersubband energy spacing.

The functional consequences of non-genetic diversity in cellular navigation

NASA Astrophysics Data System (ADS)

Emonet, Thierry; Waite, Adam J.; Frankel, Nicholas W.; Dufour, Yann; Johnston, Jessica F.

Substantial non-genetic diversity in complex behaviors, such as chemotaxis in E. coli, has been observed for decades, but the relevance of this diversity for the population is not well understood. Here, we use microfluidics to show that non-genetic diversity leads to significant structuring of the population in space and time, which confirms predictions made by our detailed mathematical model of chemotaxis. We then use genetic tools to show that altering the expression level of a single chemotaxis protein is sufficient to alter the distribution of swimming behaviors, which directly determines the performance of a population in a gradient of attractant, a result also predicted by our model. Supported by NIH 1R01GM106189, the James S McDonnell Foundation, and the Paul Allen foundation.

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2014-01-01

A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

Ordinary differential equation for local accumulation time.

PubMed

Berezhkovskii, Alexander M

2011-08-21

Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics

A non-local structural derivative model for characterization of ultraslow diffusion in dense colloids

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen

2018-03-01

Ultraslow diffusion has been observed in numerous complicated systems. Its mean squared displacement (MSD) is not a power law function of time, but instead a logarithmic function, and in some cases grows even more slowly than the logarithmic rate. The distributed-order fractional diffusion equation model simply does not work for the general ultraslow diffusion. Recent study has used the local structural derivative to describe ultraslow diffusion dynamics by using the inverse Mittag-Leffler function as the structural function, in which the MSD is a function of inverse Mittag-Leffler function. In this study, a new stretched logarithmic diffusion law and its underlying non-local structural derivative diffusion model are proposed to characterize the ultraslow diffusion in aging dense colloidal glass at both the short and long waiting times. It is observed that the aging dynamics of dense colloids is a class of the stretched logarithmic ultraslow diffusion processes. Compared with the power, the logarithmic, and the inverse Mittag-Leffler diffusion laws, the stretched logarithmic diffusion law has better precision in fitting the MSD of the colloidal particles at high densities. The corresponding non-local structural derivative diffusion equation manifests clear physical mechanism, and its structural function is equivalent to the first-order derivative of the MSD.

Influence of heat conducting substrates on explosive crystallization in thin layers

NASA Astrophysics Data System (ADS)

Schneider, Wilhelm

2017-09-01

Crystallization in a thin, initially amorphous layer is considered. The layer is in thermal contact with a substrate of very large dimensions. The energy equation of the layer contains source and sink terms. The source term is due to liberation of latent heat in the crystallization process, while the sink term is due to conduction of heat into the substrate. To determine the latter, the heat diffusion equation for the substrate is solved by applying Duhamel's integral. Thus, the energy equation of the layer becomes a heat diffusion equation with a time integral as an additional term. The latter term indicates that the heat loss due to the substrate depends on the history of the process. To complete the set of equations, the crystallization process is described by a rate equation for the degree of crystallization. The governing equations are then transformed to a moving co-ordinate system in order to analyze crystallization waves that propagate with invariant properties. Dual solutions are found by an asymptotic expansion for large activation energies of molecular diffusion. By introducing suitable variables, the results can be presented in a universal form that comprises the influence of all non-dimensional parameters that govern the process. Of particular interest for applications is the prediction of a critical heat loss parameter for the existence of crystallization waves with invariant properties.

Estimation of Knudsen diffusion coefficients from tracer experiments conducted with a binary gas system and a porous medium.

PubMed

Hibi, Yoshihiko; Kashihara, Ayumi

2018-03-01

A previous study has reported that Knudsen diffusion coefficients obtained by tracer experiments conducted with a binary gas system and a porous medium are consistently smaller than those obtained by permeability experiments conducted with a single-gas system and a porous medium. To date, however, that study is the only one in which tracer experiments have been conducted with a binary gas system. Therefore, to confirm this difference in Knudsen diffusion coefficients, we used a method we had developed previously to conduct tracer experiments with a binary carbon dioxide-nitrogen gas system and five porous media with permeability coefficients ranging from 10 -13 to 10 -11  m 2 . The results showed that the Knudsen diffusion coefficient of N 2 (D N2 ) (cm 2 /s) was related to the effective permeability coefficient k e (m 2 ) as D N2  = 7.39 × 10 7 k e 0.767 . Thus, the Knudsen diffusion coefficients of N 2 obtained by our tracer experiments were consistently 1/27 of those obtained by permeability experiments conducted with many porous media and air by other researchers. By using an inversion simulation to fit the advection-diffusion equation to the distribution of concentrations at observation points calculated by mathematically solving the equation, we confirmed that the method used to obtain the Knudsen diffusion coefficient in this study yielded accurate values. Moreover, because the Knudsen diffusion coefficient did not differ when columns with two different lengths, 900 and 1500 mm, were used, this column property did not influence the flow of gas in the column. The equation of the dusty gas model already includes obstruction factors for Knudsen diffusion and molecular diffusion, which relate to medium heterogeneity and tortuosity and depend only on the structure of the porous medium. Furthermore, there is no need to take account of any additional correction factor for molecular diffusion except the obstruction factor because molecular diffusion is only treated in a multicomponent gas system. Thus, molecular diffusion considers only the obstruction factor related to tortuosity. Therefore, we introduced a correction factor for a multicomponent gas system into the DGM equation, multiplying the Knudsen diffusion coefficient, which includes the obstruction factor related to tortuosity, by this correction factor. From the present experimental results, the value of this correction factor was 1/27, and it depended only on the structure of the gas system in the porous medium. Copyright © 2018 Elsevier B.V. All rights reserved.

Estimation of Knudsen diffusion coefficients from tracer experiments conducted with a binary gas system and a porous medium

NASA Astrophysics Data System (ADS)

Hibi, Yoshihiko; Kashihara, Ayumi

2018-03-01

A previous study has reported that Knudsen diffusion coefficients obtained by tracer experiments conducted with a binary gas system and a porous medium are consistently smaller than those obtained by permeability experiments conducted with a single-gas system and a porous medium. To date, however, that study is the only one in which tracer experiments have been conducted with a binary gas system. Therefore, to confirm this difference in Knudsen diffusion coefficients, we used a method we had developed previously to conduct tracer experiments with a binary carbon dioxide-nitrogen gas system and five porous media with permeability coefficients ranging from 10-13 to 10-11 m2. The results showed that the Knudsen diffusion coefficient of N2 (DN2) (cm2/s) was related to the effective permeability coefficient ke (m2) as DN2 = 7.39 × 107ke0.767. Thus, the Knudsen diffusion coefficients of N2 obtained by our tracer experiments were consistently 1/27 of those obtained by permeability experiments conducted with many porous media and air by other researchers. By using an inversion simulation to fit the advection-diffusion equation to the distribution of concentrations at observation points calculated by mathematically solving the equation, we confirmed that the method used to obtain the Knudsen diffusion coefficient in this study yielded accurate values. Moreover, because the Knudsen diffusion coefficient did not differ when columns with two different lengths, 900 and 1500 mm, were used, this column property did not influence the flow of gas in the column. The equation of the dusty gas model already includes obstruction factors for Knudsen diffusion and molecular diffusion, which relate to medium heterogeneity and tortuosity and depend only on the structure of the porous medium. Furthermore, there is no need to take account of any additional correction factor for molecular diffusion except the obstruction factor because molecular diffusion is only treated in a multicomponent gas system. Thus, molecular diffusion considers only the obstruction factor related to tortuosity. Therefore, we introduced a correction factor for a multicomponent gas system into the DGM equation, multiplying the Knudsen diffusion coefficient, which includes the obstruction factor related to tortuosity, by this correction factor. From the present experimental results, the value of this correction factor was 1/27, and it depended only on the structure of the gas system in the porous medium.

A stability analysis of the power-law steady state of marine size spectra.

PubMed

Datta, Samik; Delius, Gustav W; Law, Richard; Plank, Michael J

2011-10-01

This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth" equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints on the parameters. This provides new knowledge of the stability properties of the power-law steady state. It is shown analytically that the steady state of the McKendrick-von Foerster equation without the diffusion term is always unstable. Furthermore, numerical plots show that eigenvalue spectra of the McKendrick-von Foerster equation with diffusion give a good approximation to those of the jump-growth equation. The steady state is more likely to be stable with a low preferred predator:prey mass ratio, a large diet breadth and a high feeding efficiency. The effects of demographic stochasticity are also investigated and it is concluded that these are likely to be small in real systems.

The nature and role of advection in advection-diffusion equations used for modelling bed load transport

NASA Astrophysics Data System (ADS)

Ancey, Christophe; Bohorquez, Patricio; Heyman, Joris

2016-04-01

The advection-diffusion equation arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Stochastic models can also be used to derive this equation, with the significant advantage that they provide information on the statistical properties of particle activity. Stochastic models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. We develop an approach based on birth-death Markov processes, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received little attention. We show that particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

Subdiffusion in Membrane Permeation of Small Molecules.

PubMed

Chipot, Christophe; Comer, Jeffrey

2016-11-02

Within the solubility-diffusion model of passive membrane permeation of small molecules, translocation of the permeant across the biological membrane is traditionally assumed to obey the Smoluchowski diffusion equation, which is germane for classical diffusion on an inhomogeneous free-energy and diffusivity landscape. This equation, however, cannot accommodate subdiffusive regimes, which have long been recognized in lipid bilayer dynamics, notably in the lateral diffusion of individual lipids. Through extensive biased and unbiased molecular dynamics simulations, we show that one-dimensional translocation of methanol across a pure lipid membrane remains subdiffusive on timescales approaching typical permeation times. Analysis of permeant motion within the lipid bilayer reveals that, in the absence of a net force, the mean squared displacement depends on time as t 0.7 , in stark contrast with the conventional model, which assumes a strictly linear dependence. We further show that an alternate model using a fractional-derivative generalization of the Smoluchowski equation provides a rigorous framework for describing the motion of the permeant molecule on the pico- to nanosecond timescale. The observed subdiffusive behavior appears to emerge from a crossover between small-scale rattling of the permeant around its present position in the membrane and larger-scale displacements precipitated by the formation of transient voids.

Diffuse sorption modeling.

PubMed

Pivovarov, Sergey

2009-04-01

This work presents a simple solution for the diffuse double layer model, applicable to calculation of surface speciation as well as to simulation of ionic adsorption within the diffuse layer of solution in arbitrary salt media. Based on Poisson-Boltzmann equation, the Gaines-Thomas selectivity coefficient for uni-bivalent exchange on clay, K(GT)(Me(2+)/M(+))=(Q(Me)(0.5)/Q(M)){M(+)}/{Me(2+)}(0.5), (Q is the equivalent fraction of cation in the exchange capacity, and {M(+)} and {Me(2+)} are the ionic activities in solution) may be calculated as [surface charge, mueq/m(2)]/0.61. The obtained solution of the Poisson-Boltzmann equation was applied to calculation of ionic exchange on clays and to simulation of the surface charge of ferrihydrite in 0.01-6 M NaCl solutions. In addition, a new model of acid-base properties was developed. This model is based on assumption that the net proton charge is not located on the mathematical surface plane but diffusely distributed within the subsurface layer of the lattice. It is shown that the obtained solution of the Poisson-Boltzmann equation makes such calculations possible, and that this approach is more efficient than the original diffuse double layer model.

Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions

NASA Astrophysics Data System (ADS)

Elwakil, S. A.; El-Labany, S. K.; Zahran, M. A.; Sabry, R.

2004-04-01

The modified extended tanh-function method were applied to the general class of nonlinear diffusion-convection equations where the concentration-dependent diffusivity, D( u), was taken to be a constant while the concentration-dependent hydraulic conductivity, K( u) were taken to be in a power law. The obtained solutions include rational-type, triangular-type, singular-type, and solitary wave solutions. In fact, the profile of the obtained solitary wave solutions resemble the characteristics of a shock-wave like structure for an arbitrary m (where m>1 is the power of the nonlinear convection term).

Mathematical modeling of microbially induced crown corrosion in wastewater collection systems and laboratory investigation and modeling of sulfuric acid corrosion of concrete

NASA Astrophysics Data System (ADS)

Jahani, Fereidoun

In the model for microbially induced crown corrosion, the diffusion of sulfide inside the concrete pores, its biological conversion to sulfuric acid, and the corrosion of calcium carbonate aggregates are represented. The corrosion front is modeled as a moving boundary. The location of the interface between the corrosion layer and the concrete is determined as part of the solution to the model equations. This model consisted of a system of one dimensional reaction-diffusion equations coupled to an equation describing the movement of the corrosion front. The equations were solved numerically using finite element Galerkin approximation. The concentration profiles of sulfide in the air and the liquid phases, the pH as a function of concrete depth, and the position of the corrosion front. A new equation for the corrosion rate was also derived. A more specific model for the degradation of a concrete specimen exposed to a sulfuric acid solution was also studied. In this model, diffusion of hydrogen ions and their reaction with alkaline components of concrete were expressed using Fick's Law of diffusion. The model equations described the moving boundary, the dissolution rate of alkaline components in the concrete, volume increase of sulfuric acid solution over the concrete specimen, and the boundary conditions on the surface of the concrete. An apparatus was designed and experiments were performed to measure pH changes on the surface of concrete. The data were used to calculate the dissolution rate of the concrete and, with the model, to determine the diffusion rate of sulfuric acid in the corrosion layer and corrosion layer thickness. Electrochemical Impedance Spectroscopy (EIS) was used to study the corrosion rate of iron pins embedded in the concrete sample. The open circuit potential (OCP) determined the onset of corrosion on the surface of the pins. Visual observation of the corrosion layer thickness was in good agreement with the simulation results.

Particle Transport through Scattering Regions with Clear Layers and Inclusions

NASA Astrophysics Data System (ADS)

Bal, Guillaume

2002-08-01

This paper introduces generalized diffusion models for the transport of particles in scattering media with nonscattering inclusions. Classical diffusion is known as a good approximation of transport only in scattering media. Based on asymptotic expansions and the coupling of transport and diffusion models, generalized diffusion equations with nonlocal interface conditions are proposed which offer a computationally cheap, yet accurate, alternative to solving the full phase-space transport equations. The paper shows which computational model should be used depending on the size and shape of the nonscattering inclusions in the simplified setting of two space dimensions. An important application is the treatment of clear layers in near-infrared (NIR) spectroscopy, an imaging technique based on the propagation of NIR photons in human tissues.

Chemotaxis-defective mutants of the nematode Caenorhabditis elegans.

PubMed

Dusenbery, D B; Sheridan, R E; Russell, R L

1975-06-01

The technique of countercurrent separation has been used to isolate 17 independent chemotaxis-defective mutants of the nematode Caenorhabditis elegans. The mutants, selected to be relatively insensitive to the normally attractive salt NaCl, show varying degrees of residual sensitivity; some are actually weakly repelled by NaCl. The mutants are due to single gene defects, are autosomal and recessive, and identify at least five complementation groups.

The first boundary-value problem for a fractional diffusion-wave equation in a non-cylindrical domain

NASA Astrophysics Data System (ADS)

Pskhu, A. V.

2017-12-01

We solve the first boundary-value problem in a non-cylindrical domain for a diffusion-wave equation with the Dzhrbashyan- Nersesyan operator of fractional differentiation with respect to the time variable. We prove an existence and uniqueness theorem for this problem, and construct a representation of the solution. We show that a sufficient condition for unique solubility is the condition of Hölder smoothness for the lateral boundary of the domain. The corresponding results for equations with Riemann- Liouville and Caputo derivatives are particular cases of results obtained here.

Solution of the modified Helmholtz equation in a triangular domain and an application to diffusion-limited coalescence.

PubMed

ben-Avraham, D; Fokas, A S

2001-07-01

A new transform method for solving boundary value problems for linear and integrable nonlinear partial differential equations recently introduced in the literature is used here to obtain the solution of the modified Helmholtz equation q(xx)(x,y)+q(yy)(x,y)-4 beta(2)q(x,y)=0 in the triangular domain 0< or =x< or =L-y< or =L, with mixed boundary conditions. This solution is applied to the problem of diffusion-limited coalescence, A+A<==>A, in the segment (-L/2,L/2), with traps at the edges.

Singular solution of the Feller diffusion equation via a spectral decomposition.

PubMed

Gan, Xinjun; Waxman, David

2015-01-01

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

An improved model of fission gas atom transport in irradiated uranium dioxide

NASA Astrophysics Data System (ADS)

Shea, J. H.

2018-04-01

The hitherto standard approach to predicting fission gas release has been a pure diffusion gas atom transport model based upon Fick's law. An additional mechanism has subsequently been identified from experimental data at high burnup and has been summarised in an empirical model that is considered to embody a so-called fuel matrix 'saturation' phenomenon whereby the fuel matrix has become saturated with fission gas so that the continued addition of extra fission gas atoms results in their expulsion from the fuel matrix into the fuel rod plenum. The present paper proposes a different approach by constructing an enhanced fission gas transport law consisting of two components: 1) Fick's law and 2) a so-called drift term. The new transport law can be shown to be effectively identical in its predictions to the 'saturation' approach and is more readily physically justifiable. The method introduces a generalisation of the standard diffusion equation which is dubbed the Drift Diffusion Equation. According to the magnitude of a dimensionless Péclet number, P, the new equation can vary from pure diffusion to pure drift, which latter represents a collective motion of the fission gas atoms through the fuel matrix at a translational velocity. Comparison is made between the saturation and enhanced transport approaches. Because of its dependence on P, the Drift Diffusion Equation is shown to be more effective at managing the transition from one type of limiting transport phenomenon to the other. Thus it can adapt appropriately according to the reactor operation.

Singular solution of the Feller diffusion equation via a spectral decomposition

NASA Astrophysics Data System (ADS)

Gan, Xinjun; Waxman, David

2015-01-01

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

THE EFFECT OF DIFFUSION ON THE PARTICLE SPECTRA IN PULSAR WIND NEBULAE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vorster, M. J.; Moraal, H., E-mail: 12792322@nwu.ac.za

2013-03-01

A possible way to calculate particle spectra as a function of position in pulsar wind nebulae is to solve a Fokker-Planck transport equation. This paper presents numerical solutions to the transport equation with the processes of convection, diffusion, adiabatic losses, and synchrotron radiation included. In the first part of the paper, the steady-state version of the transport equation is solved as a function of position and energy. This is done to distinguish the various effects of the aforementioned processes on the solutions to the transport equation. The second part of the paper deals with a time-dependent solution to the transportmore » equation, specifically taking into account the effect of a moving outer boundary. The paper highlights the fact that diffusion can play a significant role in reducing the amount of synchrotron losses, leading to a modification in the expected particle spectra. These modified spectra can explain the change in the photon index of the synchrotron emission as a function of position. The solutions presented in this paper are not limited to pulsar wind nebulae, but can be applied to any similar central source system, e.g., globular clusters.« less

Fractional calculus phenomenology in two-dimensional plasma models

NASA Astrophysics Data System (ADS)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

Modeling of adsorption dynamics at air-liquid interfaces using statistical rate theory (SRT).

PubMed

Biswas, M E; Chatzis, I; Ioannidis, M A; Chen, P

2005-06-01

A large number of natural and technological processes involve mass transfer at interfaces. Interfacial properties, e.g., adsorption, play a key role in such applications as wetting, foaming, coating, and stabilizing of liquid films. The mechanistic understanding of surface adsorption often assumes molecular diffusion in the bulk liquid and subsequent adsorption at the interface. Diffusion is well described by Fick's law, while adsorption kinetics is less understood and is commonly described using Langmuir-type empirical equations. In this study, a general theoretical model for adsorption kinetics/dynamics at the air-liquid interface is developed; in particular, a new kinetic equation based on the statistical rate theory (SRT) is derived. Similar to many reported kinetic equations, the new kinetic equation also involves a number of parameters, but all these parameters are theoretically obtainable. In the present model, the adsorption dynamics is governed by three dimensionless numbers: psi (ratio of adsorption thickness to diffusion length), lambda (ratio of square of the adsorption thickness to the ratio of adsorption to desorption rate constant), and Nk (ratio of the adsorption rate constant to the product of diffusion coefficient and bulk concentration). Numerical simulations for surface adsorption using the proposed model are carried out and verified. The difference in surface adsorption between the general and the diffusion controlled model is estimated and presented graphically as contours of deviation. Three different regions of adsorption dynamics are identified: diffusion controlled (deviation less than 10%), mixed diffusion and transfer controlled (deviation in the range of 10-90%), and transfer controlled (deviation more than 90%). These three different modes predominantly depend on the value of Nk. The corresponding ranges of Nk for the studied values of psi (10(-2)

Generalized Fourier analyses of the advection-diffusion equation - Part I: one-dimensional domains

NASA Astrophysics Data System (ADS)

Christon, Mark A.; Martinez, Mario J.; Voth, Thomas E.

2004-07-01

This paper presents a detailed multi-methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. The errors are reported in terms of non-dimensional phase and group speed, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy. It is demonstrated that Fourier analysis provides an automatic process for separating the discrete advective operator into its symmetric and skew-symmetric components and characterizing the spectral behaviour of each operator. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. It is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, the streamline upwind control-volume method, produce both an artificial diffusivity and a concomitant phase speed adjustment in addition to the usual semi-discrete artifacts observed in the phase speed, group speed and diffusivity. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behaviour in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behaviour. In Part II of this paper, we consider two-dimensional semi-discretizations of the advection-diffusion equation and also assess the affects of grid-induced anisotropy observed in the non-dimensional phase speed, and the discrete and artificial diffusivities. Although this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common analysis framework. Published in 2004 by John Wiley & Sons, Ltd.

Ecology and Physics of Bacterial Chemotaxis in the Ocean

PubMed Central

Seymour, Justin R.

2012-01-01

Summary: Intuitively, it may seem that from the perspective of an individual bacterium the ocean is a vast, dilute, and largely homogeneous environment. Microbial oceanographers have typically considered the ocean from this point of view. In reality, marine bacteria inhabit a chemical seascape that is highly heterogeneous down to the microscale, owing to ubiquitous nutrient patches, plumes, and gradients. Exudation and excretion of dissolved matter by larger organisms, lysis events, particles, animal surfaces, and fluxes from the sediment-water interface all contribute to create strong and pervasive heterogeneity, where chemotaxis may provide a significant fitness advantage to bacteria. The dynamic nature of the ocean imposes strong selective pressures on bacterial foraging strategies, and many marine bacteria indeed display adaptations that characterize their chemotactic motility as “high performance” compared to that of enteric model organisms. Fast swimming speeds, strongly directional responses, and effective turning and steering strategies ensure that marine bacteria can successfully use chemotaxis to very rapidly respond to chemical gradients in the ocean. These fast responses are advantageous in a broad range of ecological processes, including attaching to particles, exploiting particle plumes, retaining position close to phytoplankton cells, colonizing host animals, and hovering at a preferred height above the sediment-water interface. At larger scales, these responses can impact ocean biogeochemistry by increasing the rates of chemical transformation, influencing the flux of sinking material, and potentially altering the balance of biomass incorporation versus respiration. This review highlights the physical and ecological processes underpinning bacterial motility and chemotaxis in the ocean, describes the current state of knowledge of chemotaxis in marine bacteria, and summarizes our understanding of how these microscale dynamics scale up to affect ecosystem-scale processes in the sea. PMID:23204367

Tracking neutrophil intraluminal crawling, transendothelial migration and chemotaxis in tissue by intravital video microscopy.

PubMed

Xu, Najia; Lei, Xi; Liu, Lixin

2011-09-24

The recruitment of circulating leukocytes from blood stream to the inflamed tissue is a crucial and complex process of inflammation(1,2). In the postcapillary venules of inflamed tissue, leukocytes initially tether and roll on the luminal surface of venular wall. Rolling leukocytes arrest on endothelium and undergo firm adhesion in response to chemokine or other chemoattractants on the venular surface. Many adherent leukocytes relocate from the initial site of adhesion to the junctional extravasation site in endothelium, a process termed intraluminal crawling(3). Following crawling, leukocytes move across endothelium (transmigration) and migrate in extravascular tissue toward the source of chemoattractant (chemotaxis)(4). Intravital microscopy is a powerful tool for visualizing leukocyte-endothelial cell interactions in vivo and revealing cellular and molecular mechanisms of leukocyte recruitment(2,5). In this report, we provide a comprehensive description of using brightfield intravital microscopy to visualize and determine the detailed processes of neutrophil recruitment in mouse cremaster muscle in response to the gradient of a neutrophil chemoattractant. To induce neutrophil recruitment, a small piece of agarose gel (~1-mm(3) size) containing neutrophil chemoattractant MIP-2 (CXCL2, a CXC chemokine) or WKYMVm (Trp-Lys-Tyr-Val-D-Met, a synthetic analog of bacterial peptide) is placed on the muscle tissue adjacent to the observed postcapillary venule. With time-lapsed video photography and computer software ImageJ, neutrophil intraluminal crawling on endothelium, neutrophil transendothelial migration and the migration and chemotaxis in tissue are visualized and tracked. This protocol allows reliable and quantitative analysis of many neutrophil recruitment parameters such as intraluminal crawling velocity, transmigration time, detachment time, migration velocity, chemotaxis velocity and chemotaxis index in tissue. We demonstrate that using this protocol, these neutrophil recruitment parameters can be stably determined and the single cell locomotion conveniently tracked in vivo.

Ecology and physics of bacterial chemotaxis in the ocean.

PubMed

Stocker, Roman; Seymour, Justin R

2012-12-01

Intuitively, it may seem that from the perspective of an individual bacterium the ocean is a vast, dilute, and largely homogeneous environment. Microbial oceanographers have typically considered the ocean from this point of view. In reality, marine bacteria inhabit a chemical seascape that is highly heterogeneous down to the microscale, owing to ubiquitous nutrient patches, plumes, and gradients. Exudation and excretion of dissolved matter by larger organisms, lysis events, particles, animal surfaces, and fluxes from the sediment-water interface all contribute to create strong and pervasive heterogeneity, where chemotaxis may provide a significant fitness advantage to bacteria. The dynamic nature of the ocean imposes strong selective pressures on bacterial foraging strategies, and many marine bacteria indeed display adaptations that characterize their chemotactic motility as "high performance" compared to that of enteric model organisms. Fast swimming speeds, strongly directional responses, and effective turning and steering strategies ensure that marine bacteria can successfully use chemotaxis to very rapidly respond to chemical gradients in the ocean. These fast responses are advantageous in a broad range of ecological processes, including attaching to particles, exploiting particle plumes, retaining position close to phytoplankton cells, colonizing host animals, and hovering at a preferred height above the sediment-water interface. At larger scales, these responses can impact ocean biogeochemistry by increasing the rates of chemical transformation, influencing the flux of sinking material, and potentially altering the balance of biomass incorporation versus respiration. This review highlights the physical and ecological processes underpinning bacterial motility and chemotaxis in the ocean, describes the current state of knowledge of chemotaxis in marine bacteria, and summarizes our understanding of how these microscale dynamics scale up to affect ecosystem-scale processes in the sea.

Effect of nicotine from tobacco root exudates on chemotaxis, growth, biocontrol efficiency, and colonization by Pseudomonas aeruginosa NXHG29.

PubMed

Ma, Li; Zheng, Shuai Chao; Zhang, Ti Kun; Liu, Zi Yi; Wang, Xue Jian; Zhou, Xing Kui; Yang, Cheng Gang; Duo, Jin Ling; Mo, Ming He

2018-02-03

Accumulated evidence suggests that root exudates have a major role in mediating plant-microbe interactions in the rhizosphere. Here, we characterized tobacco root exudates (TREs) by GC-MS and nicotine, scopoletin, and octadecane were identified as three main components of TREs. Qualitative and quantitative chemotaxis assays revealed that Pseudomonas aeruginosa NXHG29 with antagonistic activity displayed positive chemotactic responses towards TREs and their three main components (nicotine, scopoletin, octadecane) and its enhanced chemotaxis were induced by these substances in a concentration-dependent manner. Furthermore, following GC-MS and chemotaxis analysis, nicotine was selected as the target for evaluation of the effect on NXHG29 regarding antagonism, growth, root colonization and biocontrol efficiency. Results of in vitro studies showed that nicotine as a sole carbon source could enhance growth of NXHG29 and significantly increased the antagonism of NXHG29. We also demonstrated that nicotine exerted enhancing effects on the colonization ability of NXHG29 on tobacco roots by combining CLSM observations with investigation of population level dynamics by selective dilution plating method. Results from greenhouse experiments suggested nicotine exhibited stimulatory effects on the biocontrol efficiency of NXHG29 against bacterial wilt and black shank on tobacco. The stimulatory effect of nicotine was affected by the concentration and timing of nicotine application and further supported by the results of population level of NXHG29 on tobacco roots. This is the first report on the enhancement effect of nicotine from TREs on an antagonistic bacterium for its root colonization, control of soil-borne pathogens, regarding the chemotaxis and in vitro antagonism and growth.

Ras proteins have multiple functions in vegetative cells of Dictyostelium.

PubMed

Bolourani, Parvin; Spiegelman, George; Weeks, Gerald

2010-11-01

During the aggregation of Dictyostelium cells, signaling through RasG is more important in regulating cyclic AMP (cAMP) chemotaxis, whereas signaling through RasC is more important in regulating the cAMP relay. However, RasC is capable of substituting for RasG for chemotaxis, since rasG⁻ cells are only partially deficient in chemotaxis, whereas rasC⁻/rasG⁻ cells are totally incapable of chemotaxis. In this study we have examined the possible functional overlap between RasG and RasC in vegetative cells by comparing the vegetative cell properties of rasG⁻, rasC⁻, and rasC⁻/rasG⁻ cells. In addition, since RasD, a protein not normally found in vegetative cells, is expressed in vegetative rasG⁻ and rasC⁻/rasG⁻ cells and appears to partially compensate for the absence of RasG, we have also examined the possible functional overlap between RasG and RasD by comparing the properties of rasG⁻ and rasC⁻/rasG⁻ cells with those of the mutant cells expressing higher levels of RasD. The results of these two lines of investigation show that RasD is capable of totally substituting for RasG for cytokinesis and growth in suspension, whereas RasC is without effect. In contrast, for chemotaxis to folate, RasC is capable of partially substituting for RasG, but RasD is totally without effect. Finally, neither RasC nor RasD is able to substitute for the role that RasG plays in regulating actin distribution and random motility. These specificity studies therefore delineate three distinct and none-overlapping functions for RasG in vegetative cells.

A diffuse-interface method for two-phase flows with soluble surfactants

PubMed Central

Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel

2010-01-01

A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier–Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A non-linear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed. PMID:21218125

A strictly Markovian expansion for plasma turbulence theory

NASA Technical Reports Server (NTRS)

Jones, F. C.

1976-01-01

The collision operator that appears in the equation of motion for a particle distribution function that was averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. An expansion is derived for the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest nontrivial order. The validity of this expansion is seen to be the same as that of the standard quasilinear expansion.

On linearization and preconditioning for radiation diffusion coupled to material thermal conduction equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Feng, Tao, E-mail: fengtao2@mail.ustc.edu.cn; Graduate School of China Academy Engineering Physics, Beijing 100083; An, Hengbin, E-mail: an_hengbin@iapcm.ac.cn

2013-03-01

Jacobian-free Newton–Krylov (JFNK) method is an effective algorithm for solving large scale nonlinear equations. One of the most important advantages of JFNK method is that there is no necessity to form and store the Jacobian matrix of the nonlinear system when JFNK method is employed. However, an approximation of the Jacobian is needed for the purpose of preconditioning. In this paper, JFNK method is employed to solve a class of non-equilibrium radiation diffusion coupled to material thermal conduction equations, and two preconditioners are designed by linearizing the equations in two methods. Numerical results show that the two preconditioning methods canmore » improve the convergence behavior and efficiency of JFNK method.« less

Diffusion coefficients of water in biobased hydrogel polymer matrices by nuclear magnetic resonance imaging

USDA-ARS?s Scientific Manuscript database

The diffusion coefficient of water in biobased hydrogels were measured utilizing a simple NMR method. This method tracks the migration of deuterium oxide through imaging data that is fit to a diffusion equation. The results show that a 5 wt% soybean oil based hydrogel gives aqueous diffusion of 1.37...

Methyl group turnover on methyl-accepting chemotaxis proteins during chemotaxis by Bacillus subtilis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thoelke, M.S.; Casper, J.M.; Ordal, G.W.

1990-02-05

The addition of attractant to Bacillus subtilis briefly exposed to radioactive methionine causes an increase of labeling of the methyl-accepting chemotaxis proteins. The addition of attractant to cells radiolabeled for longer times shows no change in the extent of methylation. Therefore, the increase in labeling for the briefly labeled cells is due to an increased turnover of methyl groups caused by attractant. All amino acids gave enhanced turnover. This turnover lasted for a prolonged time, probably spanning the period of smooth swimming caused by the attractant addition. Repellent did not affect the turnover when added alone or simultaneously with attractant.more » Thus, for amino acid attractants, the turnover is probably the excitatory signal, which is seen to extend long into or throughout the adaptation period, not just at the start of it.« less

Deterministic walks with inverse-square power-law scaling are an emergent property of predators that use chemotaxis to locate randomly distributed prey

NASA Astrophysics Data System (ADS)

Reynolds, A. M.

2008-07-01

The results of numerical simulations indicate that deterministic walks with inverse-square power-law scaling are a robust emergent property of predators that use chemotaxis to locate randomly and sparsely distributed stationary prey items. It is suggested that chemotactic destructive foraging accounts for the apparent Lévy flight movement patterns of Oxyrrhis marina microzooplankton in still water containing prey items. This challenges the view that these organisms are executing an innate optimal Lévy flight searching strategy. Crucial for the emergence of inverse-square power-law scaling is the tendency of chemotaxis to occasionally cause predators to miss the nearest prey item, an occurrence which would not arise if prey were located through the employment of a reliable cognitive map or if prey location were visually cued and perfect.

Methylation-independent adaptation in chemotaxis of Escherichia coli involves acetylation-dependent speed adaptation.

PubMed

Baron, Szilvia; Afanzar, Oshri; Eisenbach, Michael

2017-01-01

Chemoreceptor methylation and demethylation has been shown to be at the core of the adaptation mechanism in Escherichia coli chemotaxis. Nevertheless, mutants lacking the methylation machinery can adapt to some extent. Here we carried out an extensive quantitative analysis of chemotactic and chemokinetic methylation-independent adaptation. We show that partial or complete adaptation of the direction of flagellar rotation and the swimming speed in the absence of the methylation machinery each occurs in a small fraction of cells. Furthermore, deletion of the main enzyme responsible for acetylation of the signaling molecule CheY prevented speed adaptation but not adaptation of the direction of rotation. These results suggest that methylation-independent adaptation in bacterial chemotaxis involves chemokinetic adaptation, which is dependent on CheY acetylation. © 2016 Federation of European Biochemical Societies.

Activation of motility and chemotaxis in the spermatozoa: From invertebrates to humans

PubMed Central

YOSHIDA, MANABU

2005-01-01

Activation of the sperm motility and chemotactic behavior of sperm toward eggs are the first communication between spermatozoa and eggs at fertilization, and understanding of the phenomena is a prerequisite for progress of not only basic biology, but also clinical aspects. The nature of molecules derived from eggs by which sperm are activated and attracted towards the eggs and the molecular mechanisms underlying the sperm activation and chemotaxis have been investigated in only a few invertebrate species, sea urchins, ascidians and herring fish. However, knowledge on this phenomena has been ignored in mammalian species including humans. The current review first introduces the studies on the activation and chemotaxis of sperm in marine invertebrates, and the same phenomena in mammals including humans, are described. (Reprod Med Biol 2005; 4: 101–115) PMID:29699215