Membrane curvature at a glance
McMahon, Harvey T.; Boucrot, Emmanuel
2015-01-01
ABSTRACT Membrane curvature is an important parameter in defining the morphology of cells, organelles and local membrane subdomains. Transport intermediates have simpler shapes, being either spheres or tubules. The generation and maintenance of curvature is of central importance for maintaining trafficking and cellular functions. It is possible that local shapes in complex membranes could help to define local subregions. In this Cell Science at a Glance article and accompanying poster, we summarize how generating, sensing and maintaining high local membrane curvature is an active process that is mediated and controlled by specialized proteins using general mechanisms: (i) changes in lipid composition and asymmetry, (ii) partitioning of shaped transmembrane domains of integral membrane proteins or protein or domain crowding, (iii) reversible insertion of hydrophobic protein motifs, (iv) nanoscopic scaffolding by oligomerized hydrophilic protein domains and, finally, (v) macroscopic scaffolding by the cytoskeleton with forces generated by polymerization and by molecular motors. We also summarize some of the discoveries about the functions of membrane curvature, where in addition to providing cell or organelle shape, local curvature can affect processes like membrane scission and fusion as well as protein concentration and enzyme activation on membranes. PMID:25774051
Anisotropic Membrane Curvature Sensing by Amphipathic Peptides
Gómez-Llobregat, Jordi; Elías-Wolff, Federico; Lindén, Martin
2016-01-01
Many proteins and peptides have an intrinsic capacity to sense and induce membrane curvature, and play crucial roles for organizing and remodeling cell membranes. However, the molecular driving forces behind these processes are not well understood. Here, we describe an approach to study curvature sensing by simulating the interactions of single molecules with a buckled lipid bilayer. We analyze three amphipathic antimicrobial peptides, a class of membrane-associated molecules that specifically target and destabilize bacterial membranes, and find qualitatively different sensing characteristics that would be difficult to resolve with other methods. Our findings provide evidence for direction-dependent curvature sensing mechanisms in amphipathic peptides and challenge existing theories of hydrophobic insertion. The buckling approach is generally applicable to a wide range of curvature-sensing molecules, and our results provide strong motivation to develop new experimental methods to track position and orientation of membrane proteins. PMID:26745422
Cholesterol Mediates Membrane Curvature during Fusion Events
NASA Astrophysics Data System (ADS)
Ivankin, Andrey; Kuzmenko, Ivan; Gidalevitz, David
2012-06-01
Biomembranes undergo extensive shape changes as they perform vital cellular functions. The mechanisms by which lipids and proteins control membrane curvature remain unclear. We use x-ray reflectivity, grazing incidence x-ray diffraction, and epifluorescence microscopy to study binding of HIV-1 glycoprotein gp41’s membrane-bending domain to DPPC/cholesterol monolayers of various compositions at the air-liquid interface. The results offer a new insight into how membrane curvature could be regulated by cholesterol during fusion of the viral lipid envelope and the host cell membranes.
Nanoscale manipulation of membrane curvature for probing endocytosis in live cells.
Zhao, Wenting; Hanson, Lindsey; Lou, Hsin-Ya; Akamatsu, Matthew; Chowdary, Praveen D; Santoro, Francesca; Marks, Jessica R; Grassart, Alexandre; Drubin, David G; Cui, Yi; Cui, Bianxiao
2017-08-01
Clathrin-mediated endocytosis (CME) involves nanoscale bending and inward budding of the plasma membrane, by which cells regulate both the distribution of membrane proteins and the entry of extracellular species. Extensive studies have shown that CME proteins actively modulate the plasma membrane curvature. However, the reciprocal regulation of how the plasma membrane curvature affects the activities of endocytic proteins is much less explored, despite studies suggesting that membrane curvature itself can trigger biochemical reactions. This gap in our understanding is largely due to technical challenges in precisely controlling the membrane curvature in live cells. In this work, we use patterned nanostructures to generate well-defined membrane curvatures ranging from +50 nm to -500 nm radius of curvature. We find that the positively curved membranes are CME hotspots, and that key CME proteins, clathrin and dynamin, show a strong preference towards positive membrane curvatures with a radius <200 nm. Of ten CME-related proteins we examined, all show preferences for positively curved membrane. In contrast, other membrane-associated proteins and non-CME endocytic protein caveolin1 show no such curvature preference. Therefore, nanostructured substrates constitute a novel tool for investigating curvature-dependent processes in live cells.
Membrane Curvature Sensing by Amphipathic Helices
Jensen, Martin Borch; Bhatia, Vikram Kjøller; Jao, Christine C.; Rasmussen, Jakob Ewald; Pedersen, Søren L.; Jensen, Knud J.; Langen, Ralf; Stamou, Dimitrios
2011-01-01
Preferential binding of proteins on curved membranes (membrane curvature sensing) is increasingly emerging as a general mechanism whereby cells may effect protein localization and trafficking. Here we use a novel single liposome fluorescence microscopy assay to examine a common sensing motif, the amphipathic helix (AH), and provide quantitative measures describing and distinguishing membrane binding and sensing behavior. By studying two AH-containing proteins, α-synuclein and annexin B12, as well as a range of AH peptide mutants, we reveal that both the hydrophobic and hydrophilic faces of the helix greatly influence binding and sensing. Although increased hydrophobic and electrostatic interactions with the membrane both lead to greater densities of bound protein, the former yields membrane curvature-sensitive binding, whereas the latter is not curvature-dependent. However, the relative contributions of both components determine the sensing of AHs. In contrast, charge density in the lipid membrane seems important primarily in attracting AHs to the membrane but does not significantly influence sensing. These observations were made possible by the ability of our assay to distinguish within our samples liposomes with and without bound protein as well as the density of bound protein. Our findings suggest that the description of membrane curvature-sensing requires consideration of several factors such as short and long range electrostatic interactions, hydrogen bonding, and the volume and structure of inserted hydrophobic residues. PMID:21953452
Intrinsically disordered proteins drive membrane curvature
Busch, David J.; Houser, Justin R.; Hayden, Carl C.; Sherman, Michael B.; Lafer, Eileen M.; Stachowiak, Jeanne C.
2015-01-01
Assembly of highly curved membrane structures is essential to cellular physiology. The prevailing view has been that proteins with curvature-promoting structural motifs, such as wedge-like amphipathic helices and crescent-shaped BAR domains, are required for bending membranes. Here we report that intrinsically disordered domains of the endocytic adaptor proteins, Epsin1 and AP180 are highly potent drivers of membrane curvature. This result is unexpected since intrinsically disordered domains lack a well-defined three-dimensional structure. However, in vitro measurements of membrane curvature and protein diffusivity demonstrate that the large hydrodynamic radii of these domains generate steric pressure that drives membrane bending. When disordered adaptor domains are expressed as transmembrane cargo in mammalian cells, they are excluded from clathrin-coated pits. We propose that a balance of steric pressure on the two surfaces of the membrane drives this exclusion. These results provide quantitative evidence for the influence of steric pressure on the content and assembly of curved cellular membrane structures. PMID:26204806
Intrinsically disordered proteins drive membrane curvature
NASA Astrophysics Data System (ADS)
Busch, David J.; Houser, Justin R.; Hayden, Carl C.; Sherman, Michael B.; Lafer, Eileen M.; Stachowiak, Jeanne C.
2015-07-01
Assembly of highly curved membrane structures is essential to cellular physiology. The prevailing view has been that proteins with curvature-promoting structural motifs, such as wedge-like amphipathic helices and crescent-shaped BAR domains, are required for bending membranes. Here we report that intrinsically disordered domains of the endocytic adaptor proteins, Epsin1 and AP180 are highly potent drivers of membrane curvature. This result is unexpected since intrinsically disordered domains lack a well-defined three-dimensional structure. However, in vitro measurements of membrane curvature and protein diffusivity demonstrate that the large hydrodynamic radii of these domains generate steric pressure that drives membrane bending. When disordered adaptor domains are expressed as transmembrane cargo in mammalian cells, they are excluded from clathrin-coated pits. We propose that a balance of steric pressure on the two surfaces of the membrane drives this exclusion. These results provide quantitative evidence for the influence of steric pressure on the content and assembly of curved cellular membrane structures.
Intrinsically disordered proteins drive membrane curvature.
Busch, David J; Houser, Justin R; Hayden, Carl C; Sherman, Michael B; Lafer, Eileen M; Stachowiak, Jeanne C
2015-07-24
Assembly of highly curved membrane structures is essential to cellular physiology. The prevailing view has been that proteins with curvature-promoting structural motifs, such as wedge-like amphipathic helices and crescent-shaped BAR domains, are required for bending membranes. Here we report that intrinsically disordered domains of the endocytic adaptor proteins, Epsin1 and AP180 are highly potent drivers of membrane curvature. This result is unexpected since intrinsically disordered domains lack a well-defined three-dimensional structure. However, in vitro measurements of membrane curvature and protein diffusivity demonstrate that the large hydrodynamic radii of these domains generate steric pressure that drives membrane bending. When disordered adaptor domains are expressed as transmembrane cargo in mammalian cells, they are excluded from clathrin-coated pits. We propose that a balance of steric pressure on the two surfaces of the membrane drives this exclusion. These results provide quantitative evidence for the influence of steric pressure on the content and assembly of curved cellular membrane structures.
On the curvature effect of thin membranes
NASA Astrophysics Data System (ADS)
Wang, Duo; Jiao, Xiangmin; Conley, Rebecca; Glimm, James
2013-01-01
We investigate the curvature effect of a thin, curved elastic interface that separates two subdomains and exerts a pressure due to a curvature effect. This pressure, which we refer to as interface pressure, is similar to the surface tension in fluid mechanics. It is important in some applications, such as the canopy of parachutes, biological membranes of cells, balloons, airbags, etc., as it partially balances a pressure jump between the two sides of an interface. In this paper, we show that the interface pressure is equal to the trace of the matrix product of the curvature tensor and the Cauchy stress tensor in the tangent plane. We derive the theory for interfaces in both 2-D and 3-D, and present numerical discretizations for computing the quality over triangulated surfaces.
Protein-Induced Membrane Curvature Alters Local Membrane Tension
Rangamani, Padmini; Mandadap, Kranthi K.; Oster, George
2014-01-01
Adsorption of proteins onto membranes can alter the local membrane curvature. This phenomenon has been observed in biological processes such as endocytosis, tubulation, and vesiculation. However, it is not clear how the local surface properties of the membrane, such as membrane tension, change in response to protein adsorption. In this article, we show that the partial differential equations arising from classical elastic model of lipid membranes, which account for simultaneous changes in shape and membrane tension due to protein adsorption in a local region, cannot be solved for nonaxisymmetric geometries using straightforward numerical techniques; instead, a viscous-elastic formulation is necessary to fully describe the system. Therefore, we develop a viscous-elastic model for inhomogeneous membranes of the Helfrich type. Using the newly available viscous-elastic model, we find that the lipids flow to accommodate changes in membrane curvature during protein adsorption. We show that, at the end of protein adsorption process, the system sustains a residual local tension to balance the difference between the actual mean curvature and the imposed spontaneous curvature. We also show that this change in membrane tension can have a functional impact such as altered response to pulling forces in the presence of proteins. PMID:25099814
Transmembrane protein sorting driven by membrane curvature
NASA Astrophysics Data System (ADS)
Strahl, H.; Ronneau, S.; González, B. Solana; Klutsch, D.; Schaffner-Barbero, C.; Hamoen, L. W.
2015-11-01
The intricate structure of prokaryotic and eukaryotic cells depends on the ability to target proteins to specific cellular locations. In most cases, we have a poor understanding of the underlying mechanisms. A typical example is the assembly of bacterial chemoreceptors at cell poles. Here we show that the classical chemoreceptor TlpA of Bacillus subtilis does not localize according to the consensus stochastic nucleation mechanism but accumulates at strongly curved membrane areas generated during cell division. This preference was confirmed by accumulation at non-septal curved membranes. Localization appears to be an intrinsic property of the protein complex and does not rely on chemoreceptor clustering, as was previously shown for Escherichia coli. By constructing specific amino-acid substitutions, we demonstrate that the preference for strongly curved membranes arises from the curved shape of chemoreceptor trimer of dimers. These findings demonstrate that the intrinsic shape of transmembrane proteins can determine their cellular localization.
Transmembrane protein sorting driven by membrane curvature.
Strahl, H; Ronneau, S; González, B Solana; Klutsch, D; Schaffner-Barbero, C; Hamoen, L W
2015-11-02
The intricate structure of prokaryotic and eukaryotic cells depends on the ability to target proteins to specific cellular locations. In most cases, we have a poor understanding of the underlying mechanisms. A typical example is the assembly of bacterial chemoreceptors at cell poles. Here we show that the classical chemoreceptor TlpA of Bacillus subtilis does not localize according to the consensus stochastic nucleation mechanism but accumulates at strongly curved membrane areas generated during cell division. This preference was confirmed by accumulation at non-septal curved membranes. Localization appears to be an intrinsic property of the protein complex and does not rely on chemoreceptor clustering, as was previously shown for Escherichia coli. By constructing specific amino-acid substitutions, we demonstrate that the preference for strongly curved membranes arises from the curved shape of chemoreceptor trimer of dimers. These findings demonstrate that the intrinsic shape of transmembrane proteins can determine their cellular localization.
Preference for Curvature: A Historical and Conceptual Framework
Gómez-Puerto, Gerardo; Munar, Enric; Nadal, Marcos
2016-01-01
That people find curved contours and lines more pleasurable than straight ones is a recurrent observation in the aesthetic literature. Although such observation has been tested sporadically throughout the history of scientific psychology, only during the last decade has it been the object of systematic research. Recent studies lend support to the idea that human preference for curved contours is biologically determined. However, it has also been argued that this preference is a cultural phenomenon. In this article, we review the available evidence, together with different attempts to explain the nature of preference for curvature: sensoriomotor-based and valuation-based approaches. We also argue that the lack of a unifying framework and clearly defined concepts might be undermining our efforts towards a better understanding of the nature of preference for curvature. Finally, we point to a series of unresolved matters as the starting point to further develop a consistent research program. PMID:26793092
Curvature-driven lateral segregation of membrane constituents in Golgi cisternae
NASA Astrophysics Data System (ADS)
Derganc, Jure
2007-12-01
Lateral segregation of mobile membrane constituents (e.g. lipids, proteins or membrane domains) into the regions of their preferred curvature relaxes stresses in the membrane. The equilibrium distribution of the constituents in the membrane is thus a balance between the gains in the membrane elastic energy and the segregation-induced loss of entropy. The membrane in the Golgi cisternae is particularly susceptible to the curvature-driven segregation because it possesses two very different curvatures—the highly curved membrane in the cisternal rims and the flat membrane in the cisternal sides. In this work, we calculate the extent of lateral segregation in the Golgi cisternae in the case where the segregation is driven by the Helfrich bending energy. It is assumed that the membrane bending constant and spontaneous curvature depend on the local membrane composition. A simple analytical expression for the extent of the lateral segregation is derived. The results show that the segregation depends on the ratio between the bending constant and the thermal energy, the difference of the preferred curvatures of the constituents and the sizes of the constituents. Applying the model to a typical Golgi cisterna, it was found that entropy can effectively limit the extent of the curvature-driven lateral segregation.
Nanoscale Membrane Curvature detected by Polarized Localization Microscopy
NASA Astrophysics Data System (ADS)
Kelly, Christopher; Maarouf, Abir; Woodward, Xinxin
Nanoscale membrane curvature is a necessary component of countless cellular processes. Here we present Polarized Localization Microscopy (PLM), a super-resolution optical imaging technique that enables the detection of nanoscale membrane curvature with order-of-magnitude improvements over comparable optical techniques. PLM combines the advantages of polarized total internal reflection fluorescence microscopy and fluorescence localization microscopy to reveal single-fluorophore locations and orientations without reducing localization precision by point spread function manipulation. PLM resolved nanoscale membrane curvature of a supported lipid bilayer draped over polystyrene nanoparticles on a glass coverslip, thus creating a model membrane with coexisting flat and curved regions and membrane radii of curvature as small as 20 nm. Further, PLM provides single-molecule trajectories and the aggregation of curvature-inducing proteins with super-resolution to reveal the correlated effects of membrane curvature, dynamics, and molecular sorting. For example, cholera toxin subunit B has been observed to induce nanoscale membrane budding and concentrate at the bud neck. PLM reveals a previously hidden and critical information of membrane topology.
Zemel, Assaf; Ben-Shaul, Avinoam; May, Sylvio
2008-06-12
Amphipathic alpha-helical peptides are often ascribed an ability to induce curvature stress in lipid membranes. This may lead directly to a bending deformation of the host membrane, or it may promote the formation of defects that involve highly curved lipid layers present in membrane pores, fusion intermediates, and solubilized peptide-micelle complexes. The driving force is the same in all cases: peptides induce a spontaneous curvature in the host lipid layer, the sign of which depends sensitively on the peptide's structural properties. We provide a quantitative account for this observation on the basis of a molecular-level method. To this end, we consider a lipid membrane with peptides interfacially adsorbed onto one leaflet at high peptide-to-lipid ratio. The peptides are modeled generically as rigid cylinders that interact with the host membrane through a perturbation of the conformational properties of the lipid chains. Through the use of a molecular-level chain packing theory, we calculate the elastic properties, that is, the spontaneous curvature and bending stiffness, of the peptide-decorated lipid membrane as a function of the peptide's insertion depth. We find a positive spontaneous curvature (preferred bending of the membrane away from the peptide) for small penetration depths of the peptide. At a penetration depth roughly equal to half-insertion into the hydrocarbon core, the spontaneous curvature changes sign, implying negative spontaneous curvature (preferred bending of the membrane toward the peptide) for large penetration depths. Despite thinning of the membrane upon peptide insertion, we find an increase in the bending stiffness. We discuss these findings in terms of how the peptide induces elastic stress.
Relationship between peptide membrane curvature generation and bactericidal activities
NASA Astrophysics Data System (ADS)
Schmidt, Nathan; Lee, Michelle; Kuo, David; Ouellette, Andre; Wong, Gerard
2013-03-01
Many amphipathic peptides and amphipathic domains in proteins can restructure biological membranes. Two examples are host defense antimicrobial peptides (AMPs) which disrupt and destabilize the cell membranes of microbes, and apolipoproteins which help stabilize nanoscale lipid aggregates. We use complementary x-ray and bacterial cell assays to elucidate the molecular length scale membrane deformations generated by amphipathic peptides with different structural motifs and relate these deformations to their activities on bacteria. Small angle x-ray scattering is used to study the interactions of model membranes with prototypical AMPs and consensus peptides from the amphipathic domains in apolipoproteins. By characterizing the nanoscale curvature deformations induced by these two distinct classes of membrane restructuring peptides we will discuss the role of amino acid composition on curvature generation. Bactericidal assays are used to access the in vivo activities of different amphipathic peptide motifs in order to understand the relationships between cell viability and membrane curvature generation.
The role of membrane curvature for the wrapping of nanoparticles.
Bahrami, Amir Houshang; Lipowsky, Reinhard; Weikl, Thomas R
2016-01-14
Cellular internalization of nanoparticles requires the full wrapping of the nanoparticles by the cell membrane. This wrapping process can occur spontaneously if the adhesive interactions between the nanoparticles and the membranes are sufficiently strong to compensate for the cost of membrane bending. In this article, we show that the membrane curvature prior to wrapping plays a key role for the wrapping process, besides the size and shape of the nanoparticles that have been investigated in recent years. For membrane segments that initially bulge away from nanoparticles by having a mean curvature of the same sign as the mean curvature of the particle surface, we find strongly stable partially wrapped states that can prevent full wrapping. For membrane segments that initially bulge towards the nanoparticles, in contrast, partially wrapped states can constitute a significant energetic barrier for the wrapping process.
Sculpting membranes: a mechanism of curvature generation by proteins
NASA Astrophysics Data System (ADS)
Campelo, Felix
2010-03-01
A wide spectrum of intracellular processes is dependent on the ability of cells to dynamically regulate membrane shape. Membrane bending by proteins is necessary for the generation of intracellular transport carriers and for the maintenance of otherwise intrinsically unstable regions of high membrane curvature in cell organelles. Understanding the mechanisms by which proteins curve membranes is therefore of primary importance. Crescent shaped N-BAR domains containing amphipathic helices can induce membrane curvature by two mechanisms: the scaffolding mechanism due to the very shape of the BAR dimer, and the hydrophobic insertion mechanism by which small shallow inclusions penetrate the membrane matrix and act as a wedge changing the local membrane curvature. We will focus on this latter mechanism, and study it from a quantitative point of view. We use an elastic model of the lipid bilayer, taking into account the internal strains and stresses generated by the presence of an inclusion. We show that large membrane curvatures found in in vitro experiments can be ascribed to this mechanism, and that shallow insertions are more powerful curvature generators than lipids.
A multiscale approach to curvature modulated sorting in biological membranes.
Mercker, M; Ptashnyk, M; Kühnle, J; Hartmann, D; Weiss, M; Jäger, W
2012-05-21
Combining different theoretical approaches, curvature modulated sorting in lipid bilayers fixed on non-planar surfaces is investigated. First, we present a continuous model of lateral membrane dynamics, described by a nonlinear PDE of fourth order. We then prove the existence and uniqueness of solutions of the presented model and simulate membrane dynamics using a finite element approach. Adopting a truly multiscale approach, we use dissipative particle dynamics (DPD) to parameterize the continuous model, i.e. to derive a corresponding macroscopic model. Our model predicts that curvature modulated sorting can occur if lipids or proteins differ in at least one of their macroscopic elastic moduli. Gradients in the spontaneous curvature, the bending rigidity or the Gaussian rigidity create characteristic (metastable) curvature dependent patterns. The structure and dynamics of these membrane patterns are investigated qualitatively and quantitatively using simulations. These show that the decomposition time decreases and the stability of patterns increases with enlarging moduli differences or curvature gradients. Presented phase diagrams allow to estimate if and how stable curvature modulated sorting will occur for a given geometry and set of elastic parameters. In addition, we find that the use of upscaled models is imperative studying membrane dynamics. Compared with common linear approximations the system can evolve to different (meta)stable patterns. This emphasizes the importance of parameters and realistic dynamics in mathematical modeling of biological membranes. Copyright © 2012 Elsevier Ltd. All rights reserved.
Relationship between peptide amino acid sequence and membrane curvature generation
NASA Astrophysics Data System (ADS)
Schmidt, Nathan; Kuo, David; Hwee Lai, Ghee; Mishra, Abhijit; Wong, Gerard
2012-02-01
Amphipathic peptides and amphipathic domains in proteins can perturb and restructure biological membranes. For example, it is believed that the cationic, amphipathic motif found in membrane active antimicrobial peptides (AMPs) is responsible for their membrane disruption mechanisms of action. And ApoA-I, the main apolipoprotein in high density lipoprotein contains a series of amphipathic α-helical repeats which are responsible for its lipid associating properties. We use small angle x-ray scattering (SAXS) to investigate the interaction of model cell membranes with prototypical AMPs and consensus peptides derived from the helical structural motif of ApoA-I. The relationship between peptide sequence and the peptide-induced changes in membrane curvature and topology is examined. By comparing the membrane rearrangement and corresponding phase behavior induced by these two distinct classes of membrane restructuring peptides we will discuss the role of amino acid sequence on membrane curvature generation.
NASA Astrophysics Data System (ADS)
Liu, Jin; Tourdot, Richard; Ramanan, Vyas; Agrawal, Neeraj J.; Radhakrishanan, Ravi
2012-06-01
The membrane-surface migration of curvature-inducing proteins in response to membrane curvature gradients has been investigated using Monte Carlo simulations of a curvilinear membrane model based on the Helfrich Hamiltonian. Consistent with theoretical and experimental data, we find the proteins that generate curvature can also sense the background membrane curvature, wherein they preferentially partition to the high curvature regions. The partitioning strength depends linearly on local membrane curvature and the slope (or the coupling constant) of the partitioning probability versus mean curvature depends on the membrane bending rigidity and instantaneous curvature field caused by different proteins. Our simulation study allows us to quantitatively characterize and identify the important factors affecting the coupling constant (slope), which may be difficult to determine in experiments. Furthermore, the membrane model is used to study budding of vesicles where it is found that in order to stabilize a mature vesicle with a stable 'neck-region' (or stable membrane overhangs), the area (extent) of the intrinsic curvature region needs to exceed a threshold-critical value. The migration and partitioning of curvature-inducing proteins in a budding vesicle with a stable neck (with a characteristic negative value of the Gaussian curvature) is investigated.
Liu, Jin; Tourdot, Richard; Ramanan, Vyas; Agrawal, Neeraj J.; Radhakrishanan, Ravi
2015-01-01
The membrane-surface migration of curvature-inducing proteins in response to membrane curvature gradients has been investigated using Monte Carlo simulations of a curvilinear membrane model based on the Helfrich Hamiltonian. Consistent with theoretical and experimental data, we find the proteins that generate curvature can also sense the background membrane curvature, wherein they preferentially partition to the high curvature regions. The partitioning strength depends linearly on local membrane curvature and the slope (or the coupling constant) of the partitioning probability versus mean curvature depends on the membrane bending rigidity and instantaneous curvature field caused by different proteins. Our simulation study allows us to quantitatively characterize and identify the important factors affecting the coupling constant (slope), which may be difficult to determine in experiments. Furthermore, the membrane model is used to study budding of vesicles where it is found that in order to stabilize a mature vesicle with a stable ‘neck-region’ (or stable membrane overhangs), the area (extent) of the intrinsic curvature region needs to exceed a threshold-critical value. The migration and partitioning of curvature-inducing proteins in a budding vesicle with a stable neck (with a characteristic negative value of the Gaussian curvature) is investigated. PMID:26500377
Liu, Jin; Tourdot, Richard; Ramanan, Vyas; Agrawal, Neeraj J; Radhakrishanan, Ravi
2012-06-01
The membrane-surface migration of curvature-inducing proteins in response to membrane curvature gradients has been investigated using Monte Carlo simulations of a curvilinear membrane model based on the Helfrich Hamiltonian. Consistent with theoretical and experimental data, we find the proteins that generate curvature can also sense the background membrane curvature, wherein they preferentially partition to the high curvature regions. The partitioning strength depends linearly on local membrane curvature and the slope (or the coupling constant) of the partitioning probability versus mean curvature depends on the membrane bending rigidity and instantaneous curvature field caused by different proteins. Our simulation study allows us to quantitatively characterize and identify the important factors affecting the coupling constant (slope), which may be difficult to determine in experiments. Furthermore, the membrane model is used to study budding of vesicles where it is found that in order to stabilize a mature vesicle with a stable 'neck-region' (or stable membrane overhangs), the area (extent) of the intrinsic curvature region needs to exceed a threshold-critical value. The migration and partitioning of curvature-inducing proteins in a budding vesicle with a stable neck (with a characteristic negative value of the Gaussian curvature) is investigated.
Changes in lipid density induce membrane curvature.
de Jesus, Armando J; Kastelowitz, Noah; Yin, Hang
2013-09-07
Highly curved bilayer lipid membranes make up the shell of many intra- and extracellular compartments, including organelles and vesicles. Using all-atom molecular dynamics simulations, we show that increasing the density of lipids in the bilayer membrane can induce the membrane to form a curved shape.
Sorting of Lipids and Proteins in Membrane Curvature Gradients
Tian, A.; Baumgart, T.
2009-01-01
The sorting of lipids and proteins in cellular trafficking pathways is a process of central importance in maintaining compartmentalization in eukaryotic cells. However, the mechanisms behind these sorting phenomena are currently far from being understood. Among several mechanistic suggestions, membrane curvature has been invoked as a means to segregate lipids and proteins in cellular sorting centers. To assess this hypothesis, we investigate the sorting of lipid analog dye trace components between highly curved tubular membranes and essentially flat membranes of giant unilamellar vesicles. Our experimental findings indicate that intracellular lipid sorting, contrary to frequent assumptions, is unlikely to occur by lipids fitting into membrane regions of appropriate curvature. This observation is explained in the framework of statistical mechanical lattice models that show that entropy, rather than curvature energy, dominates lipid distribution in the absence of strongly preferential lateral intermolecular interactions. Combined with previous findings of curvature induced phase segregation, we conclude that lipid cooperativity is required to enable efficient sorting. In contrast to lipid analog dyes, the peripheral membrane binding protein Cholera toxin subunit B is effectively curvature-sorted. The sorting of Cholera toxin subunit B is rationalized by statistical models. We discuss the implications of our findings for intracellular sorting mechanisms. PMID:19348750
Spatial Control of Epsin-induced Clathrin Assembly by Membrane Curvature*♦
Holkar, Sachin S.; Kamerkar, Sukrut C.; Pucadyil, Thomas J.
2015-01-01
Epsins belong to the family of highly conserved clathrin-associated sorting proteins that are indispensable for clathrin-mediated endocytosis, but their precise functions remain unclear. We have developed an assay system of budded supported membrane tubes displaying planar and highly curved membrane surfaces to analyze intrinsic membrane curvature preference shown by clathrin-associated sorting proteins. Using real-time fluorescence microscopy, we find that epsin preferentially partitions to and assembles clathrin on highly curved membrane surfaces. Sorting of epsin to regions of high curvature strictly depends on binding to phosphatidylinositol 4,5-bisphosphate. Fluorescently labeled clathrins rapidly assemble as foci, which in turn cluster epsin, while maintaining tube integrity. Clathrin foci grow in intensity with a typical time constant of ∼75 s, similar to the time scales for coated pit formation seen in cells. Epsin therefore effectively senses membrane curvature to spatially control clathrin assembly. Our results highlight the potential role of membrane curvature in orchestrating the myriad molecular interactions necessary for the success of clathrin-mediated membrane budding. PMID:25837255
Spatial Control of Epsin-induced Clathrin Assembly by Membrane Curvature.
Holkar, Sachin S; Kamerkar, Sukrut C; Pucadyil, Thomas J
2015-06-05
Epsins belong to the family of highly conserved clathrin-associated sorting proteins that are indispensable for clathrin-mediated endocytosis, but their precise functions remain unclear. We have developed an assay system of budded supported membrane tubes displaying planar and highly curved membrane surfaces to analyze intrinsic membrane curvature preference shown by clathrin-associated sorting proteins. Using real-time fluorescence microscopy, we find that epsin preferentially partitions to and assembles clathrin on highly curved membrane surfaces. Sorting of epsin to regions of high curvature strictly depends on binding to phosphatidylinositol 4,5-bisphosphate. Fluorescently labeled clathrins rapidly assemble as foci, which in turn cluster epsin, while maintaining tube integrity. Clathrin foci grow in intensity with a typical time constant of ∼75 s, similar to the time scales for coated pit formation seen in cells. Epsin therefore effectively senses membrane curvature to spatially control clathrin assembly. Our results highlight the potential role of membrane curvature in orchestrating the myriad molecular interactions necessary for the success of clathrin-mediated membrane budding. © 2015 by The American Society for Biochemistry and Molecular Biology, Inc.
Curvature Sorting of Peripheral Proteins on Solid-Supported Wavy Membranes
Hsieh, Wan-Ting; Hsu, Chih-Jung; Capraro, Benjamin R.; Wu, Tingting; Chen, Chi-Mon; Yang, Shu; Baumgart, Tobias
2013-01-01
Cellular membrane deformation and the associated redistribution of membrane-bound proteins are important aspects of membrane function. Current model membrane approaches for studying curvature sensing are limited to positive curvatures, and often require complex and delicate experimental setups. To overcome these challenges, we fabricated a wavy substrate imposing a range of curvatures onto an adhering lipid bilayer membrane. We examined the curvature sorting of several peripheral proteins binding to the wavy membrane and observed them to partition into distinct regions of curvature. Furthermore, single molecule imaging experiments suggested that curvature sensing of proteins on low-curvature substrates requires cooperative interactions. PMID:22881196
Membrane tension controls the assembly of curvature-generating proteins
NASA Astrophysics Data System (ADS)
Simunovic, Mijo; Voth, Gregory A.
2015-05-01
Proteins containing a Bin/Amphiphysin/Rvs (BAR) domain regulate membrane curvature in the cell. Recent simulations have revealed that BAR proteins assemble into linear aggregates, strongly affecting membrane curvature and its in-plane stress profile. Here, we explore the opposite question: do mechanical properties of the membrane impact protein association? By using coarse-grained molecular dynamics simulations, we show that increased surface tension significantly impacts the dynamics of protein assembly. While tensionless membranes promote a rapid formation of long-living linear aggregates of N-BAR proteins, increase in tension alters the geometry of protein association. At high tension, protein interactions are strongly inhibited. Increasing surface density of proteins leads to a wider range of protein association geometries, promoting the formation of meshes, which can be broken apart with membrane tension. Our work indicates that surface tension may play a key role in recruiting proteins to membrane-remodelling sites in the cell.
Membrane curvature in cell biology: An integration of molecular mechanisms.
Jarsch, Iris K; Daste, Frederic; Gallop, Jennifer L
2016-08-15
Curving biological membranes establishes the complex architecture of the cell and mediates membrane traffic to control flux through subcellular compartments. Common molecular mechanisms for bending membranes are evident in different cell biological contexts across eukaryotic phyla. These mechanisms can be intrinsic to the membrane bilayer (either the lipid or protein components) or can be brought about by extrinsic factors, including the cytoskeleton. Here, we review examples of membrane curvature generation in animals, fungi, and plants. We showcase the molecular mechanisms involved and how they collaborate and go on to highlight contexts of curvature that are exciting areas of future research. Lessons from how membranes are bent in yeast and mammals give hints as to the molecular mechanisms we expect to see used by plants and protists.
Membrane curvature in cell biology: An integration of molecular mechanisms
Daste, Frederic
2016-01-01
Curving biological membranes establishes the complex architecture of the cell and mediates membrane traffic to control flux through subcellular compartments. Common molecular mechanisms for bending membranes are evident in different cell biological contexts across eukaryotic phyla. These mechanisms can be intrinsic to the membrane bilayer (either the lipid or protein components) or can be brought about by extrinsic factors, including the cytoskeleton. Here, we review examples of membrane curvature generation in animals, fungi, and plants. We showcase the molecular mechanisms involved and how they collaborate and go on to highlight contexts of curvature that are exciting areas of future research. Lessons from how membranes are bent in yeast and mammals give hints as to the molecular mechanisms we expect to see used by plants and protists. PMID:27528656
Novel tilt-curvature coupling in lipid membranes
NASA Astrophysics Data System (ADS)
Terzi, M. Mert; Deserno, Markus
2017-08-01
On mesoscopic scales, lipid membranes are well described by continuum theories whose main ingredients are the curvature of a membrane's reference surface and the tilt of its lipid constituents. In particular, Hamm and Kozlov [Eur. Phys. J. E 3, 323 (2000)] have shown how to systematically derive such a tilt-curvature Hamiltonian based on the elementary assumption of a thin fluid elastic sheet experiencing internal lateral pre-stress. Performing a dimensional reduction, they not only derive the basic form of the effective surface Hamiltonian but also express its emergent elastic couplings as trans-membrane moments of lower-level material parameters. In the present paper, we argue, though, that their derivation unfortunately missed a coupling term between curvature and tilt. This term arises because, as one moves along the membrane, the curvature-induced change of transverse distances contributes to the area strain—an effect that was believed to be small but nevertheless ends up contributing at the same (quadratic) order as all other terms in their Hamiltonian. We illustrate the consequences of this amendment by deriving the monolayer and bilayer Euler-Lagrange equations for the tilt, as well as the power spectra of shape, tilt, and director fluctuations. A particularly curious aspect of our new term is that its associated coupling constant is the second moment of the lipid monolayer's lateral stress profile—which within this framework is equal to the monolayer Gaussian curvature modulus, κ¯ m. On the one hand, this implies that many theoretical predictions now contain a parameter that is poorly known (because the Gauss-Bonnet theorem limits access to the integrated Gaussian curvature); on the other hand, the appearance of κ¯ m outside of its Gaussian curvature provenance opens opportunities for measuring it by more conventional means, for instance by monitoring a membrane's undulation spectrum at short scales.
Relaxation and curvature-induced molecular flows within multicomponent membranes
NASA Astrophysics Data System (ADS)
Morris, Richard G.
2014-06-01
The quantitative understanding of membranes is still rooted in work performed in the 1970s by Helfrich and others, concerning amphiphilic bilayers. However, most biological membranes contain a wide variety of nonamphiphilic molecules too. Drawing analogy with the physics of nematic-non-nematic mixtures, we present a dynamical (out-of-equilibrium) description of such multicomponent membranes. The approach combines nematohydrodynamics in the linear regime and a proper use of (differential-) geometry. The main result is to demonstrate that one can obtain equations describing a cross-diffusion effect (similar to the Soret and Dufour effects) between curvature and the (in-membrane) flow of amphiphilic molecules relative to nonamphiphilic ones. Surprisingly, the shape of a membrane relaxes according to a simple heat equation in the mean curvature, a process that is accompanied by a simultaneous boost to the diffusion of amphiphiles away from regions of high curvature. The model also predicts the inverse process, by which the forced bending of a membrane induces a flow of amphiphilic molecules towards areas of high curvature. In principle, numerical values for the relevant diffusion coefficients should be verifiable by experiment.
Relaxation and curvature-induced molecular flows within multicomponent membranes.
Morris, Richard G
2014-06-01
The quantitative understanding of membranes is still rooted in work performed in the 1970s by Helfrich and others, concerning amphiphilic bilayers. However, most biological membranes contain a wide variety of nonamphiphilic molecules too. Drawing analogy with the physics of nematic-non-nematic mixtures, we present a dynamical (out-of-equilibrium) description of such multicomponent membranes. The approach combines nematohydrodynamics in the linear regime and a proper use of (differential-) geometry. The main result is to demonstrate that one can obtain equations describing a cross-diffusion effect (similar to the Soret and Dufour effects) between curvature and the (in-membrane) flow of amphiphilic molecules relative to nonamphiphilic ones. Surprisingly, the shape of a membrane relaxes according to a simple heat equation in the mean curvature, a process that is accompanied by a simultaneous boost to the diffusion of amphiphiles away from regions of high curvature. The model also predicts the inverse process, by which the forced bending of a membrane induces a flow of amphiphilic molecules towards areas of high curvature. In principle, numerical values for the relevant diffusion coefficients should be verifiable by experiment.
Curvature Forces in Membrane Lipid-Protein Interactions
NASA Astrophysics Data System (ADS)
Brown, Michael F.
2012-02-01
Membrane protein conformational changes, folding, and stability may all involve elastic deformation of the bilayer. Non-specific properties of the bilayer play a significant role in modulating protein conformational energetics. A flexible-surface model (FSM) describes the balance of curvature and hydrophobic forces in lipid-protein interactions. The FSM describes elastic coupling of membrane lipids to integral membrane proteins. Curvature and hydrophobic matching to the lipid bilayer entails a stress field that explains membrane protein stability. Rhodopsin provides an important example, where solid-state NMR and FTIR spectroscopy characterize the energy landscape of the dynamically activated receptor. Time-resolved UV-visible and FTIR spectroscopic studies show how membrane lipids affect the metarhodopsin equilibrium due to non-specific material properties. Influences of bilayer thickness, nonlamellar-forming lipids, detergents, and osmotic stress on rhodopsin function are all explained by the new biomembrane model. By contrast, the older fluid-mosaic model fails to account for such effects on membrane protein activity. According to the FSM proteins are regulated by membrane lipids whose spontaneous curvature most closely matches the activated state within the lipid membrane.
Micron-scale plasma membrane curvature is recognized by the septin cytoskeleton
Bridges, Andrew A.; Jentzsch, Maximilian S.; Oakes, Patrick W.; Occhipinti, Patricia
2016-01-01
Cells change shape in response to diverse environmental and developmental conditions, creating topologies with micron-scale features. Although individual proteins can sense nanometer-scale membrane curvature, it is unclear if a cell could also use nanometer-scale components to sense micron-scale contours, such as the cytokinetic furrow and base of neuronal branches. Septins are filament-forming proteins that serve as signaling platforms and are frequently associated with areas of the plasma membrane where there is micron-scale curvature, including the cytokinetic furrow and the base of cell protrusions. We report here that fungal and human septins are able to distinguish between different degrees of micron-scale curvature in cells. By preparing supported lipid bilayers on beads of different curvature, we reconstitute and measure the intrinsic septin curvature preference. We conclude that micron-scale curvature recognition is a fundamental property of the septin cytoskeleton that provides the cell with a mechanism to know its local shape. PMID:27044896
Curvature forces in membrane lipid-protein interactions.
Brown, Michael F
2012-12-11
Membrane biochemists are becoming increasingly aware of the role of lipid-protein interactions in diverse cellular functions. This review describes how conformational changes in membrane proteins, involving folding, stability, and membrane shape transitions, potentially involve elastic remodeling of the lipid bilayer. Evidence suggests that membrane lipids affect proteins through interactions of a relatively long-range nature, extending beyond a single annulus of next-neighbor boundary lipids. It is assumed the distance scale of the forces is large compared to the molecular range of action. Application of the theory of elasticity to flexible soft surfaces derives from classical physics and explains the polymorphism of both detergents and membrane phospholipids. A flexible surface model (FSM) describes the balance of curvature and hydrophobic forces in lipid-protein interactions. Chemically nonspecific properties of the lipid bilayer modulate the conformational energetics of membrane proteins. The new biomembrane model challenges the standard model (the fluid mosaic model) found in biochemistry texts. The idea of a curvature force field based on data first introduced for rhodopsin gives a bridge between theory and experiment. Influences of bilayer thickness, nonlamellar-forming lipids, detergents, and osmotic stress are all explained by the FSM. An increased awareness of curvature forces suggests that research will accelerate as structural biology becomes more closely entwined with the physical chemistry of lipids in explaining membrane structure and function.
Curvature Forces in Membrane Lipid-Protein Interactions
Brown, Michael F.
2012-01-01
Membrane biochemists are becoming increasingly aware of the role of lipid-protein interactions in diverse cellular functions. This review describes how conformational changes of membrane proteins—involving folding, stability, and membrane shape transitions—potentially involve elastic remodeling of the lipid bilayer. Evidence suggests that membrane lipids affect proteins through interactions of a relatively long-range nature, extending beyond a single annulus of next-neighbor boundary lipids. It is assumed the distance scale of the forces is large compared to the molecular range of action. Application of the theory of elasticity to flexible soft surfaces derives from classical physics, and explains the polymorphism of both detergents and membrane phospholipids. A flexible surface model (FSM) describes the balance of curvature and hydrophobic forces in lipid-protein interactions. Chemically nonspecific properties of the lipid bilayer modulate the conformational energetics of membrane proteins. The new biomembrane model challenges the standard model (the fluid mosaic model) found in biochemistry texts. The idea of a curvature force field based on data first introduced for rhodopsin gives a bridge between theory and experiment. Influences of bilayer thickness, nonlamellar-forming lipids, detergents, and osmotic stress are all explained by the FSM. An increased awareness of curvature forces suggests that research will accelerate as structural biology becomes more closely entwined with the physical chemistry of lipids in explaining membrane structure and function. PMID:23163284
Sar1 GTPase Activity Is Regulated by Membrane Curvature.
Hanna, Michael G; Mela, Ioanna; Wang, Lei; Henderson, Robert M; Chapman, Edwin R; Edwardson, J Michael; Audhya, Anjon
2016-01-15
The majority of biosynthetic secretory proteins initiate their journey through the endomembrane system from specific subdomains of the endoplasmic reticulum. At these locations, coated transport carriers are generated, with the Sar1 GTPase playing a critical role in membrane bending, recruitment of coat components, and nascent vesicle formation. How these events are appropriately coordinated remains poorly understood. Here, we demonstrate that Sar1 acts as the curvature-sensing component of the COPII coat complex and highlight the ability of Sar1 to bind more avidly to membranes of high curvature. Additionally, using an atomic force microscopy-based approach, we further show that the intrinsic GTPase activity of Sar1 is necessary for remodeling lipid bilayers. Consistent with this idea, Sar1-mediated membrane remodeling is dramatically accelerated in the presence of its guanine nucleotide-activating protein (GAP), Sec23-Sec24, and blocked upon addition of guanosine-5'-[(β,γ)-imido]triphosphate, a poorly hydrolysable analog of GTP. Our results also indicate that Sar1 GTPase activity is stimulated by membranes that exhibit elevated curvature, potentially enabling Sar1 membrane scission activity to be spatially restricted to highly bent membranes that are characteristic of a bud neck. Taken together, our data support a stepwise model in which the amino-terminal amphipathic helix of GTP-bound Sar1 stably penetrates the endoplasmic reticulum membrane, promoting local membrane deformation. As membrane bending increases, Sar1 membrane binding is elevated, ultimately culminating in GTP hydrolysis, which may destabilize the bilayer sufficiently to facilitate membrane fission. © 2016 by The American Society for Biochemistry and Molecular Biology, Inc.
Bcl-2 apoptosis proteins, mitochondrial membrane curvature, and cancer
NASA Astrophysics Data System (ADS)
Hwee Lai, Ghee; Schmidt, Nathan; Sanders, Lori; Mishra, Abhijit; Wong, Gerard; Ivashyna, Olena; Christenson, Eric; Schlesinger, Paul; Akabori, Kiyotaka; Santangelo, Christian
2012-02-01
Critical interactions between Bcl-2 family proteins permeabilize the outer mitochondrial membrane, a common decision point early in the intrinsic apoptotic pathway that irreversibly commits the cell to death. However, a unified picture integrating the essential non-passive role of lipid membranes with the contested dynamics of Bcl-2 regulation remains unresolved. Correlating results between synchrotron x-ray diffraction and microscopy in cell-free assays, we report activation of pro-apoptotic Bax induces strong pure negative Gaussian membrane curvature topologically necessary for pore formation and membrane remodeling events. Strikingly, Bcl-xL suppresses not only Bax-induced pore formation, but also membrane remodeling by disparate systems including cell penetrating, antimicrobial or viral fusion peptides, and bacterial toxin, none of which have BH3 allosteric domains to mediate direct binding. We propose a parallel mode of Bcl-2 pore regulation in which Bax and Bcl-xL induce antagonistic and mutually interacting Gaussian membrane curvatures. The universal nature of curvature-mediated interactions allows synergy with direct binding mechanisms, and potentially accounts for the Bcl-2 family modulation of mitochondrial fission/fusion dynamics.
Membrane curvature regulates ligand-specific membrane sorting of GPCRs in living cells.
Rosholm, Kadla R; Leijnse, Natascha; Mantsiou, Anna; Tkach, Vadym; Pedersen, Søren L; Wirth, Volker F; Oddershede, Lene B; Jensen, Knud J; Martinez, Karen L; Hatzakis, Nikos S; Bendix, Poul Martin; Callan-Jones, Andrew; Stamou, Dimitrios
2017-07-01
The targeted spatial organization (sorting) of Gprotein-coupled receptors (GPCRs) is essential for their biological function and often takes place in highly curved membrane compartments such as filopodia, endocytic pits, trafficking vesicles or endosome tubules. However, the influence of geometrical membrane curvature on GPCR sorting remains unknown. Here we used fluorescence imaging to establish a quantitative correlation between membrane curvature and sorting of three prototypic class A GPCRs (the neuropeptide Y receptor Y2, the β1 adrenergic receptor and the β2 adrenergic receptor) in living cells. Fitting of a thermodynamic model to the data enabled us to quantify how sorting is mediated by an energetic drive to match receptor shape and membrane curvature. Curvature-dependent sorting was regulated by ligands in a specific manner. We anticipate that this curvature-dependent biomechanical coupling mechanism contributes to the sorting, trafficking and function of transmembrane proteins in general.
Membrane curvature and its generation by BAR proteins
Mim, Carsten; Unger, Vinzenz M
2012-01-01
Membranes are flexible barriers that surround the cell and its compartments. To execute vital functions such as locomotion or receptor turnover, cells need to control the shapes of their membranes. In part, this control is achieved through membrane-bending proteins, such as the bin/amphiphysin/rvs domain (BAR) proteins. Many open questions remain about the mechanisms by which membrane-bending proteins function. Addressing this shortfall, recent structures of BAR protein:membrane complexes support existing mechanistic models, but also produced novel insights into how BAR-domain proteins sense, stabilize and generate curvature. Here we review these recent findings, focusing on how BAR proteins interact with the membrane, and how the resulting scaffold structures might aid the recruitment of other proteins to the sites where membranes are bent. PMID:23058040
Curvature-mediated interactions between membrane proteins.
Kim, K S; Neu, J; Oster, G
1998-01-01
Membrane proteins can deform the lipid bilayer in which they are embedded. If the bilayer is treated as an elastic medium, then these deformations will generate elastic interactions between the proteins. The interaction between a single pair is repulsive. However, for three or more proteins, we show that there are nonpairwise forces whose magnitude is similar to the pairwise forces. When there are five or more proteins, we show that the nonpairwise forces permit the existence of stable protein aggregates, despite their pairwise repulsions. PMID:9788923
Różycki, Bartosz; Lipowsky, Reinhard
2015-02-07
Biomimetic and biological membranes consist of molecular bilayers with two leaflets which are typically exposed to different aqueous environments and may differ in their molecular density or composition. Because of these asymmetries, the membranes prefer to curve in a certain manner as quantitatively described by their spontaneous curvature. Here, we study such asymmetric membranes via coarse-grained molecular dynamics simulations. We consider two mechanisms for the generation of spontaneous curvature: (i) different lipid densities within the two leaflets and (ii) leaflets exposed to different concentrations of adsorbing particles. We focus on membranes that experience no mechanical tension and describe two methods to compute the spontaneous curvature. The first method is based on the detailed structure of the bilayer's stress profile which can hardly be measured experimentally. The other method starts from the intuitive view that the bilayer represents a thin fluid film bounded by two interfaces and reduces the complexity of the stress profile to a few membrane parameters that can be measured experimentally. For the case of asymmetric adsorption, we introduce a simulation protocol based on two bilayers separated by two aqueous compartments with different adsorbate concentrations. The adsorption of small particles with a size below 1 nm is shown to generate large spontaneous curvatures up to about 1/(24 nm). Our computational approach is quite general: it can be applied to any molecular model of bilayer membranes and can be extended to other mechanisms for the generation of spontaneous curvatures as provided, e.g., by asymmetric lipid composition or depletion layers of solute molecules.
Lipid membrane-mediated attraction between curvature inducing objects
NASA Astrophysics Data System (ADS)
van der Wel, Casper; Vahid, Afshin; Šarić, Anđela; Idema, Timon; Heinrich, Doris; Kraft, Daniela J.
2016-09-01
The interplay of membrane proteins is vital for many biological processes, such as cellular transport, cell division, and signal transduction between nerve cells. Theoretical considerations have led to the idea that the membrane itself mediates protein self-organization in these processes through minimization of membrane curvature energy. Here, we present a combined experimental and numerical study in which we quantify these interactions directly for the first time. In our experimental model system we control the deformation of a lipid membrane by adhering colloidal particles. Using confocal microscopy, we establish that these membrane deformations cause an attractive interaction force leading to reversible binding. The attraction extends over 2.5 times the particle diameter and has a strength of three times the thermal energy (-3.3 kBT). Coarse-grained Monte-Carlo simulations of the system are in excellent agreement with the experimental results and prove that the measured interaction is independent of length scale. Our combined experimental and numerical results reveal membrane curvature as a common physical origin for interactions between any membrane-deforming objects, from nanometre-sized proteins to micrometre-sized particles.
Lipid membrane-mediated attraction between curvature inducing objects
van der Wel, Casper; Vahid, Afshin; Šarić, Anđela; Idema, Timon; Heinrich, Doris; Kraft, Daniela J.
2016-01-01
The interplay of membrane proteins is vital for many biological processes, such as cellular transport, cell division, and signal transduction between nerve cells. Theoretical considerations have led to the idea that the membrane itself mediates protein self-organization in these processes through minimization of membrane curvature energy. Here, we present a combined experimental and numerical study in which we quantify these interactions directly for the first time. In our experimental model system we control the deformation of a lipid membrane by adhering colloidal particles. Using confocal microscopy, we establish that these membrane deformations cause an attractive interaction force leading to reversible binding. The attraction extends over 2.5 times the particle diameter and has a strength of three times the thermal energy (−3.3 kBT). Coarse-grained Monte-Carlo simulations of the system are in excellent agreement with the experimental results and prove that the measured interaction is independent of length scale. Our combined experimental and numerical results reveal membrane curvature as a common physical origin for interactions between any membrane-deforming objects, from nanometre-sized proteins to micrometre-sized particles. PMID:27618764
Tonnesen, Asger; Christensen, Sune M; Tkach, Vadym; Stamou, Dimitrios
2014-01-07
Transmembrane proteins are embedded in cellular membranes of varied lipid composition and geometrical curvature. Here, we studied for the first time the allosteric effect of geometrical membrane curvature on transmembrane protein structure and function. We used single-channel optical analysis of the prototypic transmembrane β-barrel α-hemolysin (α-HL) reconstituted on immobilized single small unilamellar liposomes of different diameter and therefore curvature. Our data demonstrate that physiologically abundant geometrical membrane curvatures can enforce a dramatic allosteric regulation (1000-fold inhibition) of α-HL permeability. High membrane curvatures (1/diameter ~1/40 nm(-1)) compressed the effective pore diameter of α-HL from 14.2 ± 0.8 Å to 11.4 ± 0.6 Å. This reduction in effective pore area (~40%) when combined with the area compressibility of α-HL revealed an effective membrane tension of ~50 mN/m and a curvature-imposed protein deformation energy of ~7 kBT. Such substantial energies have been shown to conformationally activate, or unfold, β-barrel and α-helical transmembrane proteins, suggesting that membrane curvature could likely regulate allosterically the structure and function of transmembrane proteins in general. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Alterations of membrane curvature during influenza virus budding.
Martyna, Agnieszka; Rossman, Jeremy
2014-10-01
Influenza A virus belongs to the Orthomyxoviridae family. It is an enveloped virus that contains a segmented and negative-sense RNA genome. Influenza A viruses cause annual epidemics and occasional major pandemics, are a major cause of morbidity and mortality worldwide, and have a significant financial impact on society. Assembly and budding of new viral particles are a complex and multi-step process involving several host and viral factors. Influenza viruses use lipid raft domains in the apical plasma membrane of polarized epithelial cells as sites of budding. Two viral glycoproteins, haemagglutinin and neuraminidase, concentrate in lipid rafts, causing alterations in membrane curvature and initiation of the budding process. Matrix protein 1 (M1), which forms the inner structure of the virion, is then recruited to the site followed by incorporation of the viral ribonucleoproteins and matrix protein 2 (M2). M1 can alter membrane curvature and progress budding, whereas lipid raft-associated M2 stabilizes the site of budding, allowing for proper assembly of the virion. In the later stages of budding, M2 is localized to the neck of the budding virion at the lipid phase boundary, where it causes negative membrane curvature, leading to scission and virion release.
Maier, Oana; Galan, Debra L.; Wodrich, Harald; Wiethoff, Christopher M.
2010-01-01
Adenovirus (Ad) membrane penetration during cell entry is poorly understood. Here we show that antibodies which neutralize the membrane lytic activity of the Ad capsid protein VI interfere with Ad endosomal membrane penetration. In vitro studies using a peptide corresponding to an N-terminal amphipathic α-helix of protein VI (VI-Φ), as well as other truncated forms of protein VI suggest that VI-Φ is largely responsible for protein VI binding to and lysing of membranes. Additional studies suggest that VI-Φ lies nearly parallel to the membrane surface. Protein VI fragments membranes and induces highly curved structures. Further studies suggest that Protein VI induces positive membrane curvature. These data support a model in which protein VI binds membranes, inducing positive curvature strain which ultimately leads to membrane fragmentation. These results agree with previous observations of Ad membrane permeabilization during cell entry and provide an initial mechanistic description of a nonenveloped virus membrane lytic protein. PMID:20409568
Membrane-mediated aggregation of curvature-inducing nematogens and membrane tubulation.
Ramakrishnan, N; Sunil Kumar, P B; Ipsen, John H
2013-03-05
The shapes of cell membranes are largely regulated by membrane-associated, curvature-active proteins. Herein, we use a numerical model of the membrane, recently developed by us, with elongated membrane inclusions possessing spontaneous directional curvatures that could be different along, and perpendicular to, the membrane's long axis. We show that, due to membrane-mediated interactions, these curvature-inducing membrane-nematogens can aggregate spontaneously, even at low concentrations, and change the local shape of the membrane. We demonstrate that for a large group of such inclusions, where the two spontaneous curvatures have equal sign, the tubular conformation and sometimes the sheet conformation of the membrane are the common equilibrium shapes. We elucidate the factors necessary for the formation of these protein lattices. Furthermore, the elastic properties of the tubes, such as their compressional stiffness and persistence length, are calculated. Finally, we discuss the possible role of nematic disclination in capping and branching of the tubular membranes. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Tanaka, Masafumi; Takamura, Yuki; Kawakami, Toru; Aimoto, Saburo; Saito, Hiroyuki; Mukai, Takahiro
2013-03-01
Amphipathic helix, which senses membrane curvature, is of growing interest. Here we explore the effect of amino acid distribution of amphipathic helical peptide derived from the C-terminal region (residues 220-241) of human apolipoprotein (apo) A-I on membrane curvature sensing. This peptide preferred a curved membrane in a manner similar to full-length apoA-I, although its model peptide did not sense membrane curvature. Substitution of several residues both on the polar and non-polar faces of the amphipathic helix had no significant effect on sensing, suggestive of the elaborate molecular architecture in the C-terminal helical region of apoA-I to exert lipid efflux function. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.
Curvature-Induced Spatial Ordering of Composition in Lipid Membranes
Katz, Shimrit
2017-01-01
Phase segregation of membranal components, such as proteins, lipids, and cholesterols, leads to the formation of aggregates or domains that are rich in specific constituents. This process is important in the interaction of the cell with its surroundings and in determining the cell's behavior and fate. Motivated by published experiments on curvature-modulated phase separation in lipid membranes, we formulate a mathematical model aiming at studying the spatial ordering of composition in a two-component biomembrane that is subjected to a prescribed (imposed) geometry. Based on this model, we identified key nondimensional quantities that govern the biomembrane response and performed numerical simulations to quantitatively explore their influence. We reproduce published experimental observations and extend them to surfaces with geometric features (imposed geometry) and lipid phases beyond those used in the experiments. In addition, we demonstrate the possibility for curvature-modulated phase separation above the critical temperature and propose a systematic procedure to determine which mechanism, the difference in bending stiffness or difference in spontaneous curvatures of the two phases, dominates the coupling between shape and composition. PMID:28473867
Synaptobrevin transmembrane domain influences exocytosis by perturbing vesicle membrane curvature.
Chang, Che-Wei; Jackson, Meyer B
2015-07-07
Membrane fusion requires that nearly flat lipid bilayers deform into shapes with very high curvature. This makes membrane bending a critical force in determining fusion mechanisms. A lipid bilayer will bend spontaneously when material is distributed asymmetrically between its two monolayers, and its spontaneous curvature (C0) will influence the stability of curved fusion intermediates. Prior work on Ca(2+)-triggered exocytosis revealed that fusion pore lifetime (τ) varies with vesicle content (Q), and showed that this relation reflects membrane bending energetics. Lipids that alter C0 change the dependence of τ on Q. These results suggested that the greater stability of an initial exocytotic fusion pore associated with larger vesicles reflects the need to bend more membrane during fusion pore dilation. In this study, we explored the possibility of manipulating C0 by mutating the transmembrane domain (TMD) of the vesicle membrane protein synaptobrevin 2 (syb2). Amperometric measurements of exocytosis in mouse chromaffin cells revealed that syb2 TMD mutations altered the relation between τ and Q. The effects of these mutations showed a striking periodicity, changing sign as the structural perturbation moved through the inner and outer leaflets. Some glycine and charge mutations also influenced the dependence of τ on Q in a manner consistent with expected changes in C0. These results suggest that side chains in the syb2 TMD influence the kinetics of exocytosis by perturbing the packing of the surrounding lipids. The present results support the view that membrane bending occurs during fusion pore expansion rather than during fusion pore formation. This supports the view of an initial fusion pore through two relatively flat membranes formed by protein. Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Membrane-Mediated Aggregation of Curvature-Inducing Nematogens and Membrane Tubulation
Ramakrishnan, N.; Sunil Kumar, P.B.; Ipsen, John H.
2013-01-01
The shapes of cell membranes are largely regulated by membrane-associated, curvature-active proteins. Herein, we use a numerical model of the membrane, recently developed by us, with elongated membrane inclusions possessing spontaneous directional curvatures that could be different along, and perpendicular to, the membrane’s long axis. We show that, due to membrane-mediated interactions, these curvature-inducing membrane-nematogens can aggregate spontaneously, even at low concentrations, and change the local shape of the membrane. We demonstrate that for a large group of such inclusions, where the two spontaneous curvatures have equal sign, the tubular conformation and sometimes the sheet conformation of the membrane are the common equilibrium shapes. We elucidate the factors necessary for the formation of these protein lattices. Furthermore, the elastic properties of the tubes, such as their compressional stiffness and persistence length, are calculated. Finally, we discuss the possible role of nematic disclination in capping and branching of the tubular membranes. PMID:23473484
The Gaussian curvature elastic energy of intermediates in membrane fusion.
Siegel, David P
2008-12-01
The Gaussian curvature elastic energy contribution to the energy of membrane fusion intermediates has usually been neglected because the Gaussian curvature elastic modulus, kappa, was unknown. It is now possible to measure kappa for phospholipids that form bicontinuous inverted cubic (Q(II)) phases. Here, it is shown that one can estimate kappa for lipids that do not form Q(II) phases by studying the phase behavior of lipid mixtures. The method is used to estimate kappa for several lipid compositions in excess water. The values of kappa are used to compute the curvature elastic energies of stalks and catenoidal fusion pores according to recent models. The Gaussian curvature elastic contribution is positive and similar in magnitude to the bending energy contribution: it increases the total curvature energy of all the fusion intermediates by 100 units of k(B)T or more. It is important to note that this contribution makes the predicted intermediate energies compatible with observed lipid phase behavior in excess water. An order-of-magnitude fusion rate equation is used to estimate whether the predicted stalk energies are consistent with the observed rates of stalk-mediated processes in pure lipid systems. The current theory predicts a stalk energy that is slightly too large, by approximately 30 k(B)T, to rationalize the observed rates of stalk-mediated processes in phosphatidylethanolamine or N-monomethylated dioleoylphosphatidylethanolamine systems. Despite this discrepancy, the results show that models of fusion intermediate energy are accurate enough to make semiquantitative predictions about how proteins mediate biomembrane fusion. The same rate model shows that for proteins to drive biomembrane fusion at observed rates, they have to perform mediating functions corresponding to a reduction in the energy of a purely lipidic stalk by several tens of k(B)T. By binding particular peptide sequences to the monolayer surface, proteins could lower fusion intermediate
How curvature-generating proteins build scaffolds on membrane nanotubes
Evergren, Emma; Golushko, Ivan; Prévost, Coline; Renard, Henri-François; Johannes, Ludger; McMahon, Harvey T.; Lorman, Vladimir; Voth, Gregory A.; Bassereau, Patricia
2016-01-01
Bin/Amphiphysin/Rvs (BAR) domain proteins control the curvature of lipid membranes in endocytosis, trafficking, cell motility, the formation of complex subcellular structures, and many other cellular phenomena. They form 3D assemblies that act as molecular scaffolds to reshape the membrane and alter its mechanical properties. It is unknown, however, how a protein scaffold forms and how BAR domains interact in these assemblies at protein densities relevant for a cell. In this work, we use various experimental, theoretical, and simulation approaches to explore how BAR proteins organize to form a scaffold on a membrane nanotube. By combining quantitative microscopy with analytical modeling, we demonstrate that a highly curving BAR protein endophilin nucleates its scaffolds at the ends of a membrane tube, contrary to a weaker curving protein centaurin, which binds evenly along the tube’s length. Our work implies that the nature of local protein–membrane interactions can affect the specific localization of proteins on membrane-remodeling sites. Furthermore, we show that amphipathic helices are dispensable in forming protein scaffolds. Finally, we explore a possible molecular structure of a BAR-domain scaffold using coarse-grained molecular dynamics simulations. Together with fluorescence microscopy, the simulations show that proteins need only to cover 30–40% of a tube’s surface to form a rigid assembly. Our work provides mechanical and structural insights into the way BAR proteins may sculpt the membrane as a high-order cooperative assembly in important biological processes. PMID:27655892
How curvature-generating proteins build scaffolds on membrane nanotubes.
Simunovic, Mijo; Evergren, Emma; Golushko, Ivan; Prévost, Coline; Renard, Henri-François; Johannes, Ludger; McMahon, Harvey T; Lorman, Vladimir; Voth, Gregory A; Bassereau, Patricia
2016-10-04
Bin/Amphiphysin/Rvs (BAR) domain proteins control the curvature of lipid membranes in endocytosis, trafficking, cell motility, the formation of complex subcellular structures, and many other cellular phenomena. They form 3D assemblies that act as molecular scaffolds to reshape the membrane and alter its mechanical properties. It is unknown, however, how a protein scaffold forms and how BAR domains interact in these assemblies at protein densities relevant for a cell. In this work, we use various experimental, theoretical, and simulation approaches to explore how BAR proteins organize to form a scaffold on a membrane nanotube. By combining quantitative microscopy with analytical modeling, we demonstrate that a highly curving BAR protein endophilin nucleates its scaffolds at the ends of a membrane tube, contrary to a weaker curving protein centaurin, which binds evenly along the tube's length. Our work implies that the nature of local protein-membrane interactions can affect the specific localization of proteins on membrane-remodeling sites. Furthermore, we show that amphipathic helices are dispensable in forming protein scaffolds. Finally, we explore a possible molecular structure of a BAR-domain scaffold using coarse-grained molecular dynamics simulations. Together with fluorescence microscopy, the simulations show that proteins need only to cover 30-40% of a tube's surface to form a rigid assembly. Our work provides mechanical and structural insights into the way BAR proteins may sculpt the membrane as a high-order cooperative assembly in important biological processes.
Nonlinear Sorting, Curvature Generation, and Crowding of Endophilin N-BAR on Tubular Membranes
Zhu, Chen; Das, Sovan L.; Baumgart, Tobias
2012-01-01
The curvature of biological membranes is controlled by membrane-bound proteins. For example, during endocytosis, the sorting of membrane components, vesicle budding, and fission from the plasma membrane are mediated by adaptor and accessory proteins. Endophilin is a peripherally binding membrane protein that functions as an endocytic accessory protein. Endophilin's membrane tubulation capacity is well known. However, to understand the thermodynamic and mechanical aspects of endophilin function, experimental measurements need to be compared to quantitative theoretical models. We present measurements of curvature sorting and curvature generation of the endophilin A1 N-BAR domain on tubular membranes pulled from giant unilamellar vesicles. At low concentration, endophilin functions primarily as a membrane curvature sensor; at high concentrations, it also generates curvature. We determine the spontaneous curvature induced by endophilin and observe sigmoidal curvature/composition coupling isotherms that saturate at high membrane tensions and protein solution concentrations. The observation of saturation is supported by a strong dependence of lateral diffusion coefficients on protein density on the tether membrane. We develop a nonlinear curvature/composition coupling model that captures our experimental observations. Our model predicts a curvature-induced phase transition among two states with varying protein density and membrane curvature. This transition could act as a switch during endocytosis. PMID:22768939
The transport along membrane nanotubes driven by the spontaneous curvature of membrane components.
Kabaso, Doron; Bobrovska, Nataliya; Góźdź, Wojciech; Gongadze, Ekaterina; Kralj-Iglič, Veronika; Zorec, Robert; Iglič, Aleš
2012-10-01
Intercellular membrane nanotubes (ICNs) serve as a very specific transport system between neighboring cells. The underlying mechanisms responsible for the transport of membrane components and vesicular dilations along the ICNs are not clearly understood. The present study investigated the spatial distribution of anisotropic membrane components of tubular shapes and isotropic membrane components of spherical shapes. Experimental results revealed the preferential distribution of CTB (cholera toxin B)-GM1 complexes mainly on the spherical cell membrane, and cholesterol-sphingomyelin at the membrane leading edge and ICNs. In agreement with previous studies, we here propose that the spatial distribution of CTB-GM1 complexes and cholesterol-sphingomyelin rafts were due to their isotropic and anisotropic shapes, respectively. To elucidate the relationship between a membrane component shape and its spatial distribution, a two-component computational model was constructed. The minimization of the membrane bending (free) energy revealed the enrichment of the anisotropic component along the ICN and the isotropic component in the parent cell membrane, which was due to the curvature mismatch between the ICN curvature and the spontaneous curvature of the isotropic component. The equations of motion, derived from the differentiation of the membrane free energy, revealed a curvature-dependent flux of the isotropic component and a curvature-dependent force exerted on a vesicular dilation along the ICN. Finally, the effects of possible changes in the orientational ordering of the anisotropic component attendant to the transport of the vesicular dilation were discussed with connection to the propagation of electrical and chemical signals. Copyright © 2012 Elsevier B.V. All rights reserved.
Bhatia, Vikram Kjøller; Hatzakis, Nikos S; Stamou, Dimitrios
2010-06-01
The discovery of proteins that recognize membrane curvature created a paradigm shift by suggesting that membrane shape may act as a cue for protein localization that is independent of lipid or protein composition. Here we review recent data on membrane curvature sensing by three structurally unrelated motifs: BAR domains, amphipathic helices and membrane-anchored proteins. We discuss the conclusion that the curvature of the BAR dimer is not responsible for sensing and that the sensing properties of all three motifs can be rationalized by the physicochemical properties of the curved membrane itself. We thus anticipate that membrane curvature will promote the redistribution of proteins that are anchored in membranes through any type of hydrophobic moiety, a thesis that broadens tremendously the implications of membrane curvature for protein sorting, trafficking and signaling in cell biology.
Defining the free-energy landscape of curvature-inducing proteins on membrane bilayers
Tourdot, Richard W.; Ramakrishnan, N.; Radhakrishnan, Ravi
2015-01-01
Curvature-sensing and curvature-remodeling proteins, such as Amphiphysin, Epsin, and Exo70, are known to reshape cell membranes, and this remodeling event is essential for key biophysical processes such as tubulation, exocytosis, and endocytosis. Curvature-inducing proteins can act as curvature sensors; they aggregate to membrane regions matching their intrinsic curvature; as well as induce curvature in cell membranes to stabilize emergent high curvature, nonspherical, structures such as tubules, discs, and caveolae. A definitive understanding of the interplay between protein recruitment and migration, the evolution of membrane curvature, and membrane morphological transitions is emerging but remains incomplete. Here, within a continuum framework and using the machinery of Monte Carlo simulations, we introduce and compare three free-energy methods to delineate the free-energy landscape of curvature-inducing proteins on bilayer membranes. We demonstrate the utility of the Widom test particle (or field) insertion methodology in computing the excess chemical potentials associated with curvature-inducing proteins on the membrane—in particular, we use this method to track the onset of morphological transitions in the membrane at elevated protein densities. We validate this approach by comparing the results from the Widom method with those of thermodynamic integration and Bennett acceptance ratio methods. Furthermore, the predictions from the Widom method have been tested against analytical calculations of the excess chemical potential at infinite dilution. Our results are useful in precisely quantifying the free-energy landscape, and also in determining the phase boundaries associated with curvature-induction, curvature-sensing, and morphological transitions. This approach can be extended to studies exploring the role of thermal fluctuations and other external (control) variables, such as membrane excess area, in shaping curvature-mediated interactions on bilayer
Defining the free-energy landscape of curvature-inducing proteins on membrane bilayers
NASA Astrophysics Data System (ADS)
Tourdot, Richard W.; Ramakrishnan, N.; Radhakrishnan, Ravi
2014-08-01
Curvature-sensing and curvature-remodeling proteins, such as Amphiphysin, Epsin, and Exo70, are known to reshape cell membranes, and this remodeling event is essential for key biophysical processes such as tubulation, exocytosis, and endocytosis. Curvature-inducing proteins can act as curvature sensors; they aggregate to membrane regions matching their intrinsic curvature; as well as induce curvature in cell membranes to stabilize emergent high curvature, nonspherical, structures such as tubules, discs, and caveolae. A definitive understanding of the interplay between protein recruitment and migration, the evolution of membrane curvature, and membrane morphological transitions is emerging but remains incomplete. Here, within a continuum framework and using the machinery of Monte Carlo simulations, we introduce and compare three free-energy methods to delineate the free-energy landscape of curvature-inducing proteins on bilayer membranes. We demonstrate the utility of the Widom test particle (or field) insertion methodology in computing the excess chemical potentials associated with curvature-inducing proteins on the membrane—in particular, we use this method to track the onset of morphological transitions in the membrane at elevated protein densities. We validate this approach by comparing the results from the Widom method with those of thermodynamic integration and Bennett acceptance ratio methods. Furthermore, the predictions from the Widom method have been tested against analytical calculations of the excess chemical potential at infinite dilution. Our results are useful in precisely quantifying the free-energy landscape, and also in determining the phase boundaries associated with curvature-induction, curvature-sensing, and morphological transitions. This approach can be extended to studies exploring the role of thermal fluctuations and other external (control) variables, such as membrane excess area, in shaping curvature-mediated interactions on bilayer
Thermodynamics and mechanics of membrane curvature generation and sensing by proteins and lipids.
Baumgart, Tobias; Capraro, Benjamin R; Zhu, Chen; Das, Sovan L
2011-01-01
Research investigating lipid membrane curvature generation and sensing is a rapidly developing frontier in membrane physical chemistry and biophysics. The fast recent progress is based on the discovery of a plethora of proteins involved in coupling membrane shape to cellular membrane function, the design of new quantitative experimental techniques to study aspects of membrane curvature, and the development of analytical theories and simulation techniques that allow a mechanistic interpretation of quantitative measurements. The present review first provides an overview of important classes of membrane proteins for which function is coupled to membrane curvature. We then survey several mechanisms that are assumed to underlie membrane curvature sensing and generation. Finally, we discuss relatively simple thermodynamic/mechanical models that allow quantitative interpretation of experimental observations.
Thermodynamics and Mechanics of Membrane Curvature Generation and Sensing by Proteins and Lipids
Baumgart, Tobias; Capraro, Benjamin R.; Zhu, Chen; Das, Sovan L.
2014-01-01
Research investigating lipid membrane curvature generation and sensing is a rapidly developing frontier in membrane physical chemistry and biophysics. The fast recent progress is based on the discovery of a plethora of proteins involved in coupling membrane shape to cellular membrane function, the design of new quantitative experimental techniques to study aspects of membrane curvature, and the development of analytical theories and simulation techniques that allow a mechanistic interpretation of quantitative measurements. The present review first provides an overview of important classes of membrane proteins for which function is coupled to membrane curvature. We then survey several mechanisms that are assumed to underlie membrane curvature sensing and generation. Finally, we discuss relatively simple thermodynamic/mechanical models that allow quantitative interpretation of experimental observations. PMID:21219150
Dymond, Marcus K
2016-08-01
Several theories of phospholipid homeostasis have postulated that cells regulate the molecular composition of their bilayer membranes, such that a common biophysical membrane parameter is under homeostatic control. Two commonly cited theories are the intrinsic curvature hypothesis, which states that cells control membrane curvature elastic stress, and the theory of homeoviscous adaptation, which postulates cells control acyl chain packing order (membrane order). In this paper, we present evidence from data-driven modelling studies that these two theories correlate in vivo. We estimate the curvature elastic stress of mammalian cells to be 4-7 × 10(-12) N, a value high enough to suggest that in mammalian cells the preservation of membrane order arises through a mechanism where membrane curvature elastic stress is controlled. These results emerge from analysing the molecular contribution of individual phospholipids to both membrane order and curvature elastic stress in nearly 500 cellular compositionally diverse lipidomes. Our model suggests that the de novo synthesis of lipids is the dominant mechanism by which cells control curvature elastic stress and hence membrane order in vivo These results also suggest that cells can increase membrane curvature elastic stress disproportionately to membrane order by incorporating polyunsaturated fatty acids into lipids. © 2016 The Author(s).
2016-01-01
Several theories of phospholipid homeostasis have postulated that cells regulate the molecular composition of their bilayer membranes, such that a common biophysical membrane parameter is under homeostatic control. Two commonly cited theories are the intrinsic curvature hypothesis, which states that cells control membrane curvature elastic stress, and the theory of homeoviscous adaptation, which postulates cells control acyl chain packing order (membrane order). In this paper, we present evidence from data-driven modelling studies that these two theories correlate in vivo. We estimate the curvature elastic stress of mammalian cells to be 4–7 × 10−12 N, a value high enough to suggest that in mammalian cells the preservation of membrane order arises through a mechanism where membrane curvature elastic stress is controlled. These results emerge from analysing the molecular contribution of individual phospholipids to both membrane order and curvature elastic stress in nearly 500 cellular compositionally diverse lipidomes. Our model suggests that the de novo synthesis of lipids is the dominant mechanism by which cells control curvature elastic stress and hence membrane order in vivo. These results also suggest that cells can increase membrane curvature elastic stress disproportionately to membrane order by incorporating polyunsaturated fatty acids into lipids. PMID:27534697
IRSp53 senses negative membrane curvature and phase separates along membrane tubules
Prévost, Coline; Zhao, Hongxia; Manzi, John; Lemichez, Emmanuel; Lappalainen, Pekka; Callan-Jones, Andrew; Bassereau, Patricia
2015-01-01
BAR domain proteins contribute to membrane deformation in diverse cellular processes. The inverted-BAR (I-BAR) protein IRSp53, for instance, is found on the inner leaflet of the tubular membrane of filopodia; however its role in the formation of these structures is incompletely understood. Here we develop an original assay in which proteins are encapsulated in giant unilamellar vesicles connected to membrane nanotubes. Our results demonstrate that I-BAR dimers sense negative membrane curvature. Experiment and theory reveal that the I-BAR displays a non-monotonic sorting with curvature, and expands the tube at high imposed tension while constricting it at low tension. Strikingly, at low protein density and tension, protein-rich domains appear along the tube. This peculiar behaviour is due to the shallow intrinsic curvature of I-BAR dimers. It allows constriction of weakly curved membranes coupled to local protein enrichment at biologically relevant conditions. This might explain how IRSp53 contributes in vivo to the initiation of filopodia. PMID:26469246
Curvature of Double-Membrane Organelles Generated by Changes in Membrane Size and Composition
Knorr, Roland L.; Dimova, Rumiana; Lipowsky, Reinhard
2012-01-01
Transient double-membrane organelles are key players in cellular processes such as autophagy, reproduction, and viral infection. These organelles are formed by the bending and closure of flat, double-membrane sheets. Proteins are believed to be important in these morphological transitions but the underlying mechanism of curvature generation is poorly understood. Here, we describe a novel mechanism for this curvature generation which depends primarily on three membrane properties: the lateral size of the double-membrane sheets, the molecular composition of their highly curved rims, and a possible asymmetry between the two flat faces of the sheets. This mechanism is evolutionary advantageous since it does not require active processes and is readily available even when resources within the cell are restricted as during starvation, which can induce autophagy and sporulation. We identify pathways for protein-assisted regulation of curvature generation, organelle size, direction of bending, and morphology. Our theory also provides a mechanism for the stabilization of large double-membrane sheet-like structures found in the endoplasmic reticulum and in the Golgi cisternae. PMID:22427874
Schmidt, Nathan W.; Wong, Gerard C. L.
2013-01-01
Short cationic, amphipathic antimicrobial peptides are multi-functional molecules that have roles in host defense as direct microbicides and modulators of the immune response. While a general mechanism of microbicidal activity involves the selective disruption and permeabilization of cell membranes, the relationships between peptide sequence and membrane activity are still under investigation. Here, we review the diverse functions that AMPs collectively have in host defense, and show that these functions can be multiplexed with a membrane mechanism of activity derived from the generation of negative Gaussian membrane curvature. As AMPs preferentially generate this curvature in model bacterial cell membranes, the selective generation of negative Gaussian curvature provides AMPs with a broad mechanism to target microbial membranes. The amino acid constraints placed on AMPs by the geometric requirement to induce negative Gaussian curvature are consistent with known AMP sequences. This ‘saddle-splay curvature selection rule’ is not strongly restrictive so AMPs have significant compositional freedom to multiplex membrane activity with other useful functions. The observation that certain proteins involved in cellular processes which require negative Gaussian curvature contain domains with similar motifs as AMPs, suggests this rule may be applicable to other curvature-generating proteins. Since our saddle-splay curvature design rule is based upon both a mechanism of activity and the existing motifs of natural AMPs, we believe it will assist the development of synthetic antimicrobials. PMID:24778573
Aggregation and vesiculation of membrane proteins by curvature-mediated interactions
NASA Astrophysics Data System (ADS)
Reynwar, Benedict J.; Illya, Gregoria; Harmandaris, Vagelis A.; Müller, Martin M.; Kremer, Kurt; Deserno, Markus
2007-05-01
Membrane remodelling plays an important role in cellular tasks such as endocytosis, vesiculation and protein sorting, and in the biogenesis of organelles such as the endoplasmic reticulum or the Golgi apparatus. It is well established that the remodelling process is aided by specialized proteins that can sense as well as create membrane curvature, and trigger tubulation when added to synthetic liposomes. Because the energy needed for such large-scale changes in membrane geometry significantly exceeds the binding energy between individual proteins and between protein and membrane, cooperative action is essential. It has recently been suggested that curvature-mediated attractive interactions could aid cooperation and complement the effects of specific binding events on membrane remodelling. But it is difficult to experimentally isolate curvature-mediated interactions from direct attractions between proteins. Moreover, approximate theories predict repulsion between isotropically curving proteins. Here we use coarse-grained membrane simulations to show that curvature-inducing model proteins adsorbed on lipid bilayer membranes can experience attractive interactions that arise purely as a result of membrane curvature. We find that once a minimal local bending is realized, the effect robustly drives protein cluster formation and subsequent transformation into vesicles with radii that correlate with the local curvature imprint. Owing to its universal nature, curvature-mediated attraction can operate even between proteins lacking any specific interactions, such as newly synthesized and still immature membrane proteins in the endoplasmic reticulum.
Kegulian, Natalie C.; Sankhagowit, Shalene; Apostolidou, Melania; Jayasinghe, Sajith A.; Malmstadt, Noah; Butler, Peter C.; Langen, Ralf
2015-01-01
Islet amyloid polypeptide (IAPP) is a 37-amino acid amyloid protein intimately associated with pancreatic islet β-cell dysfunction and death in type II diabetes. In this study, we combine spectroscopic methods and microscopy to investigate α-helical IAPP-membrane interactions. Using light scattering and fluorescence microscopy, we observe that larger vesicles become smaller upon treatment with human or rat IAPP. Electron microscopy shows the formation of various highly curved structures such as tubules or smaller vesicles in a membrane-remodeling process, and spectrofluorometric detection of vesicle leakage shows disruption of membrane integrity. This effect is stronger for human IAPP than for the less toxic rat IAPP. From CD spectra in the presence of different-sized vesicles, we also uncover the membrane curvature-sensing ability of IAPP and find that it transitions from inducing to sensing membrane curvature when lipid negative charge is decreased. Our in vivo EM images of immunogold-labeled rat IAPP and human IAPP show both forms to localize to mitochondrial cristae, which contain not only locally curved membranes but also phosphatidylethanolamine and cardiolipin, lipids with high spontaneous negative curvature. Disruption of membrane integrity by induction of membrane curvature could apply more broadly to other amyloid proteins and be responsible for membrane damage observed in other amyloid diseases as well. PMID:26283787
Single Lipid Molecule Dynamics on Supported Lipid Bilayers with Membrane Curvature
Cheney, Philip P.; Weisgerber, Alan W.; Feuerbach, Alec M.; Knowles, Michelle K.
2017-01-01
The plasma membrane is a highly compartmentalized, dynamic material and this organization is essential for a wide variety of cellular processes. Nanoscale domains allow proteins to organize for cell signaling, endo- and exocytosis, and other essential processes. Even in the absence of proteins, lipids have the ability to organize into domains as a result of a variety of chemical and physical interactions. One feature of membranes that affects lipid domain formation is membrane curvature. To directly test the role of curvature in lipid sorting, we measured the accumulation of two similar lipids, 1,2-Dihexadecanoyl-sn-glycero-3-phosphoethanolamine (DHPE) and hexadecanoic acid (HDA), using a supported lipid bilayer that was assembled over a nanopatterned surface to obtain regions of membrane curvature. Both lipids studied contain 16 carbon, saturated tails and a head group tag for fluorescence microscopy measurements. The accumulation of lipids at curvatures ranging from 28 nm to 55 nm radii was measured and fluorescein labeled DHPE accumulated more than fluorescein labeled HDA at regions of membrane curvature. We then tested whether single biotinylated DHPE molecules sense curvature using single particle tracking methods. Similar to groups of fluorescein labeled DHPE accumulating at curvature, the dynamics of single molecules of biotinylated DHPE was also affected by membrane curvature and highly confined motion was observed. PMID:28294967
Measuring the composition-curvature coupling in binary lipid membranes by computer simulations
Barragán Vidal, I. A. Müller, M.; Rosetti, C. M.; Pastorino, C.
2014-11-21
The coupling between local composition fluctuations in binary lipid membranes and curvature affects the lateral membrane structure. We propose an efficient method to compute the composition-curvature coupling in molecular simulations and apply it to two coarse-grained membrane models—a minimal, implicit-solvent model and the MARTINI model. Both the weak-curvature behavior that is typical for thermal fluctuations of planar bilayer membranes as well as the strong-curvature regime corresponding to narrow cylindrical membrane tubes are studied by molecular dynamics simulation. The simulation results are analyzed by using a phenomenological model of the thermodynamics of curved, mixed bilayer membranes that accounts for the change of the monolayer area upon bending. Additionally the role of thermodynamic characteristics such as the incompatibility between the two lipid species and asymmetry of composition are investigated.
Measuring the composition-curvature coupling in binary lipid membranes by computer simulations.
Barragán Vidal, I A; Rosetti, C M; Pastorino, C; Müller, M
2014-11-21
The coupling between local composition fluctuations in binary lipid membranes and curvature affects the lateral membrane structure. We propose an efficient method to compute the composition-curvature coupling in molecular simulations and apply it to two coarse-grained membrane models-a minimal, implicit-solvent model and the MARTINI model. Both the weak-curvature behavior that is typical for thermal fluctuations of planar bilayer membranes as well as the strong-curvature regime corresponding to narrow cylindrical membrane tubes are studied by molecular dynamics simulation. The simulation results are analyzed by using a phenomenological model of the thermodynamics of curved, mixed bilayer membranes that accounts for the change of the monolayer area upon bending. Additionally the role of thermodynamic characteristics such as the incompatibility between the two lipid species and asymmetry of composition are investigated.
Aguilar Gutierrez, Oscar F; Herrera Valencia, Edtson E; Rey, Alejandro D
2017-10-01
Curvature dissipation is relevant in synthetic and biological processes, from fluctuations in semi-flexible polymer solutions, to buckling of liquid columns, tomembrane cell wall functioning. We present a micromechanical model of curvature dissipation relevant to fluid membranes and liquid surfaces based on a parallel surface parameterization and a stress constitutive equation appropriate for anisotropic fluids and fluid membranes.The derived model, aimed at high curvature and high rate of change of curvature in liquid surfaces and membranes, introduces additional viscous modes not included in the widely used 2D Boussinesq-Scriven rheological constitutive equation for surface fluids.The kinematic tensors that emerge from theparallel surface parameterization are the interfacial rate of deformation and the surface co-rotational Zaremba-Jaumann derivative of the curvature, which are used to classify all possibledissipative planar and non-planar modes. The curvature dissipation function that accounts for bending, torsion and twist rates is derived and analyzed under several constraints, including the important inextensional bending mode.A representative application of the curvature dissipation model to the periodic oscillation in nano-wrinkled outer hair cells show how and why curvature dissipation decreases with frequency, and why the 100kHz frequency range is selected. These results contribute to characterize curvature dissipation in membranes and liquid surfaces. Copyright © 2017 Elsevier Inc. All rights reserved.
Spontaneous Behaviors and Wall-Curvature Lead to Apparent Wall Preference in Planarian.
Akiyama, Yoshitaro; Agata, Kiyokazu; Inoue, Takeshi
2015-01-01
The planarian Dugesia japonica tends to stay near the walls of its breeding containers and experimental dishes in the laboratory, a phenomenon called "wall preference". This behavior is thought to be important for environmental adaptation, such as hiding by planarians in nature. However, the mechanisms regulating wall-preference behavior are not well understood, since this behavior occurs in the absence of any particular stimulation. Here we show the mechanisms of wall-preference behavior. Surprisingly, planarian wall-preference behavior was also shown even by the head alone and by headless planarians. These results indicate that planarian "wall-preference" behavior only appears to be a "preference" behavior, and is actually an outcome of spontaneous behaviors, rather than of brain function. We found that in the absence of environmental cues planarians moved basically straight ahead until they reached a wall, and that after reaching a wall, they changed their direction of movement to one tangential to the wall, suggesting that this spontaneous behavior may play a critical role in the wall preference. When we tested another spontaneous behavior, the wigwag movement of the planarian head, using computer simulation with various wigwag angles and wigwag intervals, large wigwag angle and short wigwag interval reduced wall-preference behavior. This indicated that wigwag movement may determine the probability of staying near the wall or leaving the wall. Furthermore, in accord with this simulation, when we tested planarian wall-preference behavior using several assay fields with different curvature of the wall, we found that concavity and sharp curvature of walls negatively impacted wall preference by affecting the permissible angle of the wigwag movement. Together, these results indicate that planarian wall preference may be involuntarily caused by the combination of two spontaneous planarian behaviors: moving straight ahead until reaching a wall and then moving along it
Ho, Ruoya; Stroupe, Christopher
2016-10-01
Membrane tethering is a physical association of two membranes before their fusion. Many membrane tethering factors have been identified, but the interactions that mediate inter-membrane associations remain largely a matter of conjecture. Previously, we reported that the homotypic fusion and protein sorting/Class C vacuolar protein sorting (HOPS/Class C Vps) complex, which has two binding sites for the yeast vacuolar Rab GTPase Ypt7p, can tether two low-curvature liposomes when both membranes bear Ypt7p. Here, we show that HOPS tethers highly curved liposomes to Ypt7p-bearing low-curvature liposomes even when the high-curvature liposomes are protein-free. Phosphorylation of the curvature-sensing amphipathic lipid-packing sensor (ALPS) motif from the Vps41p HOPS subunit abrogates tethering of high-curvature liposomes. A HOPS complex without its Vps39p subunit, which contains one of the Ypt7p binding sites in HOPS, lacks tethering activity, though it binds high-curvature liposomes and Ypt7p-bearing low-curvature liposomes. Thus, HOPS tethers highly curved membranes via a direct protein-membrane interaction. Such high-curvature membranes are found at the sites of vacuole tethering and fusion. There, vacuole membranes bend sharply, generating large areas of vacuole-vacuole contact. We propose that HOPS localizes via the Vps41p ALPS motif to these high-curvature regions. There, HOPS binds via Vps39p to Ypt7p in an apposed vacuole membrane. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
Membrane Curvature Sensing by Amphipathic Helices Is Modulated by the Surrounding Protein Backbone
Doucet, Christine M.; Esmery, Nina; de Saint-Jean, Maud; Antonny, Bruno
2015-01-01
Membrane curvature is involved in numerous biological pathways like vesicle trafficking, endocytosis or nuclear pore complex assembly. In addition to its topological role, membrane curvature is sensed by specific proteins, enabling the coordination of biological processes in space and time. Amongst membrane curvature sensors are the ALPS (Amphipathic Lipid Packing Sensors). ALPS motifs are short peptides with peculiar amphipathic properties. They are found in proteins targeted to distinct curved membranes, mostly in the early secretory pathway. For instance, the ALPS motif of the golgin GMAP210 binds trafficking vesicles, while the ALPS motif of Nup133 targets nuclear pores. It is not clear if, besides curvature sensitivity, ALPS motifs also provide target specificity, or if other domains in the surrounding protein backbone are involved. To elucidate this aspect, we studied the subcellular localization of ALPS motifs outside their natural protein context. The ALPS motifs of GMAP210 or Nup133 were grafted on artificial fluorescent probes. Importantly, ALPS motifs are held in different positions and these contrasting architectures were mimicked by the fluorescent probes. The resulting chimeras recapitulated the original proteins localization, indicating that ALPS motifs are sufficient to specifically localize proteins. Modulating the electrostatic or hydrophobic content of Nup133 ALPS motif modified its avidity for cellular membranes but did not change its organelle targeting properties. In contrast, the structure of the backbone surrounding the helix strongly influenced targeting. In particular, introducing an artificial coiled-coil between ALPS and the fluorescent protein increased membrane curvature sensitivity. This coiled-coil domain also provided membrane curvature sensitivity to the amphipathic helix of Sar1. The degree of curvature sensitivity within the coiled-coil context remains correlated to the natural curvature sensitivity of the helices. This suggests
Membrane Curvature Sensing by Amphipathic Helices Is Modulated by the Surrounding Protein Backbone.
Doucet, Christine M; Esmery, Nina; de Saint-Jean, Maud; Antonny, Bruno
2015-01-01
Membrane curvature is involved in numerous biological pathways like vesicle trafficking, endocytosis or nuclear pore complex assembly. In addition to its topological role, membrane curvature is sensed by specific proteins, enabling the coordination of biological processes in space and time. Amongst membrane curvature sensors are the ALPS (Amphipathic Lipid Packing Sensors). ALPS motifs are short peptides with peculiar amphipathic properties. They are found in proteins targeted to distinct curved membranes, mostly in the early secretory pathway. For instance, the ALPS motif of the golgin GMAP210 binds trafficking vesicles, while the ALPS motif of Nup133 targets nuclear pores. It is not clear if, besides curvature sensitivity, ALPS motifs also provide target specificity, or if other domains in the surrounding protein backbone are involved. To elucidate this aspect, we studied the subcellular localization of ALPS motifs outside their natural protein context. The ALPS motifs of GMAP210 or Nup133 were grafted on artificial fluorescent probes. Importantly, ALPS motifs are held in different positions and these contrasting architectures were mimicked by the fluorescent probes. The resulting chimeras recapitulated the original proteins localization, indicating that ALPS motifs are sufficient to specifically localize proteins. Modulating the electrostatic or hydrophobic content of Nup133 ALPS motif modified its avidity for cellular membranes but did not change its organelle targeting properties. In contrast, the structure of the backbone surrounding the helix strongly influenced targeting. In particular, introducing an artificial coiled-coil between ALPS and the fluorescent protein increased membrane curvature sensitivity. This coiled-coil domain also provided membrane curvature sensitivity to the amphipathic helix of Sar1. The degree of curvature sensitivity within the coiled-coil context remains correlated to the natural curvature sensitivity of the helices. This suggests
Madsen, K L; Bhatia, V K; Gether, U; Stamou, D
2010-05-03
The internal membranes of eukaryotic cells are all twists and bends characterized by high curvature. During recent years it has become clear that specific proteins sustain these curvatures while others simply recognize membrane shape and use it as "molecular information" to organize cellular processes in space and time. Here we discuss this new important recognition process termed membrane curvature sensing (MCS). First, we review a new fluorescence-based experimental method that allows characterization of MCS using measurements on single vesicles and compare it to sensing assays that use bulk/ensemble liposome samples of different mean diameter. Next, we describe two different MCS protein motifs (amphipathic helices and BAR domains) and suggest that in both cases curvature sensitive membrane binding results from asymmetric insertion of hydrophobic amino acids in the lipid membrane. This mechanism can be extended to include the insertion of alkyl chain in the lipid membrane and consequently palmitoylated and myristoylated proteins are predicted to display similar curvature sensitive binding. Surprisingly, in all the aforementioned cases, MCS is predominantly mediated by a higher density of binding sites on curved membranes instead of higher affinity as assumed so far. Finally, we integrate these new insights into the debate about which motifs are involved in sensing versus induction of membrane curvature and what role MCS proteins may play in biology.
Curvature sensing MARCKS-ED peptides bind to membranes in a stereo-independent manner.
Yan, Lei; de Jesus, Armando Jerome; Tamura, Ryo; Li, Victoria; Cheng, Kui; Yin, Hang
2015-07-01
Membrane curvature and lipid composition plays a critical role in interchanging of matter and energy in cells. Peptide curvature sensors are known to activate signaling pathways and promote molecular transport across cell membranes. Recently, the 25-mer MARCKS-ED peptide, which is derived from the effector domain of the myristoylated alanine-rich C kinase substrate protein, has been reported to selectively recognize highly curved membrane surfaces. Our previous studies indicated that the naturally occurring L-MARCKS-ED peptide could simultaneously detect both phosphatidylserine and curvature. Here, we demonstrate that D-MARCKS-ED, composed by unnatural D-amino acids, has the same activities as its enantiomer, L-MARCKS-ED, as a curvature and lipid sensor. An atomistic molecular dynamics simulation suggests that D-MARCKS-ED may change from linear to a boat conformation upon binding to the membrane. Comparable enhancement of fluorescence intensity was observed between D- and L-MARCKS-ED peptides, indicating similar binding affinities. Meanwhile, circular dichroism spectra of D- and L-MARCKS-ED are almost symmetrical both in the presence and absence of liposomes. These results suggest similar behavior of artificial D- and natural L-MARCKS-ED peptides when binding to curved membranes. Our studies may contribute to further understanding of how MARCKS-ED senses membrane curvature as well as provide a new direction to develop novel membrane curvature probes.
Spontaneous Behaviors and Wall-Curvature Lead to Apparent Wall Preference in Planarian
Akiyama, Yoshitaro; Agata, Kiyokazu; Inoue, Takeshi
2015-01-01
The planarian Dugesia japonica tends to stay near the walls of its breeding containers and experimental dishes in the laboratory, a phenomenon called “wall preference”. This behavior is thought to be important for environmental adaptation, such as hiding by planarians in nature. However, the mechanisms regulating wall-preference behavior are not well understood, since this behavior occurs in the absence of any particular stimulation. Here we show the mechanisms of wall-preference behavior. Surprisingly, planarian wall-preference behavior was also shown even by the head alone and by headless planarians. These results indicate that planarian “wall-preference” behavior only appears to be a “preference” behavior, and is actually an outcome of spontaneous behaviors, rather than of brain function. We found that in the absence of environmental cues planarians moved basically straight ahead until they reached a wall, and that after reaching a wall, they changed their direction of movement to one tangential to the wall, suggesting that this spontaneous behavior may play a critical role in the wall preference. When we tested another spontaneous behavior, the wigwag movement of the planarian head, using computer simulation with various wigwag angles and wigwag intervals, large wigwag angle and short wigwag interval reduced wall-preference behavior. This indicated that wigwag movement may determine the probability of staying near the wall or leaving the wall. Furthermore, in accord with this simulation, when we tested planarian wall-preference behavior using several assay fields with different curvature of the wall, we found that concavity and sharp curvature of walls negatively impacted wall preference by affecting the permissible angle of the wigwag movement. Together, these results indicate that planarian wall preference may be involuntarily caused by the combination of two spontaneous planarian behaviors: moving straight ahead until reaching a wall and then
Nontopological Saddle-Splay and Curvature Instabilities from Anisotropic Membrane Inclusions
NASA Astrophysics Data System (ADS)
Fournier, J. B.
1996-06-01
Anisotropic inclusions are shown to induce spontaneous deviatoric bendings in lipidic membranes, by orienting at right angles across the bilayer. In the limit of strong membrane curvatures, a nonanalytical bending energy term is generated that favors saddlelike and cylindrical shapes, without penalizing spherical ones. An ``egg-carton'' instability results in flat membranes as well as a wormlike shape instability for vesicles.
Estimation of the bending rigidity and spontaneous curvature of fluid membranes in simulations.
Shiba, Hayato; Noguchi, Hiroshi
2011-09-01
Several numerical methods for measuring the bending rigidity and the spontaneous curvature of fluid membranes are studied using two types of meshless membrane models. The bending rigidity is estimated from the thermal undulations of planar and tubular membranes and the axial force of tubular membranes. We found a large dependence of its estimate value from the thermal undulation analysis on the upper-cutoff frequency q(cut) of the least-squares fit. The inverse power-spectrum fit with an extrapolation to q(cut)→0 yields the smallest estimation error among the investigated methods. The spontaneous curvature is estimated from the axial force of tubular membranes and the average curvature of bent membrane strips. The results of these methods show good agreement with each other.
Lipidation of the autophagy proteins LC3 and GABARAP is a membrane-curvature dependent process.
Dancourt, Julia; Melia, Thomas J
2014-08-01
The phagophore membrane is highly curved along the rim of the open cup, suggesting that the molecular mechanisms governing its formation and growth could rely on membrane curvature-dependent events. To this end, we recently reported that lipidation of the LC3 protein family is facilitated on highly curved membranes in vitro. We further showed that the conjugating enzyme ATG3 contains an amphipathic helix that is responsible for this membrane curvature dependency, and that the maintenance of this amphipathic structure is essential for ATG3 function in vivo.
Bending stiffness depends on curvature of ternary lipid mixture tubular membranes.
Tian, Aiwei; Capraro, Benjamin R; Esposito, Cinzia; Baumgart, Tobias
2009-09-16
Lipid and protein sorting and trafficking in intracellular pathways maintain cellular function and contribute to organelle homeostasis. Biophysical aspects of membrane shape coupled to sorting have recently received increasing attention. Here we determine membrane tube bending stiffness through measurements of tube radii, and demonstrate that the stiffness of ternary lipid mixtures depends on membrane curvature for a large range of lipid compositions. This observation indicates amplification by curvature of cooperative lipid demixing. We show that curvature-induced demixing increases upon approaching the critical region of a ternary lipid mixture, with qualitative differences along two roughly orthogonal compositional trajectories. Adapting a thermodynamic theory earlier developed by M. Kozlov, we derive an expression that shows the renormalized bending stiffness of an amphiphile mixture membrane tube in contact with a flat reservoir to be a quadratic function of curvature. In this analytical model, the degree of sorting is determined by the ratio of two thermodynamic derivatives. These derivatives are individually interpreted as a driving force and a resistance to curvature sorting. We experimentally show this ratio to vary with composition, and compare the model to sorting by spontaneous curvature. Our results are likely to be relevant to the molecular sorting of membrane components in vivo.
A cost-benefit analysis of the physical mechanisms of membrane curvature
Stachowiak, Jeanne C.; Brodsky, Frances M.; Miller, Elizabeth A.
2013-01-01
Many cellular membrane-bound structures exhibit distinct curvature that is driven by the physical properties of their lipid and protein constituents. Here we review how cells manipulate and control this curvature in the context of dynamic events such as vesicle-mediated membrane traffic. Lipids and cargo proteins each contribute energetic barriers that must be overcome during vesicle formation. In contrast, protein coats and their associated accessory proteins drive membrane bending using a variety of interdependent physical mechanisms. We survey the energetic costs and drivers involved in membrane curvature, drawing a contrast between the stochastic contributions of molecular crowding and the deterministic assembly of protein coats. These basic principles also apply to other cellular examples of membrane bending events, including important disease-related problems like viral egress. PMID:23999615
Quantifying Membrane Curvature Generation of Drosophila Amphiphysin N-BAR Domains
Heinrich, Michael C.; Capraro, Benjamin R.; Tian, Aiwei; Isas, Jose M.; Langen, Ralf; Baumgart, Tobias
2012-01-01
Biological membrane functions are coupled to membrane curvature, the regulation of which often involves membrane-associated proteins. The membrane-binding N-terminal amphipathic helix-containing BIN/Amphiphysin/Rvs (N-BAR) domain of amphiphysin is implicated in curvature generation and maintenance. Improving the mechanistic understanding of membrane curvature regulation by N-BAR domains requires quantitative experimental characterization. We have measured tube pulling force modulation by the N-BAR domain of Drosophila amphiphysin (DA-N-BAR) bound to tubular membranes pulled from micropipette-aspirated giant vesicles. We observed that fluorescently-labeled DA-N-BAR showed significantly higher protein density on tubules compared to the connected low-curvature vesicle membrane. Furthermore, we found the equilibrium tube pulling force to be systematically dependent on the aqueous solution concentration of DA-N-BAR, thereby providing the first quantitative assessment of spontaneous curvature generation. At sufficiently high protein concentrations, pulled tubes required no external force to maintain mechanical equilibrium, in agreement with the qualitative spontaneous tubulation previously reported for amphiphysin. PMID:23772271
When physics takes over: BAR proteins and membrane curvature
Simunovic, Mijo; Voth, Gregory A.; Callan-Jones, Andrew; Bassereau, Patricia
2016-01-01
Cell membranes become highly curved during membrane trafficking, cytokinesis, infection, immune response or cell motion. Bin/amphiphysin/Rvs (BAR) domain proteins with their intrinsically curved and anisotropic shape are involved in many of these processes, but with a large spectrum of modes of action. In vitro experiments and multiscale computer simulations have contributed in identifying a minimal set of physical parameters, namely protein density on the membrane, membrane tension, and membrane shape, that control how bound BAR domain proteins behave on the membrane. In this review, we summarize the multifaceted coupling of BAR proteins to membrane mechanics and propose a simple phase diagram that recapitulates the effects of these parameters. PMID:26519988
Curvature sorting of proteins on a cylindrical lipid membrane tether connected to a reservoir
NASA Astrophysics Data System (ADS)
Singh, Pankaj; Mahata, Paritosh; Baumgart, Tobias; Das, Sovan Lal
2012-05-01
Membrane curvature of a biological cell is actively involved in various fundamental cell biological functions. It has been discovered that membrane curvature and binding of peripheral membrane proteins follow a symbiotic relationship. The exact mechanism behind this interplay of protein binding and membrane curvature has not yet been properly understood. To improve understanding of the mechanism, we study curvature sorting of proteins in a model system consisting of a tether pulled from a giant unilamellar vesicle using mechanical-thermodynamic models. The concentration of proteins bound to the membrane changes significantly due to curvature. This has also been observed in experiments by other researchers. We also find that there is a phase transition based on protein concentration and we discuss the coexistence of phases and stability of solutions. Furthermore, when sorting is favorable, the increase in protein concentration stabilizes the tether in the sense that less pulling force is required to maintain the tether. A similar mechanism may be in place, when motor proteins pull tethers from donor membranes.
Putta, Priya; Rankenberg, Johanna; Korver, Ruud A; van Wijk, Ringo; Munnik, Teun; Testerink, Christa; Kooijman, Edgar E
2016-11-01
Phosphatidic acid (PA) is a crucial membrane phospholipid involved in de novo lipid synthesis and numerous intracellular signaling cascades. The signaling function of PA is mediated by peripheral membrane proteins that specifically recognize PA. While numerous PA-binding proteins are known, much less is known about what drives specificity of PA-protein binding. Previously, we have described the ionization properties of PA, summarized in the electrostatic-hydrogen bond switch, as one aspect that drives the specific binding of PA by PA-binding proteins. Here we focus on membrane curvature stress induced by phosphatidylethanolamine and show that many PA-binding proteins display enhanced binding as a function of negative curvature stress. This result is corroborated by the observation that positive curvature stress, induced by lyso phosphatidylcholine, abolishes PA binding of target proteins. We show, for the first time, that a novel plant PA-binding protein, Arabidopsis Epsin-like Clathrin Adaptor 1 (ECA1) displays curvature-dependence in its binding to PA. Other established PA targets examined in this study include, the plant proteins TGD2, and PDK1, the yeast proteins Opi1 and Spo20, and, the mammalian protein Raf-1 kinase and the C2 domain of the mammalian phosphatidylserine binding protein Lact as control. Based on our observations, we propose that liposome binding assays are the preferred method to investigate lipid binding compared to the popular lipid overlay assays where membrane environment is lost. The use of complex lipid mixtures is important to elucidate further aspects of PA binding proteins. Copyright © 2016. Published by Elsevier B.V.
Tarahovsky, Yury S.; Koynova, Rumiana; MacDonald, Robert C.
2010-01-18
DNA release from lipoplexes is an essential step during lipofection and is probably a result of charge neutralization by cellular anionic lipids. As a model system to test this possibility, fluorescence resonance energy transfer between DNA and lipid covalently labeled with Cy3 and BODIPY, respectively, was used to monitor the release of DNA from lipid surfaces induced by anionic liposomes. The separation of DNA from lipid measured this way was considerably slower and less complete than that estimated with noncovalently labeled DNA, and depends on the lipid composition of both lipoplexes and anionic liposomes. This result was confirmed by centrifugal separation of released DNA and lipid. X-ray diffraction revealed a clear correlation of the DNA release capacity of the anionic lipids with the interfacial curvature of the mesomorphic structures developed when the anionic and cationic liposomes were mixed. DNA release also correlated with the rate of fusion of anionic liposomes with lipoplexes. It is concluded that the tendency to fuse and the phase preference of the mixed lipid membranes are key factors for the rate and extent of DNA release. The approach presented emphasizes the importance of the lipid composition of both lipoplexes and target membranes and suggests optimal transfection may be obtained by tailoring lipoplex composition to the lipid composition of target cells.
Tarahovsky, Yury S.; Koynova, Rumiana; MacDonald, Robert C.
2004-01-01
DNA release from lipoplexes is an essential step during lipofection and is probably a result of charge neutralization by cellular anionic lipids. As a model system to test this possibility, fluorescence resonance energy transfer between DNA and lipid covalently labeled with Cy3 and BODIPY, respectively, was used to monitor the release of DNA from lipid surfaces induced by anionic liposomes. The separation of DNA from lipid measured this way was considerably slower and less complete than that estimated with noncovalently labeled DNA, and depends on the lipid composition of both lipoplexes and anionic liposomes. This result was confirmed by centrifugal separation of released DNA and lipid. X-ray diffraction revealed a clear correlation of the DNA release capacity of the anionic lipids with the interfacial curvature of the mesomorphic structures developed when the anionic and cationic liposomes were mixed. DNA release also correlated with the rate of fusion of anionic liposomes with lipoplexes. It is concluded that the tendency to fuse and the phase preference of the mixed lipid membranes are key factors for the rate and extent of DNA release. The approach presented emphasizes the importance of the lipid composition of both lipoplexes and target membranes and suggests optimal transfection may be obtained by tailoring lipoplex composition to the lipid composition of target cells. PMID:15298910
Curvature–undulation coupling as a basis for curvature sensing and generation in bilayer membranes
Bradley, Ryan P.; Radhakrishnan, Ravi
2016-01-01
We present coarse-grained molecular dynamics simulations of the epsin N-terminal homology domain interacting with a lipid bilayer and demonstrate a rigorous theoretical formalism and analysis method for computing the induced curvature field in varying concentrations of the protein in the dilute limit. Our theory is based on the description of the height–height undulation spectrum in the presence of a curvature field. We formulated an objective function to compare the acquired undulation spectrum from the simulations to that of the theory. We recover the curvature field parameters by minimizing the objective function even in the limit where the protein-induced membrane curvature is of the same order as the amplitude due to thermal undulations. The coupling between curvature and undulations leads to significant predictions: (i) Under dilute conditions, the proteins can sense a site of spontaneous curvature at distances much larger than their size; (ii) as the density of proteins increases the coupling focuses and stabilizes the curvature field to the site of the proteins; and (iii) the mapping of the protein localization and the induction of a stable curvature is a cooperative process that can be described through a Hill function. PMID:27531962
SARS-CoV fusion peptides induce membrane surface ordering and curvature
Basso, Luis G. M.; Vicente, Eduardo F.; Crusca Jr., Edson; Cilli, Eduardo M.; Costa-Filho, Antonio J.
2016-01-01
Viral membrane fusion is an orchestrated process triggered by membrane-anchored viral fusion glycoproteins. The S2 subunit of the spike glycoprotein from severe acute respiratory syndrome (SARS) coronavirus (CoV) contains internal domains called fusion peptides (FP) that play essential roles in virus entry. Although membrane fusion has been broadly studied, there are still major gaps in the molecular details of lipid rearrangements in the bilayer during fusion peptide-membrane interactions. Here we employed differential scanning calorimetry (DSC) and electron spin resonance (ESR) to gather information on the membrane fusion mechanism promoted by two putative SARS FPs. DSC data showed the peptides strongly perturb the structural integrity of anionic vesicles and support the hypothesis that the peptides generate opposing curvature stresses on phosphatidylethanolamine membranes. ESR showed that both FPs increase lipid packing and head group ordering as well as reduce the intramembrane water content for anionic membranes. Therefore, bending moment in the bilayer could be generated, promoting negative curvature. The significance of the ordering effect, membrane dehydration, changes in the curvature properties and the possible role of negatively charged phospholipids in helping to overcome the high kinetic barrier involved in the different stages of the SARS-CoV-mediated membrane fusion are discussed. PMID:27892522
SARS-CoV fusion peptides induce membrane surface ordering and curvature.
Basso, Luis G M; Vicente, Eduardo F; Crusca, Edson; Cilli, Eduardo M; Costa-Filho, Antonio J
2016-11-28
Viral membrane fusion is an orchestrated process triggered by membrane-anchored viral fusion glycoproteins. The S2 subunit of the spike glycoprotein from severe acute respiratory syndrome (SARS) coronavirus (CoV) contains internal domains called fusion peptides (FP) that play essential roles in virus entry. Although membrane fusion has been broadly studied, there are still major gaps in the molecular details of lipid rearrangements in the bilayer during fusion peptide-membrane interactions. Here we employed differential scanning calorimetry (DSC) and electron spin resonance (ESR) to gather information on the membrane fusion mechanism promoted by two putative SARS FPs. DSC data showed the peptides strongly perturb the structural integrity of anionic vesicles and support the hypothesis that the peptides generate opposing curvature stresses on phosphatidylethanolamine membranes. ESR showed that both FPs increase lipid packing and head group ordering as well as reduce the intramembrane water content for anionic membranes. Therefore, bending moment in the bilayer could be generated, promoting negative curvature. The significance of the ordering effect, membrane dehydration, changes in the curvature properties and the possible role of negatively charged phospholipids in helping to overcome the high kinetic barrier involved in the different stages of the SARS-CoV-mediated membrane fusion are discussed.
Molecular Characterization of Caveolin-induced Membrane Curvature*
Ariotti, Nicholas; Rae, James; Leneva, Natalya; Ferguson, Charles; Loo, Dorothy; Okano, Satomi; Hill, Michelle M.; Walser, Piers; Collins, Brett M.; Parton, Robert G.
2015-01-01
The generation of caveolae involves insertion of the cholesterol-binding integral membrane protein caveolin-1 (Cav1) into the membrane, however, the precise molecular mechanisms are as yet unknown. We have speculated that insertion of the caveolin scaffolding domain (CSD), a conserved amphipathic region implicated in interactions with signaling proteins, is crucial for caveola formation. We now define the core membrane-juxtaposed region of Cav1 and show that the oligomerization domain and CSD are protected by tight association with the membrane in both mature mammalian caveolae and a model prokaryotic system for caveola biogenesis. Cryoelectron tomography reveals the core membrane-juxtaposed domain to be sufficient to maintain oligomerization as defined by polyhedral distortion of the caveolar membrane. Through mutagenesis we demonstrate the importance of the membrane association of the oligomerization domain/CSD for defined caveola biogenesis and furthermore, highlight the functional significance of the intramembrane domain and the CSD for defined caveolin-induced membrane deformation. Finally, we define the core structural domain of Cav1, constituting only 66 amino acids and of great potential to nanoengineering applications, which is required for caveolin-induced vesicle formation in a bacterial system. These results have significant implications for understanding the role of Cav1 in caveola formation and in regulating cellular signaling events. PMID:26304117
Role of curvature and phase transition in lipid sorting and fission of membrane tubules.
Roux, Aurélien; Cuvelier, Damien; Nassoy, Pierre; Prost, Jacques; Bassereau, Patricia; Goud, Bruno
2005-04-20
We have recently developed a minimal system for generating long tubular nanostructures that resemble tubes observed in vivo with biological membranes. Here, we studied membrane tube pulling in ternary mixtures of sphingomyelin, phosphatidylcholine and cholesterol. Two salient results emerged: the lipid composition is significantly different in the tubes and in the vesicles; tube fission is observed when phase separation is generated in the tubes. This shows that lipid sorting may depend critically on both membrane curvature and phase separation. Phase separation also appears to be important for membrane fission in tubes pulled out of giant liposomes or purified Golgi membranes.
Falk, Kerstin; Sedlmeier, Felix; Joly, Laurent; Netz, Roland R; Bocquet, Lydéric
2010-10-13
In this paper, we study the interfacial friction of water at graphitic interfaces with various topologies, water between planar graphene sheets, inside and outside carbon nanotubes, with the goal to disentangle confinement and curvature effects on friction. We show that the friction coefficient exhibits a strong curvature dependence; while friction is independent of confinement for the graphene slab, it decreases with carbon nanotube radius for water inside, but increases for water outside. As a paradigm the friction coefficient is found to vanish below a threshold diameter for armchair nanotubes. Using a statistical description of the interfacial friction, we highlight here a structural origin of this curvature dependence, mainly associated with a curvature-induced incommensurability between the water and carbon structures. These results support the recent experiments reporting fast transport of water in nanometric carbon nanotube membranes.
Smrt, Sean T.; Draney, Adrian W.; Lorieau, Justin L.
2015-01-01
The highly conserved N-terminal 23 residues of the hemagglutinin glycoprotein, known as the fusion peptide domain (HAfp23), is vital to the membrane fusion and infection mechanism of the influenza virus. HAfp23 has a helical hairpin structure consisting of two tightly packed amphiphilic helices that rest on the membrane surface. We demonstrate that HAfp23 is a new class of amphipathic helix that functions by leveraging the negative curvature induced by two tightly packed helices on membranes. The helical hairpin structure has an inverted wedge shape characteristic of negative curvature lipids, with a bulky hydrophobic region and a relatively small hydrophilic head region. The F3G mutation reduces this inverted wedge shape by reducing the volume of its hydrophobic base. We show that despite maintaining identical backbone structures and dynamics as the wild type HAfp23, the F3G mutant has an attenuated fusion activity that is correlated to its reduced ability to induce negative membrane curvature. The inverted wedge shape of HAfp23 is likely to play a crucial role in the initial stages of membrane fusion by stabilizing negative curvature in the fusion stalk. PMID:25398882
Steric confinement of proteins on lipid membranes can drive curvature and tubulation.
Stachowiak, Jeanne C; Hayden, Carl C; Sasaki, Darryl Y
2010-04-27
Deformation of lipid membranes into curved structures such as buds and tubules is essential to many cellular structures including endocytic pits and filopodia. Binding of specific proteins to lipid membranes has been shown to promote membrane bending during endocytosis and transport vesicle formation. Additionally, specific lipid species are found to colocalize with many curved membrane structures, inspiring ongoing exploration of a variety of roles for lipid domains in membrane bending. However, the specific mechanisms by which lipids and proteins collaborate to induce curvature remain unknown. Here we demonstrate a new mechanism for induction and amplification of lipid membrane curvature that relies on steric confinement of protein binding on membrane surfaces. Using giant lipid vesicles that contain domains with high affinity for his-tagged proteins, we show that protein crowding on lipid domain surfaces creates a protein layer that buckles outward, spontaneously bending the domain into stable buds and tubules. In contrast to previously described bending mechanisms relying on local steric interactions between proteins and lipids (i.e. helix insertion into membranes), this mechanism produces tubules whose dimensions are defined by global parameters: domain size and membrane tension. Our results suggest the intriguing possibility that confining structures, such as lipid domains and protein lattices, can amplify membrane bending by concentrating the steric interactions between bound proteins. This observation highlights a fundamental physical mechanism for initiation and control of membrane bending that may help explain how lipids and proteins collaborate to create the highly curved structures observed in vivo.
Schmidt, Nathan W.; Lis, Michael; Zhao, Kun; Lai, Ghee Hwee; Alexandrova, Anastassia; Tew, Gregory N.; Wong, Gerard C. L.
2013-01-01
We investigate the physical origin of peptide-induced membrane curvature by contrasting differences between H-bonding interactions of prototypical cationic amino acids, arginine (Arg) and lysine (Lys), with phosphate groups of phospholipid heads using quantum mechanical (QM) calculations of a minimum model, and test the results via synthetic oxaorbornene-based transporter sequences without the geometric constraints of polypeptide backbones. QM calculations suggest that although individual Lys can in principle coordinate two phosphates, they are not able to do so at small inter-Lys distances without drastic energetic penalties. In contrast, Arg can coordinate two phosphates down to less than 5 Å, where guanidinium groups can stack ‘face to face’. In agreement with these observations, poly-Lys cannot generate the nanoscale positive curvature necessary for inducing negative Gaussian membrane curvature, in contrast to poly-Arg. Also consistent with QM calculations, polyguanidine-oxanorbornene homopolymers (PGONs) showed that curvature generation is exquisitely sensitive to the guanidinium group spacing when the phosphate groups are near close packing. Addition of phenyl or butyl hydrophobic groups into guanidine-oxanorbornene polymers increased the amount of induced saddle-splay membrane curvature, and broadened the range of lipid compositions where saddle-splay curvature was induced. The enhancement of saddle-splay curvature generation and relaxation of lipid composition requirements via addition of hydrophobicity is consistent with activity profiles. While PGON polymers displayed selective antimicrobial activity against prototypical (Gram positive and negative) bacteria, polymers with phenyl and butyl groups were also active against red blood cells. Our results suggest that it is possible to achieve deterministic molecular design of pore forming peptides. PMID:23061419
The apoptotic protein tBid promotes leakage by altering membrane curvature.
Epand, Raquel F; Martinou, Jean-Claude; Fornallaz-Mulhauser, Monique; Hughes, Donald W; Epand, Richard M
2002-09-06
The apoptotic protein tBid is effective in promoting both leakage and lipid mixing in liposomes composed of cardiolipin and phosphatidylcholine at a molar ratio of 1:2 in the presence of calcium. When half of the phosphatidylcholine component of these liposomes is replaced with phosphatidylethanolamine, a lipid that promotes negative membrane curvature, the rates of both leakage and lipid mixing caused by tBid are substantially increased. Replacement of cardiolipin with phosphatidylglycerol, a lipid that is structurally similar to cardiolipin but does not promote negative membrane curvature in the presence of calcium, prevents the tBid from promoting leakage. The promotion of leakage by tBid is also inhibited by several substances that promote positive membrane curvature, including lysophosphatidylcholine, tritrpticin, a potent antimicrobial peptide, and cyclosporin A, a known inhibitor of cytochrome c release from mitochondria. We directly measured the effect of tBid on membrane curvature by (31)P NMR. We found that tBid promotes the formation of highly curved non-lamellar phases. All of these data are consistent with the hypothesis that tBid promotes negative curvature, and as a result it destabilizes bilayer membranes. Bcl-X(L) inhibits leakage and lipid mixing induced by tBid. Bcl-X(L) is anti-apoptotic. It reduces the promotion of non-bilayer phases by tBid, although by itself Bcl-X(L) is capable of promoting their formation. Bcl-X(L) has little effect on liposomal integrity. Our results suggest that the anti-apoptotic activity of Bcl-X(L) is not a consequence of its interaction with membranes, but rather with other proteins, such as tBid.
BAR Domains as Sensors of Membrane Curvature: The Amphiphysin BAR Structure
NASA Astrophysics Data System (ADS)
Peter, Brian J.; Kent, Helen M.; Mills, Ian G.; Vallis, Yvonne; Butler, P. Jonathan G.; Evans, Philip R.; McMahon, Harvey T.
2004-01-01
The BAR (Bin/amphiphysin/Rvs) domain is the most conserved feature in amphiphysins from yeast to human and is also found in endophilins and nadrins. We solved the structure of the Drosophila amphiphysin BAR domain. It is a crescent-shaped dimer that binds preferentially to highly curved negatively charged membranes. With its N-terminal amphipathic helix and BAR domain (N-BAR), amphiphysin can drive membrane curvature in vitro and in vivo. The structure is similar to that of arfaptin2, which we find also binds and tubulates membranes. From this, we predict that BAR domains are in many protein families, including sorting nexins, centaurins, and oligophrenins. The universal and minimal BAR domain is a dimerization, membrane-binding, and curvature-sensing module.
NASA Astrophysics Data System (ADS)
Angel, J. Roger P.; Burge, James H.; Hege, E. Keith; Kenworthy, Matthew A.; Woolf, Neville J.
2000-07-01
Very large space telescopes with primary mirrors made of flat segments have been recently proposed. The segments would be extremely lightweight, made like pellicles from stretched, reflective membranes. Here we consider the use of such membrane primary mirrors in which slight concave curvature is induced by electrostatic force, by application of a potential difference between the membrane and a control electrode behind. In this way segmented spherical or paraboloidal primaries of long focal length can be made directly, eliminating the correction optics needed when flat segments are used. The electric potential would be spatially and temporally controlled to obtain uniform curvature despite non-uniformity in membrane tension, to create slight asphericity if needed and to provide active damping of vibrations. We report the operation of a small prototype telescope with a SEMC primary.
NASA Astrophysics Data System (ADS)
Junesch, Juliane; Emilsson, Gustav; Xiong, Kunli; Kumar, Shailabh; Sannomiya, Takumi; Pace, Hudson; Vörös, Janos; Oh, Sang-Hyun; Bally, Marta; Dahlin, Andreas B.
2015-09-01
The biochemical processes of cell membranes are sensitive to the geometry of the lipid bilayer. We show how plasmonic ``nanowells'' provide label-free real-time analysis of molecules on membranes with detection of preferential binding at negative curvature. It is demonstrated that norovirus accumulate in invaginations due to multivalent interactions with glycosphingolipids.The biochemical processes of cell membranes are sensitive to the geometry of the lipid bilayer. We show how plasmonic ``nanowells'' provide label-free real-time analysis of molecules on membranes with detection of preferential binding at negative curvature. It is demonstrated that norovirus accumulate in invaginations due to multivalent interactions with glycosphingolipids. Electronic supplementary information (ESI) available: Additional plasmonic sensing results, numerical electromagnetic simulations, quartz crystal microbalance data, fluorescence recovery after photobleaching, additional electron microscopy images, experimental methodology and materials used. See DOI: 10.1039/c5nr04208a
Schmidt, Nathan W.; Mishra, Abhijit; Wang, Jun; DeGrado, William F.; Wong, Gerard C. L.
2013-01-01
The M2 protein is a multi-functional protein, which plays several roles in the replication cycle of the influenza A virus. Here we focus on its ability to promote budding of the mature virus from the cell surface. Using high resolution small angle X-ray scattering we show that M2 can restructure lipid membranes into bicontinuous cubic phases which are rich in negative Gaussian curvature (NGC). The active generation of negative Gaussian membrane curvature by M2 is essential to influenza virus budding. M2 has been observed to colocalize with the region of high NGC at the neck of a bud. The structural requirements for scission are even more stringent than those for budding, as the neck must be considerably smaller than the virus during ‘pinch off’. Consistent with this, the amount of NGC in the induced cubic phases suggests that M2 proteins can generate high curvatures comparable to those on a neck with size 10x smaller than a spherical influenza virus. Similar experiments on variant proteins containing different M2 domains show that the cytoplasmic amphipathic helix is necessary and sufficient for NGC generation. Mutations to the helix which reduce its amphiphilicity and are known to diminish budding attenuated NGC generation. An M2 construct comprising the membrane interactive domains, the transmembrane helix and the cytoplasmic helix, displayed enhanced ability to generate NGC, suggesting that other domains cooperatively promote membrane curvature. These studies establish the importance of M2-induced negative Gaussian curvature during budding and suggest that antagonizing this curvature is a viable anti-influenza strategy. PMID:23962302
Bavi, Omid; Cox, Charles D.; Vossoughi, Manouchehr; Naghdabadi, Reza; Jamali, Yousef; Martinac, Boris
2016-01-01
Mechanosensitive (MS) channels are ubiquitous molecular force sensors that respond to a number of different mechanical stimuli including tensile, compressive and shear stress. MS channels are also proposed to be molecular curvature sensors gating in response to bending in their local environment. One of the main mechanisms to functionally study these channels is the patch clamp technique. However, the patch of membrane surveyed using this methodology is far from physiological. Here we use continuum mechanics to probe the question of how curvature, in a standard patch clamp experiment, at different length scales (global and local) affects a model MS channel. Firstly, to increase the accuracy of the Laplace’s equation in tension estimation in a patch membrane and to be able to more precisely describe the transient phenomena happening during patch clamping, we propose a modified Laplace’s equation. Most importantly, we unambiguously show that the global curvature of a patch, which is visible under the microscope during patch clamp experiments, is of negligible energetic consequence for activation of an MS channel in a model membrane. However, the local curvature (RL < 50) and the direction of bending are able to cause considerable changes in the stress distribution through the thickness of the membrane. Not only does local bending, in the order of physiologically relevant curvatures, cause a substantial change in the pressure profile but it also significantly modifies the stress distribution in response to force application. Understanding these stress variations in regions of high local bending is essential for a complete understanding of the effects of curvature on MS channels. PMID:26861405
Bavi, Omid; Cox, Charles D; Vossoughi, Manouchehr; Naghdabadi, Reza; Jamali, Yousef; Martinac, Boris
2016-02-05
Mechanosensitive (MS) channels are ubiquitous molecular force sensors that respond to a number of different mechanical stimuli including tensile, compressive and shear stress. MS channels are also proposed to be molecular curvature sensors gating in response to bending in their local environment. One of the main mechanisms to functionally study these channels is the patch clamp technique. However, the patch of membrane surveyed using this methodology is far from physiological. Here we use continuum mechanics to probe the question of how curvature, in a standard patch clamp experiment, at different length scales (global and local) affects a model MS channel. Firstly, to increase the accuracy of the Laplace's equation in tension estimation in a patch membrane and to be able to more precisely describe the transient phenomena happening during patch clamping, we propose a modified Laplace's equation. Most importantly, we unambiguously show that the global curvature of a patch, which is visible under the microscope during patch clamp experiments, is of negligible energetic consequence for activation of an MS channel in a model membrane. However, the local curvature (RL < 50) and the direction of bending are able to cause considerable changes in the stress distribution through the thickness of the membrane. Not only does local bending, in the order of physiologically relevant curvatures, cause a substantial change in the pressure profile but it also significantly modifies the stress distribution in response to force application. Understanding these stress variations in regions of high local bending is essential for a complete understanding of the effects of curvature on MS channels.
NASA Astrophysics Data System (ADS)
Lee, Sin-Doo
2015-10-01
Soft matters such as liquid crystals and biological molecules exhibit a variety of interesting physical phenomena as well as new applications. Recently, in mimicking biological systems that have the ability to sense, regulate, grow, react, and regenerate in a highly responsive and self-adaptive manner, the significance of the liquid crystal order in living organisms, for example, a biological membrane possessing the lamellar order, is widely recognized from the viewpoints of physics and chemistry of interfaces and membrane biophysics. Lipid bilayers, resembling cell membranes, provide primary functions for the transport of biological components of ions and molecules in various cellular activities, including vesicle budding and membrane fusion, through lateral organization of the membrane components such as proteins. In this lecture, I will describe how the liquid crystal-analog curvature elasticity of a lipid bilayer plays a critical role in developing a new platform for understanding diverse biological functions at a cellular level. The key concept is to manipulate the local curvature at an interface between a solid substrate and a model membrane. Two representative examples will be demonstrated: one of them is the topographic control of lipid rafts in a combinatorial array where the ligand-receptor binding event occurs and the other concerns the reconstitution of a ring-type lipid raft in bud-mimicking architecture within the framework of the curvature elasticity.
A PH domain in ACAP1 possesses key features of the BAR domain in promoting membrane curvature
Pang, Xiaoyun; Fan, Jun; Zhang, Yan; Zhang, Kai; Gao, Bingquan; Ma, Jun; Li, Jian; Deng, Yuchen; Zhou, Qiangjun; Egelman, Edward H.; Hsu, Victor W.; Sun, Fei
2014-01-01
SUMMARY The BAR (Bin-Amphiphysin-Rvs) domain undergoes dimerization to produce a curved protein structure, which superimposes onto membrane through electrostatic interactions to sense and impart membrane curvature. In some cases, a BAR domain also possesses an amphipathic helix that inserts into the membrane to induce curvature. ACAP1 (Arfgap with Coil coil, Ankyrin repeat and PH domain protein 1) contains a BAR domain. Here, we show that this BAR domain can neither bind membrane nor impart curvature, but instead, requires a neighboring PH (Pleckstrin Homology) domain to achieve these functions. Specific residues within the PH domain are responsible for both membrane binding and curvature generation. The BAR domain adjacent to the PH domain instead interacts with the BAR domains of neighboring ACAP1 proteins to enable clustering at the membrane. Thus, we have uncovered the molecular basis for an unexpected and unconventional collaboration between PH and BAR domains in membrane bending. PMID:25284369
A PH domain in ACAP1 possesses key features of the BAR domain in promoting membrane curvature.
Pang, Xiaoyun; Fan, Jun; Zhang, Yan; Zhang, Kai; Gao, Bingquan; Ma, Jun; Li, Jian; Deng, Yuchen; Zhou, Qiangjun; Egelman, Edward H; Hsu, Victor W; Sun, Fei
2014-10-13
The BAR (Bin-Amphiphysin-Rvs) domain undergoes dimerization to produce a curved protein structure, which superimposes onto membrane through electrostatic interactions to sense and impart membrane curvature. In some cases, a BAR domain also possesses an amphipathic helix that inserts into the membrane to induce curvature. ACAP1 (Arfgap with Coil coil, Ankyrin repeat, and PH domain protein 1) contains a BAR domain. Here, we show that this BAR domain can neither bind membrane nor impart curvature, but instead requires a neighboring PH (Pleckstrin Homology) domain to achieve these functions. Specific residues within the PH domain are responsible for both membrane binding and curvature generation. The BAR domain adjacent to the PH domain instead interacts with the BAR domains of neighboring ACAP1 proteins to enable clustering at the membrane. Thus, we have uncovered the molecular basis for an unexpected and unconventional collaboration between PH and BAR domains in membrane bending. Copyright © 2014 Elsevier Inc. All rights reserved.
Chang-Ileto, Belle; Frere, Samuel G.; Chan, Robin B.; Voronov, Sergey V.; Roux, Aurélien; Di Paolo, Gilbert
2011-01-01
SUMMARY Phosphatidylinositol-4,5-bisphosphate [PI(4,5)P2] plays a fundamental role in clathrin-mediated endocytosis. However, precisely how PI(4,5)P2 metabolism is spatially and temporally regulated during membrane internalization and the functional consequences of endocytosis-coupled PI(4,5)P2 dephosphorylation remain to be explored. Using cell free assays with liposomes of varying curvatures, we show that the major synaptic phosphoinositide phosphatase, synaptojanin 1 (Synj1), acts with membrane curvature generators/sensors, such as the BAR protein endophilin, to preferentially remove PI(4,5)P2 from curved membranes as opposed to relatively flat ones. Moreover, in vivo recruitment of Synj1’s inositol 5-phosphatase domain to endophilin-induced membrane tubules results in fragmentation and condensation of these structures largely in a dynamin-dependent fashion. Our study raises the possibility that geometry-based mechanisms may contribute to spatially restricting PI(4,5)P2 elimination during membrane internalization and suggests that the PI(4,5)P2-to-PI4P conversion achieved by Synj1 at sites of high curvature may cooperate with dynamin to achieve membrane fission. PMID:21316588
Arenavirus budding resulting from viral-protein-associated cell membrane curvature.
Schley, David; Whittaker, Robert J; Neuman, Benjamin W
2013-09-06
Viral replication occurs within cells, with release (and onward infection) primarily achieved through two alternative mechanisms: lysis, in which virions emerge as the infected cell dies and bursts open; or budding, in which virions emerge gradually from a still living cell by appropriating a small part of the cell membrane. Virus budding is a poorly understood process that challenges current models of vesicle formation. Here, a plausible mechanism for arenavirus budding is presented, building on recent evidence that viral proteins embed in the inner lipid layer of the cell membrane. Experimental results confirm that viral protein is associated with increased membrane curvature, whereas a mathematical model is used to show that localized increases in curvature alone are sufficient to generate viral buds. The magnitude of the protein-induced curvature is calculated from the size of the amphipathic region hypothetically removed from the inner membrane as a result of translation, with a change in membrane stiffness estimated from observed differences in virion deformation as a result of protein depletion. Numerical results are based on experimental data and estimates for three arenaviruses, but the mechanisms described are more broadly applicable. The hypothesized mechanism is shown to be sufficient to generate spontaneous budding that matches well both qualitatively and quantitatively with experimental observations.
Arenavirus budding resulting from viral-protein-associated cell membrane curvature
Schley, David; Whittaker, Robert J.; Neuman, Benjamin W.
2013-01-01
Viral replication occurs within cells, with release (and onward infection) primarily achieved through two alternative mechanisms: lysis, in which virions emerge as the infected cell dies and bursts open; or budding, in which virions emerge gradually from a still living cell by appropriating a small part of the cell membrane. Virus budding is a poorly understood process that challenges current models of vesicle formation. Here, a plausible mechanism for arenavirus budding is presented, building on recent evidence that viral proteins embed in the inner lipid layer of the cell membrane. Experimental results confirm that viral protein is associated with increased membrane curvature, whereas a mathematical model is used to show that localized increases in curvature alone are sufficient to generate viral buds. The magnitude of the protein-induced curvature is calculated from the size of the amphipathic region hypothetically removed from the inner membrane as a result of translation, with a change in membrane stiffness estimated from observed differences in virion deformation as a result of protein depletion. Numerical results are based on experimental data and estimates for three arenaviruses, but the mechanisms described are more broadly applicable. The hypothesized mechanism is shown to be sufficient to generate spontaneous budding that matches well both qualitatively and quantitatively with experimental observations. PMID:23864502
Membrane nanotubes induced by aqueous phase separation and stabilized by spontaneous curvature
Li, Yanhong; Lipowsky, Reinhard; Dimova, Rumiana
2011-01-01
Tubular membrane structures are widespread in eukaryotic cells, but the mechanisms underlying their formation and stability are not well understood. Previous work has focused on tube extrusion from cells and model membranes under the application of external forces. Here, we present novel membrane/polymer systems, where stable tubes form in the absence of externally applied forces. Solutions of two water-soluble polymers, polyethylene glycol and dextran, were encapsulated in giant lipid vesicles, cell-size model systems. Hypertonic deflation induced phase separation of the enclosed solution. The excess membrane area created during the deflation process was stored in a large number of membrane nanotubes inside the vesicle. The tubes had a diameter below optical resolution and became visible only when fluorescently labeled. The tubes were rather stable: In the absence of external forces, they existed for several days. A theoretical analysis of the shapes of the deflated vesicles reveals that these shapes would be unstable if the membranes had no spontaneous curvature. Using the large separation of length scales between the tube diameter and the overall size of the vesicles, the spontaneous curvature can be calculated and is found to be about -1/(240 nm) for a certain range of polymer concentrations. The nanotubes could also be retracted back into the mother vesicle by increasing the membrane tension via micropipette aspiration of the vesicle. Membrane tubes, which can form and be retracted easily, should be relevant for lipid storage in cells. PMID:21383120
On ripples and rafts: Curvature induced nanoscale structures in lipid membranes
NASA Astrophysics Data System (ADS)
Schmid, Friederike; Dolezel, Stefan; Lenz, Olaf; Meinhardt, Sebastian
2014-03-01
We develop an elastic theory that predicts the spontaneous formation of nanoscale structures in lipid bilayers which locally phase separate between two phases with different spontaneous monolayer curvature. The theory rationalizes in a unified manner the observation of a variety of nanoscale structures in lipid membranes: Rippled states in one-component membranes, lipid rafts in multicomponent membranes. Furthermore, we report on recent observations of rippled states and rafts in simulations of a simple coarse-grained model for lipid bilayers, which are compatible with experimental observations and with our elastic model.
NASA Astrophysics Data System (ADS)
RóŻycki, Bartosz; Lipowsky, Reinhard
2016-08-01
Biomimetic and biological membranes consist of molecular bilayers with two leaflets that are typically exposed to different aqueous solutions. We consider solutions of "particles" that experience effectively repulsive interactions with these membranes and form depletion layers in front of the membrane leaflets. The particles considered here are water-soluble, have a size between a few angstrom and a few nanometers as well as a rigid, more or less globular shape, and do neither adsorb onto the membranes nor permeate these membranes. Examples are provided by ions, small sugar molecules, globular proteins, or inorganic nanoparticles with a hydrophilic surface. We first study depletion layers in a hard-core system based on ideal particle solutions as well as hard-wall interactions between these particles and the membrane. For this system, we obtain exact expressions for the coverages and tensions of the two leaflets as well as for the spontaneous curvature of the bilayer membrane. All of these quantities depend linearly on the particle concentrations. The exact results for the hard-core system also show that the spontaneous curvature can be directly deduced from the planar membrane geometry. Our results for the hard-core system apply both to ions and solutes that are small compared to the membrane thickness and to nanoparticles with a size that is comparable to the membrane thickness, provided the particle solutions are sufficiently dilute. We then corroborate the different relationships found for the hard-core system by extensive simulations of a soft-core particle system using dissipative particle dynamics. The simulations confirm the linear relationships obtained for the hard-core system. Both our analytical and our simulation results show that the spontaneous curvature induced by a single particle species can be quite large. When one leaflet of the membrane is exposed, e.g., to a 100 mM solution of glucose, a lipid bilayer can acquire a spontaneous curvature of ±1
Shen, Chong; Meng, Qin; Zhang, Guoliang
2013-08-01
Tissue engineering devices as in vitro cell culture systems in scaffolds has encountered the bottleneck due to their much lower cell functions than real tissues/organs in vivo. Such situation has been improved in some extent by mimicking the cell microenvironments in vivo from either chemical or physical ways. However, microenvironmental curvature, commonly seen in real tissues/organs, has never been manipulated to regulate the cell performance in vitro. In this regard, this paper fabricated polysulfone membranes with or without polyethylene glycol modification to investigate the impact of curvature on two renal tubular cells. Regardless the varying membrane curvatures among hollow fiber membranes of different diameters and flat membrane of zero curvature, both renal cells could well attach at 4 h of seeding and form similar confluent layers at 6 days on each membrane. Nevertheless, the renal cells on hollow fibers, though showing confluent morphology as those on flat membranes, expressed higher renal functions and, moreover, the renal functions significantly increased with the membrane curvature among hollow fibers. Such upregulation on functions was unassociated with mass transport barrier of hollow fibers, because the cultures on lengthwise cut hollow fibers without mass transfer barrier showed same curvature effect on renal functions as whole hollow fibers. It could be proposed that the curvature of hollow fiber membrane approaching to the large curvature in kidney tubules increased the mechanical stress in the renal cells and thus might up-regulate the renal cell functions. In conclusion, the increase of substrate curvature could up-regulate the cell functions without altering the confluent cell morphology and this finding will facilitate the design of functional tissue engineering devices.
Ward, Katherine E.; Ropa, James P.; Adu-Gyamfi, Emmanuel; Stahelin, Robert V.
2012-01-01
Group IVA cytosolic phospholipase A2 (cPLA2α) is an 85 kDa enzyme that regulates the release of arachidonic acid (AA) from the sn-2 position of membrane phospholipids. It is well established that cPLA2α binds zwitterionic lipids such as phosphatidylcholine in a Ca2+-dependent manner through its N-terminal C2 domain, which regulates its translocation to cellular membranes. In addition to its role in AA synthesis, it has been shown that cPLA2α promotes tubulation and vesiculation of the Golgi and regulates trafficking of endosomes. Additionally, the isolated C2 domain of cPLA2α is able to reconstitute Fc receptor-mediated phagocytosis, suggesting that C2 domain membrane binding is sufficient for phagosome formation. These reported activities of cPLA2α and its C2 domain require changes in membrane structure, but the ability of the C2 domain to promote changes in membrane shape has not been reported. Here we demonstrate that the C2 domain of cPLA2α is able to induce membrane curvature changes to lipid vesicles, giant unilamellar vesicles, and membrane sheets. Biophysical assays combined with mutagenesis of C2 domain residues involved in membrane penetration demonstrate that membrane insertion by the C2 domain is required for membrane deformation, suggesting that C2 domain-induced membrane structural changes may be an important step in signaling pathways mediated by cPLA2α. PMID:22991194
Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins
NASA Astrophysics Data System (ADS)
Ramakrishnan, N.; Sunil Kumar, P. B.; Radhakrishnan, Ravi
2014-10-01
Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham-Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this description, the
Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins
Ramakrishnan, N.; Sunil Kumar, P. B.; Radhakrishnan, Ravi
2014-01-01
Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham - Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this
Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins.
Ramakrishnan, N; Sunil Kumar, P B; Radhakrishnan, Ravi
2014-10-01
Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham - Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this
Stachowiak, Jeanne C.; Hayden, Carl C.; Negrete, Oscar.; Davis, Ryan Wesley; Sasaki, Darryl Y
2013-10-01
Pathogenic viruses are a primary threat to our national security and to the health and economy of our world. Effective defense strategies to combat viral infection and spread require the development of understanding of the mechanisms that these pathogens use to invade the host cell. We present in this report results of our research into viral particle recognition and fusion to cell membranes and the role that protein affinity and confinement in lipid domains plays in membrane curvature in cellular fusion and fission events. Herein, we describe 1) the assembly of the G attachment protein of Nipah virus using point mutation studies to define its role in viral particle fusion to the cell membrane, 2) how lateral pressure of membrane bound proteins induce curvature in model membrane systems, and 3) the role of membrane curvature in the selective partitioning of molecular receptors and specific affinity of associated proteins.
Lee, Hwankyu
2013-10-14
We performed coarse-grained (CG) molecular dynamics (MD) simulations of single-walled carbon nanotubes (SWNTs) with lipid bilayers to understand the effect of the SWNT diameter, length, and concentration on membrane curvature and penetration. Starting with different orientations of multiple SWNTs near lipid bilayers, simulations show that SWNTs insert into the bilayer and induce membrane curvature, which is much larger than that observed from previous simulations of a single SWNT. Longer and thicker SWNTs at higher concentration cause larger membrane curvature, indicating the effect of the SWNT size and concentration, in qualitative agreement with experiments. In particular, thicker SWNTs significantly increase the bilayer height and the difference of the projected and contour bilayer areas, decrease the area compressibility, and disorder lipids. When inserted into the bilayer, thinner SWNTs mainly contact the entire tails of lipids, while thicker SWNTs are wrapped mainly by the ending tail-carbons, leading to the larger membrane curvature. This indicates the effect of SWNT diameter on the SWNT-lipid interaction, yielding different extents of membrane curvature. These findings imply that the SWNT-induced membrane penetration and curvature are modulated by a combination of SWNT length, diameter, and concentration.
Koldsø, Heidi; Shorthouse, David; Hélie, Jean; Sansom, Mark S. P.
2014-01-01
Cell membranes are complex multicomponent systems, which are highly heterogeneous in the lipid distribution and composition. To date, most molecular simulations have focussed on relatively simple lipid compositions, helping to inform our understanding of in vitro experimental studies. Here we describe on simulations of complex asymmetric plasma membrane model, which contains seven different lipids species including the glycolipid GM3 in the outer leaflet and the anionic lipid, phosphatidylinositol 4,5-bisphophate (PIP2), in the inner leaflet. Plasma membrane models consisting of 1500 lipids and resembling the in vivo composition were constructed and simulations were run for 5 µs. In these simulations the most striking feature was the formation of nano-clusters of GM3 within the outer leaflet. In simulations of protein interactions within a plasma membrane model, GM3, PIP2, and cholesterol all formed favorable interactions with the model α-helical protein. A larger scale simulation of a model plasma membrane containing 6000 lipid molecules revealed correlations between curvature of the bilayer surface and clustering of lipid molecules. In particular, the concave (when viewed from the extracellular side) regions of the bilayer surface were locally enriched in GM3. In summary, these simulations explore the nanoscale dynamics of model bilayers which mimic the in vivo lipid composition of mammalian plasma membranes, revealing emergent nanoscale membrane organization which may be coupled both to fluctuations in local membrane geometry and to interactions with proteins. PMID:25340788
Koldsø, Heidi; Shorthouse, David; Hélie, Jean; Sansom, Mark S P
2014-10-01
Cell membranes are complex multicomponent systems, which are highly heterogeneous in the lipid distribution and composition. To date, most molecular simulations have focussed on relatively simple lipid compositions, helping to inform our understanding of in vitro experimental studies. Here we describe on simulations of complex asymmetric plasma membrane model, which contains seven different lipids species including the glycolipid GM3 in the outer leaflet and the anionic lipid, phosphatidylinositol 4,5-bisphophate (PIP2), in the inner leaflet. Plasma membrane models consisting of 1500 lipids and resembling the in vivo composition were constructed and simulations were run for 5 µs. In these simulations the most striking feature was the formation of nano-clusters of GM3 within the outer leaflet. In simulations of protein interactions within a plasma membrane model, GM3, PIP2, and cholesterol all formed favorable interactions with the model α-helical protein. A larger scale simulation of a model plasma membrane containing 6000 lipid molecules revealed correlations between curvature of the bilayer surface and clustering of lipid molecules. In particular, the concave (when viewed from the extracellular side) regions of the bilayer surface were locally enriched in GM3. In summary, these simulations explore the nanoscale dynamics of model bilayers which mimic the in vivo lipid composition of mammalian plasma membranes, revealing emergent nanoscale membrane organization which may be coupled both to fluctuations in local membrane geometry and to interactions with proteins.
Sankhagowit, Shalene; Lee, Ernest Y; Wong, Gerard C L; Malmstadt, Noah
2016-03-15
Oxidation is associated with conditions related to chronic inflammations and aging. Cubic structures have been observed in the smooth endoplasmic reticulum and mitochondrial membranes of cells under oxidative stress (e.g., tumor cells and virus-infected cells). It has been previously suspected that oxidation can result in the rearrangement of lipids from a fluid lamellar phase to a cubic structure in organelles containing membranes enriched with amphiphiles that have nonzero intrinsic curvature, such as phosphatidylethanolamine (PE) and cardiolipin. This study focuses on the oxidation of 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE), a lipid that natively forms an inverted hexagonal phase at physiological conditions. The oxidized samples contain an approximately 3:2 molar ratio of nonoxidized to oxidized DOPE. Optical microscopy images collected during the hydration of this mixture from a dried film suggest that the system evolves into a coexistence of a stable fluid lamellar phase and transient square lattice structures with unit cell sizes of 500-600 nm. Small-angle X-ray scattering of the same lipid mixture yielded a body-centered Im3m cubic phase with the lattice parameter of 14.04 nm. On average, the effective packing parameter of the oxidized DOPE species was estimated to be 0.657 ± 0.069 (standard deviation). This suggests that the oxidation of PE leads to a group of species with inverted molecular intrinsic curvature. Oxidation can create amphiphilic subpopulations that potently impact the integrity of the membrane, since negative Gaussian curvature intrinsic to cubic phases can enable membrane destabilization processes.
NASA Astrophysics Data System (ADS)
Lee, Michelle; Hwee Lai, Ghee; Schmidt, Nathan; Xian, Wujing; Wong, Gerard C. L.
2013-03-01
Mitochondria form a dynamic and interconnected network, which disintegrates during apoptosis to generate numerous smaller mitochondrial fragments. This process is at present not well understood. Yeast mitochondrial fission machinery proteins, Dnm1 and Fis1, are believed to regulate programmed cell death in yeast. Yeast Dnm1 has been previously shown to promote mitochondrial fragmentation and degradation characteristic of apoptotic cells, while yeast Fis1 inhibits cell death by limiting the mitochondrial fission induced by Dnm1 [Fannjiang et al, Genes & Dev. 2004. 18: 2785-2797]. To better understand the mechanisms of these antagonistic fission proteins, we use synchrotron small angle x-ray scattering (SAXS) to investigate their interaction with model cell membranes. The relationship between each protein, Dnm1 and Fis1, and protein-induced changes in membrane curvature and topology is examined. Through the comparison of the membrane rearrangement and phase behavior induced by each protein, we will discuss their respective roles in the regulation of mitochondrial fission.
Picard, G.; Schneider-Henriquez, J.E.; Fendler, J.H. )
1990-01-25
Two-exposure interferometric holograms have been shown to sensitively report ultrasmall-pressure (10 natm)-induced curvature changes in glyceryl monooleate (GMO) bilayer lipid membranes (BLMs). The number of concentric fringes observed, and hence the lateral distance between the plane of the Teflon and the BLM, increased linearly with increasing transmembrane pressure and led to a value of 1.1 {plus minus} 0.05 dyn/cm for the surface tension of the BLM. BLMs with appreciable Plateau-Gibbs borders have been shown to undergo nonuniform deformation; the bilayer portion is distorted less than the surrounding Plateau-Gibbs border upon the application of a transmembrane pressure gradient.
Lipid exchange between membranes: effects of membrane surface charge, composition, and curvature.
Zhu, Tao; Jiang, Zhongying; Ma, Yuqiang
2012-09-01
Intermembrane lipid exchange is critical to membrane functions and pharmaceutical applications. The exchange process is not fully understood and it is explored by quartz crystal microbalance with dissipation monitor method in this research. It is found that intermembrane lipid exchange is accelerated with the decrease of vesicle size and the increase of charge and liquid crystalline lipid composition ratio. Vesicle adsorption rate, membrane lateral pressure gradient, and lipid lateral diffusion coefficient are inferred to be critical in deciding the lipid exchange kinetics between membranes. Besides that, the membrane contact situation during lipid exchange is also studied. The maximum total membrane contact area is found to increase with the decrease of vesicle size, charged and liquid crystalline lipid composition ratio. A competition mechanism between the vesicle adsorption rate and the intermembrane lipid exchange rate was proposed to control the maximum total membrane contact area.
Beltrán-Heredia, Elena; Almendro-Vedia, Víctor G.; Monroy, Francisco; Cao, Francisco J.
2017-01-01
Many cell division processes have been conserved throughout evolution and are being revealed by studies on model organisms such as bacteria, yeasts, and protozoa. Cellular membrane constriction is one of these processes, observed almost universally during cell division. It happens similarly in all organisms through a mechanical pathway synchronized with the sequence of cytokinetic events in the cell interior. Arguably, such a mechanical process is mastered by the coordinated action of a constriction machinery fueled by biochemical energy in conjunction with the passive mechanics of the cellular membrane. Independently of the details of the constriction engine, the membrane component responds against deformation by minimizing the elastic energy at every constriction state following a pathway still unknown. In this paper, we address a theoretical study of the mechanics of membrane constriction in a simplified model that describes a homogeneous membrane vesicle in the regime where mechanical work due to osmotic pressure, surface tension, and bending energy are comparable. We develop a general method to find approximate analytical expressions for the main descriptors of a symmetrically constricted vesicle. Analytical solutions are obtained by combining a perturbative expansion for small deformations with a variational approach that was previously demonstrated valid at the reference state of an initially spherical vesicle at isotonic conditions. The analytic approximate results are compared with the exact solution obtained from numerical computations, getting a good agreement for all the computed quantities (energy, area, volume, constriction force). We analyze the effects of the spontaneous curvature, the surface tension and the osmotic pressure in these quantities, focusing especially on the constriction force. The more favorable conditions for vesicle constriction are determined, obtaining that smaller constriction forces are required for positive spontaneous
Beltrán-Heredia, Elena; Almendro-Vedia, Víctor G; Monroy, Francisco; Cao, Francisco J
2017-01-01
Many cell division processes have been conserved throughout evolution and are being revealed by studies on model organisms such as bacteria, yeasts, and protozoa. Cellular membrane constriction is one of these processes, observed almost universally during cell division. It happens similarly in all organisms through a mechanical pathway synchronized with the sequence of cytokinetic events in the cell interior. Arguably, such a mechanical process is mastered by the coordinated action of a constriction machinery fueled by biochemical energy in conjunction with the passive mechanics of the cellular membrane. Independently of the details of the constriction engine, the membrane component responds against deformation by minimizing the elastic energy at every constriction state following a pathway still unknown. In this paper, we address a theoretical study of the mechanics of membrane constriction in a simplified model that describes a homogeneous membrane vesicle in the regime where mechanical work due to osmotic pressure, surface tension, and bending energy are comparable. We develop a general method to find approximate analytical expressions for the main descriptors of a symmetrically constricted vesicle. Analytical solutions are obtained by combining a perturbative expansion for small deformations with a variational approach that was previously demonstrated valid at the reference state of an initially spherical vesicle at isotonic conditions. The analytic approximate results are compared with the exact solution obtained from numerical computations, getting a good agreement for all the computed quantities (energy, area, volume, constriction force). We analyze the effects of the spontaneous curvature, the surface tension and the osmotic pressure in these quantities, focusing especially on the constriction force. The more favorable conditions for vesicle constriction are determined, obtaining that smaller constriction forces are required for positive spontaneous
Shih, Yu-Ling; Huang, Kai-Fa; Lai, Hsin-Mei; Liao, Jiahn-Haur; Lee, Chai-Siah; Chang, Chiao-Min; Mak, Huey-Ming; Hsieh, Cheng-Wei; Lin, Chu-Chi
2011-01-01
Pole-to-pole oscillations of the Min proteins in Escherichia coli are required for the proper placement of the division septum. Direct interaction of MinE with the cell membrane is critical for the dynamic behavior of the Min system. In vitro, this MinE-membrane interaction led to membrane deformation; however, the underlying mechanism remained unclear. Here we report that MinE-induced membrane deformation involves the formation of an amphipathic helix of MinE2–9, which, together with the adjacent basic residues, function as membrane anchors. Biochemical evidence suggested that the membrane association induces formation of the helix, with the helical face, consisting of A2, L3, and F6, inserted into the membrane. Insertion of this helix into the cell membrane can influence local membrane curvature and lead to drastic changes in membrane topology. Accordingly, MinE showed characteristic features of protein-induced membrane tubulation and lipid clustering in in vitro reconstituted systems. In conclusion, MinE shares common protein signatures with a group of membrane trafficking proteins in eukaryotic cells. These MinE signatures appear to affect membrane curvature. PMID:21738659
Shlyonsky, V Gh; Markin, V S; Andreeva, I; Pedersen, S E; Simon, S A; Benos, D J; Ismailov, I I
2006-11-01
We describe the phenomenon of mechanoelectrical transduction in macroscopic lipid bilayer membranes modified by two cation-selective ionophores, valinomycin and nonactin. We found that bulging these membranes, while maintaining the membrane tension constant, produced a marked supralinear increase in specific carrier-mediated conductance. Analyses of the mechanisms involved in mechanoelectrical transduction induced by the imposition of a hydrostatic pressure gradient or by an amphipathic compound chlorpromazine reveal similar changes in the charge carrier motility and carrier reaction rates at the interface(s). Furthermore, the relative change in membrane conductance was independent of membrane diameter, but was directly proportional to the square of membrane curvature, thus relating the observed phenomena to the bilayer bending energy. Extrapolated to biological membranes, these findings indicate that ion transport in cells can be influenced simply by changing shape of the membrane, without a change in membrane tension.
NASA Astrophysics Data System (ADS)
Golushko, I. Yu.; Rochal, S. B.
2016-01-01
Conditions of joint equilibrium and stability are derived for a spherical lipid vesicle and a tubular lipid membrane (TLM) pulled from this vesicle. The obtained equations establish relationships between the geometric and physical characteristics of the system and the external parameters, which have been found to be controllable in recent experiments. In particular, the proposed theory shows that, in addition to the pressure difference between internal and external regions of the system, the variable spontaneous average curvature of the lipid bilayer (forming the TLM) also influences the stability of the lipid tube. The conditions for stability of the cylindrical phase of TLMs after switching off the external force that initially formed the TLM from a vesicle are discussed. The loss of system stability under the action of a small axial force compressing the TLM is considered.
Golushko, I. Yu. Rochal, S. B.
2016-01-15
Conditions of joint equilibrium and stability are derived for a spherical lipid vesicle and a tubular lipid membrane (TLM) pulled from this vesicle. The obtained equations establish relationships between the geometric and physical characteristics of the system and the external parameters, which have been found to be controllable in recent experiments. In particular, the proposed theory shows that, in addition to the pressure difference between internal and external regions of the system, the variable spontaneous average curvature of the lipid bilayer (forming the TLM) also influences the stability of the lipid tube. The conditions for stability of the cylindrical phase of TLMs after switching off the external force that initially formed the TLM from a vesicle are discussed. The loss of system stability under the action of a small axial force compressing the TLM is considered.
Lowengrub, John; Allard, Jun; Aland, Sebastian
2016-03-15
The formation of membrane vesicles from a larger membrane that occurs during endocytosis and other cell processes are typically orchestrated by curvature-inducing molecules attached to the membrane. Recent reports demonstrate that vesicles can form de novo in a few milliseconds. Membrane dynamics at these scales are strongly influenced by hydrodynamic interactions. To study this problem, we develop new diffuse interface models for the dynamics of inextensible vesicles in a viscous fluid with stiff, curvature-inducing molecules. The model couples the Navier-Stokes equations with membrane-induced bending forces that incorporate concentration-dependent bending stiffness coefficients and spontaneous curvatures, with equations for molecule transport and for a Lagrange multiplier to enforce local inextensibility. Two forms of surface transport equations are considered: Fickian surface diffusion and Cahn-Hilliard surface dynamics, with the former being more appropriate for small molecules and the latter being better for large molecules. The system is solved using adaptive finite element methods in 3D axisymmetric geometries. The results demonstrate that hydrodynamics can indeed enable the rapid formation of a small vesicle attached to the membrane by a narrow neck. When the Fickian model is used, this is a transient state with the steady state being a flat membrane with a uniformly distributed molecule concentration due to diffusion. When the Cahn-Hilliard model is used, molecule concentration gradients are sustained, the neck stabilizes and the system evolves to a steady-state with a small, compact vesicle attached to the membrane. By varying the membrane coverage of molecules in the Cahn-Hilliard model, we find that there is a critical (smallest) neck radius and a critical (fastest) budding time. These critical points are associated with changes in the vesicle morphology from spherical to mushroom-like as the molecule coverage on the membrane is increased.
NASA Astrophysics Data System (ADS)
Lowengrub, John; Allard, Jun; Aland, Sebastian
2016-03-01
The formation of membrane vesicles from a larger membrane that occurs during endocytosis and other cell processes is typically orchestrated by curvature-inducing molecules attached to the membrane. Recent reports demonstrate that vesicles can form de novo in a few milliseconds. Membrane dynamics at these scales are strongly influenced by hydrodynamic interactions. To study this problem, we develop new diffuse interface models for the dynamics of inextensible vesicles in a viscous fluid with stiff, curvature-inducing molecules. The model couples the Navier-Stokes equations with membrane-induced bending forces that incorporate concentration-dependent bending stiffness coefficients and spontaneous curvatures, with equations for molecule transport and for a Lagrange multiplier to enforce local inextensibility. Two forms of surface transport equations are considered: Fickian surface diffusion and Cahn-Hilliard surface dynamics, with the former being more appropriate for small molecules and the latter being better for large molecules. The system is solved using adaptive finite element methods in 3D axisymmetric geometries. The results demonstrate that hydrodynamics can indeed enable the rapid formation of a small vesicle attached to the membrane by a narrow neck. When the Fickian model is used, this is a transient state with the steady state being a flat membrane with a uniformly distributed molecule concentration due to diffusion. When the Cahn-Hilliard model is used, molecule concentration gradients are sustained, the neck stabilizes and the system evolves to a steady-state with a small, compact vesicle attached to the membrane. By varying the membrane coverage of molecules in the Cahn-Hilliard model, we find that there is a critical (smallest) neck radius and a critical (fastest) budding time. These critical points are associated with changes in the vesicle morphology from spherical to mushroom-like as the molecule coverage on the membrane is increased.
NASA Astrophysics Data System (ADS)
Gupta, Sanju; Saxena, Avadh
2012-12-01
Soft, polymeric and biological systems are self-assembled and hierarchical that involves a multitude of length scales, geometrical shapes and topological variation besides being elastically soft and easily deformable unlike their inorganic solid counterparts. Within the framework of topology and geometry applied to nanocarbons in our recent work [Gupta and Saxena, J. Appl. Phys. 109, 074316 (2011)], we invoke a similar approach to understanding soft/bio-macromolecular systems having structural diversity specifically within the context of minimal surfaces (i.e., mean curvature H = 0 and Gaussian curvature K < 0 everywhere). The systems of interest include non-periodic and periodic minimal surfaces such as catenoids (synthetic or natural ion-channel membrane proteins), helicoids (β-sheet proteins), and Schwarzites, respectively, which are analyzed within the framework of differential geometry to obtain the information about Gaussian curvature variation, Gaussian bending rigidity, elastic bending energy, and corresponding topological features. Specifically, we study the negative Gaussian curvature distribution providing surface structure of membrane proteins and Schwarzites and corresponding bending energy cost. We focus on ion-channel membrane proteins approximated as a symmetric catenoid, biological sheets as a helicoid and negatively curved carbons and certain mixed di- or triblock copolymers as periodic minimal surfaces, e.g., gyroids. Through these analyses, we identify the role of geometry (shape) and topology in energy storage and catalysis, nanomedicine and drug delivery applications and derive an overarching geometry/topology → property → functionality relationship paradigm.
NASA Astrophysics Data System (ADS)
Zidovska, Alexandra; Ewert, Kai K.; Safinya, Cyrus R.; Quispe, Joel; Carragher, Bridget; Potter, Clinton S.
2008-03-01
Recently, we have reported block liposomes (BLs), a new vesicle phase formed in mixtures of MVLBG2, DOPC and water (A. Zidovska et al., Submitted, 2007), where MVLBG2 is a newly synthesized highly charged (16+) lipid (K. Ewert et al., JACS, 2006) with giant dendrimer-like headgroup. BLs are liposomes consisting of distinctly shaped nanoscale spheres, pears, tubes, or rods connected into blocks. In this work we investigate the contribution of spontaneous curvature and membrane charge density to the formation of BLs. By comparing with a system of matching membrane charge density but zero spontaneous curvature and by screening the charge of MVLBG2 but keeping the curvature constant, we were able to identify both, spontaneous curvature and membrane charge, as critical parameters for BLs-formation. The effect of salt and pH on the shape evolution of the BLs was also carefully studied. Funding provided by DOE DE-FG-02-06ER46314, NIH GM-59288, NSF DMR-0503347.
Pannuzzo, Martina; Raudino, Antonio; Böckmann, Rainer A
2014-07-14
Peptide- or protein-induced curvatures of lipid membranes may be studied in molecular dynamics (MD) simulations. In these, membranes are usually modeled as infinitely extended bilayers by using periodic boundary conditions. However, the enforced periodicity results in an underestimation of the bending power of peptides, unless the patch size is much larger than the induced curvature radii. In this letter, we propose a novel approach to evaluate the bending power of a given distribution and/or density of peptides based on the use of flat open-edged lipid patches. To ensure long-lived metastable structures, the patch rim is stabilized in MD simulations by a local enrichment with short-chain lipids. By combining the theory of continuum elastic media with MD simulations, we prove that open-edged patches evolve from a planar state to a closed vesicle, with a transition rate that strongly depends on the concentration of lipid soluble peptides. For close-to-critical values for the patch size and edge energy, the response to even small changes in peptide concentration adopts a transition-like behavior (buckling instability). The usage of open-edged membrane patches amplifies the bending power of peptides, thereby enabling the analysis of the structural properties of membrane-peptide systems. We applied the presented method to investigate the curvature induced by aggregating β -amyloid peptides, unraveling a strong sensitivity of membrane deformation to the peptide concentration.
NASA Astrophysics Data System (ADS)
Pannuzzo, Martina; Raudino, Antonio; Böckmann, Rainer A.
2014-07-01
Peptide- or protein-induced curvatures of lipid membranes may be studied in molecular dynamics (MD) simulations. In these, membranes are usually modeled as infinitely extended bilayers by using periodic boundary conditions. However, the enforced periodicity results in an underestimation of the bending power of peptides, unless the patch size is much larger than the induced curvature radii. In this letter, we propose a novel approach to evaluate the bending power of a given distribution and/or density of peptides based on the use of flat open-edged lipid patches. To ensure long-lived metastable structures, the patch rim is stabilized in MD simulations by a local enrichment with short-chain lipids. By combining the theory of continuum elastic media with MD simulations, we prove that open-edged patches evolve from a planar state to a closed vesicle, with a transition rate that strongly depends on the concentration of lipid soluble peptides. For close-to-critical values for the patch size and edge energy, the response to even small changes in peptide concentration adopts a transition-like behavior (buckling instability). The usage of open-edged membrane patches amplifies the bending power of peptides, thereby enabling the analysis of the structural properties of membrane-peptide systems. We applied the presented method to investigate the curvature induced by aggregating β -amyloid peptides, unraveling a strong sensitivity of membrane deformation to the peptide concentration.
Furse, Samuel; Jakubec, Martin; Rise, Frode; Williams, Huw E; Rees, Catherine E D; Halskau, Øyvind
2017-08-14
This paper reports that the abundances of endogenous cardiolipin and phosphatidylethanolamine halve during elongation of the Gram-positive bacterium Listeria innocua. The lyotropic phase behaviour of model lipid systems that describe these modulations in lipid composition indicate that the average stored curvature elastic stress of the membrane is reduced on elongation of the cell, while the fluidity appears to be maintained. These findings suggest that phospholipid metabolism is linked to the cell cycle and that changes in membrane composition can facilitate passage to the succeding stage of the cell cycle. This therefore suggests a means by which bacteria can manage the physical properties of their membranes through the cell cycle.
NASA Astrophysics Data System (ADS)
Gardner, Jasmine M.; Deserno, Markus; Abrams, Cameron F.
2016-08-01
We use a combination of coarse-grained molecular dynamics simulations and theoretical modeling to examine three-junctions in mixed lipid bilayer membranes. These junctions are localized defect lines in which three bilayers merge in such a way that each bilayer shares one monolayer with one of the other two bilayers. The resulting local morphology is non-lamellar, resembling the threefold symmetric defect lines in inverse hexagonal phases, but it regularly occurs during membrane fission and fusion events. We realize a system of junctions by setting up a honeycomb lattice, which in its primitive cell contains two hexagons and four three-line junctions, permitting us to study their stability as well as their line tension. We specifically consider the effects of lipid composition and intrinsic curvature in binary mixtures, which contain a fraction of negatively curved lipids in a curvature-neutral background phase. Three-junction stability results from a competition between the junction and an open edge, which arises if one of the three bilayers detaches from the other two. We show that the stable phase is the one with the lower defect line tension. The strong and opposite monolayer curvatures present in junctions and edges enhance the mole fraction of negatively curved lipids in junctions and deplete it in edges. This lipid sorting affects the two line tensions and in turn the relative stability of the two phases. It also leads to a subtle entropic barrier for the transition between junction and edge that is absent in uniform membranes.
Gardner, Jasmine M; Deserno, Markus; Abrams, Cameron F
2016-08-21
We use a combination of coarse-grained molecular dynamics simulations and theoretical modeling to examine three-junctions in mixed lipid bilayer membranes. These junctions are localized defect lines in which three bilayers merge in such a way that each bilayer shares one monolayer with one of the other two bilayers. The resulting local morphology is non-lamellar, resembling the threefold symmetric defect lines in inverse hexagonal phases, but it regularly occurs during membrane fission and fusion events. We realize a system of junctions by setting up a honeycomb lattice, which in its primitive cell contains two hexagons and four three-line junctions, permitting us to study their stability as well as their line tension. We specifically consider the effects of lipid composition and intrinsic curvature in binary mixtures, which contain a fraction of negatively curved lipids in a curvature-neutral background phase. Three-junction stability results from a competition between the junction and an open edge, which arises if one of the three bilayers detaches from the other two. We show that the stable phase is the one with the lower defect line tension. The strong and opposite monolayer curvatures present in junctions and edges enhance the mole fraction of negatively curved lipids in junctions and deplete it in edges. This lipid sorting affects the two line tensions and in turn the relative stability of the two phases. It also leads to a subtle entropic barrier for the transition between junction and edge that is absent in uniform membranes.
NASA Astrophysics Data System (ADS)
Kawamoto, Shuhei; Klein, Michael L.; Shinoda, Wataru
2015-12-01
The effects of membrane curvature on the free energy barrier for membrane fusion have been investigated using coarse-grained molecular dynamics (CG-MD) simulations, assuming that fusion takes place through a stalk intermediate. Free energy barriers were estimated for stalk formation as well as for fusion pore formation using the guiding potential method. Specifically, the three different geometries of two apposed membranes were considered: vesicle-vesicle, vesicle-planar, and planar-planar membranes. The free energy barriers for the resulting fusion were found to depend importantly on the fusing membrane geometries; the lowest barrier was obtained for vesicular membranes. Further, lipid sorting was observed in fusion of the mixed membranes of dimyristoyl phosphatidylcholine and dioleoyl phosphatidylethanolamine (DOPE). Specifically, DOPE molecules were found to assemble around the stalk to support the highly negative curved membrane surface. A consistent result for lipid sorting was observed when a simple continuum model (CM) was used, where the Helfrich energy and mixing entropy of the lipids were taken into account. However, the CM predicts a much higher free energy barrier than found using CG-MD. This discrepancy originates from the conformational changes of lipids, which were not considered in the CM. The results of the CG-MD simulations reveal that a large conformational change in the lipid takes place around the stalk region, which results in a reduction of free energy barriers along the stalk mechanism of membrane fusion.
Kawamoto, Shuhei; Shinoda, Wataru; Klein, Michael L.
2015-12-28
The effects of membrane curvature on the free energy barrier for membrane fusion have been investigated using coarse-grained molecular dynamics (CG-MD) simulations, assuming that fusion takes place through a stalk intermediate. Free energy barriers were estimated for stalk formation as well as for fusion pore formation using the guiding potential method. Specifically, the three different geometries of two apposed membranes were considered: vesicle–vesicle, vesicle–planar, and planar–planar membranes. The free energy barriers for the resulting fusion were found to depend importantly on the fusing membrane geometries; the lowest barrier was obtained for vesicular membranes. Further, lipid sorting was observed in fusion of the mixed membranes of dimyristoyl phosphatidylcholine and dioleoyl phosphatidylethanolamine (DOPE). Specifically, DOPE molecules were found to assemble around the stalk to support the highly negative curved membrane surface. A consistent result for lipid sorting was observed when a simple continuum model (CM) was used, where the Helfrich energy and mixing entropy of the lipids were taken into account. However, the CM predicts a much higher free energy barrier than found using CG-MD. This discrepancy originates from the conformational changes of lipids, which were not considered in the CM. The results of the CG-MD simulations reveal that a large conformational change in the lipid takes place around the stalk region, which results in a reduction of free energy barriers along the stalk mechanism of membrane fusion.
Kawamoto, Shuhei; Klein, Michael L; Shinoda, Wataru
2015-12-28
The effects of membrane curvature on the free energy barrier for membrane fusion have been investigated using coarse-grained molecular dynamics (CG-MD) simulations, assuming that fusion takes place through a stalk intermediate. Free energy barriers were estimated for stalk formation as well as for fusion pore formation using the guiding potential method. Specifically, the three different geometries of two apposed membranes were considered: vesicle-vesicle, vesicle-planar, and planar-planar membranes. The free energy barriers for the resulting fusion were found to depend importantly on the fusing membrane geometries; the lowest barrier was obtained for vesicular membranes. Further, lipid sorting was observed in fusion of the mixed membranes of dimyristoyl phosphatidylcholine and dioleoyl phosphatidylethanolamine (DOPE). Specifically, DOPE molecules were found to assemble around the stalk to support the highly negative curved membrane surface. A consistent result for lipid sorting was observed when a simple continuum model (CM) was used, where the Helfrich energy and mixing entropy of the lipids were taken into account. However, the CM predicts a much higher free energy barrier than found using CG-MD. This discrepancy originates from the conformational changes of lipids, which were not considered in the CM. The results of the CG-MD simulations reveal that a large conformational change in the lipid takes place around the stalk region, which results in a reduction of free energy barriers along the stalk mechanism of membrane fusion.
Kazama, Itsuro; Maruyama, Yoshio; Baba, Asuka
2014-02-01
Microparticles produced from the membrane surface of adipocytes promote lipid biosynthesis and angiogenesis in adipose tissues. Thus, they are deeply associated with the onset of metabolic disorders. Despite our understanding of their roles in physiological or pathological responses, we know little about the mechanism by which microparticles are produced from adipocytes. Based on our previous studies using rat megakaryocytes or mast cells during exocytosis, we proposed that membrane curvature induced by amphiphilic reagents, such as chlorpromazine or salicylate, facilitate or inhibit the formation of microparticles. Since the plasma membranes in adipocytes share many common biophysiological features with those in megakaryocytes or mast cells during exocytosis, the same stimulatory or inhibitory mechanism of microparticle formation would exist in adipocytes. Therefore, we hypothesize here that amphiphilic reagents would also change the membrane curvature in adipocytes, and that such changes would facilitate or inhibit the microparticle formation from adipocytes. Our hypothesis is unique because it sheds light for the first time on the physiological mechanism by which microparticles are produced in adipocytes. It is also important because the idea could have novel therapeutic implications for metabolic disorders that are triggered by increases in the microparticle formation. Copyright © 2013 Elsevier Ltd. All rights reserved.
Yang, L.; Gordon, V.D.; Trinkle, D.R.; Schmidt, N.W.; Davis, M.A.; DeVries, C.; Som, A.; Cronan, J.E., Jr.; Tew, G.N.; Wong, G.C.L.
2009-05-28
Phenylene ethynylenes comprise a prototypical class of synthetic antimicrobial compounds that mimic antimicrobial peptides produced by eukaryotes and have broad-spectrum antimicrobial activity. We show unambiguously that bacterial membrane permeation by these antimicrobials depends on the presence of negative intrinsic curvature lipids, such as phosphatidylethanolamine (PE) lipids, found in high concentrations within bacterial membranes. Plate-killing assays indicate that a PE-knockout mutant strain of Escherichia coli drastically out-survives the wild type against the membrane-active phenylene ethynylene antimicrobials, whereas the opposite is true when challenged with traditional metabolic antibiotics. That the PE deletion is a lethal mutation in normative environments suggests that resistant bacterial strains do not evolve because a lethal mutation is required to gain immunity. PE lipids allow efficient generation of negative curvature required for the circumferential barrel of an induced membrane pore; an inverted hexagonal HII phase, which consists of arrays of water channels, is induced by a small number of antimicrobial molecules. The estimated antimicrobial occupation in these water channels is nonlinear and jumps from {approx}1 to 3 per 4 nm of induced water channel length as the global antimicrobial concentration is increased. By comparing to exactly solvable 1D spin models for magnetic systems, we quantify the cooperativity of these antimicrobials.
Nonadditive Compositional Curvature Energetics of Lipid Bilayers
NASA Astrophysics Data System (ADS)
Sodt, A. J.; Venable, R. M.; Lyman, E.; Pastor, R. W.
2016-09-01
The unique properties of the individual lipids that compose biological membranes together determine the energetics of the surface. The energetics of the surface, in turn, govern the formation of membrane structures and membrane reshaping processes, and thus they will underlie cellular-scale models of viral fusion, vesicle-dependent transport, and lateral organization relevant to signaling. The spontaneous curvature, to the best of our knowledge, is always assumed to be additive. We describe observations from simulations of unexpected nonadditive compositional curvature energetics of two lipids essential to the plasma membrane: sphingomyelin and cholesterol. A model is developed that connects molecular interactions to curvature stress, and which explains the role of local composition. Cholesterol is shown to lower the number of effective Kuhn segments of saturated acyl chains, reducing lateral pressure below the neutral surface of bending and favoring positive curvature. The effect is not observed for unsaturated (flexible) acyl chains. Likewise, hydrogen bonding between sphingomyelin lipids leads to positive curvature, but only at sufficient concentration, below which the lipid prefers negative curvature.
Nonadditive Compositional Curvature Energetics of Lipid Bilayers.
Sodt, A J; Venable, R M; Lyman, E; Pastor, R W
2016-09-23
The unique properties of the individual lipids that compose biological membranes together determine the energetics of the surface. The energetics of the surface, in turn, govern the formation of membrane structures and membrane reshaping processes, and thus they will underlie cellular-scale models of viral fusion, vesicle-dependent transport, and lateral organization relevant to signaling. The spontaneous curvature, to the best of our knowledge, is always assumed to be additive. We describe observations from simulations of unexpected nonadditive compositional curvature energetics of two lipids essential to the plasma membrane: sphingomyelin and cholesterol. A model is developed that connects molecular interactions to curvature stress, and which explains the role of local composition. Cholesterol is shown to lower the number of effective Kuhn segments of saturated acyl chains, reducing lateral pressure below the neutral surface of bending and favoring positive curvature. The effect is not observed for unsaturated (flexible) acyl chains. Likewise, hydrogen bonding between sphingomyelin lipids leads to positive curvature, but only at sufficient concentration, below which the lipid prefers negative curvature.
Agrawal, Neeraj J.; Weinstein, Joshua; Radhakrishnan, Ravi
2011-01-01
Using a recently developed multiscale simulation methodology, we describe the equilibrium behaviour of bilayer membranes under the influence of curvature-inducing proteins using a linearized elastic free energy model. In particular, we describe how the cooperativity associated with a multitude of protein–membrane interactions and protein diffusion on a membrane-mediated energy landscape elicits emergent behaviour in the membrane phase. Based on our model simulations, we predict that, depending on the density of membrane-bound proteins and the degree to which a single protein molecule can induce intrinsic mean curvature in the membrane, a range of membrane phase behaviour can be observed including two different modes of vesicle-bud nucleation and repressed membrane undulations. A state diagram as a function of experimentally tunable parameters to classify the underlying states is proposed. PMID:21243078
Fossati, Matteo; Goud, Bruno; Borgese, Nica; Manneville, Jean-Baptiste
2014-01-01
Sorting of membrane proteins within the secretory pathway of eukaryotic cells is a complex process involving discrete sorting signals as well as physico-chemical properties of the transmembrane domain (TMD). Previous work demonstrated that tail-anchored (TA) protein sorting at the interface between the Endoplasmic Reticulum (ER) and the Golgi complex is exquisitely dependent on the length and hydrophobicity of the transmembrane domain, and suggested that an imbalance between TMD length and bilayer thickness (hydrophobic mismatch) could drive long TMD-containing proteins into curved membrane domains, including ER exit sites, with consequent export of the mismatched protein out of the ER. Here, we tested a possible role of curvature in TMD-dependent sorting in a model system consisting of Giant Unilamellar Vesicles (GUVs) from which narrow membrane tubes were pulled by micromanipulation. Fluorescent TA proteins differing in TMD length were incorporated into GUVs of uniform lipid composition or made of total ER lipids, and TMD-dependent sorting and diffusion, as well as the bending rigidity of bilayers made of microsomal lipids, were investigated. Long and short TMD-containing constructs were inserted with similar orientation, diffused equally rapidly in GUVs and in tubes pulled from GUVs, and no difference in their final distribution between planar and curved regions was detected. These results indicate that curvature alone is not sufficient to drive TMD-dependent sorting at the ER-Golgi interface, and set the basis for the investigation of the additional factors that must be required. PMID:25210649
Fossati, Matteo; Goud, Bruno; Borgese, Nica; Manneville, Jean-Baptiste
2014-01-01
Sorting of membrane proteins within the secretory pathway of eukaryotic cells is a complex process involving discrete sorting signals as well as physico-chemical properties of the transmembrane domain (TMD). Previous work demonstrated that tail-anchored (TA) protein sorting at the interface between the Endoplasmic Reticulum (ER) and the Golgi complex is exquisitely dependent on the length and hydrophobicity of the transmembrane domain, and suggested that an imbalance between TMD length and bilayer thickness (hydrophobic mismatch) could drive long TMD-containing proteins into curved membrane domains, including ER exit sites, with consequent export of the mismatched protein out of the ER. Here, we tested a possible role of curvature in TMD-dependent sorting in a model system consisting of Giant Unilamellar Vesicles (GUVs) from which narrow membrane tubes were pulled by micromanipulation. Fluorescent TA proteins differing in TMD length were incorporated into GUVs of uniform lipid composition or made of total ER lipids, and TMD-dependent sorting and diffusion, as well as the bending rigidity of bilayers made of microsomal lipids, were investigated. Long and short TMD-containing constructs were inserted with similar orientation, diffused equally rapidly in GUVs and in tubes pulled from GUVs, and no difference in their final distribution between planar and curved regions was detected. These results indicate that curvature alone is not sufficient to drive TMD-dependent sorting at the ER-Golgi interface, and set the basis for the investigation of the additional factors that must be required.
Fuller, N; Rand, R P
2001-07-01
The effects of lysolipids on phospholipid layer curvature and bending elasticity were examined using x-ray diffraction and the osmotic stress method. Lysolipids with two different head groups, phosphatidylcholine (PC) and phosphatidylethanolamine (PE), and differing hydrocarbon chains were mixed with the hexagonal-forming lipid, dioleoylphosphatidylethanolamine (DOPE). With up to 30 mole% lysolipid in DOPE, the mixture maintains the inverted hexagonal (H(II)) phase in excess water, where increasing levels of lysolipid result in a systematic increase in the H(II) lattice dimension. Analysis of the structural changes imposed by lysolipids show that, opposite to DOPE itself, which has an spontaneous radius of curvature (R(0)) of -30 A, PC lysolipids add high positive curvature, with R(0) = +38 to +60 A, depending on chain length. LysoPEs, in contrast, add very small curvatures. When both polar group and hydrocarbon chains of the added lysolipid mismatch those of DOPE, the structural effects are qualitatively different from otherwise. Such mismatched lysolipids "reshape" the effective combination molecule into a longer and more cylindrical configuration compared to those lysolipids with either matching polar group or hydrocarbon chain.
Molecular Modeling of Lipid Membrane Curvature Induction by a Peptide: More than Simply Shape
Sodt, Alexander J.; Pastor, Richard W.
2014-01-01
Molecular dynamics simulations of an amphipathic helix embedded in a lipid bilayer indicate that it will induce substantial positive curvature (e.g., a tube of diameter 20 nm at 16% surface coverage). The induction is twice that of a continuum model prediction that only considers the shape of the inclusion. The discrepancy is explained in terms of the additional presence of specific interactions described only by the molecular model. The conclusion that molecular shape alone is insufficient to quantitatively model curvature is supported by contrasting molecular and continuum models of lipids with large and small headgroups (choline and ethanolamine, respectively), and of the removal of a lipid tail (modeling a lyso-lipid). For the molecular model, curvature propensity is analyzed by computing the derivative of the free energy with respect to bending. The continuum model predicts that the inclusion will soften the bilayer near the headgroup region, an effect that may weaken curvature induction. The all-atom predictions are consistent with experimental observations of the degree of tubulation by amphipathic helices and variation of the free energy of binding to liposomes. PMID:24806928
Molecular modeling of lipid membrane curvature induction by a peptide: more than simply shape.
Sodt, Alexander J; Pastor, Richard W
2014-05-06
Molecular dynamics simulations of an amphipathic helix embedded in a lipid bilayer indicate that it will induce substantial positive curvature (e.g., a tube of diameter 20 nm at 16% surface coverage). The induction is twice that of a continuum model prediction that only considers the shape of the inclusion. The discrepancy is explained in terms of the additional presence of specific interactions described only by the molecular model. The conclusion that molecular shape alone is insufficient to quantitatively model curvature is supported by contrasting molecular and continuum models of lipids with large and small headgroups (choline and ethanolamine, respectively), and of the removal of a lipid tail (modeling a lyso-lipid). For the molecular model, curvature propensity is analyzed by computing the derivative of the free energy with respect to bending. The continuum model predicts that the inclusion will soften the bilayer near the headgroup region, an effect that may weaken curvature induction. The all-atom predictions are consistent with experimental observations of the degree of tubulation by amphipathic helices and variation of the free energy of binding to liposomes. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Khattree, Nidhi; Ritter, Linda M; Goldberg, Andrew F X
2013-10-15
Vertebrate vision requires photon absorption by photoreceptor outer segments (OSs), structurally elaborate membranous organelles derived from non-motile sensory cilia. The structure and function of OSs depends on a precise stacking of hundreds of membranous disks. Each disk is fully (as in rods) or partially (as in cones) bounded by a rim, at which the membrane is distorted into an energetically unfavorable high-curvature bend; however, the mechanism(s) underlying disk rim structure is (are) not established. Here, we demonstrate that the intrinsically disordered cytoplasmic C-terminus of the photoreceptor tetraspanin peripherin-2/rds (P/rds) can directly generate membrane curvature. A P/rds C-terminal domain and a peptide mimetic of an amphipathic helix contained within it each generated curvature in liposomes with a composition similar to that of OS disks and in liposomes generated from native OS lipids. Association of the C-terminal domain with liposomes required conical phospholipids, and was promoted by membrane curvature and anionic surface charge, results suggesting that the P/rds C-terminal amphipathic helix can partition into the cytosolic membrane leaflet to generate curvature by a hydrophobic insertion (wedging) mechanism. This activity was evidenced in full-length P/rds by its induction of small-diameter tubulovesicular membrane foci in cultured cells. In sum, the findings suggest that curvature generation by the P/rds C-terminus contributes to the distinctive structure of OS disk rims, and provide insight into how inherited defects in P/rds can disrupt organelle structure to cause retinal disease. They also raise the possibility that tethered amphipathic helices can function for shaping cellular membranes more generally.
Baptist, Matilda; Panagabko, Candace; Nickels, Jonathan D.; Katsaras, John; Atkinson, Jeffrey
2015-01-21
Previous work revealed that α-tocopherol transfer protein (α-TTP) co-localizes with bis(monoacylglycero)phosphate (BMP) in late endosomes. BMP is a lipid unique to late endosomes and is believed to induce membrane curvature and support the multivesicular nature of this organelle. In this paper, we examined the effect of BMP on α-TTP binding to membranes using dual polarization interferometry and vesicle-binding assay. α-TTP binding to membranes is increased by the curvature-inducing lipid BMP. Finally, α-TTP binds to membranes with greater affinity when they contain the 2,2'-BMP versus 3,1'-BMP isomers.
Dorn, Jonas F.; Zhang, Li; Phi, Tan-Trao; Lacroix, Benjamin; Maddox, Paul S.; Liu, Jian; Maddox, Amy Shaub
2016-01-01
During cytokinesis, the cell undergoes a dramatic shape change as it divides into two daughter cells. Cell shape changes in cytokinesis are driven by a cortical ring rich in actin filaments and nonmuscle myosin II. The ring closes via actomyosin contraction coupled with actin depolymerization. Of interest, ring closure and hence the furrow ingression are nonconcentric (asymmetric) within the division plane across Metazoa. This nonconcentricity can occur and persist even without preexisting asymmetric cues, such as spindle placement or cellular adhesions. Cell-autonomous asymmetry is not explained by current models. We combined quantitative high-resolution live-cell microscopy with theoretical modeling to explore the mechanistic basis for asymmetric cytokinesis in the Caenorhabditis elegans zygote, with the goal of uncovering basic principles of ring closure. Our theoretical model suggests that feedback among membrane curvature, cytoskeletal alignment, and contractility is responsible for asymmetric cytokinetic furrowing. It also accurately predicts experimental perturbations of conserved ring proteins. The model further suggests that curvature-mediated filament alignment speeds up furrow closure while promoting energy efficiency. Collectively our work underscores the importance of membrane–cytoskeletal anchoring and suggests conserved molecular mechanisms for this activity. PMID:26912796
Lee, Il-Hyung; Kai, Hiroyuki; Carlson, Lars-Anders; Groves, Jay T; Hurley, James H
2015-12-29
The endosomal sorting complexes required for transport (ESCRT) machinery functions in HIV-1 budding, cytokinesis, multivesicular body biogenesis, and other pathways, in the course of which it interacts with concave membrane necks and bud rims. To test the role of membrane shape in regulating ESCRT assembly, we nanofabricated templates for invaginated supported lipid bilayers. The assembly of the core ESCRT-III subunit CHMP4B/Snf7 is preferentially nucleated in the resulting 100-nm-deep membrane concavities. ESCRT-II and CHMP6 accelerate CHMP4B assembly by increasing the concentration of nucleation seeds. Superresolution imaging was used to visualize CHMP4B/Snf7 concentration in a negatively curved annulus at the rim of the invagination. Although Snf7 assemblies nucleate slowly on flat membranes, outward growth onto the flat membrane is efficiently nucleated at invaginations. The nucleation behavior provides a biophysical explanation for the timing of ESCRT-III recruitment and membrane scission in HIV-1 budding.
Rhinow, Daniel; Hampp, Norbert
2010-01-14
Purple membrane (PM) from Halobacterium salinarum has been studied by many groups and is commonly described as a flat 2-D crystalline membrane microdomain which contains a hexagonal crystalline lattice of bacteriorhodopsin (BR) trimers in a stoichiometric ratio of 10:1 between lipids and BR. BR is the key protein in the halobacterial photosynthetic system and acts as a light-driven proton pump. Upon absorption of a photon, BR undergoes a cyclic series of intramolecular changes, among them a transient "wedge-like" geometrical change of the protein due to a tilt in helix F, one of the seven alpha-helical domains of BR. Due to the strong coupling between the BRs in the crystalline lattice, this may affect membrane topography. In nature, only low light levels occur and the total number of BRs in the "wedge-shaped" state is negligible. For mutated PMs like PM-D85T and PM-D85N (PM-D85X, X = neutral residue), the change of the membrane topography can be triggered in a pH-dependent manner. PMs containing BR-D85X look like "cups" at certain pH values. How does nature deal with a mutated PM like PM-D96G/F171C/F219L (PM-Tri) which comprises permanently "wedge-shaped" BRs and how does this influence membrane assembly? Astonishingly, we observed that PM-Tri is flat. Obviously, the morphology of Halobacterium salinarum is highly conserved and requires flat PMs to be assembled. We found that the lipid content of PM-Tri is specifically altered to assemble a hexagonal crystalline PM-Tri lattice of flat topography.
Hariri, Hanaa; Bhattacharya, Nilakshee; Johnson, Kerri; Noble, Alex J; Stagg, Scott M.
2014-01-01
The small GTPase protein Sar1 is known to be involved in both the initiation of COPII coated vesicle formation and scission of the nascent vesicle from the ER. The molecular details for the mechanism of membrane remodeling by Sar1 remain unresolved. Here we show that Sar1 transforms synthetic liposomes into structures of different morphologies including tubules and detached vesicles. We demonstrate that Sar1 alone is competent for vesicle scission in a manner that depends on the concentration of Sar1 molecules occupying the membrane. Sar1 molecules align on low curvature membranes to form an extended lattice. The continuity of this lattice breaks down as the curvature locally increases. The smallest repeating unit constituting the ordered lattice is a Sar1 dimer. The three dimensional structure of the Sar1 lattice was reconstructed by substituting spherical liposomes with galactoceramide lipid tubules of homogeneous diameter. These data suggest that Sar1 dimerization is responsible for the formation of constrictive membrane curvature. We propose a model whereby Sar1 dimers assemble into ordered arrays to promote membrane constriction and COPII-directed vesicle scission. PMID:25193674
Constitutive equations of erythrocyte membrane incorporating evolving preferred configuration.
Tözeren, A; Skalak, R; Fedorciw, B; Sung, K L; Chien, S
1984-01-01
The erythrocyte membrane is modeled as a two-dimensional viscoelastic continuum that evolves under the application of stress. The present analysis of the erythrocyte membrane is motivated by the recent development of knowledge about its molecular structure. The constitutive equations proposed in the present analysis explain in a consistent manner the data on both the deformation and recovery phases of the micropipette experiment. The rheological equations of the present study are applied in a later section to the analysis of a plane membrane deformation that is quantitatively similar to the tank-treading motion of the erythrocytes in a shear field. The computations yield useful information on how the membrane viscosity becomes a more dominant feature in tank-treading motion. The material constants appearing in the proposed constitutive equations may be useful indications of the biochemical state of the membrane in health and disease. PMID:6713066
Non-additive compositional curvature energetics of lipid bilayers
Sodt, A.J.; Venable, R.M.; Lyman, E.; Pastor, R.W.
2016-01-01
The unique properties of the individual lipids that compose biological membranes together determine the energetics of the surface. The energetics of the surface in turn govern the formation of membrane structures and membrane reshaping processes, and will thus underlie cellular-scale models of viral fusion, vesicle-dependent transport, and lateral organization relevant to signaling. The spontaneous curvature, to the best of our knowledge, is always assumed to be additive. The letter describes observations from simulations of unexpected non-additive compositional curvature energetics of two lipids essential to the plasma membrane: sphingomyelin and cholesterol. A model is developed that connects molecular interactions to curvature stress, and which explains the role of local composition. Cholesterol is shown to lower the number of effective Kuhn segments of saturated acyl chains, reducing lateral pressure below the neutral surface of bending and favoring positive curvature. The effect is not observed for unsaturated (flexible) acyl chains. Likewise, hydrogen bonding between sphingomyelin lipids leads to positive curvature, but only at sufficient concentration, below which the lipid prefers negative curvature. PMID:27715135
Effects of membrane curvature and pH on proton pumping activity of single cytochrome bo3 enzymes.
Li, Mengqiu; Khan, Sanobar; Rong, Honglin; Tuma, Roman; Hatzakis, Nikos S; Jeuken, Lars J C
2017-09-01
The molecular mechanism of proton pumping by heme-copper oxidases (HCO) has intrigued the scientific community since it was first proposed. We have recently reported a novel technology that enables the continuous characterisation of proton transport activity of a HCO and ubiquinol oxidase from Escherichia coli, cytochrome bo3, for hundreds of seconds on the single enzyme level (Li et al. J Am Chem Soc 137 (2015) 16055-16063). Here, we have extended these studies by additional experiments and analyses of the proton transfer rate as a function of proteoliposome size and pH at the N- and P-side of single HCOs. Proton transport activity of cytochrome bo3 was found to decrease with increased curvature of the membrane. Furthermore, proton uptake at the N-side (proton entrance) was insensitive to pH between pH6.4-8.4, while proton release at the P-side had an optimum pH of ~7.4, suggesting that the pH optimum is related to proton release from the proton exit site. Our previous single-enzyme experiments identified rare, long-lived conformation states of cytochrome bo3 where protons leak back under turn-over conditions. Here, we analyzed and found that ~23% of cytochrome bo3 proteoliposomes show ΔpH half-lives below 50s after stopping turnover, while only ~5% of the proteoliposomes containing a non-pumping mutant, E286C cytochrome bo3 exhibit such fast decays. These single-enzyme results confirm our model in which HCO exhibit heterogeneous pumping rates and can adopt rare leak states in which protons are able to rapidly flow back. Copyright © 2017 Elsevier B.V. All rights reserved.
da Hora, G C A; Archilha, N L; Lopes, J L S; Müller, D M; Coutinho, K; Itri, R; Soares, T A
2016-11-04
Antimicrobial peptides (AMPs) are cationic peptides that kill bacteria with a broad spectrum of action, low toxicity to mammalian cells and exceptionally low rates of bacterial resistance. These features have led to considerable efforts in developing AMPs as an alternative antibacterial therapy. In vitro studies have shown that AMPs interfere with membrane bilayer integrity via several possible mechanisms, which are not entirely understood. We have performed the synthesis, membrane lysis measurements, and biophysical characterization of a novel hybrid peptide. These measurements show that PA-Pln149 does not form nanopores, but instead promotes membrane rupture. It causes fast rupture of the bacterial model membrane (POPG-rich) at concentrations 100-fold lower than that required for the disruption of mammalian model membranes (POPC-rich). Atomistic molecular dynamics (MD) simulations were performed for single and multiple copies of PA-Pln149 in the presence of mixed and pure POPC/POPG bilayers to investigate the concentration-dependent membrane disruption by the hybrid peptide. These simulations reproduced the experimental trend and provided a potential mechanism of action for PA-Pln149. It shows that the PA-Pln149 does not form nanopores, but instead promotes membrane destabilization through peptide aggregation and induction of membrane negative curvature with the collapse of the lamellar arrangement. The sequence of events depicted for PA-Pln149 may offer insights into the mechanism of action of AMPs previously shown to induce negative deformation of membrane curvature and often associated with peptide translocation via non-bilayer intermediate structures.
Wang, Tuo; Hong, Mei
2015-04-07
A wide variety of membrane proteins induce membrane curvature for function; thus, it is important to develop new methods to simultaneously determine membrane curvature and protein binding sites in membranes with multiple curvatures. We introduce solid-state nuclear magnetic resonance (NMR) methods based on magnetically oriented bicelles and off-magic-angle spinning (OMAS) to measure membrane curvature and the binding site of proteins in mixed-curvature membranes. We demonstrate these methods on the influenza virus M2 protein, which not only acts as a proton channel but also mediates virus assembly and membrane scission. An M2 peptide encompassing the transmembrane (TM) domain and an amphipathic helix, M2(21-61), was studied and compared with the TM peptide (M2TM). Static (31)P NMR spectra of magnetically oriented 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC)/1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC) bicelles exhibit a temperature-independent isotropic chemical shift in the presence of M2(21-61) but not M2TM, indicating that the amphipathic helix confers the ability to generate a high-curvature phase. Two-dimensional (2D) (31)P spectra indicate that this high-curvature phase is associated with the DHPC bicelle edges, suggestive of the structure of budding viruses from the host cell. (31)P- and (13)C-detected (1)H relaxation times of the lipids indicate that the majority of M2(21-61) is bound to the high-curvature phase. Using OMAS experiments, we resolved the (31)P signals of lipids with identical headgroups based on their distinct chemical shift anisotropies. On the basis of this resolution, 2D (1)H-(31)P correlation spectra show that the amide protons in M2(21-61) correlate with the DMPC but not DHPC (31)P signal of the bicelle, indicating that a small percentage of M2(21-61) partitions into the planar region of the bicelles. These results show that the amphipathic helix induces high membrane curvature and localizes the protein to this phase, in good
Wang, Tuo; Hong, Mei
2015-01-01
A wide variety of membrane proteins induce membrane curvature for function, thus it is important to develop new methods to simultaneously determine membrane curvature and protein binding sites in membranes with multiple curvatures. We introduce solid-state NMR methods based on magnetically oriented bicelles and off-magic-angle spinning (OMAS) to measure membrane curvature and the binding site of proteins in mixed-curvature membranes. We demonstrate these methods on the influenza virus M2 protein, which not only acts as a proton channel but also mediates virus assembly and membrane scission. An M2 peptide encompassing the transmembrane (TM) domain and an amphipathic helix, M2(21-61), was studied and compared with the TM peptide (M2TM). Static 31P NMR spectra of magnetically oriented DMPC/DHPC bicelles exhibit a temperature-independent isotropic chemical shift in the presence of M2(21-61) but not M2TM, indicating that the amphipathic helix confers the peptide with the ability to generate a high-curvature phase. 2D 31P spectra indicate that this high-curvature phase is associated with the DHPC bicelle edges, suggestive of the structure of budding viruses from the host cell. 31P- and 13C-detected 1H relaxation times of the lipids indicate that the majority of M2(21-61) is bound to the high-curvature phase. Using OMAS experiments, we resolved the 31P signals of lipids with identical headgroups based on their distinct chemical shift anisotropies. Based on this resolution, 2D 1H-31P correlation spectra show that the amide protons in M2(21-61) correlate with the DMPC but not the DHPC 31P signal of the bicelle, indicating that a small percentage of M2(21-61) partitions into the planar region of the bicelles. These results show that the M2 amphipathic helix induces high membrane curvature and localizes the protein to this phase, in excellent agreement with the membrane-scission function of the protein. These bicelle-based relaxation and OMAS solid-state NMR techniques are
Shi, Junli; Xia, Yonggao; Yuan, Zhizhang; Hu, Huasheng; Li, Xianfeng; Zhang, Huamin; Liu, Zhaoping
2015-01-01
Separators with high reliability and security are in urgent demand for the advancement of high performance lithium ion batteries. Here, we present a new and practical porous membrane with three-dimension (3D) heat-resistant skeleton and high curvature pore structure as a promising separator candidate to facilitate advances in battery safety and performances beyond those obtained from the conventional separators. The unique material properties combining with the well-developed structural characteristics enable the 3D porous skeleton to own several favorable properties, including superior thermal stability, good wettability with liquid electrolyte, high ion conductivity and internal short-circuit protection function, etc. which give rise to acceptable battery performances. Considering the simply and cost-effective preparation process, the porous membrane is deemed to be an interesting direction for the future lithium ion battery separator. PMID:25653104
Shi, Junli; Xia, Yonggao; Yuan, Zhizhang; Hu, Huasheng; Li, Xianfeng; Zhang, Huamin; Liu, Zhaoping
2015-02-05
Separators with high reliability and security are in urgent demand for the advancement of high performance lithium ion batteries. Here, we present a new and practical porous membrane with three-dimension (3D) heat-resistant skeleton and high curvature pore structure as a promising separator candidate to facilitate advances in battery safety and performances beyond those obtained from the conventional separators. The unique material properties combining with the well-developed structural characteristics enable the 3D porous skeleton to own several favorable properties, including superior thermal stability, good wettability with liquid electrolyte, high ion conductivity and internal short-circuit protection function, etc. which give rise to acceptable battery performances. Considering the simply and cost-effective preparation process, the porous membrane is deemed to be an interesting direction for the future lithium ion battery separator.
Katayama, Sayaka; Nakase, Ikuhiko; Yano, Yoshiaki; Murayama, Tomo; Nakata, Yasushi; Matsuzaki, Katsumi; Futaki, Shiroh
2013-09-01
Arginine-rich cell-penetrating peptides, including octaarginine (R8) and HIV-1 TAT peptides, have the ability to translocate through cell membranes and transport exogenous bioactive molecules into cells. Hydrophobic counteranions such as pyrenebutyrate (PyB) have been reported to markedly promote the membrane translocation of these peptides. In this study, using model membranes having liquid-ordered (Lo) and liquid-disordered (Ld) phases, we explored the effects of PyB on the promotion of R8 translocation. Confocal microscopic observations of giant unilamellar vesicles (GUVs) showed that PyB significantly accelerated the accumulation of R8 on membranes containing negatively charged lipids, leading to the internalization of R8 without collapse of the GUV structures. PyB displayed an alternative activity, increasing the fluidity of the negatively charged membranes, which diminished the distinct Lo/Ld phase separation on GUVs. This was supported by the decrease in fluorescence anisotropy of 1,6-diphenyl-1,3,5-hexatriene (DPH). Additionally, PyB induced membrane curvature, which has been suggested as a possible mechanism of membrane translocation for R8. Taken together, our results indicate that PyB may have multiple effects that promote R8 translocation through cell membranes. Copyright © 2013 Elsevier B.V. All rights reserved.
Torsion and curvature of FtsZ filaments.
González de Prado Salas, Pablo; Hörger, Ines; Martín-García, Fernando; Mendieta, Jesús; Alonso, Álvaro; Encinar, Mario; Gómez-Puertas, Paulino; Vélez, Marisela; Tarazona, Pedro
2014-03-28
FtsZ filaments participate in bacterial cell division, but it is still not clear how their dynamic polymerization and shape exert force on the underlying membrane. We present a theoretical description of individual filaments that incorporates information from molecular dynamic simulations. The structure of the crystallized Methanococcus jannaschii FtsZ dimer was used to model a FtsZ pentamer that showed a curvature and a twist. The estimated bending and torsion angles between monomers and their fluctuations were included in the theoretical description. The MD data also permitted positioning the curvature with respect to the protein coordinates and allowed us to explore the effect of the relative orientation of the preferred curvature with respect to the surface plane. We find that maximum tension is attained when filaments are firmly attached and oriented with their curvature perpendicular to the surface and that the twist serves as a valve to release or to tighten the tension exerted by the curved filaments on the membrane. The theoretical model also shows that the presence of torsion can explain the shape distribution of short filaments observed by Atomic Force Microscopy in previously published experiments. New experiments with FtsZ covalently attached to lipid membranes show that the filament on-plane curvature depends on lipid head charge, confirming the predicted monomer orientation effects. This new model underlines the fact that the combination of the three elements, filament curvature, twist and the strength and orientation of its surface attachment, can modulate the force exerted on the membrane during cell division.
Clancy, Eileen K.; Barry, Chris; Ciechonska, Marta; Duncan, Roy
2010-02-05
The reovirus fusion-associated small transmembrane (FAST) proteins evolved to induce cell-cell, rather than virus-cell, membrane fusion. It is unclear whether the FAST protein fusion reaction proceeds in the same manner as the enveloped virus fusion proteins. We now show that fluorescence-based cell-cell and cell-RBC hemifusion assays are unsuited for detecting lipid mixing in the absence of content mixing during FAST protein-mediated membrane fusion. Furthermore, membrane curvature agents that inhibit hemifusion or promote pore formation mediated by influenza hemagglutinin had no effect on p14-induced cell-cell fusion, even under conditions of limiting p14 concentrations. Standard assays used to detect fusion intermediates induced by enveloped virus fusion proteins are therefore not applicable to the FAST proteins. These results suggest the possibility that the nature of the fusion intermediates or the mechanisms used to transit through the various stages of the fusion reaction may differ between these distinct classes of viral fusogens.
Galic, Milos; Tsai, Feng-Chiao; Collins, Sean R; Matis, Maja; Bandara, Samuel; Meyer, Tobias
2014-01-01
In the vertebrate central nervous system, exploratory filopodia transiently form on dendritic branches to sample the neuronal environment and initiate new trans-neuronal contacts. While much is known about the molecules that control filopodia extension and subsequent maturation into functional synapses, the mechanisms that regulate initiation of these dynamic, actin-rich structures have remained elusive. Here, we find that filopodia initiation is suppressed by recruitment of ArhGAP44 to actin-patches that seed filopodia. Recruitment is mediated by binding of a membrane curvature-sensing ArhGAP44 N-BAR domain to plasma membrane sections that were deformed inward by acto-myosin mediated contractile forces. A GAP domain in ArhGAP44 triggers local Rac-GTP hydrolysis, thus reducing actin polymerization required for filopodia formation. Additionally, ArhGAP44 expression increases during neuronal development, concurrent with a decrease in the rate of filopodia formation. Together, our data reveals a local auto-regulatory mechanism that limits initiation of filopodia via protein recruitment to nanoscale membrane deformations. DOI: http://dx.doi.org/10.7554/eLife.03116.001 PMID:25498153
NASA Astrophysics Data System (ADS)
Noguchi, Hiroshi
2016-05-01
The assembly of curved protein rods on fluid membranes is studied using implicit-solvent meshless membrane simulations. As the rod curvature increases, the rods on a membrane tube assemble along the azimuthal direction first and subsequently along the longitudinal direction. Here, we show that both transition curvatures decrease with increasing rod stiffness. For comparison, curvature-inducing isotropic inclusions are also simulated. When the isotropic inclusions have the same bending rigidity as the other membrane regions, the inclusions are uniformly distributed on the membrane tubes and vesicles even for large spontaneous curvature of the inclusions. However, the isotropic inclusions with much larger bending rigidity induce shape deformation and are concentrated on the region of a preferred curvature. For high rod density, high rod stiffness, and/or low line tension of the membrane edge, the rod assembly induces vesicle rupture, resulting in the formation of a high-genus vesicle. A gradual change in the curvature suppresses this rupture. Hence, large stress, compared to the edge tension, induced by the rod assembly is the key factor determining rupture. For rod curvature with the opposite sign to the vesicle curvature, membrane rupture induces inversion of the membrane, leading to division into multiple vesicles as well as formation of a high-genus vesicle.
Gallop, Jennifer L; Walrant, Astrid; Cantley, Lewis C; Kirschner, Marc W
2013-04-30
The membrane-cytosol interface is the major locus of control of actin polymerization. At this interface, phosphoinositides act as second messengers to recruit membrane-binding proteins. We show that curved membranes, but not flat ones, can use phosphatidylinositol 3-phosphate [PI(3)P] along with phosphatidylinositol 4,5-bisphosphate [PI(4,5)P2] to stimulate actin polymerization. In this case, actin polymerization requires the small GTPase cell cycle division 42 (Cdc42), the nucleation-promoting factor neural Wiskott-Aldrich syndrome protein (N-WASP) and the actin nucleator the actin-related protein (Arp) 2/3 complex. In liposomes containing PI(4,5)P2 as the sole phosphoinositide, actin polymerization requires transducer of Cdc42 activation-1 (toca-1). In the presence of phosphatidylinositol 3-phosphate, polymerization is both more efficient and independent of toca-1. Under these conditions, sorting nexin 9 (Snx9) can be implicated as a specific adaptor that replaces toca-1 to mobilize neural Wiskott-Aldrich syndrome protein and the Arp2/3 complex. This switch in phosphoinositide and adaptor specificity for actin polymerization from membranes has implications for how different types of actin structures are generated at precise times and locations in the cell.
NASA Astrophysics Data System (ADS)
Crawford, David F.
Curvature Cosmology proposes a new cosmological model very different from, and more elegant than, the Big-Bang Theory. Curvature Cosmology is based on two major hypotheses that Hubble redshift is due to an interaction of photons with curved spacetime and that there is a pressure that acts to stabilise expansion and provides a static, stable universe. The main focus of this book is to describe these two hypotheses in detail and to examine all relevant cosmological data in the context of this new model of the universe. This model proposes that, though evolution of stars and galaxies is evident, the statistical properties of the universe are the same at all places and at all times. In short, the universe is ageless, has no defined beginning (unlike the Big-Bang model), and carries no evidence of expansion, despite the changeability of its components. Curvature Cosmology calls for a paradigm shift in current cosmology and requires at least basic (if not more complex) knowledge of past and current cosmological models and equations.
Siegel, D. P.; Kozlov, M. M.
2004-01-01
The energy of intermediates in fusion of phospholipid bilayers is sensitive to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\bar {{\\kappa}}}_{{\\mathrm{m}}},\\end{equation*}\\end{document} the saddle splay (Gaussian curvature) elastic modulus of the lipid monolayers. The value \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\bar {{\\kappa}}}_{{\\mathrm{m}}}\\end{equation*}\\end{document} is also important in understanding the stability of inverted cubic (QII) and rhombohedral (R) phases relative to the lamellar (Lα) and inverted hexagonal (HII) phases in phospholipids. However, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\bar {{\\kappa}}}_{{\\mathrm{m}}}\\end{equation*}\\end{document} cannot be measured directly. It was previously measured by observing changes in QII phase lattice dimensions as a function of water content. Here we use observations of the phase behavior of N-mono-methylated dioleoylphosphatidylethanolamine (DOPE-Me) to determine \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}{\\bar {{\\kappa}}}_{{\\mathrm{m}}}.\\end{equation*}\\end{document} At the temperature of the Lα/QII phase transition, TQ, the partial energies of the two phases are equal, and we can express \\documentclass[12pt
EAU guidelines on penile curvature.
Hatzimouratidis, Konstantinos; Eardley, Ian; Giuliano, François; Hatzichristou, Dimitrios; Moncada, Ignacio; Salonia, Andrea; Vardi, Yoram; Wespes, Eric
2012-09-01
Penile curvature can be congenital or acquired. Acquired curvature is secondary due to La Peyronie (Peyronie's) disease. To provide clinical guidelines on the diagnosis and treatment of penile curvature. A systematic literature search on the epidemiology, diagnosis, and treatment of penile curvature was performed. Articles with the highest evidence available were selected and formed the basis for assigning levels of evidence and grades of recommendations. The pathogenesis of congenital penile curvature is unknown. Peyronie's disease is a poorly understood connective tissue disorder most commonly attributed to repetitive microvascular injury or trauma during intercourse. Diagnosis is based on medical and sexual histories, which are sufficient to establish the diagnosis. Physical examination includes assessment of palpable nodules and penile length. Curvature is best documented by a self-photograph or pharmacologically induced erection. The only treatment option for congenital penile curvature is surgery based on plication techniques. Conservative treatment for Peyronie's disease is associated with poor outcomes. Pharmacotherapy includes oral potassium para-aminobenzoate, intralesional treatment with verapamil, clostridial collagenase or interferon, topical verapamil gel, and iontophoresis with verapamil and dexamethasone. They can be efficacious in some patients, but none of these options carry a grade A recommendation. Steroids, vitamin E, and tamoxifen cannot be recommended. Extracorporeal shock wave treatment and penile traction devices may only be used to treat penile pain and reduce penile deformity, respectively. Surgery is indicated when Peyronie's disease is stable for at least 3 mo. Tunical shortening procedures, especially plication techniques, are the first treatment options. Tunical lengthening procedures are preferred in more severe curvatures or in complex deformities. Penile prosthesis implantation is recommended in patients with erectile dysfunction
Cherniavskyi, Yevhen K; Ramseyer, Christophe; Yesylevskyy, Semen O
2016-01-07
Interaction of fullerenes with asymmetric and curved DOPC/DOPS bicelles is studied by means of coarse-grained molecular dynamics simulations. The effects caused by asymmetric lipid composition of the membrane leaflets and the curvature of the membrane are analyzed. It is shown that the aggregates of fullerenes prefer to penetrate into the membrane in the regions of the moderately positive mean curvature. Upon penetration into the hydrophobic core of the membrane fullerenes avoid the regions of the extreme positive or the negative curvature. Fullerenes increase the ordering of lipid tails, which are in direct contact with them, but do not influence other lipids significantly. Our data suggest that the effects of the membrane curvature should be taken into account in the studies concerning permeability of the membranes to fullerenes and fullerene-based drug delivery systems.
Curvature-induced lipid segregation
NASA Astrophysics Data System (ADS)
Zheng, Bin; Meng, Qing-Tian; B. Selinger Robin, L.; V. Selinger, Jonathan; Ye, Fang-Fu
2015-06-01
We investigate how an externally imposed curvature influences lipid segregation on two-phase-coexistent membranes. We show that the bending-modulus contrast of the two phases and the curvature act together to yield a reduced effective line tension. On largely curved membranes, a state of multiple domains (or rafts) forms due to a mechanism analogous to that causing magnetic-vortex formation in type-II superconductors. We determine the criterion for such a multi-domain state to occur; we then calculate respectively the size of the domains formed on cylindrically and spherically curved membranes. Project supported by the Hundred-Talent Program of the Chinese Academy of Sciences (FY) and the National Science Foundation of USA via Grant DMR-1106014 (RLBS, JVS).
Structural Insights How PIP2 Imposes Preferred Binding Orientations of FAK at Lipid Membranes.
Herzog, Florian A; Braun, Lukas; Schoen, Ingmar; Vogel, Viola
2017-04-20
Focal adhesion kinase (FAK) is a multidomain protein (FERM-kinase-FAT) with important signaling functions in the regulation of cell-substrate adhesions. Its inactive, autoinhibited form is recruited from the cytoplasm to the plasma membrane, where it becomes activated at PIP2 enriched regions. To elucidate the molecular basis of activation, we performed a systematic screening of binding orientations of FAK's autoinhibited FERM-kinase complex, as well as of the dissociated FERM and kinase domains alone, on model plasma membranes using coarse-grained scFix MARTINI simulations, partially corroborated by atomistic MD simulations. The proteins adopted many more different orientations than previously thought. The presence of PIP2 tuned and narrowed the complex map of competing interfacial orientations. The dissociated FERM domain most frequently interacted with the membrane through its autoinhibitory interface rather than with the "basic patch" residues. These findings suggest a PIP2-dependent activation mechanism in which membrane binding of the dissociated FERM domain competes with the rebinding of the kinase domain. This competition could promote FAK autophosphorylation on Y397 and subsequent Src binding. The orientation of peripheral proteins at membranes is crucial to understand cell adhesion processes and is furthermore required to exploit steered molecular dynamics to predict how tensile forces might switch their active states.
Curvature constraints from the causal entropic principle
Bozek, Brandon; Albrecht, Andreas; Phillips, Daniel
2009-07-15
Current cosmological observations indicate a preference for a cosmological constant that is drastically smaller than what can be explained by conventional particle physics. The causal entropic principle (Bousso et al.) provides an alternative approach to anthropic attempts to predict our observed value of the cosmological constant by calculating the entropy created within a causal diamond. We have extended this work to use the causal entropic principle to predict the preferred curvature within the 'multiverse'. We have found that values larger than {rho}{sub k}=40{rho}{sub m} are disfavored by more than 99.99% peak value at {rho}{sub {lambda}}=7.9x10{sup -123} and {rho}{sub k}=4.3{rho}{sub m} for open universes. For universes that allow only positive curvature or both positive and negative curvature, we find a correlation between curvature and dark energy that leads to an extended region of preferred values. Our universe is found to be disfavored to an extent depending on the priors on curvature. We also provide a comparison to previous anthropic constraints on open universes and discuss future directions for this work.
Rainaldi, Mario; Moretto, Alessandro; Peggion, Cristina; Formaggio, Fernando; Mammi, Stefano; Peggion, Evaristo; Galvez, José Antonio; Díaz-de-Villegas, Maria Dolores; Cativiela, Carlos; Toniolo, Claudio
2003-08-04
We have synthesized by solution methods and characterized the lipopeptaibol metabolite LP237-F8 extracted from the fungus Tolypocladium geodes and five selected analogues with the Etn-->Aib or Etn-->Nva replacement at position 8 and/or a triple Gln-->Glu(OMe) replacement at positions 5, 6, and 9 (Etn=Calpha-ethylnorvaline, Aib=alpha-aminoisobutyric acid, Nva=norvaline). Conformation analysis, performed by FT-IR absorption, NMR, and CD techniques, strongly supports the view that the six terminally blocked decapeptides are highly helical in solution. Helix topology and amphiphilic character are responsible for their remarkable membrane activity. At position 8 the combination of high hydrophobicity and Calpha tetrasubstitution, as in the Etn-containing LP237-F8 metabolite, has a positive effect on membrane interaction.
Heuvingh, Julien; Bonneau, Stéphanie
2009-01-01
Abstract Oxidation of unsaturated lipids is a fundamental process involved in cell bioenergetics as well as in cell death. Using giant unilamellar vesicles and a chlorin photosensitizer, we asymmetrically oxidized the outer or inner monolayers of lipid membranes. We observed different shape transitions such as oblate to prolate and budding, which are typical of membrane curvature modifications. The asymmetry of the shape transitions is in accordance with a lowered effective spontaneous curvature of the leaflet being targeted. We interpret this effect as a decrease in the preferred area of the targeted leaflet compared to the other, due to the secondary products of oxidation (cleaved-lipids). Permeabilization of giant vesicles by light-induced oxidation is observed after a lag and is characterized in relation with the photosensitizer concentration. We interpret permeabilization as the opening of a pore above a critical membrane tension, resulting from the budding of vesicles. The evolution of photosensitized giant vesicle lysis tension was measured and yields an estimation of the effective spontaneous curvature at lysis. Additionally photo-oxidation was shown to be fusogenic. PMID:19948119
Substrate curvature regulates cell migration
NASA Astrophysics Data System (ADS)
He, Xiuxiu; Jiang, Yi
2017-06-01
Cell migration is essential in many aspects of biology. Many basic migration processes, including adhesion, membrane protrusion and tension, cytoskeletal polymerization, and contraction, have to act in concert to regulate cell migration. At the same time, substrate topography modulates these processes. In this work, we study how substrate curvature at micrometer scale regulates cell motility. We have developed a 3D mechanical model of single cell migration and simulated migration on curved substrates with different curvatures. The simulation results show that cell migration is more persistent on concave surfaces than on convex surfaces. We have further calculated analytically the cell shape and protrusion force for cells on curved substrates. We have shown that while cells spread out more on convex surfaces than on concave ones, the protrusion force magnitude in the direction of migration is larger on concave surfaces than on convex ones. These results offer a novel biomechanical explanation to substrate curvature regulation of cell migration: geometric constrains bias the direction of the protrusion force and facilitates persistent migration on concave surfaces.
Substrate curvature regulates cell migration.
He, Xiuxiu; Jiang, Yi
2017-05-23
Cell migration is essential in many aspects of biology. Many basic migration processes, including adhesion, membrane protrusion and tension, cytoskeletal polymerization, and contraction, have to act in concert to regulate cell migration. At the same time, substrate topography modulates these processes. In this work, we study how substrate curvature at micrometer scale regulates cell motility. We have developed a 3D mechanical model of single cell migration and simulated migration on curved substrates with different curvatures. The simulation results show that cell migration is more persistent on concave surfaces than on convex surfaces. We have further calculated analytically the cell shape and protrusion force for cells on curved substrates. We have shown that while cells spread out more on convex surfaces than on concave ones, the protrusion force magnitude in the direction of migration is larger on concave surfaces than on convex ones. These results offer a novel biomechanical explanation to substrate curvature regulation of cell migration: geometric constrains bias the direction of the protrusion force and facilitates persistent migration on concave surfaces.
Raft Formation in Lipid Bilayers Coupled to Curvature
Sadeghi, Sina; Müller, Marcus; Vink, Richard L.C.
2014-01-01
We present computer simulations of a membrane in which the local composition is coupled to the local membrane curvature. At high temperatures (i.e., above the temperature of macroscopic phase separation), finite-sized transient domains are observed, reminiscent of lipid rafts. The domain size is in the range of hundred nanometers, and set by the membrane elastic properties. These findings are in line with the notion of the membrane as a curvature-induced microemulsion. At low temperature, the membrane phase separates. The transition to the phase-separated regime is continuous and belongs to the two-dimensional Ising universality class when the coupling to curvature is weak, but becomes first-order for strong curvature-composition coupling. PMID:25296311
Geodesic curvature driven surface microdomain formation.
Adkins, Melissa R; Zhou, Y C
2017-09-15
Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. Here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. Our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. Our results are in contrast to the surface phase separation predicted by the classical surface Cahn-Hilliard equation, which tends to generate large domains as a result of the minimizing line tension. Our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.
Geodesic curvature driven surface microdomain formation
NASA Astrophysics Data System (ADS)
Adkins, Melissa R.; Zhou, Y. C.
2017-09-01
Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. Here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. Our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. Our results are in contrast to the surface phase separation predicted by the classical surface Cahn-Hilliard equation, which tends to generate large domains as a result of the minimizing line tension. Our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.
Lipids, curvature, and nano-medicine*
Mouritsen, Ole G
2011-01-01
The physical properties of the lamellar lipid-bilayer component of biological membranes are controlled by a host of thermodynamic forces leading to overall tensionless bilayers with a conspicuous lateral pressure profile and build-in curvature-stress instabilities that may be released locally or globally in terms of morphological changes. In particular, the average molecular shape and the propensity of the different lipid and protein species for forming non-lamellar and curved structures are a source of structural transitions and control of biological function. The effects of different lipids, sterols, and proteins on membrane structure are discussed and it is shown how one can take advantage of the curvature-stress modulations brought about by specific molecular agents, such as fatty acids, lysolipids, and other amphiphilic solutes, to construct intelligent drug-delivery systems that function by enzymatic triggering via curvature. Practical applications: The simple concept of lipid molecular shape and how it impacts on the structure of lipid aggregates, in particular the curvature and curvature stress in lipid bilayers and liposomes, can be exploited to construct liposome-based drug-delivery systems, e.g., for use as nano-medicine in cancer therapy. Non-lamellar-forming lysolipids and fatty acids, some of which may be designed to be prodrugs, can be created by phospholipase action in diseased tissues thereby providing for targeted drug release and proliferation of molecular entities with conical shape that break down the permeability barrier of the target cells and may hence enhance efficacy. PMID:22164124
Wang,W.; Yang, L.; Huang, H.
2007-01-01
Recent experiments suggested that cholesterol and other lipid components of high negative spontaneous curvature facilitate membrane fusion. This is taken as evidence supporting the stalk-pore model of membrane fusion in which the lipid bilayers go through intermediate structures of high curvature. How do the high-curvature lipid components lower the free energy of the curved structure? Do the high-curvature lipid components modify the average spontaneous curvature of the relevant monolayer, thereby facilitate its bending, or do the lipid components redistribute in the curved structure so as to lower the free energy? This question is fundamental to the curvature elastic energy for lipid mixtures. Here we investigate the lipid distribution in a monolayer of a binary lipid mixture before and after bending, or more precisely in the lamellar, hexagonal, and distorted hexagonal phases. The lipid mixture is composed of 2:1 ratio of brominated di18:0PC and cholesterol. Using a newly developed procedure for the multiwavelength anomalous diffraction method, we are able to isolate the bromine distribution and reconstruct the electron density distribution of the lipid mixture in the three phases. We found that the lipid distribution is homogenous and uniform in the lamellar and hexagonal phases. But in the distorted hexagonal phase, the lipid monolayer has nonuniform curvature, and cholesterol almost entirely concentrates in the high curvature region. This finding demonstrates that the association energies between lipid molecules vary with the curvature of membrane. Thus, lipid components in a mixture may redistribute under conditions of nonuniform curvature, such as in the stalk structure. In such cases, the spontaneous curvature depends on the local lipid composition and the free energy minimum is determined by lipid distribution as well as curvature.
NASA Astrophysics Data System (ADS)
Monga, Olivier; Ayache, Nicholas; Sander, Peter T.
1991-09-01
Modern medical image techniques, such as magnetic resonance image (MRI) or x-ray computed tomography provide three dimensional images of internal structures of the body, usually by means of a stack of tomographic images. The first stage in the automatic analysis of such data is 3-D edge detection1,2 which provides points corresponding to the boundaries of the surfaces forming the 3-D structure. The next stage is to characterize the local geometry of these surfaces in order to extract points or lines on which registration and/or tracking procedures can rely.3,4,5,6 This paper presents a pipeline of processes which define a hierarchical description of the second order differential characteristics of the surfaces. The focus is on the theoretical coherence of these levels of representation. Using uncertainty, a link is established between the edge detection and the local surface approximation by addressing the uncertainties inherent to edge detection in 2-D or 3-D images; and how to incorporate these uncertainties into the computation of local geometric models. In particular, calculate the uncertainty of edge location, direction, and magnitude for the 3-D Deriche operator is calculated.1,2 Statistical results are then used as a solid theoretical foundation on which to base subsequent computations, such as the determination of local surface curvature using local geometric models for surface segmentation. From the local fitting, for each edge point the mean and Gaussian curvature, principal curvatures and directions, curvature singularities, lines of curvature singularities, and covariance matrices defining the uncertainties are calculated. Experimental results for real data using two 3-D scanner images of the same organ taken at different positions demonstrate the stability of the mean and Gaussian curvatures. Experimental results for real data showing the determination of local curvature extremes of surfaces extracted from MR images are presented.
Tani, T.; Lumme, A.; Linnala, A.; Kivilaakso, E.; Kiviluoto, T.; Burgeson, R. E.; Kangas, L.; Leivo, I.; Virtanen, I.
1997-01-01
We studied the adhesion mechanism of pancreatic carcinoma using in vitro adhesion and migration assays of stable cell lines and tumors grown from these cell lines in nude mice. We also compared the results with the expression profiles of laminins and their receptors in pancreatic carcinomas to evaluate the relevance of these mechanisms in vivo. All of the cell lines preferably adhered to laminin-5, irrespective of their capability to synthesize laminin-5. Cell migration was studied in the presence of hepatocyte growth factor, as it increased the speed of migration manyfold. Herbimycin A treatment and antibodies against the beta 1 and alpha 3 integrin subunits and laminin alpha 3 chain almost entirely blocked cell migration of the BxPC-3 cell line, whereas migration was nearly unaffected by RGD peptide and only moderately inhibited by antibody against the alpha 6 integrin subunit. Indirect immunofluorescence microscopy of wounded BxPC-3 cells suggested a rapid endocytosis of alpha 3 integrin subunit in the cells at the margin of the wound and a rapid, polarized rearrangement of the alpha 6 beta 4 integrin. Especially HGF-treated cultures showed a prominent cytoplasmic reaction for laminin-5 at the margin of the wound. Xenografted cells formed tumors that produced and deposited the same laminin chains as the in vitro cultures. Frozen sections of human pancreatic carcinomas showed reactivity for laminin chains suggestive for expression of laminin-1 and laminin-5. Both xenografted tumors and human pancreatic carcinomas also showed stromal reactivity for laminin-5. Electron microscopy of the human tumors suggested that this was due to an abundant reduplication the basement-membrane-like material around the nests of malignant cells. Our results suggest that pancreatic carcinomas synthesize and deposit laminin-5 in the basement membrane in an abnormal manner. Invading cells adhere to this newly produced basement membrane and migrate on it by using the alpha 3 beta 1
End-Stopping Predicts Curvature Tuning along the Ventral Stream.
Ponce, Carlos R; Hartmann, Till S; Livingstone, Margaret S
2017-01-18
Neurons in primate inferotemporal cortex (IT) are clustered into patches of shared image preferences. Functional imaging has shown that these patches are activated by natural categories (e.g., faces, body parts, and places), artificial categories (numerals, words) and geometric features (curvature and real-world size). These domains develop in the same cortical locations across monkeys and humans, which raises the possibility of common innate mechanisms. Although these commonalities could be high-level template-based categories, it is alternatively possible that the domain locations are constrained by low-level properties such as end-stopping, eccentricity, and the shape of the preferred images. To explore this, we looked for correlations among curvature preference, receptive field (RF) end-stopping, and RF eccentricity in the ventral stream. We recorded from sites in V1, V4, and posterior IT (PIT) from six monkeys using microelectrode arrays. Across all visual areas, we found a tendency for end-stopped sites to prefer curved over straight contours. Further, we found a progression in population curvature preferences along the visual hierarchy, where, on average, V1 sites preferred straight Gabors, V4 sites preferred curved stimuli, and many PIT sites showed a preference for curvature that was concave relative to fixation. Our results provide evidence that high-level functional domains may be mapped according to early rudimentary properties of the visual system. The macaque occipitotemporal cortex contains clusters of neurons with preferences for categories such as faces, body parts, and places. One common question is how these clusters (or "domains") acquire their cortical position along the ventral stream. We and other investigators previously established an fMRI-level correlation among these category domains, retinotopy, and curvature preferences: for example, in inferotemporal cortex, face- and curvature-preferring domains show a central visual field bias
End-Stopping Predicts Curvature Tuning along the Ventral Stream
Hartmann, Till S.; Livingstone, Margaret S.
2017-01-01
Neurons in primate inferotemporal cortex (IT) are clustered into patches of shared image preferences. Functional imaging has shown that these patches are activated by natural categories (e.g., faces, body parts, and places), artificial categories (numerals, words) and geometric features (curvature and real-world size). These domains develop in the same cortical locations across monkeys and humans, which raises the possibility of common innate mechanisms. Although these commonalities could be high-level template-based categories, it is alternatively possible that the domain locations are constrained by low-level properties such as end-stopping, eccentricity, and the shape of the preferred images. To explore this, we looked for correlations among curvature preference, receptive field (RF) end-stopping, and RF eccentricity in the ventral stream. We recorded from sites in V1, V4, and posterior IT (PIT) from six monkeys using microelectrode arrays. Across all visual areas, we found a tendency for end-stopped sites to prefer curved over straight contours. Further, we found a progression in population curvature preferences along the visual hierarchy, where, on average, V1 sites preferred straight Gabors, V4 sites preferred curved stimuli, and many PIT sites showed a preference for curvature that was concave relative to fixation. Our results provide evidence that high-level functional domains may be mapped according to early rudimentary properties of the visual system. SIGNIFICANCE STATEMENT The macaque occipitotemporal cortex contains clusters of neurons with preferences for categories such as faces, body parts, and places. One common question is how these clusters (or “domains”) acquire their cortical position along the ventral stream. We and other investigators previously established an fMRI-level correlation among these category domains, retinotopy, and curvature preferences: for example, in inferotemporal cortex, face- and curvature-preferring domains show a
Stiffness Modulation of Rayed Fins by Curvature
NASA Astrophysics Data System (ADS)
Nguyen, Khoi; Yu, Ning; Venkadesan, Madhusudhan; Bandi, Mahesh; Mandre, Shreyas
2016-11-01
Fishes with rayed fins comprise over 99% of all extant fish species. Multifunctional use of fins, from propulsion to station holding, requires substantial modulation of stiffness. We propose that fishes stiffen the fin by curving it transverse to its length. This effect is similar to stiffening a dollar bill by curling it because of curvature-induced coupling of out-of-plane bending with in-plane stretching. Unlike a piece of paper, rayed fins are a composite of rays and membranes. We model this as parallel elastic beams (rays) with springy interconnections (membranes). Our analysis shows that the key parameters stiffening the fin are the ray anisotropy to bending, the misalignment of principal bending directions of adjacent rays, and the membrane elasticity. The composite fin stiffens when the principal bending directions of adjacent rays are misaligned due to fin curvature, which necessarily causes the membrane to stretch. Unlike a homogenous thin sheet, composite rayed structures are able to mimic curvature-induced stiffening by using misaligned rays even if the fin appears geometrically flat. Preliminary radiographic evidence from the rays of fish fins supports such a mechanism. Funding by Human Frontier Science Program.
Improving the Sensitivity of Astronomical Curvature Wavefront Sensor Using Dual-Stroke Curvature
NASA Astrophysics Data System (ADS)
Guyon, Olivier; Blain, Celia; Takami, Hideki; Hayano, Yutaka; Hattori, Masayuki; Watanabe, Makoto
2008-06-01
Curvature wavefront sensors measure wavefront phase aberration by acquiring two intensity images on either side of the pupil plane. Low-order adaptive optics (AO) systems using curvature wavefront sensing (CWFS) have proved to be highly efficient for astronomical applications: they are more sensitive, use fewer detector elements, and achieve, for the same number of actuators, higher Strehl ratios than AO systems using more traditional Shack-Hartmann wavefront sensors. In higher-order systems, however, curvature wavefront sensors lose sensitivity to low spatial frequencies wavefront aberrations. This effect, often described as “noise propagation,” limits the usefulness of curvature wavefront sensing for high-order AO systems and/or large telescopes. In this paper, we first explain how this noise propagation effect occurs and then show that this limitation can be overcome by acquiring four defocused images of the pupil instead of two. This solution can be implemented without significant technology development and can run with a simple linear wavefront reconstruction algorithm at >kHz speed. We have successfully demonstrated in the laboratory that the four conjugation planes can be sequentially obtained at >kHz speed using a speaker-vibrating membrane assembly commonly used in current curvature AO systems. Closed loop simulations show that implementing this scheme is equivalent to making the guide star 1 to 1.5 magnitude brighter for the configuration tested (188 actuator elements on 8-m telescope). Higher sensitivity gains are expected on curvature systems with higher number of actuators.
Tseng, Hua-an; Nadim, Farzan
2010-08-11
Many oscillatory networks involve neurons that exhibit intrinsic rhythmicity but possess a large variety of voltage-gated currents that interact in a complex fashion, making it difficult to determine which factors control frequency. Yet these neurons often have preferred (resonance) frequencies that can be close to the network frequency. Because the preferred frequency results from the dynamics of ionic currents, it can be assumed to depend on parameters that determine the neuron's oscillatory waveform shape. The pyloric network frequency in the crab Cancer borealis is correlated with the preferred frequency of its bursting pacemaker neurons anterior burster and pyloric dilator (PD). We measured the preferred frequency of the PD neuron in voltage clamp, which allows control of the oscillation voltage range and waveforms (sine waves and realistic oscillation waveforms), and showed that (1) the preferred frequency depends on the voltage range of the oscillating voltage waveform; (2) the slope of the waveform near its peak has a strongly negative correlation with the preferred frequency; and (3) correlations between parameters of the PD neuron oscillation waveform and its preferred frequency can be used to predict shifts in the network frequency. As predicted by these results, dynamic clamp shifts of the upper or lower voltage limits of the PD neuron waveform during ongoing oscillations changed the network frequency, consistent with the predictions from the preferred frequency. These results show that the voltage waveform of oscillatory neurons can be predictive of their preferred frequency and thus the network oscillation frequency.
Tseng, Hua-an; Nadim, Farzan
2010-01-01
Many oscillatory networks involve neurons that exhibit intrinsic rhythmicity, but possess a large variety of voltage-gated currents which interact in a complex fashion making it difficult to determine which factors control frequency. Yet, these neurons often have preferred (resonance) frequencies that can be close to the network frequency. Because the preferred frequency results from the dynamics of ionic currents, it can be assumed to depend on parameters that determine the neuron’s oscillatory waveform shape. The pyloric network frequency in the crab Cancer borealis is correlated with the preferred frequency of its bursting pacemaker neurons AB and PD. We measure the preferred frequency of the PD neuron in voltage-clamp, which allows control of the oscillation voltage range and waveforms (sine waves and realistic oscillation waveforms), and showthat1) the preferred frequency depends on the voltage range of the oscillating voltage waveform; 2) the slope of the waveform near its peak has a strongly negative correlation with the preferred frequency; and 3) correlations between parameters of the PD neuron oscillation waveform and its preferred frequency can be used to predict shifts in the network frequency. As predicted by these results, dynamic clamp shifts of the upper or lower voltage limits of the PD neuron waveform during ongoing oscillations changed the network frequency, consistent with the predictions from the preferred frequency. These results show that the voltage waveform of oscillatory neurons can be predictive of their preferred frequency and thus the network oscillation frequency. PMID:20702710
Curvature-Driven Lipid Sorting in Biomembranes
Callan-Jones, Andrew; Sorre, Benoit; Bassereau, Patricia
2011-01-01
It has often been suggested that the high curvature of transport intermediates in cells may be a sufficient means to segregate different lipid populations based on the relative energy costs of forming bent membranes. In this review, we present in vitro experiments that highlight the essential physics of lipid sorting at thermal equilibrium: It is driven by a trade-off between bending energy, mixing entropy, and interactions between species. We collect evidence that lipid sorting depends strongly on lipid–lipid and protein–lipid interactions, and hence on the underlying composition of the membrane and on the presence of bound proteins. PMID:21421916
NASA Astrophysics Data System (ADS)
Chambolle, Antonin; Morini, Massimiliano; Ponsiglione, Marcello
2015-12-01
This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. We introduce a class of nonlocal generalized mean curvatures and prove the existence and uniqueness for the level set formulation of the corresponding geometric flows. We then introduce a class of generalized perimeters, whose first variation is an admissible generalized curvature. Within this class, we implement a minimizing movements scheme and we prove that it approximates the viscosity solution of the corresponding level set PDE. We also describe several examples and applications. Besides recovering and presenting in a unified way existence, uniqueness, and approximation results for several geometric motions already studied and scattered in the literature, the theory developed in this paper also allows us to establish new results.
Quantifying the Relationship between Curvature and Electric Potential in Lipid Bilayers.
Bruhn, Dennis S; Lomholt, Michael A; Khandelia, Himanshu
2016-06-02
Cellular membranes mediate vital cellular processes by being subject to curvature and transmembrane electrical potentials. Here we build upon the existing theory for flexoelectricity in liquid crystals to quantify the coupling between lipid bilayer curvature and membrane potentials. Using molecular dynamics simulations, we show that headgroup dipole moments, the lateral pressure profile across the bilayer, and spontaneous curvature all systematically change with increasing membrane potentials. In particular, there is a linear dependence between the bending moment (the product of bending rigidity and spontaneous curvature) and the applied membrane potentials. We show that biologically relevant membrane potentials can induce biologically relevant curvatures corresponding to radii of around 500 nm. The implications of flexoelectricity in lipid bilayers are thus likely to be of considerable consequence both in biology and in model lipid bilayer systems.
Forman curvature for complex networks
NASA Astrophysics Data System (ADS)
Sreejith, R. P.; Mohanraj, Karthikeyan; Jost, Jürgen; Saucan, Emil; Samal, Areejit
2016-06-01
We adapt Forman’s discretization of Ricci curvature to the case of undirected networks, both weighted and unweighted, and investigate the measure in a variety of model and real-world networks. We find that most nodes and edges in model and real networks have a negative curvature. Furthermore, the distribution of Forman curvature of nodes and edges is narrow in random and small-world networks, while the distribution is broad in scale-free and real-world networks. In most networks, Forman curvature is found to display significant negative correlation with degree and centrality measures. However, Forman curvature is uncorrelated with clustering coefficient in most networks. Importantly, we find that both model and real networks are vulnerable to targeted deletion of nodes with highly negative Forman curvature. Our results suggest that Forman curvature can be employed to gain novel insights on the organization of complex networks.
Surface precision of optical membranes with curvature.
Marker, D; Jenkins, C
1997-11-24
Space-based inflatable technology is of current interest to NASA and DOD, and in particular to the Air Force and Phillips Laboratory. Potentially large gains in lowering launch costs, through reductions in structure mass and volume, are driving this activity. Diverse groups are researching and developing this technology for radio and radar antennae, optical telescopes, and solar power and propulsion applications. Regardless of the use, one common requirement for successful application is the accuracy of the inflated surface shape. The work reported here concerns the shape control of an inflated thin circular disk through use of a nonlinear finite element analysis. First, a review of the important associated Hencky problem is given. Then we discuss a shape modification, achieved through enforced boundary displacements, which resulted in moving the inflated shape towards a desired parabolic profile. Minimization of the figure error is discussed and conclusions are drawn.
Nanoscale phase behavior on flat and curved membranes
NASA Astrophysics Data System (ADS)
Andersen, Thomas; Bahadori, Azra; Ott, Dino; Kyrsting, Anders; Reihani, S. Nader S.; Bendix, Poul M.
2014-12-01
The diverse physical properties of membranes play a critical role in many membrane associated biological processes. Proteins responsible for membrane transport can be affected by the lateral membrane order and lateral segregation of proteins is often controlled by the preference of certain membrane anchors for membrane phases having a physically ordered state. The dynamic properties of coexisting membrane phases are often studied by investigating their thermal behavior. Optical trapping of gold nanoparticles is a useful tool to generate local phase transitions in membranes. The high local temperatures surrounding an irradiated gold nanoparticle can be used to melt a part of a giant unilamellar lipid vesicle (GUV) which is then imaged using phase sensitive fluorophores embedded within the bilayer. By local melting of GUVs we reveal how a protein-free, one component lipid bilayer can mediate passive transport of fluorescent molecules by localized and transient pore formation. Also, we show how tubular membrane curvatures can be generated by optical pulling from the melted region on the GUV. This will allow us to measure the effect of membrane curvature on the phase transition temperature.
Agudo-Canalejo, Jaime; Lipowsky, Reinhard
2017-03-15
Biological membranes and lipid vesicles often display complex shapes with non-uniform membrane curvature. When adhesive nanoparticles with chemically uniform surfaces come into contact with such membranes, they exhibit four different engulfment regimes as recently shown by a systematic stability analysis. Depending on the local curvature of the membrane, the particles either remain free, become partially or completely engulfed by the membrane, or display bistability between free and completely engulfed states. Here, we go beyond stability analysis and develop an analytical theory to leading order in the ratio of particle-to-vesicle size. This theory allows us to determine the local and global energy landscapes of uniform nanoparticles that are attracted towards membranes and vesicles. While the local energy landscape depends only on the local curvature of the vesicle membrane and not on the overall membrane shape, the global energy landscape describes the variation of the equilibrium state of the particle as it probes different points along the membrane surface. In particular, we find that the binding energy of a partially engulfed particle depends on the 'unperturbed' local curvature of the membrane in the absence of the particle. This curvature dependence leads to local forces that pull the partially engulfed particles towards membrane segments with lower and higher mean curvature if the particles originate from the exterior and interior solution, respectively, corresponding to endo- and exocytosis. Thus, for partial engulfment, endocytic particles undergo biased diffusion towards the membrane segments with the lowest membrane curvature, whereas exocytic particles move towards segments with the highest curvature. The curvature-induced forces are also effective for Janus particles with one adhesive and one non-adhesive surface domain. In fact, Janus particles with a strongly adhesive surface domain are always partially engulfed which implies that they provide
NASA Astrophysics Data System (ADS)
Berry, M. V.
2013-10-01
Wave streamlines are integral curves of the local wavevector (phase gradient). An exact formula is derived, giving the curvature of streamlines as the component transverse to the local wavevector of the gradient of the logarithm of the local wavenumber. The formula is applied to quantum particles moving in a potential and classical light in the presence of a refractive-index gradient. Three limiting regimes are encompassed. The first is geometrical, in which the bending of streamlines arises solely from the classical force or optical index gradient. The second and third limits concern singularities in the pattern of wave streamlines, of two types: optical vortices, near which the streamlines are asymptotically circular, and phase saddles, near which the streamlines are asymptotically hyperbolic.
Bacterial cell curvature through mechanical control of cell growth
Cabeen, Matthew T; Charbon, Godefroid; Vollmer, Waldemar; Born, Petra; Ausmees, Nora; Weibel, Douglas B; Jacobs-Wagner, Christine
2009-01-01
The cytoskeleton is a key regulator of cell morphogenesis. Crescentin, a bacterial intermediate filament-like protein, is required for the curved shape of Caulobacter crescentus and localizes to the inner cell curvature. Here, we show that crescentin forms a single filamentous structure that collapses into a helix when detached from the cell membrane, suggesting that it is normally maintained in a stretched configuration. Crescentin causes an elongation rate gradient around the circumference of the sidewall, creating a longitudinal cell length differential and hence curvature. Such curvature can be produced by physical force alone when cells are grown in circular microchambers. Production of crescentin in Escherichia coli is sufficient to generate cell curvature. Our data argue for a model in which physical strain borne by the crescentin structure anisotropically alters the kinetics of cell wall insertion to produce curved growth. Our study suggests that bacteria may use the cytoskeleton for mechanical control of growth to alter morphology. PMID:19279668
Curvature-induced stiffening of a fish fin.
Nguyen, Khoi; Yu, Ning; Bandi, Mahesh M; Venkadesan, Madhusudhan; Mandre, Shreyas
2017-05-01
How fish modulate their fin stiffness during locomotive manoeuvres remains unknown. We show that changing the fin's curvature modulates its stiffness. Modelling the fin as bendable bony rays held together by a membrane, we deduce that fin curvature is manifested as a misalignment of the principal bending axes between neighbouring rays. An external force causes neighbouring rays to bend and splay apart, and thus stretches the membrane. This coupling between bending the rays and stretching the membrane underlies the increase in stiffness. Using three-dimensional reconstruction of a mackerel (Scomber japonicus) pectoral fin for illustration, we calculate the range of stiffnesses this fin is expected to span by changing curvature. The three-dimensional reconstruction shows that, even in its geometrically flat state, a functional curvature is embedded within the fin microstructure owing to the morphology of individual rays. As the ability of a propulsive surface to transmit force to the surrounding fluid is limited by its stiffness, the fin curvature controls the coupling between the fish and its surrounding fluid. Thereby, our results provide mechanical underpinnings and morphological predictions for the hypothesis that the spanned range of fin stiffnesses correlates with the behaviour and the ecological niche of the fish. © 2017 The Author(s).
Curvature-induced stiffening of a fish fin
2017-01-01
How fish modulate their fin stiffness during locomotive manoeuvres remains unknown. We show that changing the fin's curvature modulates its stiffness. Modelling the fin as bendable bony rays held together by a membrane, we deduce that fin curvature is manifested as a misalignment of the principal bending axes between neighbouring rays. An external force causes neighbouring rays to bend and splay apart, and thus stretches the membrane. This coupling between bending the rays and stretching the membrane underlies the increase in stiffness. Using three-dimensional reconstruction of a mackerel (Scomber japonicus) pectoral fin for illustration, we calculate the range of stiffnesses this fin is expected to span by changing curvature. The three-dimensional reconstruction shows that, even in its geometrically flat state, a functional curvature is embedded within the fin microstructure owing to the morphology of individual rays. As the ability of a propulsive surface to transmit force to the surrounding fluid is limited by its stiffness, the fin curvature controls the coupling between the fish and its surrounding fluid. Thereby, our results provide mechanical underpinnings and morphological predictions for the hypothesis that the spanned range of fin stiffnesses correlates with the behaviour and the ecological niche of the fish. PMID:28566508
On nonlinear higher spin curvature
NASA Astrophysics Data System (ADS)
Manvelyan, Ruben; Mkrtchyan, Karapet; Rühl, Werner; Tovmasyan, Murad
2011-05-01
We present the first nonlinear term of the higher spin curvature which is covariant with respect to deformed gauge transformations that are linear in the field. We consider the case of spin 3 after presenting spin 2 as an example, and then construct the general spin s quadratic term of the de Wit-Freedman curvature.
Representation of tactile curvature in macaque somatosensory area 2
Connor, Charles E.; Hsiao, Steven S.
2013-01-01
Tactile shape information is elaborated in a cortical hierarchy spanning primary (SI) and secondary somatosensory cortex (SII). Indeed, SI neurons in areas 3b and 1 encode simple contour features such as small oriented bars and edges, whereas higher order SII neurons represent large curved contour features such as angles and arcs. However, neural coding of these contour features has not been systematically characterized in area 2, the most caudal SI subdivision in the postcentral gyrus. In the present study, we analyzed area 2 neural responses to embossed oriented bars and curved contour fragments to establish whether curvature representations are generated in the postcentral gyrus. We found that many area 2 neurons (26 of 112) exhibit clear curvature tuning, preferring contours pointing in a particular direction. Fewer area 2 neurons (15 of 112) show preferences for oriented bars. Because area 2 response patterns closely resembled SII patterns, we also compared area 2 and SII response time courses to characterize the temporal dynamics of curvature synthesis in the somatosensory system. We found that curvature representations develop and peak concurrently in area 2 and SII. These results reveal that transitions from orientation tuning to curvature selectivity in the somatosensory cortical hierarchy occur within SI rather than between SI and SII. PMID:23536717
Representation of tactile curvature in macaque somatosensory area 2.
Yau, Jeffrey M; Connor, Charles E; Hsiao, Steven S
2013-06-01
Tactile shape information is elaborated in a cortical hierarchy spanning primary (SI) and secondary somatosensory cortex (SII). Indeed, SI neurons in areas 3b and 1 encode simple contour features such as small oriented bars and edges, whereas higher order SII neurons represent large curved contour features such as angles and arcs. However, neural coding of these contour features has not been systematically characterized in area 2, the most caudal SI subdivision in the postcentral gyrus. In the present study, we analyzed area 2 neural responses to embossed oriented bars and curved contour fragments to establish whether curvature representations are generated in the postcentral gyrus. We found that many area 2 neurons (26 of 112) exhibit clear curvature tuning, preferring contours pointing in a particular direction. Fewer area 2 neurons (15 of 112) show preferences for oriented bars. Because area 2 response patterns closely resembled SII patterns, we also compared area 2 and SII response time courses to characterize the temporal dynamics of curvature synthesis in the somatosensory system. We found that curvature representations develop and peak concurrently in area 2 and SII. These results reveal that transitions from orientation tuning to curvature selectivity in the somatosensory cortical hierarchy occur within SI rather than between SI and SII.
Wallace, John Paul; Myneni, Ganapati Rao; Pike, Robert
2011-03-31
The manufacturing of niobium SRF accelerator cavities is plagued by a mobile point defect, hydrogen. For efficient accelerator operation, niobium must function at both high electric and magnetic fields, and is compromised if magnetic impurities are located in the surface regions of the material. The finding that trace hydrogen in niobium can produce structures with magnetic properties is a feature that is not acceptable for a high performance cavity. X-ray diffraction has proved to be the key tool in assessing irreversible process damage to the niobium substrate. In future generations of accelerators, niobium will actually be merely the substrate for more effective superconductors that will allow for more efficient operation. The substrate analogy to the silicon wafer industry is useful since for niobium it may be possible to avoid some of the mistakes made in silicon technology. Because hydrogen attacks niobium on a number of different size scales, there is an inherent complexity in the trouble sources. There are also features in cavity design that are benign, such as local curvature considerations, requiring a fully non symmetric analysis of current flow to be appreciated.
Cosmic curvature and condensation
NASA Technical Reports Server (NTRS)
Harwit, Martin
1992-01-01
It is shown that the universe may consist of a patchwork of domains with different Riemann curvature constants k = 0, +/-1. Features of a phase transition in which flat space breaks up in a transition 2k0 - k(-) + k(+) with initial scale factors R(-) = R(+) are postulated and explored. It is shown that such a transition is energetically permitted, has the equivalent of a Curie temperature, and can lead in a natural way to the formation of voids and galaxies. It is predicted that, if the ambient universe on average is well fitted by a purely k(-) space, with only occasional domains of k(+) containing galaxies, a density parameter of (A(z sub c + 1)) super -1 should be expected, where z sub c represents the redshift of the earliest objects to have condensed, and A takes on values ranging from about 5 to 3. Present observations of quasars would suggest a density of about 0.03 or 0.05, respectively, but it could be lower if earlier condensation took place.
John Paul Wallace, Ganapati Rao Myneni, and Robert Pike
2011-03-01
The manufacturing of niobium SRF accelerator cavities is plagued by a mobile point defect, hydrogen. For efficient accelerator operation, niobium must function at both high electric and magnetic fields, and is compromised if magnetic impurities are located in the surface regions of the material. The finding that trace hydrogen in niobium can produce structures with magnetic properties is a feature that is not acceptable for a high performance cavity. X-ray diffraction has proved to be the key tool in assessing irreversible process damage to the niobium substrate. In future generations of accelerators, niobium will actually be merely the substrate for more effective superconductors that will allow for more efficient operation. The substrate analogy to the silicon wafer industry is useful since for niobium it may be possible to avoid some of the mistakes made in silicon technology. Because hydrogen attacks niobium on a number of different size scales, there is an inherent complexity in the trouble sources. There are also features in cavity design that are benign, such as local curvature considerations, requiring a fully non symmetric analysis of current flow to be appreciated.
Membrane-mediated aggregation of anisotropically curved nanoparticles.
Olinger, Alexander D; Spangler, Eric J; Kumar, P B Sunil; Laradji, Mohamed
2016-01-01
Using systematic numerical simulations, we study the self-assembly of elongated curved nanoparticles on lipid vesicles. Our simulations are based on molecular dynamics of a coarse-grained implicit-solvent model of self-assembled lipid membranes with a Langevin thermostat. Here we consider only the case wherein the nanoparticle-nanoparticle interaction is repulsive, only the concave surface of the nanoparticle interacts attractively with the lipid head groups and only the outer surface of the vesicle is exposed to the nanoparticles. Upon their adhesion on the vesicle, the curved nanoparticles generate local curvature on the membrane. The resulting nanoparticle-generated membrane curvature leads in turn to nanoparticle self-assembly into two main types of aggregates corresponding to chain aggregates at low adhesion strengths and aster aggregates at high adhesion strength. The chain-like aggregates are due to the fact that at low values of adhesion strength, the nanoparticles prefer to lie parallel to each other. As the adhesion strength is increased, a splay angle between the nanoparticles is induced with a magnitude that increases with increasing adhesion strength. The origin of the splay angles between the nanoparticles is shown to be saddle-like membrane deformations induced by a tilt of the lipids around the nanoparticles. This phenomenon of membrane mediated self-assembly of anisotropically curved nanoparticles is explored for systems with varying nanoparticle number densities, adhesion strength, and nanoparticle intrinsic curvature.
On the edge energy of lipid membranes and the thermodynamic stability of pores
Pera, H.; Kleijn, J. M.; Leermakers, F. A. M.
2015-01-21
To perform its barrier function, the lipid bilayer membrane requires a robust resistance against pore formation. Using a self-consistent field (SCF) theory and a molecularly detailed model for membranes composed of charged or zwitterionic lipids, it is possible to predict structural, mechanical, and thermodynamical parameters for relevant lipid bilayer membranes. We argue that the edge energy in membranes is a function of the spontaneous lipid monolayer curvature, the mean bending modulus, and the membrane thickness. An analytical Helfrich-like model suggests that most bilayers should have a positive edge energy. This means that there is a natural resistance against pore formation. Edge energies evaluated explicitly in a two-gradient SCF model are consistent with this. Remarkably, the edge energy can become negative for phosphatidylglycerol (e.g., dioleoylphosphoglycerol) bilayers at a sufficiently low ionic strength. Such bilayers become unstable against the formation of pores or the formation of lipid disks. In the weakly curved limit, we study the curvature dependence of the edge energy and evaluate the preferred edge curvature and the edge bending modulus. The latter is always positive, and the former increases with increasing ionic strength. These results point to a small window of ionic strengths for which stable pores can form as too low ionic strengths give rise to lipid disks. Higher order curvature terms are necessary to accurately predict relevant pore sizes in bilayers. The electric double layer overlap across a small pore widens the window of ionic strengths for which pores are stable.
Mechanisms of membrane deformation by lipid-binding domains.
Itoh, Toshiki; Takenawa, Tadaomi
2009-09-01
Among an increasing number of lipid-binding domains, a group that not only binds to membrane lipids but also changes the shape of the membrane has been found. These domains are characterized by their strong ability to transform globular liposomes as well as flat plasma membranes into elongated membrane tubules both in vitro and in vivo. Biochemical studies on the structures of these proteins have revealed the importance of the amphipathic helix, which potentially intercalates into the lipid bilayer to induce and/or sense membrane curvature. Among such membrane-deforming domains, BAR and F-BAR/EFC domains form crescent-shaped dimers, suggesting a preference for a curved membrane, which is important for curvature sensing. Bioinformatics in combination with structural analyses has been identifying an increasing number of novel families of lipid-binding domains. This review attempts to summarize the evidence obtained by recent studies in order to gain general insights into the roles of membrane-deforming domains in a variety of biological events.
Compound curvature laser window development
NASA Technical Reports Server (NTRS)
Verhoff, Vincent G.
1993-01-01
The NASA Lewis Research Center has developed and implemented a unique process for forming flawless compound curvature laser windows. These windows represent a major part of specialized, nonintrusive laser data acquisition systems used in a variety of compressor and turbine research test facilities. This report summarizes the main aspects of compound curvature laser window development. It is an overview of the methodology and the peculiarities associated with the formulation of these windows. Included in this discussion is new information regarding procedures for compound curvature laser window development.
Sigma models with negative curvature
NASA Astrophysics Data System (ADS)
Alonso, Rodrigo; Jenkins, Elizabeth E.; Manohar, Aneesh V.
2016-05-01
We construct Higgs Effective Field Theory (HEFT) based on the scalar manifold Hn, which is a hyperbolic space of constant negative curvature. The Lagrangian has a non-compact O (n , 1) global symmetry group, but it gives a unitary theory as long as only a compact subgroup of the global symmetry is gauged. Whether the HEFT manifold has positive or negative curvature can be tested by measuring the S-parameter, and the cross sections for longitudinal gauge boson and Higgs boson scattering, since the curvature (including its sign) determines deviations from Standard Model values.
Sigma models with negative curvature
Alonso, Rodrigo; Jenkins, Elizabeth E.; Manohar, Aneesh V.
2016-03-16
Here, we construct Higgs Effective Field Theory (HEFT) based on the scalar manifold Hn, which is a hyperbolic space of constant negative curvature. The Lagrangian has a non-compact O(n, 1) global symmetry group, but it gives a unitary theory as long as only a compact subgroup of the global symmetry is gauged. Whether the HEFT manifold has positive or negative curvature can be tested by measuring the S-parameter, and the cross sections for longitudinal gauge boson and Higgs boson scattering, since the curvature (including its sign) determines deviations from Standard Model values.
Particles and curvatures in nematic liquid crystals
NASA Astrophysics Data System (ADS)
Serra, Francesca; Luo, Yimin; Yang, Shu; Kamien, Randall D.; Stebe, Kathleen J.
Elastic interactions in anisotropic fluids can be harnessed to direct particle interactions. A strategy to smoothly manipulate the director field in nematic liquid crystals is to vary the topography of the bounding surfaces. A rugged landscape with peaks and valleys create local deformations of the director field which can interact with particles in solution. We study this complex interaction in two different settings. The first consists of an array of shallow pores in a poly-dimethyl-siloxane (PDMS) membrane, whose curvature can be tuned either by swelling the PDMS membrane or by mechanical stretching. The second is a set of grooves with wavy walls, fabricated by photolithography, with various parameters of curvature and shapes. In this contexts we study how the motion of colloidal particles in nematic liquid crystals can be influenced by their interaction with the peaks and valleys of the bottom substrate or of the side walls. Particles with different associated topological defects (hedgehogs or Saturn rings) behave differently as they interact with the topographical features, favoring the docking on peaks or valleys. These experimental systems are also ideal to study the ``lock and key'' mechanism of particles in holes and to investigate a possible route for particle sorting.
Curvature Interaction in Collective Space
NASA Astrophysics Data System (ADS)
Herrmann, Richard
2012-12-01
For the Riemannian space, built from the collective coordinates used within nuclear models, an additional interaction with the metric is investigated, using the collective equivalent to Einstein's curvature scalar. The coupling strength is determined using a fit with the AME2003 ground state masses. An extended finite-range droplet model including curvature is introduced, which generates significant improvements for light nuclei and nuclei in the trans-fermium region.
Supported lipid bilayers with controlled curvature via colloidal lithography.
Sundh, Maria; Manandhar, Michal; Svedhem, Sofia; Sutherland, Duncan S
2011-09-01
Supported lipid bilayers (SLBs) at surfaces provide a route to quantitatively study molecular interactions with and at lipid membranes via different surface-based analytical techniques. Here, a method to fabricate SLBs with controlled curvatures, in the nanometer regime over large areas, is presented, utilizing lipid vesicle rupture onto nanostructured sensor substrates. Heat treated colloidal particle masks were used as templates to produce silicon dioxide films with systematically varied radius of curvature (ROC, 70 to 170 nm are demonstrated) and quartz crystal microbalance with dissipation monitoring (QCM-D) was used to confirm vesicle rupture onto such structured surfaces. Fluorescence microscopy was used to show fluidity of the supported membranes. The formation of confluent SLBs is demonstrated at the nanostructured surfaces from vesicles composed of POPC lipids. However, at surfaces with decreasing ROCs, vesicle rupture was hindered but with an increasing fraction of the positively charged lipid POEPC in the vesicles, it was possible to form good quality supported bilayers on all curvatures studied. Curved SLBs open up the possibility to systematically study the influence of curvature on molecular interactions at lipid membranes. © 2011 IEEE
Spatial curvature endgame: Reaching the limit of curvature determination
NASA Astrophysics Data System (ADS)
Leonard, C. Danielle; Bull, Philip; Allison, Rupert
2016-07-01
Current constraints on spatial curvature show that it is dynamically negligible: |ΩK|≲5 ×10-3 (95% C.L.). Neglecting it as a cosmological parameter would be premature however, as more stringent constraints on ΩK at around the 10-4 level would offer valuable tests of eternal inflation models and probe novel large-scale structure phenomena. This precision also represents the "curvature floor," beyond which constraints cannot be meaningfully improved due to the cosmic variance of horizon-scale perturbations. In this paper, we discuss what future experiments will need to do in order to measure spatial curvature to this maximum accuracy. Our conservative forecasts show that the curvature floor is unreachable—by an order of magnitude—even with Stage IV experiments, unless strong assumptions are made about dark energy evolution and the Λ CDM parameter values. We also discuss some of the novel problems that arise when attempting to constrain a global cosmological parameter like ΩK with such high precision. Measuring curvature down to this level would be an important validation of systematics characterization in high-precision cosmological analyses.
NASA Astrophysics Data System (ADS)
Kim, Dae Seok; Cha, Yun Jeong; Kim, Mun Ho; Lavrentovich, Oleg D.; Yoon, Dong Ki
2016-01-01
Soft materials with layered structure such as membranes, block copolymers and smectics exhibit intriguing morphologies with nontrivial curvatures. Here, we report restructuring the Gaussian and mean curvatures of smectic A films with free surface in the process of sintering, that is, reshaping at elevated temperatures. The pattern of alternating patches of negative, zero and positive mean curvature of the air-smectic interface has a profound effect on the rate of sublimation. As a result of sublimation, condensation and restructuring, initially equilibrium smectic films with negative and zero Gaussian curvature are transformed into structures with pronounced positive Gaussian curvature of layers packing, which are rare in the samples obtained by cooling from the isotropic melt. The observed relationship between the curvatures, bulk elastic behaviour and interfacial geometries in sintering of smectic liquid crystals might pave the way for new approaches to control soft morphologies at micron and submicron scales.
Kim, Dae Seok; Cha, Yun Jeong; Kim, Mun Ho; Lavrentovich, Oleg D.; Yoon, Dong Ki
2016-01-01
Soft materials with layered structure such as membranes, block copolymers and smectics exhibit intriguing morphologies with nontrivial curvatures. Here, we report restructuring the Gaussian and mean curvatures of smectic A films with free surface in the process of sintering, that is, reshaping at elevated temperatures. The pattern of alternating patches of negative, zero and positive mean curvature of the air–smectic interface has a profound effect on the rate of sublimation. As a result of sublimation, condensation and restructuring, initially equilibrium smectic films with negative and zero Gaussian curvature are transformed into structures with pronounced positive Gaussian curvature of layers packing, which are rare in the samples obtained by cooling from the isotropic melt. The observed relationship between the curvatures, bulk elastic behaviour and interfacial geometries in sintering of smectic liquid crystals might pave the way for new approaches to control soft morphologies at micron and submicron scales. PMID:26725975
Coupling of bending and stretching deformations in vesicle membranes.
Lipowsky, Reinhard
2014-06-01
Biomimetic membranes are fluid and can undergo two different elastic deformations, bending and stretching. The bending of a membrane is primarily governed by two elastic parameters: its spontaneous (or preferred) curvature m and its bending rigidity κ. These two parameters define an intrinsic tension scale, the spontaneous tension 2 κm². Membrane stretching and compression, on the other hand, are determined by the mechanical tension acting within the membrane. For vesicle membranes, the two elastic deformations are coupled via the enclosed vesicle volume even in the absence of mechanical forces as shown here by minimizing the combined bending and stretching energy with respect to membrane area for fixed vesicle volume. As a consequence, the mechanical tension within a vesicle membrane depends on the spontaneous curvature and on the bending rigidity. This interdependence, which is difficult to grasp intuitively, is then illustrated for a variety of simple vesicle shapes. Depending on the vesicle morphology, the magnitude of the mechanical tension can be comparable to or can be much smaller than the spontaneous tension. Copyright © 2014. Published by Elsevier B.V.
On the Weyl curvature hypothesis
Stoica, Ovidiu Cristinel
2013-11-15
The Weyl curvature hypothesis of Penrose attempts to explain the high homogeneity and isotropy, and the very low entropy of the early universe, by conjecturing the vanishing of the Weyl tensor at the Big-Bang singularity. In previous papers it has been proposed an equivalent form of Einstein’s equation, which extends it and remains valid at an important class of singularities (including in particular the Schwarzschild, FLRW, and isotropic singularities). Here it is shown that if the Big-Bang singularity is from this class, it also satisfies the Weyl curvature hypothesis. As an application, we study a very general example of cosmological models, which generalizes the FLRW model by dropping the isotropy and homogeneity constraints. This model also generalizes isotropic singularities, and a class of singularities occurring in Bianchi cosmologies. We show that the Big-Bang singularity of this model is of the type under consideration, and satisfies therefore the Weyl curvature hypothesis. -- Highlights: •The singularities we introduce are described by finite geometric/physical objects. •Our singularities have smooth Riemann and Weyl curvatures. •We show they satisfy Penrose’s Weyl curvature hypothesis (Weyl=0 at singularities). •Examples: FLRW, isotropic singularities, an extension of Schwarzschild’s metric. •Example: a large class of singularities which may be anisotropic and inhomogeneous.
Spatial curvature falsifies eternal inflation
Kleban, Matthew; Schillo, Marjorie E-mail: mls604@nyu.edu
2012-06-01
Inflation creates large-scale cosmological density perturbations that are characterized by an isotropic, homogeneous, and Gaussian random distribution about a locally flat background. Even in a flat universe, the spatial curvature measured within one Hubble volume receives contributions from long wavelength perturbations, and will not in general be zero. These same perturbations determine the Cosmic Microwave Background (CMB) temperature fluctuations, which are O(10{sup −5}). Consequently, the low-l multipole moments in the CMB temperature map predict the value of the measured spatial curvature Ω{sub k}. On this basis we argue that a measurement of |Ω{sub k}| > 10{sup −4} would rule out slow-roll eternal inflation in our past with high confidence, while a measurement of Ω{sub k} < −10{sup −4} (which is positive curvature, a locally closed universe) rules out false-vacuum eternal inflation as well, at the same confidence level. In other words, negative curvature (a locally open universe) is consistent with false-vacuum eternal inflation but not with slow-roll eternal inflation, and positive curvature falsifies both. Near-future experiments will dramatically extend the sensitivity of Ω{sub k} measurements and constitute a sharp test of these predictions.
Incisor crown bending strength correlates with diet and incisor curvature in anthropoid primates.
Deane, Andrew S
2015-02-01
Anthropoid incisors are large relative to the postcanine dentition and function in the preprocessing of food items. Previous analyses of anthropoid incisor allometry and shape demonstrate that incisor morphology is correlated with preferred foods and that more frugivorous anthropoids have larger and more curved incisors. Although the relationship between incisal crown curvature and preferred foods has been well documented in extant and fossil anthropoids, the functional significance of curvature variation has yet to be conclusively established. Given that an increase in crown curvature will increase maximum linear crown dimensions, and bending resistance is a function of linear crown dimensions, it is hypothesized that incisor crown curvature functons to increase incisor crown resistance to bending forces. This study uses beam theory to calculate the mesiodistal and labiolingual bending strengths of the maxillary and mandibular incisors of hominoid and platyrrhine taxa with differing diets and variable degrees of incisal curvature. Results indicate that bending strength correlates with incisal curvature and that frugivores have elevated incisor bending resistance relative to folivores. Maxillary central incisor bending strengths further discriminate platyrrhine and hominoid hard- and soft-object frugivores suggesting this crown is subjected to elevated occlusal loading relative to other incisors. These results are consistent with the hypothesis that incisor crown curvature functions to increase incisor crown resistance to bending forces but does not preclude the possibility that incisor bending strength is a composite function of multiple dentognathic variables including, but not limited to, incisor crown curvature. © 2014 Wiley Periodicals, Inc.
Lateral organization of membranes and cell shapes.
Markin, V S
1981-01-01
The relations among membrane structure, mechanical properties, and cell shape have been investigated. The fluid mosaic membrane models used contains several components that move freely in the membrane plane. These components interact with each other and determine properties of the membrane such as curvature and elasticity. A free energy equation is postulated for such a multicomponent membrane and the condition of free energy minimum is used to obtain differential equations relating the distribution of membrane components and the local membrane curvature. The force that moves membrane components along the membrane in a variable curvature field is calculated. A change in the intramembrane interactions can bring about phase separation or particle clustering. This, in turn, may strongly affect the local curvature. The numerical solution of the set of equations for the two dimensional case allows determination of the cell shape and the component distribution along the membrane. The model has been applied to describe certain erythrocytes shape transformations. PMID:7284547
Curvature generation in nematic surfaces
NASA Astrophysics Data System (ADS)
Mostajeran, Cyrus
2015-06-01
In recent years there has been a growing interest in the study of shape formation using modern responsive materials that can be preprogrammed to undergo spatially inhomogeneous local deformations. In particular, nematic liquid crystalline solids offer exciting possibilities in this context. Considerable recent progress has been made in achieving a variety of shape transitions in thin sheets of nematic solids by engineering isolated points of concentrated Gaussian curvature using topological defects in the nematic director field across textured surfaces. In this paper, we consider ways of achieving shape transitions in thin sheets of nematic glass by generation of nonlocalized Gaussian curvature in the absence of topological defects in the director field. We show how one can blueprint any desired Gaussian curvature in a thin nematic sheet by controlling the nematic alignment angle across the surface and highlight specific patterns which present feasible initial targets for experimental verification of the theory.
Mixed lipid bilayers with locally varying spontaneous curvature and bending.
Gueguen, Guillaume; Destainville, Nicolas; Manghi, Manoel
2014-08-01
A model of lipid bilayers made of a mixture of two lipids with different average compositions on both leaflets, is developed. A Landau Hamiltonian describing the lipid-lipid interactions on each leaflet, with two lipidic fields ψ 1 and ψ 2, is coupled to a Helfrich one, accounting for the membrane elasticity, via both a local spontaneous curvature, which varies as C 0 + C 1(ψ 1 - ψ 2/2), and a bending modulus equal to κ 0 + κ 1(ψ 1 + ψ 2)/2. This model allows us to define curved patches as membrane domains where the asymmetry in composition, ψ 1 - ψ 2, is large, and thick and stiff patches where ψ 1 + ψ 2 is large. These thick patches are good candidates for being lipidic rafts, as observed in cell membranes, which are composed primarily of saturated lipids forming a liquid-ordered domain and are known to be thick and flat nano-domains. The lipid-lipid structure factors and correlation functions are computed for globally spherical membranes and planar ones and for a whole set of parameters including the surface tension and the coupling in the two leaflet compositions. Phase diagrams are established, within a Gaussian approximation, showing the occurrence of two types of Structure Disordered phases, with correlations between either curved or thick patches, and an Ordered phase, corresponding to the divergence of the structure factor at a finite wave vector. The varying bending modulus plays a central role for curved membranes, where the driving force κ 1 C 0 (2) is balanced by the line tension, to form raft domains of size ranging from 10 to 100 nm. For planar membranes, raft domains emerge via the cross-correlation with curved domains. A global picture emerges from curvature-induced mechanisms, described in the literature for planar membranes, to coupled curvature- and bending-induced mechanisms in curved membranes forming a closed vesicle.
Actin filament curvature biases branching direction
Risca, Viviana I.; Wang, Evan B.; Chaudhuri, Ovijit; Chia, Jia Jun; Geissler, Phillip L.; Fletcher, Daniel A.
2012-01-01
Mechanical cues affect many important biological processes in metazoan cells, such as migration, proliferation, and differentiation. Such cues are thought to be detected by specialized mechanosensing molecules linked to the cytoskeleton, an intracellular network of protein filaments that provide mechanical rigidity to the cell and drive cellular shape change. The most abundant such filament, actin, forms branched networks nucleated by the actin-related protein (Arp) 2/3 complex that support or induce membrane protrusions and display adaptive behavior in response to compressive forces. Here we show that filamentous actin serves in a mechanosensitive capacity itself, by biasing the location of actin branch nucleation in response to filament bending. Using an in vitro assay to measure branching from curved sections of immobilized actin filaments, we observed preferential branch formation by the Arp2/3 complex on the convex face of the curved filament. To explain this behavior, we propose a fluctuation gating model in which filament binding or branch nucleation by Arp2/3 occur only when a sufficiently large, transient, local curvature fluctuation causes a favorable conformational change in the filament, and we show with Monte Carlo simulations that this model can quantitatively account for our experimental data. We also show how the branching bias can reinforce actin networks in response to compressive forces. These results demonstrate how filament curvature can alter the interaction of cytoskeletal filaments with regulatory proteins, suggesting that direct mechanotransduction by actin may serve as a general mechanism for organizing the cytoskeleton in response to force. PMID:22308368
Studying Biomolecule Localization by Engineering Bacterial Cell Wall Curvature
Renner, Lars D.; Eswaramoorthy, Prahathees; Ramamurthi, Kumaran S.; Weibel, Douglas B.
2013-01-01
In this article we describe two techniques for exploring the relationship between bacterial cell shape and the intracellular organization of proteins. First, we created microchannels in a layer of agarose to reshape live bacterial cells and predictably control their mean cell wall curvature, and quantified the influence of curvature on the localization and distribution of proteins in vivo. Second, we used agarose microchambers to reshape bacteria whose cell wall had been chemically and enzymatically removed. By combining microstructures with different geometries and fluorescence microscopy, we determined the relationship between bacterial shape and the localization for two different membrane-associated proteins: i) the cell-shape related protein MreB of Escherichia coli, which is positioned along the long axis of the rod-shaped cell; and ii) the negative curvature-sensing cell division protein DivIVA of Bacillus subtilis, which is positioned primarily at cell division sites. Our studies of intracellular organization in live cells of E. coli and B. subtilis demonstrate that MreB is largely excluded from areas of high negative curvature, whereas DivIVA localizes preferentially to regions of high negative curvature. These studies highlight a unique approach for studying the relationship between cell shape and intracellular organization in intact, live bacteria. PMID:24391905
The role of curvature in silica mesoporous crystals
Miyasaka, Keiichi; Garcia Bennett, Alfonso; Han, Lu; Han, Yu; Xiao, Changhong; Fujita, Nobuhisa; Castle, Toen; Sakamoto, Yasuhiro; Che, Shunai; Terasaki, Osamu
2012-01-01
Silica mesoporous crystals (SMCs) offer a unique opportunity to study micellar mesophases. Replication of non-equilibrium mesophases into porous silica structures allows the characterization of surfactant phases under a variety of chemical and physical perturbations, through methods not typically accessible to liquid crystal chemists. A poignant example is the use of electron microscopy and crystallography, as discussed herein, for the purpose of determining the fundamental role of amphiphile curvature, namely mean curvature and Gaussian curvature, which have been extensively studied in various fields such as polymer, liquid crystal, biological membrane, etc. The present work aims to highlight some current studies devoted to the interface curvature on SMCs, in which electron microscopy and electron crystallography (EC) are used to understand the geometry of silica wall surface in bicontinuous and cage-type mesostructures through the investigation of electrostatic potential maps. Additionally, we show that by altering the synthesis conditions during the preparation of SMCs, it is possible to isolate particles during micellar mesophase transformations in the cubic bicontinuous system, allowing us to view and study epitaxial relations under the specific synthesis conditions. By studying the relationship between mesoporous structure, interface curvature and micellar mesophases using electron microscopy and EC, we hope to bring new insights into the formation mechanism of these unique materials but also contribute a new way of understanding periodic liquid crystal systems. PMID:24098848
Lipid shape is a key factor for membrane interactions of amphipathic helical peptides.
Strandberg, Erik; Tiltak, Deniz; Ehni, Sebastian; Wadhwani, Parvesh; Ulrich, Anne S
2012-07-01
The membrane alignment of the amphiphilic alpha-helical model peptide MSI-103 (sequence [KIAGKIA]3-NH2) was examined by solid state 2H-NMR in different lipid systems by systematically varying the acyl chain length and degree of saturation, the lipid head group type, and the peptide-to-lipid molar ratio. In liquid crystalline phosphatidylcholine (PC) lipids with saturated chains, the amphiphilic helix changes its orientation from a surface-bound "S-state" to a tilted "T-state" with increasing peptide concentration. In PC lipids with unsaturated chains, on the other hand, the S-state is found throughout all concentrations. Using phosphatidylethanolamine lipids with a small head group or by addition of lyso-lipids with only one acyl chain, the spontaneous curvature of the bilayer was purposefully changed. In the first case with a negative curvature only the S-state was found, whereas in systems with a positive curvature the peptide preferred the obliquely immersed T-state at high concentration. The orientation of MSI-103 thus correlates very well with the shape of the lipid molecules constituting the membrane. Lipid charge, on the other hand, was found to affect only the initial electrostatic attraction to the membrane surface but not the alignment preferences. In bilayers that are "sealed" with 20% cholesterol, MSI-103 cannot bind in a well-oriented manner and forms immobilized aggregates instead. We conclude that the curvature properties of a membrane are a key factor in the interactions of amphiphilic helical peptides in general, whose re-alignment and immersion preferences may thus be inferred in a straightforward manner from the lipid-shape concept.
Agudo-Canalejo, Jaime; Lipowsky, Reinhard
2015-01-01
The adhesion and engulfment of nanoparticles by biomembranes is essential for many processes such as biomedical imaging, drug delivery, nanotoxicity, and viral infection. Many studies have shown that both surface chemistry, which determines the adhesive strength of the membrane-particle interactions, and particle size represent key parameters for these processes. Here, we show that the asymmetry between the two leaflets of a bilayer membrane provides another key parameter for the engulfment of nanoparticles. The asymmetric membrane prefers to curve in a certain manner as quantitatively described by its spontaneous curvature. We derive two general relationships between particle size, adhesive strength, and spontaneous curvature that determine the instabilities of (i) the nonadhering or free state and (ii) the completely engulfed state of the particle. For model membranes such as lipid or polymer bilayers with a uniform composition, the two relationships lead to two critical particle sizes that determine four distinct engulfment regimes, both for the endocytic and for the exocytic engulfment process. For strong adhesion, the critical particle sizes are on the order of 10 nm, while they are on the order of 1000 nm for weak or ultraweak adhesion. Our theoretical results are therefore accessible to both experimental studies and computer simulations of model membranes. In order to address the more complex process of receptor-mediated endocytosis, we take the adhesion-induced segregation of membrane components into account and consider bound and unbound membrane segments that differ in their spontaneous curvatures. To model protein coats as formed during clathrin-dependent endocytosis, we focus on the case in which the bound membrane segments have a large spontaneous curvature compared to the unbound ones. We derive explicit expressions for the engulfment rate and the uptake of nanoparticles, which both depend on the particle size in a nonmonotonic manner, and provide a
Model-independent Constraints on Cosmic Curvature and Opacity
NASA Astrophysics Data System (ADS)
Wang, Guo-Jian; Wei, Jun-Jie; Li, Zheng-Xiang; Xia, Jun-Qing; Zhu, Zong-Hong
2017-09-01
In this paper, we propose to estimate the spatial curvature of the universe and the cosmic opacity in a model-independent way with expansion rate measurements, H(z), and type Ia supernova (SNe Ia). On the one hand, using a nonparametric smoothing method Gaussian process, we reconstruct a function H(z) from opacity-free expansion rate measurements. Then, we integrate the H(z) to obtain distance modulus μ H, which is dependent on the cosmic curvature. On the other hand, distances of SNe Ia can be determined by their photometric observations and thus are opacity-dependent. In our analysis, by confronting distance moduli μ H with those obtained from SNe Ia, we achieve estimations for both the spatial curvature and the cosmic opacity without any assumptions for the cosmological model. Here, it should be noted that light curve fitting parameters, accounting for the distance estimation of SNe Ia, are determined in a global fit together with the cosmic opacity and spatial curvature to get rid of the dependence of these parameters on cosmology. In addition, we also investigate whether the inclusion of different priors for the present expansion rate (H 0: global estimation, 67.74 ± 0.46 km s‑1 Mpc‑1, and local measurement, 73.24 ± 1.74 km s‑1 Mpc‑1) exert influence on the reconstructed H(z) and the following estimations of the spatial curvature and cosmic opacity. Results show that, in general, a spatially flat and transparent universe is preferred by the observations. Moreover, it is suggested that priors for H 0 matter a lot. Finally, we find that there is a strong degeneracy between the curvature and the opacity.
Ménager, Christine; Guemghar, Dihya; Cabuil, Valérie; Lesieur, Sylviane
2010-10-05
The present study deals with the morphological modifications of giant dioleoyl phosphatidylcholine vesicles (DOPC GUVs) induced by the nonionic surfactant n-octyl β,D-glucopyranoside at sublytic levels, i.e., in the first steps of the vesicle-to-micelle transition process, when surfactant inserts into the vesicle bilayer without disruption. Experimental conditions were perfected to exactly control the surfactant bilayer composition of the vesicles, in line with former work focused on the mechanical properties of the membrane of magnetic-fluid-loaded DOPC GUVs submitted to a magnetic field. The purpose here was to systematically examine, in the absence of any external mechanical constraint, the dynamics of giant vesicle shape and membrane deformations as a function of surfactant partitioning between the aqueous phase and the lipid membrane, beforehand established by turbidity measurements from small unilamellar vesicles.
Di Natale, Giuseppe; Pappalardo, Giuseppe; Milardi, Danilo; Sciacca, Michele F M; Attanasio, Francesco; La Mendola, Diego; Rizzarelli, Enrico
2010-11-04
The flexible N-terminal domain of the prion protein (PrP(c)) is believed to play a pivotal role in both trafficking of the protein through the cell membrane and its pathogenic conversion into the β sheet-rich scrapie isoform (PrP(sc)). Unlike mammalian PrP(c), avian prion proteins are not known to undergo any pathogenic conformational conversions. Consequently, some critical advances in our understanding of the molecular mechanisms underlying prion pathogenesis are expected from comparative studies of the biophysical properties of the N-terminal domains of the two proteins. The present study addresses the role played by different environmental factors, i.e., copper(II), pH, and membrane-mimicking environments, in assisting the conformational preferences of huPrP60-91 and chPrP53-76, two soluble peptides encompassing the N-terminal copper(II) binding domains of the human and chicken prion proteins, respectively. Moreover, the membrane interactions of huPrP60-91, chPrP53-76, and their copper(II) complexes were evaluated by Trp fluorescence in conjunction with measurements of the variation in thermotropic properties of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) unilamellar vesicles. Circular dichroism experiments revealed that huPrP60-91 adopts a predominant polyproline II conformation in aqueous solution that is destabilized at basic pH or in the presence of trifluoroethanol (TFE). Unlike anionic sodium dodecyl sulfate (SDS), which seems to stabilize the polyproline II conformation further, zwitterionic dodecylphosphocholine (DPC) micelles do not affect the peptide structure. On the contrary, copper(II) promptly promotes an increase in β-turn-rich structures. Differential scanning calorimetry (DSC) and Trp fluorescence assays carried out on DPPC model membranes after incubation with huPrP60-91 showed a marked tendency of the peptide to slowly penetrate the lipid bilayer with a concomitant conformational transition toward an extended β-sheet-like structure
Space Curvature and the "Heavy Banana 'Paradox.'"
ERIC Educational Resources Information Center
Gruber, Ronald P.; And Others
1991-01-01
Two ways to visually enhance the concept of space curvature are described. Viewing space curvature as a meterstick contraction and the heavy banana "paradox" are discussed. The meterstick contraction is mathematically explained. (KR)
Space Curvature and the "Heavy Banana 'Paradox.'"
ERIC Educational Resources Information Center
Gruber, Ronald P.; And Others
1991-01-01
Two ways to visually enhance the concept of space curvature are described. Viewing space curvature as a meterstick contraction and the heavy banana "paradox" are discussed. The meterstick contraction is mathematically explained. (KR)
Classification and quantification of leaf curvature
Liu, Zhongyuan; Jia, Liguo; Mao, Yanfei; He, Yuke
2010-01-01
Various mutants of Arabidopsis thaliana deficient in polarity, cell division, and auxin response are characterized by certain types of leaf curvature. However, comparison of curvature for clarification of gene function can be difficult without a quantitative measurement of curvature. Here, a novel method for classification and quantification of leaf curvature is reported. Twenty-two mutant alleles from Arabidopsis mutants and transgenic lines deficient in leaf flatness were selected. The mutants were classified according to the direction, axis, position, and extent of leaf curvature. Based on a global measure of whole leaves and a local measure of four regions in the leaves, the curvature index (CI) was proposed to quantify the leaf curvature. The CI values accounted for the direction, axis, position, and extent of leaf curvature in all of the Arabidopsis mutants grown in growth chambers. Comparison of CI values between mutants reveals the spatial and temporal variations of leaf curvature, indicating the strength of the mutant alleles and the activities of the corresponding genes. Using the curvature indices, the extent of curvature in a complicated genetic background becomes quantitative and comparable, thus providing a useful tool for defining the genetic components of leaf development and to breed new varieties with leaf curvature desirable for the efficient capture of sunlight for photosynthesis and high yields. PMID:20400533
Classification and quantification of leaf curvature.
Liu, Zhongyuan; Jia, Liguo; Mao, Yanfei; He, Yuke
2010-06-01
Various mutants of Arabidopsis thaliana deficient in polarity, cell division, and auxin response are characterized by certain types of leaf curvature. However, comparison of curvature for clarification of gene function can be difficult without a quantitative measurement of curvature. Here, a novel method for classification and quantification of leaf curvature is reported. Twenty-two mutant alleles from Arabidopsis mutants and transgenic lines deficient in leaf flatness were selected. The mutants were classified according to the direction, axis, position, and extent of leaf curvature. Based on a global measure of whole leaves and a local measure of four regions in the leaves, the curvature index (CI) was proposed to quantify the leaf curvature. The CI values accounted for the direction, axis, position, and extent of leaf curvature in all of the Arabidopsis mutants grown in growth chambers. Comparison of CI values between mutants reveals the spatial and temporal variations of leaf curvature, indicating the strength of the mutant alleles and the activities of the corresponding genes. Using the curvature indices, the extent of curvature in a complicated genetic background becomes quantitative and comparable, thus providing a useful tool for defining the genetic components of leaf development and to breed new varieties with leaf curvature desirable for the efficient capture of sunlight for photosynthesis and high yields.
Barenboim, Gabriela; Martínez, Enrique Fernández; Mena, Olga; Verde, Licia E-mail: enfmarti@mppmu.mpg.de E-mail: liciaverde@icc.ub.edu
2010-03-01
Geometrical tests such as the combination of the Hubble parameter H(z) and the angular diameter distance d{sub A}(z) can, in principle, break the degeneracy between the dark energy equation of state parameter w(z), and the spatial curvature Ω{sub k} in a direct, model-independent way. In practice, constraints on these quantities achievable from realistic experiments, such as those to be provided by Baryon Acoustic Oscillation (BAO) galaxy surveys in combination with CMB data, can resolve the cosmic confusion between the dark energy equation of state parameter and curvature only statistically and within a parameterized model for w(z). Combining measurements of both H(z) and d{sub A}(z) up to sufficiently high redshifts z ∼ 2 and employing a parameterization of the redshift evolution of the dark energy equation of state are the keys to resolve the w(z)−Ω{sub k} degeneracy.
Quantum complexity and negative curvature
NASA Astrophysics Data System (ADS)
Brown, Adam R.; Susskind, Leonard; Zhao, Ying
2017-02-01
As time passes, once simple quantum states tend to become more complex. For strongly coupled k -local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we show that the same pattern is exhibited by a much simpler system—classical geodesics on a compact two-dimensional geometry of uniform negative curvature. This striking parallel persists whether the system is allowed to evolve naturally or is perturbed from the outside.
Curvatures Estimation in Orientation Selection
1991-01-31
than is-obtained in length-tuning measurements . Hence, over a limited range, increasing the size or gain of the small RF has a similar effect . The...the remaining larger, lower curvature units to represent the curve. An indirect test involves measuring the time for the effect to set in, with and...31Jan 91 By, Steen .Zcke * ax . Cnadr tDistribution/ Steen .Zcke *MaxS. ynaer ~ Availability Codes Dist Special Computer Vision and Robotics Laboratory
Disformal invariance of curvature perturbation
Motohashi, Hayato; White, Jonathan E-mail: jwhite@post.kek.jp
2016-02-01
We show that under a general disformal transformation the linear comoving curvature perturbation is not identically invariant, but is invariant on superhorizon scales for any theory that is disformally related to Horndeski's theory. The difference between disformally related curvature perturbations is found to be given in terms of the comoving density perturbation associated with a single canonical scalar field. In General Relativity it is well-known that this quantity vanishes on superhorizon scales through the Poisson equation that is obtained on combining the Hamiltonian and momentum constraints, and we confirm that a similar result holds for any theory that is disformally related to Horndeski's scalar-tensor theory so long as the invertibility condition for the disformal transformation is satisfied. We also consider the curvature perturbation at full nonlinear order in the unitary gauge, and find that it is invariant under a general disformal transformation if we assume that an attractor regime has been reached. Finally, we also discuss the counting of degrees of freedom in theories disformally related to Horndeski's.
Shape and curvature error estimation in polished surfaces of ground glass molds
NASA Astrophysics Data System (ADS)
Savio, Gianpaolo; Pal, Raj Kumar; Meneghello, Roberto; D'Angelo, Luciano; Concheri, Gianmaria
2017-02-01
In the fabrication process of aspheric glass lens and molds, shape characterization is a fundamental task to control geometrical errors. Nevertheless, the more significant geometrical functional aspect related to the optical properties is the curvature, which is rarely investigated in the manufacturing process of lenses. Algorithms for the assessment of shape and curvature errors on aspheric surface profile are presented. The method has been investigated on profiles measured before and at different steps of the membrane polishing process. The results show how surface roughness, shape, and curvature change during the polishing process as a function of the machining time.
Origins of chemoreceptor curvature sorting in Escherichia coli
Draper, Will; Liphardt, Jan
2017-01-01
Bacterial chemoreceptors organize into large clusters at the cell poles. Despite a wealth of structural and biochemical information on the system's components, it is not clear how chemoreceptor clusters are reliably targeted to the cell pole. Here, we quantify the curvature-dependent localization of chemoreceptors in live cells by artificially deforming growing cells of Escherichia coli in curved agar microchambers, and find that chemoreceptor cluster localization is highly sensitive to membrane curvature. Through analysis of multiple mutants, we conclude that curvature sensitivity is intrinsic to chemoreceptor trimers-of-dimers, and results from conformational entropy within the trimer-of-dimers geometry. We use the principles of the conformational entropy model to engineer curvature sensitivity into a series of multi-component synthetic protein complexes. When expressed in E. coli, the synthetic complexes form large polar clusters, and a complex with inverted geometry avoids the cell poles. This demonstrates the successful rational design of both polar and anti-polar clustering, and provides a synthetic platform on which to build new systems. PMID:28322223
Effect of Gaussian curvature modulus on the shape of deformed hollow spherical objects.
Quilliet, C; Farutin, A; Marmottant, P
2016-06-01
A popular description of soft membranes uses the surface curvature energy introduced by Helfrich, which includes a spontaneous curvature parameter. In this paper we show how the Helfrich formula can also be of interest for a wider class of spherical elastic surfaces, namely with shear elasticity, and likely to model other deformable hollow objects. The key point is that when a stress-free state with spherical symmetry exists before subsequent deformation, its straightforwardly determined curvature ("geometrical spontaneous curvature") differs most of the time from the Helfrich spontaneous curvature parameter that should be considered in order to have the model being correctly used. Using the geometrical curvature in a set of independent parameters unveils the role of the Gaussian curvature modulus, which appears to play on the shape of an elastic surface even though this latter is closed, contrary to what happens for surfaces without spontaneous curvature. In appendices, clues are given to apply this alternative and convenient formulation of the elastic surface model to the particular case of thin spherical shells of isotropic material (TSSIMs).
Proteins interacting with Membranes: Protein Sorting and Membrane Shaping
NASA Astrophysics Data System (ADS)
Callan-Jones, Andrew
2015-03-01
Membrane-bound transport in cells requires generating membrane curvature. In addition, transport is selective, in order to establish spatial gradients of membrane components in the cell. The mechanisms underlying cell membrane shaping by proteins and the influence of curvature on membrane composition are active areas of study in cell biophysics. In vitro approaches using Giant Unilamellar Vesicles (GUVs) are a useful tool to identify the physical mechanisms that drive sorting of membrane components and membrane shape change by proteins. I will present recent work on the curvature sensing and generation of IRSp53, a protein belonging to the BAR family, whose members, sharing a banana-shaped backbone, are involved in endocytosis. Pulling membrane tubes with 10-100 nm radii from GUVs containing encapsulated IRSp53 have, unexpectedly, revealed a non-monotonic dependence of the protein concentration on the tube as a function of curvature. Experiments also show that bound proteins alter the tube mechanics and that protein phase separation along the tube occurs at low tensions. I will present accompanying theoretical work that can explain these findings based on the competition between the protein's intrinsic curvature and the effective rigidity of a membrane-protein patch.
Salvage penile curvature correction surgery.
Hsieh, Cheng-Hsing; Chen, Heng-Shuen; Lee, Wen-Yuan; Chen, Kuo-Liang; Chang, Chao-Hsiang; Hsu, Geng-Long
2010-01-01
It is commonly believed that coarser suture materials should be used to provide sufficient tenacity in surgery for penile curvature correction. We report our 15-year experience of fine sutures in a second operation in 31 patients who underwent prior curvature correction elsewhere with coarser sutures, resulting in recurrent penile curvature. Suture materials used in prior surgeries in these patients were either 2-0 or 3-0 nylon sutures. In this series, all 31 patients underwent a modified Nesbit procedure at the level of the collagen bundles using finer sutures. Prior to July 1998, 10 men underwent salvage surgery using 4-0 polyglactin sutures. Thereafter, we adapted 6-0 nylon sutures for another 21 patients. We categorized the patients into the polyglactin (n = 10) and nylon (n = 21) groups respectively. Overall, 29 patients were available for follow-up while using the abridged 5-item version of the International Index of Erectile Function (IIEF-5) scoring system, with 21 patients in the nylon group. We have found cavernosography a practical and reliable method to objectively assess penile morphology in these patients. The penile morphology both subjectively and objectively was excellent in all patients, except for 1 in each group. Erectile function restoration showed a trend of satisfaction in the polyglactin group and based on IIEF-5 was significantly improved in the nylon group (14.2 ± 3.6 vs 21.9 ± 2.1, n = 20, P < .001). These results suggest that in penile tunical surgery, fine sutures such as 6-0 nylon may result in better penile morphology and functional outcomes.
Schmeiser, Christian; Winkler, Christoph
2015-09-07
The crawling motility of many cell types relies on lamellipodia, flat protrusions spreading on flat substrates but (on cells in suspension) also growing into three-dimensional space. Lamellipodia consist of a plasma membrane wrapped around an oriented actin filament meshwork. It is well known that the actin density is controlled by coordinated polymerization, branching, and capping processes, but the mechanisms producing the small aspect ratios of lamellipodia (hundreds of nm thickness vs. several μm lateral and inward extension) remain unclear. The main hypothesis of this work is a strong influence of the local geometry of the plasma membrane on the actin dynamics. This is motivated by observations of co-localization of proteins with I-BAR domains (like IRSp53) with polymerization and branching agents along the membrane. The I-BAR domains are known to bind to the membrane and to prefer and promote membrane curvature. This hypothesis is translated into a stochastic mathematical model where branching and capping rates, and polymerization speeds depend on the local membrane geometry and branching directions are influenced by the principal curvature directions. This requires the knowledge of the deformation of the membrane, being described in a quasi-stationary approximation by minimization of a modified Helfrich energy, subject to the actin filaments acting as obstacles. Simulations with this model predict pieces of flat lamellipodia without any prescribed geometric restrictions. Copyright © 2015 Elsevier Ltd. All rights reserved.
Molecular basis of endosomal-membrane association for the dengue virus envelope protein
Rogers, David M.; Kent, Michael S.; Rempe, Susan B.
2015-01-02
Dengue virus is coated by an icosahedral shell of 90 envelope protein dimers that convert to trimers at low pH and promote fusion of its membrane with the membrane of the host endosome. We provide the first estimates for the free energy barrier and minimum for two key steps in this process: host membrane bending and protein–membrane binding. Both are studied using complementary membrane elastic, continuum electrostatics and all-atom molecular dynamics simulations. The predicted host membrane bending required to form an initial fusion stalk presents a 22–30 kcal/mol free energy barrier according to a constrained membrane elastic model. Combined continuummore » and molecular dynamics results predict a 15 kcal/mol free energy decrease on binding of each trimer of dengue envelope protein to a membrane with 30% anionic phosphatidylglycerol lipid. The bending cost depends on the preferred curvature of the lipids composing the host membrane leaflets, while the free energy gained for protein binding depends on the surface charge density of the host membrane. The fusion loop of the envelope protein inserts exactly at the level of the interface between the membrane's hydrophobic and head-group regions. As a result, the methods used in this work provide a means for further characterization of the structures and free energies of protein-assisted membrane fusion.« less
The curvature elastic-energy function of the lipid-water cubic mesophase
NASA Astrophysics Data System (ADS)
Chung, Hesson; Caffrey, Martin
1994-03-01
CELL and lipid membranes are able to bend, as manifested during membrane fusion and the formation of non-lamellar lyotropic mesopbases in water. But there is an energy cost to bending of lipid layers, called the curvature elastic energy. Although the functional form of this energy is known1, a complete quantitative knowledge of the curvature elastic energy, which is central to predicting the relative stability of the large number of phases that lipid membranes can adopt, has been lacking. Here we use X-ray synchrotron diffraction measurements of the variation of lattice parameter with pressure and temperature for the periodic Ia3d (Q230) cubic phase of hydrated monoolein to calculate the complete curvature elastic-energy function for the lipid cubic mesophase. This allows us to predict the stabilities of different cubic and lamellar phases for this system as a function of composition.
Mirror with thermally controlled radius of curvature
Neil, George R.; Shinn, Michelle D.
2010-06-22
A radius of curvature controlled mirror for controlling precisely the focal point of a laser beam or other light beam. The radius of curvature controlled mirror provides nearly spherical distortion of the mirror in response to differential expansion between the front and rear surfaces of the mirror. The radius of curvature controlled mirror compensates for changes in other optical components due to heating or other physical changes. The radius of curvature controlled mirror includes an arrangement for adjusting the temperature of the front surface and separately adjusting the temperature of the rear surface to control the radius of curvature. The temperature adjustment arrangements can include cooling channels within the mirror body or convection of a gas upon the surface of the mirror. A control system controls the differential expansion between the front and rear surfaces to achieve the desired radius of curvature.
Galassi, Vanesa V; Salinas, Silvina R; Montich, Guillermo G
2017-07-27
We studied the conformational changes of the fatty acid-binding protein ReP1-NCXSQ in the interface of anionic lipid membranes. ReP1-NCXSQ is an acidic protein that regulates the activity of the Na(+)/Ca(2+) exchanger in squid axon. The structure is a flattened barrel composed of two orthogonal β-sheets delimiting an inner cavity and a domain of two α-helix segments arranged as a hairpin. FTIR and CD spectroscopy showed that the interactions with several anionic lipids in the form of small unilamellar vesicles (SUVs) induced an increase in the proportion of helix secondary structure. Lower amount or no increase in α-helix was observed upon the interaction with anionic lipids in the form of large unilamellar vesicles (LUVs). The exception was 1,2-dimyristoyl-sn-glycero-3-phosphoglycerol (DMPG) that was equally efficien to to induce the conformational change both in SUVs and in LUVs. In solution, the infrared spectra of ReP1-NCXSQ at temperatures above the unfolding displayed a band at 1617 cm(-1) characteristic of aggregated strands. This band was not observed when the protein interacted with DMPG, indicating inhibition of aggregation in the interface. Similarly to the observed in L-BABP, another member of the fatty acid binding proteins, a conformational change in ReP1-NCXSQ was coupled to the gel to liquid-crystalline lipid phase transition.
Continuum electromechanical modeling of protein-membrane interactions.
Zhou, Y C; Lu, Benzhuo; Gorfe, Alemayehu A
2010-10-01
A continuum electromechanical model is proposed to describe the membrane curvature induced by electrostatic interactions in a solvated protein-membrane system. The model couples the macroscopic strain energy of membrane and the electrostatic solvation energy of the system, and equilibrium membrane deformation is obtained by minimizing the electroelastic energy functional with respect to the dielectric interface. The model is illustrated with the systems with increasing geometry complexity and captures the sensitivity of membrane curvature to the permanent and mobile charge distributions.
Radius of curvature controlled mirror
Neil, George R.; Rathke, John Wickham; Schultheiss, Thomas John; Shinn, Michelle D.; Dillon-Townes, Lawrence A.
2006-01-17
A controlled radius of curvature mirror assembly comprising: a distortable mirror having a reflective surface and a rear surface; and in descending order from the rear surface; a counter-distortion plate; a flow diverter having a flow diverter aperture at the center thereof; a flow return plate having a flow return aperture at the center thereof; a thermal isolation plate having a thermal isolation plate aperture at the center thereof and a flexible heater having a rear surface and a flexible heater aperture at the center thereof; a double walled tube defining a coolant feed chamber and a coolant return chamber; said coolant feed chamber extending to and through the flow diverter aperture and terminating at the counter-distortion plate and the coolant return chamber extending to and through the thermal isolation backplate and terminating at the flow diverter; and a coolant feed and a coolant return exit at the rear of said flexible heater.
Determining wave direction using curvature parameters.
de Queiroz, Eduardo Vitarelli; de Carvalho, João Luiz Baptista
2016-01-01
The curvature of the sea wave was tested as a parameter for estimating wave direction in the search for better results in estimates of wave direction in shallow waters, where waves of different sizes, frequencies and directions intersect and it is difficult to characterize. We used numerical simulations of the sea surface to determine wave direction calculated from the curvature of the waves. Using 1000 numerical simulations, the statistical variability of the wave direction was determined. The results showed good performance by the curvature parameter for estimating wave direction. Accuracy in the estimates was improved by including wave slope parameters in addition to curvature. The results indicate that the curvature is a promising technique to estimate wave directions.•In this study, the accuracy and precision of curvature parameters to measure wave direction are analyzed using a model simulation that generates 1000 wave records with directional resolution.•The model allows the simultaneous simulation of time-series wave properties such as sea surface elevation, slope and curvature and they were used to analyze the variability of estimated directions.•The simultaneous acquisition of slope and curvature parameters can contribute to estimates wave direction, thus increasing accuracy and precision of results.
Streamline curvature effects on turbulent boundary layers
NASA Technical Reports Server (NTRS)
Wilcox, D. C.; Chambers, T. L.
1976-01-01
A theoretical tool has been developed for predicting, in a nonempirical manner, effects of streamline curvature and coordinate-system rotation on turbulent boundary layers. The second-order closure scheme developed by Wilcox and Traci has been generalized for curved streamline flow and for flow in a rotating coordinate system. A physically based straightforward argument shows that curvature/rotation primarily affects the turbulent mixing energy; the argument yields suitable curvature/rotation terms which are added to the mixing-energy equation. Singular-perturbation solutions valid in the wall layer of a curved-wall boundary layer and a fully developed rotating channel flow demonstrate that, with the curvature/rotation terms, the model predicts the curved-wall and the rotating coordinate system laws of the wall. Results of numerical computations of curved-wall boundary layers and of rotating channel flow show that curvature/rotation effects can be computed accurately with second-order closure.
Importance of plan curvature in watershed modeling
NASA Astrophysics Data System (ADS)
Boll, J.; Ribail, J.; Zhao, M.
2016-12-01
A hillslope's hydrologic response to precipitation events is largely controlled by the topographic features of a given hillslope, specifically the profile and plan curvature. Many models simplify hillslope topography and ignore the curvature properties, and some use alternate measures such as a topographic index or the hillslope width function. Models that ignore curvature properties may be calibrated to produce the statistically acceptable integrated response of runoff at a watershed outlet, but incorporating these properties is necessary to model accurately hydrologic processes such as surface flow, erosion, subsurface lateral flow, location of runoff generation and drainage response. In this study, we evaluated the sensitivity of rainfall-runoff modelling to profile and plan curvature in two models. In the first model, the Water Erosion Prediction Project (WEPP) model, hillslope uses a representative width to the hillslope by dividing the drainage area by the average surface channel length. Profile curvature is preserved with a limited spatial resolution due to the number of overland flow elements. In the second model, the distributed Soil Moisture Routing (SMR) model, the geographic information system uses the D8 algorithm to capture profile and plan curvature. Sensitivity to topographic features was tested for three profile curvatures (convex, concave, straight) combined with three plan curvatures (diverging, converging, uniform) resulting in a total of nine hillslopes. Each hillslope was subjected to different rainfall events to detect threshold behavior for when topographic features cannot be ignored. Our findings indicate that concave and convex plan curvature need to be included when subsurface flow processes are the dominant flow process for surface flow runoff generation. We present thresholds for acceptable cases when profile and plan curvature can be simplified in larger spatial hydrologic units.
Conversion of radius of curvature to power (and vice versa)
NASA Astrophysics Data System (ADS)
Wickenhagen, Sven; Endo, Kazumasa; Fuchs, Ulrike; Youngworth, Richard N.; Kiontke, Sven R.
2015-09-01
Manufacturing optical components relies on good measurements and specifications. One of the most precise measurements routinely required is the form accuracy. In practice, form deviation from the ideal surface is effectively low frequency errors, where the form error most often accounts for no more than a few undulations across a surface. These types of errors are measured in a variety of ways including interferometry and tactile methods like profilometry, with the latter often being employed for aspheres and general surface shapes such as freeforms. This paper provides a basis for a correct description of power and radius of curvature tolerances, including best practices and calculating the power value with respect to the radius deviation (and vice versa) of the surface form. A consistent definition of the sagitta is presented, along with different cases in manufacturing that are of interest to fabricators and designers. The results make clear how the definitions and results should be documented, for all measurement setups. Relationships between power and radius of curvature are shown that allow specifying the preferred metric based on final accuracy and measurement method. Results shown include all necessary equations for conversion to give optical designers and manufacturers a consistent and robust basis for decision-making. The paper also gives guidance on preferred methods for different scenarios for surface types, accuracy required, and metrology methods employed.
Gao, Dengliang
2013-03-01
In 3D seismic interpretation, curvature is a popular attribute that depicts the geometry of seismic reflectors and has been widely used to detect faults in the subsurface; however, it provides only part of the solutions to subsurface structure analysis. This study extends the curvature algorithm to a new curvature gradient algorithm, and integrates both algorithms for fracture detection using a 3D seismic test data set over Teapot Dome (Wyoming). In fractured reservoirs at Teapot Dome known to be formed by tectonic folding and faulting, curvature helps define the crestal portion of the reservoirs that is associated with strong seismic amplitude and high oil productivity. In contrast, curvature gradient helps better define the regional northwest-trending and the cross-regional northeast-trending lineaments that are associated with weak seismic amplitude and low oil productivity. In concert with previous reports from image logs, cores, and outcrops, the current study based on an integrated seismic curvature and curvature gradient analysis suggests that curvature might help define areas of enhanced potential to form tensile fractures, whereas curvature gradient might help define zones of enhanced potential to develop shear fractures. In certain fractured reservoirs such as at Teapot Dome where faulting and fault-related folding contribute dominantly to the formation and evolution of fractures, curvature and curvature gradient attributes can be potentially applied to differentiate fracture mode, to predict fracture intensity and orientation, to detect fracture volume and connectivity, and to model fracture networks.
Curvature-driven capillary migration and assembly of rod-like particles.
Cavallaro, Marcello; Botto, Lorenzo; Lewandowski, Eric P; Wang, Marisa; Stebe, Kathleen J
2011-12-27
Capillarity can be used to direct anisotropic colloidal particles to precise locations and to orient them by using interface curvature as an applied field. We show this in experiments in which the shape of the interface is molded by pinning to vertical pillars of different cross-sections. These interfaces present well-defined curvature fields that orient and steer particles along complex trajectories. Trajectories and orientations are predicted by a theoretical model in which capillary forces and torques are related to Gaussian curvature gradients and angular deviations from principal directions of curvature. Interface curvature diverges near sharp boundaries, similar to an electric field near a pointed conductor. We exploit this feature to induce migration and assembly at preferred locations, and to create complex structures. We also report a repulsive interaction, in which microparticles move away from planar bounding walls along curvature gradient contours. These phenomena should be widely useful in the directed assembly of micro- and nanoparticles with potential application in the fabrication of materials with tunable mechanical or electronic properties, in emulsion production, and in encapsulation.
Curvature-driven capillary migration and assembly of rod-like particles
Cavallaro, Marcello; Botto, Lorenzo; Lewandowski, Eric P.; Wang, Marisa; Stebe, Kathleen J.
2011-01-01
Capillarity can be used to direct anisotropic colloidal particles to precise locations and to orient them by using interface curvature as an applied field. We show this in experiments in which the shape of the interface is molded by pinning to vertical pillars of different cross-sections. These interfaces present well-defined curvature fields that orient and steer particles along complex trajectories. Trajectories and orientations are predicted by a theoretical model in which capillary forces and torques are related to Gaussian curvature gradients and angular deviations from principal directions of curvature. Interface curvature diverges near sharp boundaries, similar to an electric field near a pointed conductor. We exploit this feature to induce migration and assembly at preferred locations, and to create complex structures. We also report a repulsive interaction, in which microparticles move away from planar bounding walls along curvature gradient contours. These phenomena should be widely useful in the directed assembly of micro- and nanoparticles with potential application in the fabrication of materials with tunable mechanical or electronic properties, in emulsion production, and in encapsulation. PMID:22184218
Magnetophoretic Induction of Root Curvature
NASA Technical Reports Server (NTRS)
Hasenstein, Karl H.
1997-01-01
The last year of the grant period concerned the consolidation of previous experiments to ascertain that the theoretical premise apply not just to root but also to shoots. In addition, we verified that high gradient magnetic fields do not interfere with regular cellular activities. Previous results have established that: (1) intracellular magnetophoresis is possible; and (2) HGMF lead to root curvature. In order to investigate whether HGMF affect the assembly and/or organization of structural proteins, we examined the arrangement of microtubules in roots exposed to HGMF. The cytoskeletal investigations were performed with fomaldehyde-fixed, nonembedded tissue segments that were cut with a vibratome. Microtubules (MTs) were stained with rat anti-yeast tubulin (YOL 1/34) and DTAF-labeled antibody against rat IgG. Microfilaments (MFs) were visualized by incubation in rhodamine-labeled phalloidin. The distribution and arrangement of both components of the cytoskeleton were examined with a confocal microscope. Measurements of growth rates and graviresponse were done using a video-digitizer. Since HGMF repel diamagnetic substances including starch-filled amyloplasts and most The second aspect of the work includes studies of the effect of cytoskeletal inhibitors on MTs and MFs. The analysis of the effect of micotubular inhibitors on the auxin transport in roots showed that there is very little effect of MT-depolymerizing or stabilizing drugs on auxin transport. This is in line with observations that application of such drugs is not immediately affecting the graviresponsiveness of roots.
Programming curvature using origami tessellations
NASA Astrophysics Data System (ADS)
Dudte, Levi H.; Vouga, Etienne; Tachi, Tomohiro; Mahadevan, L.
2016-05-01
Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one-degree-of-freedom collapsible structures--we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the difficulty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-off between the accuracy to which the pattern conforms to the target surface, and the effort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, as well as the quantification of the energetic and material cost of doing so.
Ionic liquid tunes microemulsion curvature.
Liu, Liping; Bauduin, Pierre; Zemb, Thomas; Eastoe, Julian; Hao, Jingcheng
2009-02-17
Middle-phase microemulsions formed from cationic dioctadecyldimethylammonium chloride (DODMAC), anionic sodium dodecylsulfate (SDS), n-butanol, and n-heptane were studied. An ionic liquid (IL), 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]), was employed as the electrolyte in the aqueous media instead of inorganic salts usually used in microemulsion formulation. Studies have been carried out as a function of the concentrations of [bmim][BF4], n-butanol, total surfactant (cDODMAC+SDS), and temperature on the phase behavior and the ultralow interfacial tensions in which the anionic component is present in excess in the catanionic film. Ultralow interfacial tension measurements confirmed the formation of middle-phase microemulsions and the necessary conditions for stabilizing middle-phase microemulsions. Electrical conductivity, small-angle X-ray scattering (SAXS), and small-angle neutron scattering (SANS) experiments were also performed, indicating that the typical heptane domain size has an average radius of 360 A and the ionic liquid induces softening of the charged catanionic film. Most interestingly, the IL concentration (cIL) is shown to act as an effective interfacial curvature-control parameter, representing a new approach to tuning the formulation of microemulsions and emulsions. The results expand the potential uses of ILs but also point to the design of new ILs that may achieve superefficient control over interfacial and self-assembly systems.
Curvature function and coarse graining
NASA Astrophysics Data System (ADS)
Díaz-Marín, Homero; Zapata, José A.
2010-12-01
A classic theorem in the theory of connections on principal fiber bundles states that the evaluation of all holonomy functions gives enough information to characterize the bundle structure (among those sharing the same structure group and base manifold) and the connection up to a bundle equivalence map. This result and other important properties of holonomy functions have encouraged their use as the primary ingredient for the construction of families of quantum gauge theories. However, in these applications often the set of holonomy functions used is a discrete proper subset of the set of holonomy functions needed for the characterization theorem to hold. We show that the evaluation of a discrete set of holonomy functions does not characterize the bundle and does not constrain the connection modulo gauge appropriately. We exhibit a discrete set of functions of the connection and prove that in the abelian case their evaluation characterizes the bundle structure (up to equivalence), and constrains the connection modulo gauge up to "local details" ignored when working at a given scale. The main ingredient is the Lie algebra valued curvature function F_S (A) defined below. It covers the holonomy function in the sense that exp {F_S (A)} = Hol(l= partial S, A).
Curvature function and coarse graining
Diaz-Marin, Homero; Zapata, Jose A.
2010-12-15
A classic theorem in the theory of connections on principal fiber bundles states that the evaluation of all holonomy functions gives enough information to characterize the bundle structure (among those sharing the same structure group and base manifold) and the connection up to a bundle equivalence map. This result and other important properties of holonomy functions have encouraged their use as the primary ingredient for the construction of families of quantum gauge theories. However, in these applications often the set of holonomy functions used is a discrete proper subset of the set of holonomy functions needed for the characterization theorem to hold. We show that the evaluation of a discrete set of holonomy functions does not characterize the bundle and does not constrain the connection modulo gauge appropriately. We exhibit a discrete set of functions of the connection and prove that in the abelian case their evaluation characterizes the bundle structure (up to equivalence), and constrains the connection modulo gauge up to ''local details'' ignored when working at a given scale. The main ingredient is the Lie algebra valued curvature function F{sub S}(A) defined below. It covers the holonomy function in the sense that expF{sub S}(A)=Hol(l={partial_derivative}S,A).
Conformation of charged vesicles: the Debye Huckel and the low curvature limit
NASA Astrophysics Data System (ADS)
Sinha, Kumari Priti; Thaokar, Rochish M., , Prof.
The shape as well as tension and pressure inside an uncharged vesicle are determined by the reduced volume. These parameters are important for a vesicle or a biological cell, since it can affect bio-physical processes such as osmosis and permeation, interaction with external agents such as bio- macromolecules and thermal fluctuations of the bilayer membrane of a vesicle. Charged membranes are ubiquitous in nature, most biological cell bio-membranes are charged, and therefore the knowledge of shape, tension and pressure of charged vesicles is critical. Additionally, the distribution of charges in the inner and outer leaflets is also important as it can affect the spatial interaction of a bilayer membrane with proteins. This work addresses these issues in the low charge and curvature limit. Our analysis indicates that despite a very strong two-way coupling between the charge and the curvature, the shapes of charged vesicles remain similar to that of uncharged vesicles at comparable reduced volumes, even for reasonable values of total charge. However, the tension and pressure values are higher, and are accurately estimated. Similarly the charge distribution on the outer and inner leaflet is strongly affected by the curvature. The value of spontaneous curvature due to charge redistribution is estimated. The insensitivity of the shape to charges persists even when only the outer leaflet is charged instead of charged inner and outer leaflets
Soliton curvatures of surfaces and spaces
Konopelchenko, B.G.
1997-01-01
An intrinsic geometry of surfaces and three-dimensional Riemann spaces is discussed. In the geodesic coordinates the Gauss equation for two-dimensional Riemann spaces (surfaces) is reduced to the one-dimensional Schr{umlt o}dinger equation, where the Gaussian curvature plays a role of potential. The use of this fact provides an infinite set of explicit expressions for curvature and metric of surface. A special case is governed by the KdV equation for the Gaussian curvature. Integrable dynamics of curvature via the KdV equation, higher KdV equations, and 2+1-dimensional integrable equations with breaking solitons is considered. For a special class of three-dimensional Riemann spaces the relation between metric and scalar curvature is given by the two-dimensional stationary Schr{umlt o}dinger or perturbed string equations. This provides us an infinite family of Riemann spaces with explicit scalar curvature and metric. Particular class of spaces and their integrable evolutions are described by the Nizhnik{endash}Veselov{endash}Novikov equation and its higher analogs. Surfaces and three-dimensional Riemann spaces with large curvature and slow dependence on the variable are considered. They are associated with the Burgers and Kadomtsev{endash}Petviashvili equations, respectively. {copyright} {ital 1997 American Institute of Physics.}
Curvature and torsion in growing actin networks
NASA Astrophysics Data System (ADS)
Shaevitz, Joshua W.; Fletcher, Daniel A.
2008-06-01
Intracellular pathogens such as Listeria monocytogenes and Rickettsia rickettsii move within a host cell by polymerizing a comet-tail of actin fibers that ultimately pushes the cell forward. This dense network of cross-linked actin polymers typically exhibits a striking curvature that causes bacteria to move in gently looping paths. Theoretically, tail curvature has been linked to details of motility by considering force and torque balances from a finite number of polymerizing filaments. Here we track beads coated with a prokaryotic activator of actin polymerization in three dimensions to directly quantify the curvature and torsion of bead motility paths. We find that bead paths are more likely to have low rather than high curvature at any given time. Furthermore, path curvature changes very slowly in time, with an autocorrelation decay time of 200 s. Paths with a small radius of curvature, therefore, remain so for an extended period resulting in loops when confined to two dimensions. When allowed to explore a three-dimensional (3D) space, path loops are less evident. Finally, we quantify the torsion in the bead paths and show that beads do not exhibit a significant left- or right-handed bias to their motion in 3D. These results suggest that paths of actin-propelled objects may be attributed to slow changes in curvature, possibly associated with filament debranching, rather than a fixed torque.
Curvature and torsion in growing actin networks
Shaevitz, Joshua W; Fletcher, Daniel A
2011-01-01
Intracellular pathogens such as Listeria monocytogenes and Rickettsia rickettsii move within a host cell by polymerizing a comet-tail of actin fibers that ultimately pushes the cell forward. This dense network of cross-linked actin polymers typically exhibits a striking curvature that causes bacteria to move in gently looping paths. Theoretically, tail curvature has been linked to details of motility by considering force and torque balances from a finite number of polymerizing filaments. Here we track beads coated with a prokaryotic activator of actin polymerization in three dimensions to directly quantify the curvature and torsion of bead motility paths. We find that bead paths are more likely to have low rather than high curvature at any given time. Furthermore, path curvature changes very slowly in time, with an autocorrelation decay time of 200 s. Paths with a small radius of curvature, therefore, remain so for an extended period resulting in loops when confined to two dimensions. When allowed to explore a three-dimensional (3D) space, path loops are less evident. Finally, we quantify the torsion in the bead paths and show that beads do not exhibit a significant left- or right-handed bias to their motion in 3D. These results suggest that paths of actin-propelled objects may be attributed to slow changes in curvature, possibly associated with filament debranching, rather than a fixed torque. PMID:18560043
Curvature in solid oxide fuel cells
NASA Astrophysics Data System (ADS)
Li, Wenxia; Hasinska, Kathy; Seabaugh, Matt; Swartz, Scott; Lannutti, John
At this point in history, curvature is inherent to the laminated components that comprise solid oxide fuel cells (SOFCs). Surprisingly, however, this fact has never been previously quantified in the literature. In addition, potential curvature changes associated with NiO reduction and re-oxidation during operation have not been investigated. In this report, an optical profilometer was employed to non-destructively quantify the surface curvature or cracking behavior observed on a large scale in industrially manufactured cells. This provides insights into the challenges that the component materials face as well as additional appreciation for why, in spite of a concerted effort to commercialize SOFC power generation, all currently manufactured SOFC stacks fail. Our results demonstrate that cracked electrolyte areas (caused by differential sintering) are flatter than uncracked regions. The height of the electrolyte surface ranged from 86 to 289 μm above the baseline following sintering. Reduction typically results in increases in curvature of up to 214 μm. Initial crack density appears to affect curvature evolution during reduction; the higher the crack density, the smaller the curvature increase following reduction at 600 °C. In general, however, we observed that the electrolyte layer is remarkably resistant to further cracking during these typographic changes. Following oxidation at 750 °C, large changes in curvature (up to 280 μm) are noted that appear to be related to the strength of the bond between the electrolyte and the underlying anode.
Magnetic curvature effects on plasma interchange turbulence
Li, B. Liao, X.; Sun, C. K.; Ou, W.; Liu, D.; Gui, G.; Wang, X. G.
2016-06-15
The magnetic curvature effects on plasma interchange turbulence and transport in the Z-pinch and dipole-like systems are explored with two-fluid global simulations. By comparing the transport levels in the systems with a different magnetic curvature, we show that the interchange-mode driven transport strongly depends on the magnetic geometry. For the system with large magnetic curvature, the pressure and density profiles are strongly peaked in a marginally stable state and the nonlinear evolution of interchange modes produces the global convective cells in the azimuthal direction, which lead to the low level of turbulent convective transport.
Impact of curvature on topological defects
NASA Astrophysics Data System (ADS)
Mesarec, L.; Góźdź, W.; Iglič, A.; Kralj, S.
2017-01-01
We analyze the impact of extrinsic and intrinsic curvature on positions of topological defects (TDs) in two-dimensional (2D) nematic films. We demonstrate that both these curvature contributions are commonly present and are expected to be weighted by comparable elastic constants. A simple Landau-de Gennes approach in terms of tensor nematic order parameter is used to numerically demonstrate impact of the curvatures on position of TDs on 2D ellipsoidal nematic shells. In particular, in oblate ellipsoids the extrinsic and intrinsic elastic terms enforce conflicting tendencies to positions of TDs.
ERIC Educational Resources Information Center
National Commission on the Observance of International Women's Year, Washington, DC.
This document considers sexual preference as it specifically relates to women. Divided into two parts, the document presents a fact sheet about lesbianism and contains a workshop resource guide on sexual preference. The fact sheet, arranged in a question-answer format, focuses on the following concerns: (1) lesbianism as a woman's issue; (2) legal…
Curve Appeal: Exploring Individual Differences in Preference for Curved Versus Angular Objects
Cotter, Katherine N.; Bertamini, Marco; Palumbo, Letizia; Vartanian, Oshin
2017-01-01
A preference for smooth curvature, as opposed to angularity, is a well-established finding for lines, two-dimensional shapes, and complex objects, but little is known about individual differences. We used two-dimensional black-and-white shapes—randomly generated irregular polygons, and arrays of circles and hexagons—and measured many individual differences, including artistic expertise, personality, and cognitive style. As expected, people preferred curved over angular stimuli, and people’s degree of curvature preference correlated across the two sets of shapes. Multilevel models showed varying patterns of interaction between shape and individual differences. For the irregular polygons, people higher in artistic expertise or openness to experience showed a greater preference for curvature. This pattern was not evident for the arrays of circles and hexagons. We discuss the results in relation to the nature of the stimuli, and we conclude that individual differences do play a role in moderating the preference for smooth curvature. PMID:28491269
Detonation front curvatures and detonation rates
NASA Astrophysics Data System (ADS)
Lauderbach, Lisa M.; Lorenz, K. Thomas; Lee, Edward L.; Souers, P. Clark
2017-01-01
Many detonation front curvatures are reviewed. Most are of the Shock Dynamics type, which are described as a combination of quadratic and 8th power-of-the-radius curves. The integrated fraction of the 8th power curve is taken as a measure of curvature, which we are able to relate to the logarithm of the detonation rate. This provides a means of estimating the rates of some unknown explosives from the curvature. Using the edge lag divided by the radius is an even better way. A second group of curvatures are almost or purely quadratic. This is probably not associated with density gradients but may be caused by low sound speeds. A final group of "sombreros" show curvy fronts for ideal explosives, which appear to be caused by density gradients.
Helical Microfilaments with Alternating Imprinted Intrinsic Curvatures.
Silva, Pedro Emanuel Santos; Godinho, Maria Helena
2017-03-01
There has been an intense research for developing techniques that can produce filaments with helical shapes, given the widespread of potential applications. In this work, how helices with different curvatures can be precisely imprinted in microfilaments is shown. It is also shown that using this technique, it is possible to produce, in a single fiber, helices with different curvatures. This striking and innovative behavior is observed when one side of the stretched filaments is irradiated with UV light, modifying the mechanical properties at surface. Upon release, the regions with higher curvature start to curl first, while regions with lower intrinsic curvature remain stretched until start to curl later. The results presented here can be important to understand why structures adopt a helical shape in general, which can be of interest in nanotechnology, biomolecular science, or even to understand why plant filaments curl. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Role of feature curvature in contact guidance
Mathur, Anurag; Moore, Simon W.; Sheetz, Michael P.; Hone, James
2012-01-01
This study examines the role of feature curvature in cellular topography sensing. To separate the effects of feature size and curvature, we have developed a method to fabricate grooved substrates whose radius of curvature (r) is varied from under 10 nm to 400 nm, while all other dimensions are kept constant. With increasing r up to 200 nm, mouse embryonic fibroblasts increased their spread area, but reduced their polarization (aspect ratio). Interestingly, on features with an r of 200 and 400 nm - where there was very little effect on spreading area and polarization - we find that internal structures such as stress fibers are nevertheless still strongly aligned to the topography. These findings are of importance to studies of both tissue engineering and curvature sensing proteins. PMID:22426288
Gravitational energy in quadratic-curvature gravities.
Deser, S; Tekin, Bayram
2002-09-02
We define energy (E) and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For D=4, all purely quadratic models admit constant curvature vacua with arbitrary Lambda, and E is the "cosmological" Abbott-Deser (AD) expression; instead, E always vanishes in flat, Lambda=0, background. For combined Einstein-quadratic curvature systems without explicit Lambda-term vacuum must be flat space, and E has the usual Arnowitt-Deser-Misner form. A Lambda-term forces unique de Sitter vacuum, with E the sum of contributions from Einstein and quadratic parts to the AD form. We also discuss the effects on energy definition of higher curvature terms and of higher dimension.
Spline-Based Smoothing of Airfoil Curvatures
NASA Technical Reports Server (NTRS)
Li, W.; Krist, S.
2008-01-01
Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been
Hess, Samuel T; Gudheti, Manasa V; Mlodzianoski, Michael; Baumgart, Tobias
2007-01-01
Membrane shape parameters such as curvature, bending elasticity, and lateral tension, are relevant to the lateral organization and function of biomembranes, and may critically influence the formation of lateral clustering patterns observed in living cells. Fluorescence laser-scanning microscopy can be used to image vesicles and cell membranes, and from shape analysis of these images mechanical membrane parameters can be quantified. Methods to analyze images of equatorial sections obtained by confocal or multiphoton microscopy are detailed, in order to estimate curvature, lateral tension, line tension, relative differences in mean curvature and Gaussian curvature bending moduli, and fluorescence dye intensity profiles, typically within coexisting liquid-ordered and liquid-disordered membrane domains. A variety of shape tracing and shape fitting methods are compared.
Curvature Analysis of Cardiac Excitation Wavefronts
2013-04-01
computational cardiac-cell network accurately reproduces a particular kind of cardiac arrhythmia , such as ventricular fibrillation. Curvature Analysis of Cardiac...network accurately reproduces a particular kind of cardiac arrhythmia , such as ventricular fibrillation. Index Terms Cardiac excitation waves...isopotentials, Bézier curves, curvature, cardiac arrhythmia and fibrillation Ç 1 INTRODUCTION AN estimated 81,000,000 American adults, more than onein three
Curvature tensors unified field equations on SEXn
NASA Astrophysics Data System (ADS)
Chung, Kyung Tae; Lee, Il Young
1988-09-01
We study the curvature tensors and field equations in the n-dimensional SE manifold SEXn. We obtain several basic properties of the vectors S λ and U λ and then of the SE curvature tensor and its contractions, such as a generalized Ricci identity, a generalized Bianchi identity, and two variations of the Bianchi identity satisfied by the SE Einstein tensor. Finally, a system of field equations is discussed in SEXn and one of its particular solutions is constructed and displayed.
Curvature adaptive optics and low light imaging
NASA Astrophysics Data System (ADS)
Ftaclas, C.; Chun, M.; Kuhn, J.; Ritter, J.
We review the basic approach of curvature adaptive optics (AO) and show how its many advantages arise. A curvature wave front sensor (WFS) measures exactly what a curvature deformable mirror (DM) generates. This leads to the computational and operational simplicity of a nearly diagonal control matrix. The DM automatically reconstructs the wave front based on WFS curvature measurements. Thus, there is no formal wave front reconstruction. This poses an interesting challenge to post-processing of AO images. Physical continuity of the DM and the reconstruction of phase from wave front curvature data assure that each actuated region of the DM corrects local phase, tip-tilt and focus. This gain in per-channel correction efficiency, combined with the need for only one pixel per channel detector reads in the WFS allows the use of photon counting detectors for wave front sensing. We note that the use of photon counting detectors implies penalty-free combination of correction channels either in the WFS or on the DM. This effectively decouples bright and faint source performance in that one no longer predicts the other. The application of curvature AO to the low light moving target detection problem, and explore the resulting challenges to components and control systems. Rapidly moving targets impose high-speed operation posing new requirements unique to curvature components. On the plus side, curvature wave front sensors, unlike their Shack-Hartmann counterparts, are tunable for optimum sensitivity to seeing and we are examining autonomous optimization of the WFS to respond to rapid changes in seeing.
Instant curvature measurement for microcantilever sensors
Jeon, Sangmin; Thundat, Thomas
2004-08-09
A multiple-point deflection technique has been developed for the instant measurement of microcantilever curvature. Eight light-emitting diodes are focused on various positions of a gold-coated silicon cantilever through optical fibers, and temperature change or chemical adsorption induces cantilever bending. The deflection at each point on the cantilever is measured with subnanometer precision by a position-sensitive detector, and thus the curvature of the cantilever is obtained.
Spherical gravitational curvature boundary-value problem
NASA Astrophysics Data System (ADS)
Šprlák, Michal; Novák, Pavel
2016-08-01
Values of scalar, vector and second-order tensor parameters of the Earth's gravitational field have been collected by various sensors in geodesy and geophysics. Such observables have been widely exploited in different parametrization methods for the gravitational field modelling. Moreover, theoretical aspects of these quantities have extensively been studied and well understood. On the other hand, new sensors for observing gravitational curvatures, i.e., components of the third-order gravitational tensor, are currently under development. As the gravitational curvatures represent new types of observables, their exploitation for modelling of the Earth's gravitational field is a subject of this study. Firstly, the gravitational curvature tensor is decomposed into six parts which are expanded in terms of third-order tensor spherical harmonics. Secondly, gravitational curvature boundary-value problems defined for four combinations of the gravitational curvatures are formulated and solved in spectral and spatial domains. Thirdly, properties of the corresponding sub-integral kernels are investigated. The presented mathematical formulations reveal some important properties of the gravitational curvatures and extend the so-called Meissl scheme, i.e., an important theoretical framework that relates various parameters of the Earth's gravitational field.
The role of curvature in entanglement
NASA Astrophysics Data System (ADS)
Buck, Gregory
2015-10-01
Which tangles more readily: curly hair or straight hair? A perhaps natural thought, supported by some theoretical evidence, is to associate curvature and entanglement, and assume that they would grow together-that an increase in one fosters an increase in the other. However we have biological examples such as DNA in the chromosome, and mechanical examples such as coiled telephone cords, in which much more curvature is employed than is required for the packing, and in which tangling is presumably detrimental. We offer a resolution to this conundrum. We show, that at least for simple but generally applicable models, the relationship between curvature and entanglement is subtle: if we keep filament density constant and increase curvature, the entanglement initially increases, passes through a maximum, then decreases, so there is a regime where increasing curvature increases entanglement, and there is also a regime where increasing curvature decreases entanglement. This has implications for filament packing in many circumstances, and in particular for the compaction structure of DNA in the cell-it provides a straightforward argument for the view that one purpose of DNA coiling and supercoiling is to inhibit entanglement. It also tells us to expect that wavy hair-neither the straightest nor the curliest-tangles most readily.
Anisotropic Cosmology and Curvature Invariants.
NASA Astrophysics Data System (ADS)
Skea, James E. F.
greater when non-axisymmetric cosmologies are considered. In the limit where the particle production is switched on at the Planck time (t _{rm Pl}), isotropisation is found to occur at _{Omega } 10^5 t_ {rm Pl}, compatible with restrictions on anistropy at that time. Particle production is not found to isotropise Bianchi VIII and IX cosmologies. In Part 3, we study the structure of various curvature invariants and, following a suggestion by Karlhede, we investigate their relationship to horizons in particular space-times. (Abstract shortened by UMI.).
On classical thermal stability of black holes with a dynamical extrinsic curvature
NASA Astrophysics Data System (ADS)
Capistrano, Abraão J. S.; Gutiérrez-Piñeres, Antonio C.; Ulhoa, Sergio C.; Amorim, Ronni G. G.
2017-05-01
We study the deformation caused by the influence of the extrinsic curvature on a vacuum spherically symmetric metric embedded in a five-dimensional bulk. We investigate the resulting black-holes obtaining general characteristics such as their masses, horizons, singularities and thermal properties by using a dynamical extrinsic curvature leading to different results as those from rigid embedded models. As a test, we also study the bending of light near such black-holes analyzing the movement of a test particle and the modification caused by extrinsic curvature on its movement. Accordingly, using the asymptotically conformal flat condition, we show that such black holes must be large and constrained by the allowed number range - 1 / 2 ≤ n ≤ 1.8 for a set of n-scalar potentials. As a result, they are locally thermodynamically stable, but not globally preferred.
Bender, Ruben R.; Muth, Anke; Schneider, Irene C.; Friedel, Thorsten; Hartmann, Jessica; Plückthun, Andreas; Maisner, Andrea; Buchholz, Christian J.
2016-01-01
Receptor-targeted lentiviral vectors (LVs) can be an effective tool for selective transfer of genes into distinct cell types of choice. Moreover, they can be used to determine the molecular properties that cell surface proteins must fulfill to act as receptors for viral glycoproteins. Here we show that LVs pseudotyped with receptor-targeted Nipah virus (NiV) glycoproteins effectively enter into cells when they use cell surface proteins as receptors that bring them closely enough to the cell membrane (less than 100 Å distance). Then, they were flexible in receptor usage as demonstrated by successful targeting of EpCAM, CD20, and CD8, and as selective as LVs pseudotyped with receptor-targeted measles virus (MV) glycoproteins, the current standard for cell-type specific gene delivery. Remarkably, NiV-LVs could be produced at up to two orders of magnitude higher titers compared to their MV-based counterparts and were at least 10,000-fold less effectively neutralized than MV glycoprotein pseudotyped LVs by pooled human intravenous immunoglobulin. An important finding for NiV-LVs targeted to Her2/neu was an about 100-fold higher gene transfer activity when particles were targeted to membrane-proximal regions as compared to particles binding to a more membrane-distal epitope. Likewise, the low gene transfer activity mediated by NiV-LV particles bound to the membrane distal domains of CD117 or the glutamate receptor subunit 4 (GluA4) was substantially enhanced by reducing receptor size to below 100 Å. Overall, the data suggest that the NiV glycoproteins are optimally suited for cell-type specific gene delivery with LVs and, in addition, for the first time define which parts of a cell surface protein should be targeted to achieve optimal gene transfer rates with receptor-targeted LVs. PMID:27281338
The effect of spontaneous curvature on a two-phase vesicle
NASA Astrophysics Data System (ADS)
Cox, Geoffrey; Lowengrub, John
2015-03-01
Vesicles are membrane-bound structures commonly known for their roles in cellular transport and the shape of a vesicle is determined by its surrounding membrane (lipid bilayer). When the membrane is composed of different lipids, it is natural for the lipids of similar molecular structure to migrate towards one another (via spinodal decomposition), creating a multi-phase vesicle. In this article, we consider a two-phase vesicle model which is driven by nature's propensity to maintain a minimal state of elastic energy. The model assumes a continuum limit, thereby treating the membrane as a closed three-dimensional surface. The main purpose of this study is to reveal the complexity of the Helfrich two-phase vesicle model with non-zero spontaneous curvature and provide further evidence to support the relevance of spontaneous curvature as a modelling parameter. In this paper, we illustrate the complexity of the Helfrich two-phase model by providing multiple examples of undocumented solutions and energy hysteresis. We also investigate the influence of spontaneous curvature on morphological effects and membrane phenomena such as budding and fusion.
The effect of spontaneous curvature on a two-phase vesicle
Cox, Geoffrey; Lowengrub, John
2015-01-01
Vesicles are membrane-bound structures commonly known for their roles in cellular transport and the shape of a vesicle is determined by its surrounding membrane (lipid bilayer). When the membrane is composed of different lipids, it is natural for the lipids of similar molecular structure to migrate towards one another (via spinodal decomposition), creating a multi-phase vesicle. In this article, we consider a two-phase vesicle model which is driven by nature’s propensity to maintain a minimal state of elastic energy. The model assumes a continuum limit, thereby treating the membrane as a closed three-dimensional surface. The main purpose of this study is to reveal the complexity of the Helfrich two-phase vesicle model with non-zero spontaneous curvature and provide further evidence to support the relevance of spontaneous curvature as a modelling parameter. In this paper, we illustrate the complexity of the Helfrich two-phase model by providing multiple examples of undocumented solutions and energy hysteresis. We also investigate the influence of spontaneous curvature on morphological effects and membrane phenomena such as budding and fusion. PMID:26097287
Formation, Stability, and Mobility of One-Dimensional Lipid Bilayer on High Curvature Substrates
Huang, J; Martinez, J; Artyukhin, A; Sirbuly, D; Wang, Y; Ju, J W; Stroeve, P; Noy, A
2007-03-23
Curved lipid membranes are ubiquitous in living systems and play an important role in many biological processes. To understand how curvature and lipid composition affect membrane formation and fluidity we have assembled and studied mixed 1,2-Dioleoyl-sn-Glycero-3-Phosphocholine (DOPC) and 1,2-Dioleoyl-sn-Glycero-3-Phosphoethanolamine (DOPE) supported lipid bilayers on amorphous silicon nanowires with controlled diameters ranging from 20 nm to 200 nm. Addition of cone-shaped DOPE molecules to cylindrical DOPC molecules promotes vesicle fusion and bilayer formation on smaller diameter nanowires. Our experiments demonstrate that nanowire-supported bilayers are mobile, exhibit fast recovery after photobleaching, and have low concentration of defects. Lipid diffusion coefficients in these high-curvature tubular membranes are comparable to the values reported for flat supported bilayers and increase with decreasing nanowire diameter.
Strong curvature effects in Neumann wave problems
Willatzen, M.; Pors, A.; Gravesen, J.
2012-08-15
Waveguide phenomena play a major role in basic sciences and engineering. The Helmholtz equation is the governing equation for the electric field in electromagnetic wave propagation and the acoustic pressure in the study of pressure dynamics. The Schroedinger equation simplifies to the Helmholtz equation for a quantum-mechanical particle confined by infinite barriers relevant in semiconductor physics. With this in mind and the interest to tailor waveguides towards a desired spectrum and modal pattern structure in classical structures and nanostructures, it becomes increasingly important to understand the influence of curvature effects in waveguides. In this work, we demonstrate analytically strong curvature effects for the eigenvalue spectrum of the Helmholtz equation with Neumann boundary conditions in cases where the waveguide cross section is a circular sector. It is found that the linear-in-curvature contribution originates from parity symmetry breaking of eigenstates in circular-sector tori and hence vanishes in a torus with a complete circular cross section. The same strong curvature effect is not present in waveguides subject to Dirichlet boundary conditions where curvature contributions contribute to second-order in the curvature only. We demonstrate this finding by considering wave propagation in a circular-sector torus corresponding to Neumann and Dirichlet boundary conditions, respectively. Results for relative eigenfrequency shifts and modes are determined and compared with three-dimensional finite element method results. Good agreement is found between the present analytical method using a combination of differential geometry with perturbation theory and finite element results for a large range of curvature ratios.
Strong curvature effects in Neumann wave problems
NASA Astrophysics Data System (ADS)
Willatzen, M.; Pors, A.; Gravesen, J.
2012-08-01
Waveguide phenomena play a major role in basic sciences and engineering. The Helmholtz equation is the governing equation for the electric field in electromagnetic wave propagation and the acoustic pressure in the study of pressure dynamics. The Schrödinger equation simplifies to the Helmholtz equation for a quantum-mechanical particle confined by infinite barriers relevant in semiconductor physics. With this in mind and the interest to tailor waveguides towards a desired spectrum and modal pattern structure in classical structures and nanostructures, it becomes increasingly important to understand the influence of curvature effects in waveguides. In this work, we demonstrate analytically strong curvature effects for the eigenvalue spectrum of the Helmholtz equation with Neumann boundary conditions in cases where the waveguide cross section is a circular sector. It is found that the linear-in-curvature contribution originates from parity symmetry breaking of eigenstates in circular-sector tori and hence vanishes in a torus with a complete circular cross section. The same strong curvature effect is not present in waveguides subject to Dirichlet boundary conditions where curvature contributions contribute to second-order in the curvature only. We demonstrate this finding by considering wave propagation in a circular-sector torus corresponding to Neumann and Dirichlet boundary conditions, respectively. Results for relative eigenfrequency shifts and modes are determined and compared with three-dimensional finite element method results. Good agreement is found between the present analytical method using a combination of differential geometry with perturbation theory and finite element results for a large range of curvature ratios.
NASA Astrophysics Data System (ADS)
He, X.; Kadoch, B.; Apte, S.; Farge, M.; Schneider, K.
2016-12-01
Direct Numerical Simulations (DNS) of flow through a periodic face centered cubic (FCC) unit cell at Reynolds numbers of 300, 500 and 1000 are conducted to investigate porescale turbulent flow physics. The simulations are performed using a fictitious domain approach [Apte et al, J. Comp. Physics 2009], which uses non-body conforming Cartesian grids. The flowfield involves regions of rapid acceleration and decelerations, separated flow and jet-impingement like flow features. Lagrangian statistics of scale dependent curvature angle and acceleration are calculated by tracking a large number of fluid particle trajectories. For isotropic turbulence, it has been shown [Bos et al. 2015, PRL] that the mean curvature angle varies linearly with time initially, reaches an inertial range and asymptotes to a value of π /2 at long times, corresponding to the decorrelation and equipartition of the cosine of the curvature angle. Similar trends are observed at early times for turbulence in porous medium; however, the mean curvature angle asymptotes to a value larger than π /2, due to the effect of confinement on the fluid particle trajectories that result in preferred directions at large times. A Monte-Carlo based stochastic model to predict the long-time behavior of curvature angles is developed. It is shown to correctly predict an angle larger than π /2 at large times consistent with the Lagrangian statistics.
Multiscale Lagrangian Statistics of Curvature Angle in Pore-Scale Turbulence
NASA Astrophysics Data System (ADS)
He, Bryan; Kadoch, Benjamin; Apte, Sourabh; Farge, Marie; Schneider, Kai
2016-11-01
Porescale turbulent flow physics are investigated using Direct Numeric Simulation (DNS) of flow through a periodic face centered cubic (FCC) unit cell at Reynolds numbers of 300, 500 and 1000. The simulations are performed using a fictitious domain approach, which uses non-body conforming Cartesian grids. Lagrangian statistics of scale dependent curvature angle and acceleration are calculated by tracking a large number of fluid particle trajectories. For isotropic turbulence, it has been shown that the mean curvature angle varies linearly with time initially, reaches an inertial range and asymptotes to a value of π / 2 at long times, corresponding to the decorrelation and equipartition of the cosine of the curvature angle. Similar trends are observed at early times for turbulence in porous medium; however, the mean curvature angle asymptotes to a value larger than π / 2 , due to the effect of confinement on the fluid particle trajectories that result in preferred directions at large times. A Monte-Carlo based stochastic model to predict the long-time behavior of curvature angles is developed and shown to correctly predicts an angle larger than π / 2 at large times. NSF Project Numbers 1336983, 1133363.
Self-assembly of a filament by curvature-inducing proteins
NASA Astrophysics Data System (ADS)
Kwiecinski, James; Chapman, S. Jonathan; Goriely, Alain
2017-04-01
We explore a simplified macroscopic model of membrane shaping by means of curvature-sensing BAR proteins. Equations describing the interplay between the shape of a freely floating filament in a fluid and the adhesion kinetics of proteins are derived from mechanical principles. The constant curvature solutions that arise from this system are studied using weakly nonlinear analysis. We show that the stability of the filament's shape is completely characterized by the parameters associated with protein recruitment and establish that in the bistable regime, proteins aggregate on the filament forming regions of high and low curvatures. This pattern formation is then followed by phase-coarsening that resolves on a time-scale dependent on protein diffusion and drift across the filament, which contend to smooth and maintain the pattern respectively. The model is generalized for multiple species of BAR proteins and we show that the stability of the assembled shape is determined by a competition between proteins attaching on opposing sides.
The influence of solid scaffolds on flat and curved lipid membranes
NASA Astrophysics Data System (ADS)
de Jong, D. H.; Heuer, A.
2017-07-01
Solid-supported membranes have become a common tool to study lipid membrane properties in a controlled environment. One particular example is the study of membrane curvature and its effect on lipid sorting. Here we simulate solid-supported membranes using the coarse grain molecular dynamics Martini force field. We characterize basic properties of the solid surfaces and lipid membranes deposited on them. Subsequently we construct large, solid ridges and use them to induce curvature in DOPC membranes. We study membrane properties, such as lateral diffusion and tail order parameters, relative to the curved membrane. Finally, we study the effect of the induced curvature on lateral lipid sorting in a ternary lipid membrane. Thus, we obtain comprehensive and microscopic insight into the impact of curvature on a lipid membrane in terms of structure and dynamics.
Membrane with supported internal passages
NASA Technical Reports Server (NTRS)
Gonzalez-Martin, Anuncia (Inventor); Salinas, Carlos E. (Inventor); Cisar, Alan J. (Inventor); Hitchens, G. Duncan (Inventor); Murphy, Oliver J. (Inventor)
2000-01-01
The invention provides an improved proton exchange membrane for use in electrochemical cells having internal passages parallel to the membrane surface comprising permanent tubes preferably placed at the ends of the fluid passages. The invention also provides an apparatus and process for making the membrane, membrane and electrode assemblies fabricated using the membrane, and the application of the membrane and electrode assemblies to a variety of devices, both electrochemical and otherwise. The passages in the membrane extend from one edge of the membrane to another and allow fluid flow through the membrane and give access directly to the membrane.
Does a methionine-to-norleucine substitution in PGLa influence peptide-membrane interactions?
Radchenko, Dmytro S; Kattge, Saskia; Kara, Sezgin; Ulrich, Anne S; Afonin, Sergii
2016-09-01
Yes. To understand the molecular mechanisms of amphiphilic membrane-active peptides, it is essential to study their interactions with lipid bilayers under near-native conditions. Amino acid composition largely determines the non-specific properties of peptides, on the basis of the physicochemical properties of the side chains. The resultant effects on peptides' functional properties include influences on the conformation, structural dynamics and binding affinities within the peptide interactome. Here, we studied the effect of substituting oxidation-prone methionine (Met) with non-oxidizable norleucine (Nle) in the model α-helical antimicrobial peptide PGLa, through systematic comparison of PGLa with the (2)Met/(2)Nle mutant. Both peptides were evaluated for their bacteriostatic and hemolytic activities (using in situ assays), for their conformational preferences in isotropic solutions (using circular dichroism spectropolarimetry) and for their abilities to modulate membrane curvature (using a solid-state (31)P NMR assay). We determined the membrane-bound states in detail and characterized the orientational dynamics of both peptides in oriented phospholipid membranes by solid-state (19)F NMR spectroscopy. On the one hand, the bioactivity results, the structure in the diluted membrane-mimicking environments and the strong inhibition of the negative membrane curvature were comparable between PGLa and the mutant. On the other hand, the alignments in DMPC bilayer were qualitatively the same but differed in absolute values - the more hydrophobic Nle residue inserted deeper in the membrane core. Furthermore, the mutant peptide displayed a significantly reduced ability to re-orient from the monomeric, surficial to the putative dimeric, tilted state. Overall, these results confirm the functional isosterism of Nle and Met in the helical membrane-active peptides but highlight differences in the ways in which the two residues affect non-specific binding to the lipid bilayer
The Induction of Negative Curvature as a Mechanism of Cell Toxicity by Amyloidogenic Peptides
Smith, Pieter E. S.; Brender, Jeffrey R.; Ramamoorthy, Ayyalusamy
2009-01-01
The death of insulin-producing β-cells is a key step in the pathogenesis of type 2 diabetes. The amyloidogenic peptide Islet Amyloid Polypeptide (IAPP, also known as amylin) has been shown to disrupt β-cell membranes leading to β-cell death. Despite the strong evidence linking IAPP to the destruction of β-cell membrane integrity and cell death, the mechanism of IAPP toxicity is poorly understood. In particular, the effect of IAPP on the bilayer structure has largely been uncharacterized. In this study, we have determined the effect of the amyloidogenic and toxic hIAPP1-37 peptide and the non-toxic and non-amyloidogenic rIAPP1-37 peptide on membranes by a combination of DSC and solid-state NMR spectroscopy. We also characterized the toxic but largely non-amyloidogenic rIAPP1-19 and hIAPP1-19 fragments. DSC shows that both amyloidogenic (hIAPP1-37) and largely non-amyloidogenic (hIAPP1-19 and rIAPP1-19) toxic versions of the peptide strongly favor the formation of negative curvature in lipid bilayers, while the non-toxic full-length rat IAPP1-37 peptide does not. This result was confirmed by solid-state NMR spectroscopy which shows that in bicelles composed of regions of high curvature and low curvature, non-toxic rIAPP1-37 binds to the regions of low curvature while toxic rIAPP1-19 binds to regions of high curvature. Similarly, solid-state NMR spectroscopy shows that the toxic rIAPP1-19 peptide significantly disrupts the lipid bilayer structure, whereas the non-toxic rIAPP1-37 does not have a significant effect. These results indicate IAPP may induce the formation of pores by the induction of excess membrane curvature and can be used to guide the design of compounds that can prevent the cell-toxicity of IAPP. This mechanism may be important to understand the toxicity of other amyloidogenic proteins. Our solid-state NMR results also demonstrate the possibility of using bicelles to measure the affinity of biomolecules for negatively or positively curved regions of
Cosmic curvature from de Sitter equilibrium cosmology.
Albrecht, Andreas
2011-10-07
I show that the de Sitter equilibrium cosmology generically predicts observable levels of curvature in the Universe today. The predicted value of the curvature, Ω(k), depends only on the ratio of the density of nonrelativistic matter to cosmological constant density ρ(m)(0)/ρ(Λ) and the value of the curvature from the initial bubble that starts the inflation, Ω(k)(B). The result is independent of the scale of inflation, the shape of the potential during inflation, and many other details of the cosmology. Future cosmological measurements of ρ(m)(0)/ρ(Λ) and Ω(k) will open up a window on the very beginning of our Universe and offer an opportunity to support or falsify the de Sitter equilibrium cosmology.
HEREDITARY DISTAL FORELEG CURVATURE IN THE RABBIT
Pearce, Louise
1960-01-01
An inwardly directed curvature of the distal segment of both forelegs of the rabbit has been described. The condition was detected at 2 to 3 weeks of age, developed rapidly, and reached its final and permanent stage at 2 to 3 months of age. Only the distal epiphysis of the ulna was primarily affected and this in the form of a massive chondrodystrophic lesion accompanied by a progressive curvature of the shaft. The curvature of the growing radius was a secondary effect due to the firm, immovable, anatomical connection of the ulna and radius. The positional changes of the wrist and paw were likewise effects secondary to the changed form of the ulna and radius. The bowing abnormality occurred only in certain families of pure bred Beveren, Belgian, French Silver, and Dutch rabbits and was found to be inherited. The mode of inheritance was on the basis of a single recessive unit factor (5). PMID:13733755
Principal curvature for infrared small target detection
NASA Astrophysics Data System (ADS)
Zhao, Yao; Pan, Haibin; Du, Changping; Zheng, Yao
2015-03-01
Small target detection in infrared image with complex background and low signal-noise ratio is an important and difficult task in the infrared target tracking system. In this paper, a principal curvature-based method is proposed. The principal curvatures of target pixels are negative and their absolute values are larger than that of background pixels and noise pixels in a Gaussian-blurred infrared image. The proposed filter takes a composite function of the curvatures for detection. An approximate model is also built for optimizing the parameters. Experimental results show that the proposed algorithm is effective and adaptable for infrared small target detection in complex background. Compared with several popular methods, the proposed algorithm demonstrates significant improvement on detection performance in terms of the parameters of signal clutter ratio gain, background suppression factor and ROC.
Membrane shape instabilities induced by BAR domain proteins
NASA Astrophysics Data System (ADS)
Baumgart, Tobias
2014-03-01
Membrane curvature has developed into a forefront of membrane biophysics. Numerous proteins involved in membrane curvature sensing and membrane curvature generation have recently been discovered, including proteins containing the crescent-shaped BAR domain as membrane binding and shaping module. Accordingly, the structure determination of these proteins and their multimeric complexes is increasingly well-understood. Substantially less understood, however, are thermodynamic and kinetic aspects and the detailed mechanisms of how these proteins interact with membranes in a curvature-dependent manner. New experimental approaches need to be combined with established techniques to be able to fill in these missing details. Here we use model membrane systems in combination with a variety of biophysical techniques to characterize mechanistic aspects of BAR domain protein function. This includes a characterization of membrane curvature sensing and membrane generation. We also establish kinetic and thermodynamic aspects of BAR protein dimerization in solution, and investigate kinetic aspects of membrane binding. We present two new approaches to investigate membrane shape instabilities and demonstrate that membrane shape instabilities can be controlled by protein binding and lateral membrane tension. This work is supported through NIH grant GM-097552 and NSF grant CBET-1053857.
Ray Curvature and Refraction of Wave Packets.
1978-09-01
1!~~~~~ _ ‘ AD AOM 302 FLORIDA STATE UNIV TALLAHASSEE DEPT OF OCEANOGRAPHY FIG B/3 RAY CURVATURE AND REFRACTION OF WAVE PACKETS. (U) SEP 78 .J E...BREEDING N00014—77—C—0329 UNCLASSIFIED TR JE6 3 NL _ _ _ rwii__ _ ~iU ir!I I -~~ RAYOJR\\1L~[UREAND REFRACI ION OF WAVE F1~\\CKET~S ~y J. Ernest Breeding...01 29 014 -~ Technical Report No. JEB-3 Department of Oceanography • Florida State University RAY CURVATURE AND REFRACTION OF WAVE PACKETS b O G • J
NASTRAN modifications for recovering strains and curvatures
NASA Technical Reports Server (NTRS)
Hennrich, C. W.
1975-01-01
Modifications to the NASTRAN structural analysis computer program are described. The modifications allow the recovery of strain and curvature data for the general two-dimensional elements, in addition to the usual stress data. Option features allow the transformation of the strain/curvature (or stress) data to a common coordinate system and representation at the grid points of the structural model rather than at the conventional element center locations. Usage information is provided which will allow present users of NASTRAN to easily utilize the new capability.
Equal-Curvature X-Ray Telescopes
NASA Technical Reports Server (NTRS)
Saha, Timo T.; Zhang, William
2002-01-01
We introduce a new type of x-ray telescope design; an Equal-Curvature telescope. We simply add a second order axial sag to the base grazing incidence cone-cone telescope. The radius of curvature of the sag terms is the same on the primary surface and on the secondary surface. The design is optimized so that the on-axis image spot at the focal plane is minimized. The on-axis RMS (root mean square) spot diameter of two studied telescopes is less than 0.2 arc-seconds. The off-axis performance is comparable to equivalent Wolter type 1 telescopes.
Hysteresis compensation technique for POF curvature sensors
NASA Astrophysics Data System (ADS)
Leal, Arnaldo G.; Frizera, Anselmo; Pontes, Maria José
2017-04-01
Polymer optical fibers (POF) have higher strain limits, fracture toughness and flexibility in bend if compared to glass optical fibers. These characteristics enable the application of POFs as curvature sensors. However, the polymer is a viscoelastic material, which does not have a constant response with stress or strain. For this reason, a curvature sensor based on POF may present high hysteresis. This paper proposes a dynamic compensation technique based on the angular velocity of the sensor. Results show a hysteresis up to 10 times lower. Furthermore, it results on a simple calibration equation, which can be applied in real-time measurements.
Curvature suppresses the Rayleigh-Taylor instability
Trinh, Philippe H.; Kim, Hyoungsoo; Hammoud, Naima; Howell, Peter D.; Chapman, S. Jonathan; Stone, Howard A.
2014-05-01
The dynamics of a thin liquid #12;lm on the underside of a curved cylindrical substrate is studied. The evolution of the liquid layer is investigated as the #12;lm thickness and the radius of curvature of the substrate are varied. A dimensionless parameter (a modi#12;ed Bond number) that incorporates both geometric parameters, gravity, and surface tension is identified, and allows the observations to be classified according to three different flow regimes: stable films, films with transient growth of perturbations followed by decay, and unstable films. Experiments and theory confirm that, below a critical value of the Bond number, curvature of the substrate suppresses the Rayleigh-Taylor instability.
Fengjie, Xi; Zongfu, Jiang; Xiaojun, Xu; Jing, Hou; Zejin, Liu
2009-03-02
In this paper we determine the optimum propagation distance between measurement planes and the plane of the lens in a wavefront curvature sensor with the diffraction optics approach. From the diffraction viewpoint, the measured wavefront aberration can be decomposed into Fourier harmonics at various frequencies. The curvature signal produced by a single harmonic is analyzed with the wave propagation transfer function approach, which is the frequency analysis of wavefront curvature sensing. The intensity of the curvature signal is a sine function of the product of the propagation distance and the squared frequency. To maximize the curvature signal, the optimum propagation distance is proposed as one quarter of the Talbot length at the critical frequency (average power point at which the power spectrum density is the average power spectrum density). Following the determination of the propagation distance, the intensity of the curvature signal varies sinusoidally with the squared frequencies, vanishing at some higher frequency bands just like a comb filter. To cover these insensitive bands, wavefront curvature sensing with dual propagation distances or with multi-propagation distances is proposed.
Mariani, María Elisa; Madoery, Ricardo Román; Fidelio, Gerardo Daniel
2015-01-01
Two secretory phospholipase A2 (sPLA2s) from Glycine max, GmsPLA2-IXA-1 and GmsPLA2-XIB-2, have been purified as recombinant proteins and the activity was evaluated in order to obtain the optimum conditions for catalysis using mixed micelles and lipid monolayers as substrate. Both sPLA2s showed a maximum enzyme activity at pH 7 and a requirement of Ca(2+) in the micromolar range. These parameters were similar to those found for animal sPLA2s but a surprising optimum temperature for catalysis at 60 °C was observed. The effect of negative interfacial charges on the hydrolysis of organized substrates was evaluated through initial rate measurements using short chain phospholipids with different head groups. The enzymes showed subtle differences in the specificity for phospholipids with different head groups (DLPC, DLPG, DLPE, DLPA) in presence or absence of NaCl. Both recombinant enzymes showed lower activity toward anionic phospholipids and a preference for the zwitterionic ones. The values of the apparent kinetic parameters (Vmax and KM) demonstrated that these enzymes have more affinity for phosphatidylcholine compared with phosphatidylglycerol, in contrast with the results observed for pancreatic sPLA2. A hopping mode of catalysis was proposed for the action of these sPLA2 on mixed phospholipid/triton micelles. On the other hand, Langmuir-monolayers assays indicated an optimum lateral surface pressure for activity in between 13 and 16 mN/m for both recombinant enzymes. Copyright © 2014 Elsevier B.V. and Société française de biochimie et biologie Moléculaire (SFBBM). All rights reserved.
Strong curvature singularities and causal simplicity
Krolak, A. )
1992-02-01
Techniques of differential topology in Lorentzian manifolds developed by Geroch, Hawking, and Penrose are used to rule out a class of locally naked strong curvature singularities in strongly causal space-times. This result yields some support to the validity of Penrose's strong cosmic censorship hypothesis.
Graph Curvature for Differentiating Cancer Networks
Sandhu, Romeil; Georgiou, Tryphon; Reznik, Ed; Zhu, Liangjia; Kolesov, Ivan; Senbabaoglu, Yasin; Tannenbaum, Allen
2015-01-01
Cellular interactions can be modeled as complex dynamical systems represented by weighted graphs. The functionality of such networks, including measures of robustness, reliability, performance, and efficiency, are intrinsically tied to the topology and geometry of the underlying graph. Utilizing recently proposed geometric notions of curvature on weighted graphs, we investigate the features of gene co-expression networks derived from large-scale genomic studies of cancer. We find that the curvature of these networks reliably distinguishes between cancer and normal samples, with cancer networks exhibiting higher curvature than their normal counterparts. We establish a quantitative relationship between our findings and prior investigations of network entropy. Furthermore, we demonstrate how our approach yields additional, non-trivial pair-wise (i.e. gene-gene) interactions which may be disrupted in cancer samples. The mathematical formulation of our approach yields an exact solution to calculating pair-wise changes in curvature which was computationally infeasible using prior methods. As such, our findings lay the foundation for an analytical approach to studying complex biological networks. PMID:26169480
Photon Drag Effect due to Berry Curvature.
Kurosawa, Hiroyuki; Sawada, Kei; Ohno, Seigo
2016-08-19
A theoretical investigation reveals that the photon drag effect (PDE) is induced in a grating slab with deformation by the Berry curvature in phase space. It drifts the momentum of light, and gives asymmetric PDE signals in momentum space. Large PDE signals are observed even near the Γ point. This characteristic agrees well with our theoretical results.
Riemann curvature of a boosted spacetime geometry
NASA Astrophysics Data System (ADS)
Battista, Emmanuele; Esposito, Giampiero; Scudellaro, Paolo; Tramontano, Francesco
2016-10-01
The ultrarelativistic boosting procedure had been applied in the literature to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface. This paper evaluates the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Thus, for the first time in the literature, the singular limit of curvature, through Dirac’s δ distribution and its derivatives, is numerically evaluated for this class of spacetimes. Moreover, the analysis of the Kretschmann invariant and the geodesic equation shows that the spacetime possesses a “scalar curvature singularity” within a 3-sphere and it is possible to define what we here call “boosted horizon”, a sort of elastic wall where all particles are surprisingly pushed away, as numerical analysis demonstrates. This seems to suggest that such “boosted geometries” are ruled by a sort of “antigravity effect” since all geodesics seem to refuse to enter the “boosted horizon” and are “reflected” by it, even though their initial conditions are aimed at driving the particles toward the “boosted horizon” itself. Eventually, the equivalence with the coordinate shift method is invoked in order to demonstrate that all δ2 terms appearing in the Riemann curvature tensor give vanishing contribution in distributional sense.
Geometrical interpretation and curvature distribution in nanocarbons
NASA Astrophysics Data System (ADS)
Gupta, Sanju; Saxena, Avadh
2011-04-01
Despite extensive research on microscopic structure and physical property characterization of advanced nanocarbon systems, they have not been viewed as topologically distinct nanoscale materials with various geometries (curvature). This work is motivated by our recent work [S. Gupta and A. Saxena, J. Raman Spectrosc. 40, 1127 (2009)] where we introduced the notion of "global" topology for novel nanocarbons and provided systematic trends by monitoring the phonon spectra via resonance Raman spectroscopy, which led to the paradigm of curvature/topology → property → functionality relationship in these materials. Here we determined the distribution of the mean (H) and Gaussian (K) curvatures as pertinent observables for geometric characterization taking into account the observed geometrical parameters, that is, radius, polar, azimuthal, or conical angle associated with tubular (single, double-, and multi-walled nanotubes; K = 0), spherical (hypo- and hyperfullerenes; K > 0) and complex (helical nanoribbons and nanotori/nanorings; K < 0) nanocarbon geometries to quantify the interplay of intrinsic surface curvature and topology, wherein global topology of the overall sp2-bonded carbon (sp2C) constrains local topology of the constituent carbon rings. We also studied various other structures such as catenoid and saddle-shaped surfaces as interesting nanocarbons. We compared these results with highly oriented pyrolytic graphite and monolayer graphene as layered and planar systems, respectively. Moreover, nanocarbons discussed herein are their derivatives. Curvature leads to nonlinearity that manifests itself in some form of symmetry breaking which can be extrapolated to topological variation due to nanoscale defects. Thus it may either close/open the bandgap leading to the introduction of new Raman spectroscopy signatures and optical absorption peaks, changes in mechanical properties, electrical behavior, and electronic density of states and possibly inducing magnetism
Seismological Constraints on Fault Plane Curvature
NASA Astrophysics Data System (ADS)
Reynolds, K.
2015-12-01
The down-dip geometry of seismically active normal faults is not well known. Many examples of normal faults with down-dip curvature exist, such as listric faults revealed in cross-section or in seismic reflection data, or the exposed domes of core complexes. However, it is not understood: (1) whether curved faults fail in earthquakes, and (2) if those faults have generated earthquakes, is the curvature a primary feature of the rupture or due to later modification of the plane? Even if an event is surface-rupturing, because of the limited depth-extent over which observations can be made, it is difficult to reliably constrain the change in dip with depth (if any) and therefore the fault curvature. Despite the uncertainty in seismogenic normal fault geometries, published slip inversions most commonly use planar fault models. We investigate the seismological constraints on normal fault geometry using a forward-modelling approach and present a seismological technique for determining down-dip geometry. We demonstrate that complexity in the shape of teleseismic body waveforms may be used to investigate the presence of down-dip fault plane curvature. We have applied this method to a catalogue of continental and oceanic normal faulting events. Synthetic models demonstrate that the shapes of SH waveforms at along-strike stations are particularly sensitive to fault plane geometry. It is therefore important to consider the azimuthal station coverage before modelling an event. We find that none of the data require significant down-dip curvature, although the modelling results for some events remain ambiguous. In some cases we can constrain that the down-dip fault geometry is within 20° of planar.
Sequential effects in preference decision: Prior preference assimilates current preference.
Chang, Seah; Kim, Chai-Youn; Cho, Yang Seok
2017-01-01
An important factor affecting preference formation is the context in which that preference decision takes place. The current research examined whether one's preference formed for a previously presented stimulus influences the processing of a subsequent preference decision, henceforth referred to as the preference sequence effect. Using a novel sequential rating/judgment paradigm, the present study demonstrated the presence of a preference sequence effect using artistic photographs and face stimuli: A neutral stimulus was preferred more following a preferable stimulus than a less preferable stimulus. Furthermore, a similar trend was found even when the potential influence of response bias was controlled. These results suggest that an assimilative sequential effect exists even when sequential judgments are made solely based on one's subjective feeling; preference formed for a preceding stimulus modulates preference for a subsequent stimulus. This implies the need for a consideration of trial sequence as a factor creating a psychological context affecting the subsequent preference decisions.
Sequential effects in preference decision: Prior preference assimilates current preference
Chang, Seah; Kim, Chai-Youn
2017-01-01
An important factor affecting preference formation is the context in which that preference decision takes place. The current research examined whether one’s preference formed for a previously presented stimulus influences the processing of a subsequent preference decision, henceforth referred to as the preference sequence effect. Using a novel sequential rating/judgment paradigm, the present study demonstrated the presence of a preference sequence effect using artistic photographs and face stimuli: A neutral stimulus was preferred more following a preferable stimulus than a less preferable stimulus. Furthermore, a similar trend was found even when the potential influence of response bias was controlled. These results suggest that an assimilative sequential effect exists even when sequential judgments are made solely based on one’s subjective feeling; preference formed for a preceding stimulus modulates preference for a subsequent stimulus. This implies the need for a consideration of trial sequence as a factor creating a psychological context affecting the subsequent preference decisions. PMID:28817619
Miyake, Masahiro; Yamashiro, Kenji; Akagi-Kurashige, Yumiko; Oishi, Akio; Tsujikawa, Akitaka; Hangai, Masanori; Yoshimura, Nagahisa
2014-01-01
Purpose To evaluate fundus shape in highly myopic eyes using color maps created through optical coherence tomography (OCT) image analysis. Methods We retrospectively evaluated 182 highly myopic eyes from 113 patients. After obtaining 12 lines of 9-mm radial OCT scans with the fovea at the center, the Bruch’s membrane line was plotted and its curvature was measured at 1-µm intervals in each image, which was reflected as a color topography map. For the quantitative analysis of the eye shape, mean absolute curvature and variance of curvature were calculated. Results The color maps allowed staphyloma visualization as a ring of green color at the edge and as that of orange-red color at the bottom. Analyses of mean and variance of curvature revealed that eyes with myopic choroidal neovascularization tended to have relatively flat posterior poles with smooth surfaces, while eyes with chorioretinal atrophy exhibited a steep, curved shape with an undulated surface (P<0.001). Furthermore, eyes with staphylomas and those without clearly differed in terms of mean curvature and the variance of curvature: 98.4% of eyes with staphylomas had mean curvature ≥7.8×10−5 [1/µm] and variance of curvature ≥0.26×10−8 [1/µm]. Conclusions We established a novel method to analyze posterior pole shape by using OCT images to construct curvature maps. Our quantitative analysis revealed that fundus shape is associated with myopic complications. These values were also effective in distinguishing eyes with staphylomas from those without. This tool for the quantitative evaluation of eye shape should facilitate future research of myopic complications. PMID:25259853
How to calculate normal curvatures of sampled geological surfaces
NASA Astrophysics Data System (ADS)
Bergbauer, Stephan; Pollard, David D.
2003-02-01
Curvature has been used both to describe geological surfaces and to predict the distribution of deformation in folded or domed strata. Several methods have been proposed in the geoscience literature to approximate the curvature of surfaces; however we advocate a technique for the exact calculation of normal curvature for single-valued gridded surfaces. This technique, based on the First and Second Fundamental Forms of differential geometry, allows for the analytical calculation of the magnitudes and directions of principal curvatures, as well as Gaussian and mean curvature. This approach is an improvement over previous methods to calculate surface curvatures because it avoids common mathematical approximations, which introduce significant errors when calculated over sloped horizons. Moreover, the technique is easily implemented numerically as it calculates curvatures directly from gridded surface data (e.g. seismic or GPS data) without prior surface triangulation. In geological curvature analyses, problems arise because of the sampled nature of geological horizons, which introduces a dependence of calculated curvatures on the sample grid. This dependence makes curvature analysis without prior data manipulation problematic. To ensure a meaningful curvature analysis, surface data should be filtered to extract only those surface wavelengths that scale with the feature under investigation. A curvature analysis of the top-Pennsylvanian horizon at Goose Egg dome, Wyoming shows that sampled surfaces can be smoothed using a moving average low-pass filter to extract curvature information associated with the true morphology of the structure.
Membrane remodeling by the M2 amphipathic helix drives influenza virus membrane scission
Martyna, Agnieszka; Bahsoun, Basma; Badham, Matthew D.; Srinivasan, Saipraveen; Howard, Mark J.; Rossman, Jeremy S.
2017-01-01
Membrane scission is a crucial step in all budding processes, from endocytosis to viral budding. Many proteins have been associated with scission, though the underlying molecular details of how scission is accomplished often remain unknown. Here, we investigate the process of M2-mediated membrane scission during the budding of influenza viruses. Residues 50–61 of the viral M2 protein bind membrane and form an amphipathic α-helix (AH). Membrane binding requires hydrophobic interactions with the lipid tails but not charged interactions with the lipid headgroups. Upon binding, the M2AH induces membrane curvature and lipid ordering, constricting and destabilizing the membrane neck, causing scission. We further show that AHs in the cellular proteins Arf1 and Epsin1 behave in a similar manner. Together, they represent a class of membrane-induced AH domains that alter membrane curvature and fluidity, mediating the scission of constricted membrane necks in multiple biological pathways. PMID:28317901
NASA Astrophysics Data System (ADS)
Breidenich, Markus
2000-11-01
The surface of biological cells consists of a lipid membrane and a large amount of various proteins and polymers, which are embedded in the membrane or attached to it. We investigate how membranes are influenced by polymers, which are anchored to the membrane by one end. The entropic pressure exerted by the polymer induces a curvature, which bends the membrane away from the polymer. The resulting membrane shape profile is a cone in the vicinity of the anchor segment and a catenoid far away from it. The perturbative calculations are confirmed by Monte-Carlo simulations. An additional attractive interaction between polymer and membrane reduces the entropically induced curvature. In the limit of strong adsorption, the polymer is localized directly on the membrane surface and does not induce any pressure, i.e. the membrane curvature vanishes. If the polymer is not anchored directly on the membrane surface, but in a non-vanishing anchoring distance, the membrane bends towards the polymer for strong adsorption. In the last part of the thesis, we study membranes under the influence of non-anchored polymers in solution. In the limit of pure steric interactions between the membrane and free polymers, the membrane curves towards the polymers (in contrast to the case of anchored polymers). In the limit of strong adsorption the membrane bends away from the polymers. Die Oberfläche biologischer Zellen besteht aus einer Lipidmembran und einer Vielzahl von Proteinen und Polymeren, die in die Membran eingebaut sind. Die Beeinflussung der Membran durch Polymere, die mit einem Ende an der Membran verankert sind, wird im Rahmen dieser Arbeit anhand eines vereinfachten biomimetischen Systems studiert. Der entropische Druck, den das Polymer durch Stöße auf die Membran ausübt, führt dazu, dass sich die Membran vom Polymer weg krümmt. Die resultierende Membranform ist ein Kegel in der Nähe des Ankers und ein Katenoid in grossem Abstand vom Ankerpunkt. Monte Carlo-Simulationen best
Regulation of membrane-shape transitions induced by I-BAR domains.
Chen, Zhiming; Shi, Zheng; Baumgart, Tobias
2015-07-21
I-BAR proteins are well-known actin-cytoskeleton adaptors and have been observed to be involved in the formation of plasma membrane protrusions (filopodia). I-BAR proteins contain an all-helical, crescent-shaped IRSp53-MIM domain (IMD) dimer that is believed to be able to couple with a membrane shape. This coupling could involve the sensing and even the generation of negative plasma membrane curvature. Indeed, the in vitro studies have shown that IMDs can induce inward tubulation of liposomes. While N-BAR domains, which generate positive membrane curvature, have received a considerable amount of attention from both theory and experiments, the mechanisms of curvature coupling through IMDs are comparatively less studied and understood. Here we used a membrane-shape stability assay developed recently in our lab to quantitatively characterize IMD-induced membrane-shape transitions. We determined a membrane-shape stability diagram for IMDs that reveals how membrane tension and protein density can comodulate the generation of IMD-induced membrane protrusions. From comparison to analytical theory, we determine three key parameters that characterize the curvature coupling of IMD. We find that the curvature generation capacity of IMDs is significantly stronger compared to that of endophilin, an N-BAR protein known to be involved in plasma membrane shape transitions. Contrary to N-BAR domains, where amphipathic helix insertion is known to promote its membrane curvature generation, for IMDs we find that amphipathic helices inhibit membrane shape transitions, consistent with the inverse curvature that IMDs generate. Importantly, in both of these types of BAR domains, electrostatic interactions affect membrane-binding capacity, but do not appear to affect the curvature generation capacity of the protein. These two types of BAR domain proteins show qualitatively similar membrane shape stability diagrams, suggesting an underlying ubiquitous mechanism by which peripheral proteins
Ramesh, Pradeep; Baroji, Younes F.; Reihani, S. Nader S.; Stamou, Dimitrios; Oddershede, Lene B.; Bendix, Poul Martin
2013-01-01
Syndapin 1 FBAR, a member of the Bin-amphiphysin-Rvs (BAR) domain protein family, is known to induce membrane curvature and is an essential component in biological processes like endocytosis and formation and growth of neurites. We quantify the curvature sensing of FBAR on reconstituted porcine brain lipid vesicles and show that it senses membrane curvature at low density whereas it induces and reinforces tube stiffness at higher density. FBAR strongly up-concentrates on the high curvature tubes pulled out of Giant Unilamellar lipid Vesicles (GUVs), this sorting behavior is strongly amplified at low protein densities. Interestingly, FBAR from syndapin 1 has a large affinity for tubular membranes with curvatures larger than its own intrinsic concave curvature. Finally, we studied the effect of FBAR on membrane relaxation kinetics with high temporal resolution and found that the protein increases relaxation time of the tube holding force in a density-dependent fashion. PMID:23535634
Inequalities for scalar curvature of pseudo-Riemannian submanifolds
NASA Astrophysics Data System (ADS)
Tripathi, Mukut Mani; Gülbahar, Mehmet; Kılıç, Erol; Keleş, Sadık
2017-02-01
Some basic inequalities, involving the scalar curvature and the mean curvature, for a pseudo-Riemannian submanifold of a pseudo-Riemannian manifold are obtained. We also find inequalities for spacelike submanifolds. Equality cases are also discussed.
Rossman, Jeremy S.; Lamb, Robert A.
2014-01-01
Virus budding is a complex, multistep process in which viral proteins make specific alterations in membrane curvature. Many different viral proteins can deform the membrane and form a budding virion, but very few can mediate membrane scission to complete the budding process. As a result, enveloped viruses have developed numerous ways of facilitating membrane scission, including hijacking host cellular scission machinery and expressing their own scission proteins. These proteins mediate scission in very different ways, though the biophysical mechanics underlying their actions may be similar. In this review, we explore the mechanisms of membrane scission and the ways in which enveloped viruses use these systems to mediate the release of budding virions. PMID:24099087
Laser triangulation measurements of scoliotic spine curvatures.
Čelan, Dušan; Jesenšek Papež, Breda; Poredoš, Primož; Možina, Janez
2015-01-01
The main purpose of this research was to develop a new method for differentiating between scoliotic and healthy subjects by analysing the curvatures of their spines in the cranio-caudal view. The study included 247 subjects with physiological curvatures of the spine and 28 subjects with clinically confirmed scoliosis. The curvature of the spine was determined by a computer analysis of the surface of the back, measured with a non-invasive, 3D, laser-triangulation system. The determined spinal curve was represented in the transversal plane, which is perpendicular to the line segment that was defined by the initial point and the end point of the spinal curve. This was achieved using a rotation matrix. The distances between the extreme points in the antero-posterior (AP) and left-right (LR) views were calculated in relation to the length of the spine as well as the quotient of these two values LR/AP. All the measured parameters were compared between the scoliotic and control groups using the Student's t-Test in case of normal data and Kruskal-Wallis test in case of non-normal data. Besides, a comprehensive diagram representing the distances between the extreme points in the AP and LR views was introduced, which clearly demonstrated the direction and the size of the thoracic and lumbar spinal curvatures for each individual subject. While the distances between the extreme points of the spine in the AP view were found to differ only slightly between the groups (p = 0.1), the distances between the LR extreme points were found to be significantly greater in the scoliosis group, compared to the control group (p < 0.001). The quotient LR/AP was statistically significantly different in both groups (p < 0.001). The main innovation of the presented method is the ability to differentiate a scoliotic subject from a healthy subject by assessing the curvature of the spine in the cranio-caudal view. Therefore, the proposed method could be useful for human posture
Two-component membrane material properties and domain formation from dissipative particle dynamics.
Illya, G; Lipowsky, R; Shillcock, J C
2006-09-21
The material parameters (area stretch modulus and bending rigidity) of two-component amphiphilic membranes are determined from dissipative particle dynamics simulations. The preferred area per molecule for each species is varied so as to produce homogeneous mixtures or nonhomogeneous mixtures that form domains. If the latter mixtures are composed of amphiphiles with the same tail length, but different preferred areas per molecule, their material parameters increase monotonically as a function of composition. By contrast, mixtures of amphiphiles that differ in both tail length and preferred area per molecule form both homogeneous and nonhomogeneous mixtures that both exhibit smaller values of their material properties compared to the corresponding pure systems. When the same nonhomogeneous mixtures of amphiphiles are assembled into planar membrane patches and vesicles, the resulting domain shapes are different when the bending rigidities of the domains are sufficiently different. Additionally, both bilayer and monolayer domains are observed in vesicles. We conclude that the evolution of the domain shapes is influenced by the high curvature of the vesicles in the simulation, a result that may be relevant for biological vesicle membranes.
Domain Formation in Membranes Near the Onset of Instability
NASA Astrophysics Data System (ADS)
Fonseca, Irene; Hayrapetyan, Gurgen; Leoni, Giovanni; Zwicknagl, Barbara
2016-10-01
The formation of microdomains, also called rafts, in biomembranes can be attributed to the surface tension of the membrane. In order to model this phenomenon, a model involving a coupling between the local composition and the local curvature was proposed by Seul and Andelman in 1995. In addition to the familiar Cahn-Hilliard/Modica-Mortola energy, there are additional `forces' that prevent large domains of homogeneous concentration. This is taken into account by the bending energy of the membrane, which is coupled to the value of the order parameter, and reflects the notion that surface tension associated with a slightly curved membrane influences the localization of phases as the geometry of the lipids has an effect on the preferred placement on the membrane. The main result of the paper is the study of the Γ -convergence of this family of energy functionals, involving nonlocal as well as negative terms. Since the minimizers of the limiting energy have minimal interfaces, the physical interpretation is that, within a sufficiently strong interspecies surface tension and a large enough sample size, raft microdomains are not formed.
Constraining inverse-curvature gravity with supernovae.
Mena, Olga; Santiago, José; Weller, Jochen
2006-02-03
We show that models of generalized modified gravity, with inverse powers of the curvature, can explain the current accelerated expansion of the Universe without resorting to dark energy and without conflicting with solar system experiments. We have solved the Friedmann equations for the full dynamical range of the evolution of the Universe and performed a detailed analysis of supernovae data in the context of such models that results in an excellent fit. If we further include constraints on the current expansion of the Universe and on its age, we obtain that the matter content of the Universe is 0.07
Static optical designs for Wavefront Curvature Sensing
NASA Astrophysics Data System (ADS)
Bharmal, Nazim A.
2006-06-01
A bulk optic is presented, the Parallel Output Beamsplitter, which allows simultaneous imaging of two planes either side of the focus using static imaging optics. The POB is used to create novel optical configurations for Wavefront Curvature Sensing and two designs are presented. The first is suited to small-amplitude aberration measurements in situations where compactness, a large field of view, and high optical throughput are desirable. A laboratory experiment using a POB to make such a wavefront sensor was undertaken, and results are presented. The second design is a conceptual idea which offers image-scale invariant imaging of two planes whose conjugation satisfies the requirements of a conventional Wavefront Curvature Sensor concept.
Streamline curvature in supersonic shear layers
NASA Technical Reports Server (NTRS)
Kibens, V.
1992-01-01
Results of an experimental investigation in which a curved shear layer was generated between supersonic flow from a rectangular converging/diverging nozzle and the freestream in a series of open channels with varying radii of curvature are reported. The shear layers exhibit unsteady large-scale activity at supersonic pressure ratios, indicating increased mixing efficiency. This effect contrasts with supersonic flow in a straight channel, for which no large-scale vortical structure development occurs. Curvature must exceed a minimum level before it begins to affect the dynamics of the supersonic shear layer appreciably. The curved channel flows are compared with reference flows consisting of a free jet, a straight channel, and wall jets without sidewalls on a flat and a curved plate.
Effect of intrinsic curvature on semiflexible polymers
NASA Astrophysics Data System (ADS)
Ghosh, Surya K.; Singh, Kulveer; Sain, Anirban
2009-11-01
Recently many important biopolymers have been found to possess intrinsic curvature. Tubulin protofilaments in animal cells, FtsZ filaments in bacteria and double stranded DNA are examples. We examine how intrinsic curvature influences the conformational statistics of such polymers. We give exact results for the tangent-tangent spatial correlation function C(r)=⟨t̂(s).t̂(s+r)⟩ , both in two and three dimensions. Contrary to expectation, C(r) does not show any oscillatory behavior, rather decays exponentially and the effective persistence length has strong length dependence for short polymers. We also compute the distribution function P(R) of the end to end distance R and show how curved chains can be distinguished from wormlike chains using loop formation probability.
Curvature suppresses the Rayleigh-Taylor instability
Trinh, Philippe H.; Kim, Hyoungsoo; Hammoud, Naima; ...
2014-05-20
We studied the dynamics of a thin liquid film on the underside of a curved cylindrical substrate. The evolution of the liquid layer is investigated as the film thickness and the radius of curvature of the substrate are varied. A dimensionless parameter (a modified Bond number) that incorporates both geometric parameters, gravity, and surface tension is identified, and allows the observations to be classified according to three different flow regimes: stable films, films with transient growth of perturbations followed by decay, and unstable films. We found that the experiments and theory confirm that, below a critical value of the Bondmore » number, curvature of the substrate suppresses the Rayleigh-Taylor instability.« less
Tube curvature measuring probe and method
Sokol, George J.
1990-01-01
The present invention is directed to a probe and method for measuring the radius of curvature of a bend in a section of tubing. The probe includes a member with a pair of guide means, one located at each end of the member. A strain gauge is operatively connected to the member for detecting bending stress exrted on the member as the probe is drawn through and in engagement with the inner surface of a section of tubing having a bend. The method of the present invention includes steps utilizing a probe, like the aforementioned probe, which can be made to detect bends only in a single plane when having a fixed orientation relative the section of tubing to determine the maximum radius of curvature of the bend.
Measuring Intrinsic Curvature of Space with Electromagnetism
NASA Astrophysics Data System (ADS)
Mabin, Mason; Becker, Maria; Batelaan, Herman
2016-10-01
The concept of curved space is not readily observable in everyday life. The educational movie "Sphereland" attempts to illuminate the idea. The main character, a hexagon, has to go to great lengths to prove that her world is in fact curved. We present an experiment that demonstrates a new way to determine if a two-dimensional surface, the 2-sphere, is curved. The behavior of an electric field, placed on a spherical surface, is shown to be related to the intrinsic Gaussian curvature. This approach allows students to gain some understanding of Einstein's theory of general relativity, which relates the curvature of spacetime to the presence of mass and energy. Additionally, an opportunity is provided to investigate the dimensionality of Gauss's law.
Streamline curvature in supersonic shear layers
NASA Technical Reports Server (NTRS)
Kibens, V.
1992-01-01
Results of an experimental investigation in which a curved shear layer was generated between supersonic flow from a rectangular converging/diverging nozzle and the freestream in a series of open channels with varying radii of curvature are reported. The shear layers exhibit unsteady large-scale activity at supersonic pressure ratios, indicating increased mixing efficiency. This effect contrasts with supersonic flow in a straight channel, for which no large-scale vortical structure development occurs. Curvature must exceed a minimum level before it begins to affect the dynamics of the supersonic shear layer appreciably. The curved channel flows are compared with reference flows consisting of a free jet, a straight channel, and wall jets without sidewalls on a flat and a curved plate.
Cosmological signatures of anisotropic spatial curvature
Pereira, Thiago S.; Marugán, Guillermo A. Mena; Carneiro, Saulo E-mail: mena@iem.cfmac.csic.es
2015-07-01
If one is willing to give up the cherished hypothesis of spatial isotropy, many interesting cosmological models can be developed beyond the simple anisotropically expanding scenarios. One interesting possibility is presented by shear-free models in which the anisotropy emerges at the level of the curvature of the homogeneous spatial sections, whereas the expansion is dictated by a single scale factor. We show that such models represent viable alternatives to describe the large-scale structure of the inflationary universe, leading to a kinematically equivalent Sachs-Wolfe effect. Through the definition of a complete set of spatial eigenfunctions we compute the two-point correlation function of scalar perturbations in these models. In addition, we show how such scenarios would modify the spectrum of the CMB assuming that the observations take place in a small patch of a universe with anisotropic curvature.
Controlling Hamiltonian chaos via Gaussian curvature.
Oloumi, A; Teychenné, D
1999-12-01
We present a method allowing one to partly stabilize some chaotic Hamiltonians which have two degrees of freedom. The purpose of the method is to avoid the regions of V(q(1),q(2)) where its Gaussian curvature becomes negative. We show the stabilization of the Hénon-Heiles system, over a wide area, for the critical energy E=1/6. Total energy of the system varies only by a few percent.
Generalization of Seidel astigmatism and Petzval curvature.
Gaj, M
1966-06-01
In a paper probably to be published in Optika i Spektroskopiya the wave aberration for sagittal focus for the arbitrary surface of rotational symmetry has been carried out on the base of the astigmatic beam invariant D(s) = nu(s)d(s). The resulting expression for the wave aberration has been reformulated into three terms which, in the Seidel region, go over into astigmatism (the first) and into the Petzval curvature (the second) while the third disappears.
Breeding curvature from extended gauge covariance
NASA Astrophysics Data System (ADS)
Aldrovandi, R.
1991-05-01
Independence between spacetime and “internal” space in gauge theories is related to the adjoint-covariant behaviour of the gauge potential. The usual gauge scheme is modified to allow a coupling between both spaces. Gauging spacetime translations produce field equations similar to Einstein equations. A curvature-like quantity of mixed differential-algebraic character emerges. Enlarged conservation laws are present, pointing to the presence of an covariance.
Curvature of spacetime: A simple student activity
NASA Astrophysics Data System (ADS)
Wood, Monika; Smith, Warren; Jackson, Matthew
2016-12-01
The following is a description of an inexpensive and simple student experiment for measuring the differences between the three types of spacetime topology—Euclidean (flat), Riemann (spherical), and Lobachevskian (saddle) curvatures. It makes use of commonly available tools and materials, and requires only a small amount of construction. The experiment applies to astronomical topics such as gravity, spacetime, general relativity, as well as geometry and mathematics.
Phase separation in artificial vesicles driven by light and curvature
NASA Astrophysics Data System (ADS)
Rinaldin, Melissa; Pomp, Wim; Schmidt, Thomas; Giomi, Luca; Kraft, Daniela; Physics of Life Processes Team; Soft; Bio Mechanics Collaboration; Self-Assembly in Soft Matter Systems Collaboration
The role of phase-demixing in living cells, leading to the lipid-raft hypothesis, has been extensively studied. Lipid domains of higher lipid chain order are proposed to regulate protein spatial organization. Giant Unilamellar Vesicles provide an artificial model to study phase separation. So far temperature was used to initiate the process. Here we introduce a new methodology based on the induction of phase separation by light. To this aim, the composition of the lipid membrane is varied by photo-oxidation of lipids. The control of the process gained by using light allowed us to observe vesicle shape fluctuations during phase-demixing. The presence of fluctuations near the critical mixing point resembles features of a critical process. We quantitatively analyze these fluctuations using a 2d elastic model, from which we can estimate the material parameters such as bending rigidity and surface tension, demonstrating the non-equilibrium critical behaviour. Finally, I will describe recent attempts toward tuning the membrane composition by controlling the vesicle curvature.
Multiple Manifold Clustering Using Curvature Constrained Path
Babaeian, Amir; Bayestehtashk, Alireza; Bandarabadi, Mojtaba
2015-01-01
The problem of multiple surface clustering is a challenging task, particularly when the surfaces intersect. Available methods such as Isomap fail to capture the true shape of the surface near by the intersection and result in incorrect clustering. The Isomap algorithm uses shortest path between points. The main draw back of the shortest path algorithm is due to the lack of curvature constrained where causes to have a path between points on different surfaces. In this paper we tackle this problem by imposing a curvature constraint to the shortest path algorithm used in Isomap. The algorithm chooses several landmark nodes at random and then checks whether there is a curvature constrained path between each landmark node and every other node in the neighborhood graph. We build a binary feature vector for each point where each entry represents the connectivity of that point to a particular landmark. Then the binary feature vectors could be used as a input of conventional clustering algorithm such as hierarchical clustering. We apply our method to simulated and some real datasets and show, it performs comparably to the best methods such as K-manifold and spectral multi-manifold clustering. PMID:26375819
Superintegrable systems on spaces of constant curvature
Gonera, Cezary Kaszubska, Magdalena
2014-07-15
Construction and classification of two-dimensional (2D) superintegrable systems (i.e. systems admitting, in addition to two global integrals of motion guaranteeing the Liouville integrability, the third global and independent one) defined on 2D spaces of constant curvature and separable in the so-called geodesic polar coordinates are presented. The method proposed is applicable to any value of curvature including the case of Euclidean plane, sphere and hyperbolic plane. The main result is a generalization of Bertrand’s theorem on 2D spaces of constant curvature and covers most of the known separable and superintegrable models on such spaces (in particular, the so-called Tremblay–Turbiner–Winternitz (TTW) and Post–Winternitz (PW) models which have recently attracted some interest). -- Highlights: •Classifying 2D superintegrable, separable (polar coordinates) systems on S{sup 2}, R{sup 2}, H{sup 2}. •Construction of radial, angular potentials leading to superintegrability. •Generalization of Bertrand’s theorem covering known models, e.g. Higgs, TTW, PW, and Coulomb.
Effects of wall curvature on turbulence statistics
NASA Technical Reports Server (NTRS)
Moser, R. D.; Moin, P.
1985-01-01
A three-dimensional, time-dependent, direct numerical simulation of low-Reynolds number turbulent flow in a mildly curved channel was performed, and the results examined to determine the mechanism by which curvature affects wall-bounded turbulent shear flows. A spectral numerical method with about one-million modes was employed, and no explicit subgrid scale model was used. The effects of curvature on this flow were determined by comparing the concave and convex sides of the channel. The observed effects are consistent with experimental observations for mild curvature. The most significant difference in the turbulence statistics between the concave and convex sides is in the Reynolds shear stress. This is accompanied by significant differences in the terms of the Reynolds shear stress balance equations. In addition, it was found that stationary Taylor-Goertler vortices were present and that they had a significant effect on the flow by contributing to the mean Reynolds shear stress, and by enhancing the difference between the wall shear stresses.
Curvature driven flow of bi-layer interfaces
NASA Astrophysics Data System (ADS)
Gavish, Nir; Hayrapetyan, Gurgen; Promislow, Keith; Yang, Li
2011-03-01
We introduce the Functionalized Cahn-Hilliard (FCH) energy, a negative multiple of the Cahn-Hilliard energy balanced against the square of its own variational derivative, as a finite width regularization of the sharp-interface Canham-Helfrich energy. Mass-preserving gradient flows associated to the FCH energy are higher-order phase field models which develop not only single-layer, or front-type interfaces, but also bi-layer, or homoclinic interfaces with associated endcap and multi-junction structures. The single-layer interfaces manifest a fingering instability which grows into endcapped bi-layers. The meandering growth of the bi-layer interfaces and the subsequent merging lead to a multi-junction dominated network that bears a striking similarity to the phase separated domains of both perfluorosulfonic membranes and amphiphilic di-block co-polymer solutions. The bi-layers generated by the gradient flows of the FCH energy have an interfacial width which scales with ε≪1, however for fixed ε, there is a class of bi-layers parameterized by width and background state. Our primary result is the asymptotic derivation of the normal velocity of a closed bi-layer hypersurface in Rd (d≥2) coupled to the evolution for the surface width, curvature, and background state. We also show the convergence of the FCH energy to a scaled Canham-Helfrich type energy for both single and bi-layer interfaces, with the surface area coefficient of the limiting Canham-Helfrich energy coupling to the bi-layer width. Thus the bi-layer networks grow to maximize surface area while minimizing the square of curvature, up to the point that the increase in surface area stretches the bi-layers too thin.
Free-streaming radiation in cosmological models with spatial curvature
NASA Technical Reports Server (NTRS)
Wilson, M. L.
1982-01-01
The effects of spatial curvature on radiation anisotropy are examined for the standard Friedmann-Robertson-Walker model universes. The effect of curvature is found to be very important when considering fluctuations with wavelengths comparable to the horizon. It is concluded that the behavior of radiation fluctuations in models with spatial curvature is quite different from that in spatially flat models, and that models with negative curvature are most strikingly different. It is therefore necessary to take the curvature into account in careful studies of the anisotropy of the microwave background.
The role of substrate curvature in actin-based pushing forces.
Schwartz, Ian M; Ehrenberg, Morton; Bindschadler, Michael; McGrath, James L
2004-06-22
The extension of the plasma membrane during cell crawling or spreading is known to require actin polymerization; however, the question of how pushing forces derive from actin polymerization remains open. A leading theory (herein referred to as elastic propulsion) illustrates how elastic stresses in networks growing on curved surfaces can result in forces that push particles. To date all examples of reconstituted motility have used curved surfaces, raising the possibility that such squeezing forces are essential for actin-based pushing. By contrast, other theories, such as molecular ratchets, neither require nor consider surface curvature to explain pushing forces. Here, we critically test the requirement of substrate curvature by reconstituting actin-based motility on polystyrene disks. We find that disks move through extracts in a manner that indicates pushing forces on their flat surfaces and that disks typically move faster than the spheres they are manufactured from. For a subset of actin tails that form on the perimeter of disks, we find no correlation between local surface curvature and tail position. Collectively the data indicate that curvature-dependent mechanisms are not required for actin-based pushing.
The crack problem in a specially orthotropic shell with double curvature
NASA Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.
1983-01-01
The crack problem of a shallow shell with two nonzero curvatures is considered. It is assumed that the crack lies in one of the principal planes of curvature and the shell is under Mode I loading condition. The material is assumed to be specially orthotropic. After giving the general formulation of the problem the asymptotic behavior of the stress state around the crack tip is examined. The analysis is based on Reissner's transverse shear theory. Thus, as in the bending of cracked plates, the asymptotic results are shown to be consistent with that obtained from the plane elasticity solution of crack problems. Rather extensive numerical results are obtained which show the effect of material orthotropy on the stress intensity factors in cylindrical and spherical shells and in shells with double curvature. Other results include the stress intensity factors in isotropic toroidal shells with positive or negative curvature ratio, the distribution of the membrane stress resultant outside the crack, and the influence of the material orthotropy on the angular distribution of the stresses around the crack tip. Previously announced in STAR as N83-16782
The crack problem in a specially orthotropic shell with double curvature
NASA Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.
1982-01-01
The crack problem of a shallow shell with two nonzero curvatures is considered. It is assumed that the crack lies in one of the principal planes of curvature and the shell is under Mode I loading condition. The material is assumed to be specially orthotropic. After giving the general formulation of the problem the asymptotic behavior of the stress state around the crack tip is examined. The analysis is based on Reissner's transverse shear theory. Thus, as in the bending of cracked plates, the asymptotic results are shown to be consistent with that obtained from the plane elasticity solution of crack problems. Rather extensive numerical results are obtained which show the effect of material orthotropy on the stress intensity factors in cylindrical and spherical shells and in shells with double curvature. Other results include the stress intensity factors in isotropic toroidal shells with positive or negative curvature ratio, the distribution of the membrane stress resultant outside the crack, and the influence of the material orthotropy on the angular distribution of the stresses around the crack tip.
The crack problem in a specially orthotropic shell with double curvature
NASA Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.
1983-01-01
The crack problem of a shallow shell with two nonzero curvatures is considered. It is assumed that the crack lies in one of the principal planes of curvature and the shell is under Mode I loading condition. The material is assumed to be specially orthotropic. After giving the general formulation of the problem the asymptotic behavior of the stress state around the crack tip is examined. The analysis is based on Reissner's transverse shear theory. Thus, as in the bending of cracked plates, the asymptotic results are shown to be consistent with that obtained from the plane elasticity solution of crack problems. Rather extensive numerical results are obtained which show the effect of material orthotropy on the stress intensity factors in cylindrical and spherical shells and in shells with double curvature. Other results include the stress intensity factors in isotropic toroidal shells with positive or negative curvature ratio, the distribution of the membrane stress resultant outside the crack, and the influence of the material orthotropy on the angular distribution of the stresses around the crack tip. Previously announced in STAR as N83-16782
On the Riemann Curvature Operators in Randers Spaces
NASA Astrophysics Data System (ADS)
Rafie-Rad, M.
2013-05-01
The Riemann curvature in Riemann-Finsler geometry can be regarded as a collection of linear operators on the tangent spaces. The algebraic properties of these operators may be linked to the geometry and the topology of the underlying space. The principal curvatures of a Finsler space (M, F) at a point x are the eigenvalues of the Riemann curvature operator at x. They are real functions κ on the slit tangent manifold TM0. A principal curvature κ(x, y) is said to be isotropic (respectively, quadratic) if κ(x, y)/F(x, y) is a function of x only (respectively, κ(x, y) is quadratic with respect to y). On the other hand, the Randers metrics are the most popular and prominent metrics in pure and applied disciplines. Here, it is proved that if a Randers metric admits an isotropic principal curvature, then F is of isotropic S-curvature. The same result is also established for F to admit a quadratic principal curvature. These results extend Shen's verbal results about Randers metrics of scalar flag curvature K = K(x) as well as those Randers metrics with quadratic Riemann curvature operator. The Riemann curvature Rik may be broken into two operators Rik and Jik. The isotropic and quadratic principal curvature are characterized in terms of the eigenvalues of R and J.
A Novel Quantitative Measure of Breast Curvature Based on Catenary
Lee, Juhun; Chen, Si; Reece, Gregory P.; Crosby, Melissa A.; Beahm, Elisabeth K.
2012-01-01
Quantitative, objective measurements of breast curvature computed from clinical photographs could be used to investigate factors that impact reconstruction and facilitate surgical planning. This paper introduces a novel quantitative measure of breast curvature based on catenary. A catenary curve is used to approximate the overall curvature of the breast contour, and the curvature measure is extracted from the catenary curve. The catenary curve was verified by comparing its length, the area enclosed by the curve, and the curvature measure from the catenary curve to those from manual tracings of the breast contour. The evaluation of the proposed analysis employed untreated and postoperative clinical photographs of women who were undergoing tissue expander/implant (TE/Implant) reconstruction. Logistic regression models were developed to distinguish between the curvature of breasts undergoing TE/Implant reconstruction and that of untreated breasts based on the curvature measure and patient variables (age and body mass index). The relationships between the curvature measures of untreated breasts and patient variables were also investigated. The catenary curve approximates breast curvature reliably. The curvature measure contains useful information for quantifying the curvature differences between breasts undergoing TE/Implant reconstruction and untreated breasts, and identifying the effect of patient variables on the breast shape. PMID:22271826
A novel quantitative measure of breast curvature based on catenary.
Lee, Juhun; Chen, Si; Reece, Gregory P; Crosby, Melissa A; Beahm, Elisabeth K; Markey, Mia K
2012-04-01
Quantitative, objective measurements of breast curvature computed from clinical photographs could be used to investigate factors that impact reconstruction and facilitate surgical planning. This paper introduces a novel quantitative measure of breast curvature based on catenary. A catenary curve is used to approximate the overall curvature of the breast contour, and the curvature measure is extracted from the catenary curve. The catenary curve was verified by comparing its length, the area enclosed by the curve, and the curvature measure from the catenary curve to those from manual tracings of the breast contour. The evaluation of the proposed analysis employed untreated and postoperative clinical photographs of women who were undergoing tissue expander/implant (TE/Implant) reconstruction. Logistic regression models were developed to distinguish between the curvature of breasts undergoing TE/Implant reconstruction and that of untreated breasts based on the curvature measure and patient variables (age and body mass index). The relationships between the curvature measures of untreated breasts and patient variables were also investigated. The catenary curve approximates breast curvature reliably. The curvature measure contains useful information for quantifying the curvature differences between breasts undergoing TE/Implant reconstruction and untreated breasts, and identifying the effect of patient variables on the breast shape.
Fiber Fabry-Perot interferometer for curvature sensing
NASA Astrophysics Data System (ADS)
Monteiro, Catarina S.; Ferreira, Marta S.; Silva, Susana O.; Kobelke, Jens; Schuster, Kay; Bierlich, Jörg; Frazão, Orlando
2016-12-01
A curvature sensor based on an Fabry-Perot (FP) interferometer was proposed. A capillary silica tube was fusion spliced between two single mode fibers, producing an FP cavity. Two FP sensors with different cavity lengths were developed and subjected to curvature and temperature. The FP sensor with longer cavity showed three distinct operating regions for the curvature measurement. Namely, a linear response was shown for an intermediate curvature radius range, presenting a maximum sensitivity of 68.52 pm/m-1. When subjected to temperature, the sensing head produced a similar response for different curvature radii, with a sensitivity varying from 0.84 pm/°C to 0.89 pm/°C, which resulted in a small cross-sensitivity to temperature when the FP sensor was subjected to curvature. The FP cavity with shorter length presented low sensitivity to curvature.
Curvature inducing macroion condensation driven shape changes of fluid vesicles.
Sreeja, K K; Ipsen, John H; Sunil Kumar, P B
2015-11-21
We study the effect of curvature inducing macroion condensation on the shapes of charged deformable fluid interfaces using dynamically triangulated Monte Carlo simulations. In the weak electrostatic coupling regime, surface charges are weakly screened and the conformations of a vesicle, with fixed spherical topology, depend on the charge-charge interaction on the surface. While in the strong coupling regime, condensation driven curvature induction plays a dominant role in determining the conformations of these surfaces. Condensation itself is observed to be dependent on the induced curvature, with larger induced curvatures favoring increased condensation. We show that both curvature generation and curvature sensing, induced by the interplay of electrostatics and curvature energy, contribute to determination of the vesicle configurations.
Optimal Spatial Scale for Curvature Calculations in Multiphase Flows
NASA Astrophysics Data System (ADS)
Senecal, Jacob; Owkes, Mark
2016-11-01
In gas-liquid flows, the surface tension force often controls the dynamics of the flow and an accurate calculation of this force is necessary for predictive simulations. The surface tension force is directly proportional to the curvature of the gas-liquid interface, making accurate curvature calculations an essential consideration. Multiple methods have been developed to calculate the curvature of volume of fluid (VoF) interface capturing schemes, such as the height function method. These methods have been extensively tested. However, the impact of the scale or size of computational stencil on which the curvature is computed, has not been correlated with the rate at which interface perturbations relax under the surface tension force. In this work, the effect of varying the scale on which the curvature is computed has been tested and quantified. An optimal curvature scale is identified that leads to accurate and converging curvatures, and accurate timescales for surface tension induced, interface dynamics.
Lipid Geometry and Bilayer Curvature Modulate LC3/GABARAP-Mediated Model Autophagosomal Elongation
Landajuela, Ane; Hervás, Javier H.; Antón, Zuriñe; Montes, L. Ruth; Gil, David; Valle, Mikel; Rodriguez, J. Francisco; Goñi, Felix M.; Alonso, Alicia
2016-01-01
Autophagy, an important catabolic pathway involved in a broad spectrum of human diseases, implies the formation of double-membrane-bound structures called autophagosomes (AP), which engulf material to be degraded in lytic compartments. How APs form, especially how the membrane expands and eventually closes upon itself, is an area of intense research. Ubiquitin-like ATG8 has been related to both membrane expansion and membrane fusion, but the underlying molecular mechanisms are poorly understood. Here, we used two minimal reconstituted systems (enzymatic and chemical conjugation) to compare the ability of human ATG8 homologs (LC3, GABARAP, and GATE-16) to mediate membrane fusion. We found that both enzymatically and chemically lipidated forms of GATE-16 and GABARAP proteins promote extensive membrane tethering and fusion, whereas lipidated LC3 does so to a much lesser extent. Moreover, we characterize the GATE-16/GABARAP-mediated membrane fusion as a phenomenon of full membrane fusion, independently demonstrating vesicle aggregation, intervesicular lipid mixing, and intervesicular mixing of aqueous content, in the absence of vesicular content leakage. Multiple fusion events give rise to large vesicles, as seen by cryo-electron microscopy observations. We also show that both vesicle diameter and selected curvature-inducing lipids (cardiolipin, diacylglycerol, and lyso-phosphatidylcholine) can modulate the fusion process, smaller vesicle diameters and negative intrinsic curvature lipids (cardiolipin, diacylglycerol) facilitating fusion. These results strongly support the hypothesis of a highly bent structural fusion intermediate (stalk) during AP biogenesis and add to the growing body of evidence that identifies lipids as important regulators of autophagy. PMID:26789764
Membrane tension and peripheral protein density mediate membrane shape transitions
NASA Astrophysics Data System (ADS)
Shi, Zheng; Baumgart, Tobias
2015-01-01
Endocytosis is a ubiquitous eukaryotic membrane budding, vesiculation and internalization process fulfilling numerous roles including compensation of membrane area increase after bursts of exocytosis. The mechanism of the coupling between these two processes to enable homeostasis is not well understood. Recently, an ultrafast endocytosis (UFE) pathway was revealed with a speed significantly exceeding classical clathrin-mediated endocytosis (CME). Membrane tension reduction is a potential mechanism by which endocytosis can be rapidly activated at remote sites. Here, we provide experimental evidence for a mechanism whereby membrane tension reduction initiates membrane budding and tubulation mediated by endocytic proteins, such as endophilin A1. We find that shape instabilities occur at well-defined membrane tensions and surface densities of endophilin. From our data, we obtain a membrane shape stability diagram that shows remarkable consistency with a quantitative model. This model applies to all laterally diffusive curvature-coupling proteins and therefore a wide range of endocytic proteins.
Lokar, Maruša; Kabaso, Doron; Resnik, Nataša; Sepčić, Kristina; Kralj-Iglič, Veronika; Veranič, Peter; Zorec, Robert; Iglič, Aleš
2012-01-01
Intercellular membrane nanotubes (ICNs) are highly curved tubular structures that connect neighboring cells. The stability of these structures depends on the inner cytoskeleton and the cell membrane composition. Yet, due to the difficulty in the extraction of ICNs, the cell membrane composition remains elusive. In the present study, a raft marker, ostreolysin, revealed the enrichment of cholesterol-sphingomyelin membrane nanodomains along ICNs in a T24 (malignant) urothelial cancer cell line. Cholesterol depletion, due to the addition of methyl-β-cyclodextrin, caused the dispersion of cholesterol-sphingomyelin membrane nanodomains and the retraction of ICNs. The depletion of cholesterol also led to cytoskeleton reorganization and to formation of actin stress fibers. Live cell imaging data revealed the possible functional coupling between the change from polygonal to spherical shape, cell separation, and the disconnection of ICNs. The ICN was modeled as an axisymmetric tubular structure, enabling us to investigate the effects of cholesterol content on the ICN curvature. The removal of cholesterol was predicted to reduce the positive spontaneous curvature of the remaining membrane components, increasing their curvature mismatch with the tube curvature. The mechanisms by which the increased curvature mismatch could contribute to the disconnection of ICNs are discussed. PMID:22605937
FtsZ Protofilament Curvature Is the Opposite of Tubulin Rings.
Housman, Max; Milam, Sara L; Moore, Desmond A; Osawa, Masaki; Erickson, Harold P
2016-07-26
FtsZ protofilaments (pfs) form the bacterial cytokinetic Z ring. Previous work suggested that a conformational change from straight to curved pfs generated the constriction force. In the simplest model, the C-terminal membrane tether is on the outside of the curved pf, facing the membrane. Tubulin, a homologue of FtsZ, also forms pfs with a curved conformation. However, it is well-established that tubulin rings have the C terminus on the inside of the ring. Could FtsZ and tubulin rings have the opposite curvature? In this study, we explored the FtsZ curvature direction by fusing large protein tags to the FtsZ termini. Thin section electron microscopy showed that the C-terminal tag was on the outside, consistent with the bending pf model. This has interesting implications for the evolution of tubulin. Tubulin likely began with the curvature of FtsZ, but evolution managed to reverse direction to produce outward-curving rings, which are useful for pulling chromosomes.
Sehgal, Rakesh; Brinker, Charles Jeffrey
1998-01-01
Supported inorganic membranes capable of molecular sieving, and methods for their production, are provided. The subject membranes exhibit high flux and high selectivity. The subject membranes are substantially defect free and less than about 100 nm thick. The pores of the subject membranes have an average critical pore radius of less than about 5 .ANG., and have a narrow pore size distribution. The subject membranes are prepared by coating a porous substrate with a polymeric sol, preferably under conditions of low relative pressure of the liquid constituents of the sol. The coated substrate is dried and calcined to produce the subject supported membrane. Also provided are methods of derivatizing the surface of supported inorganic membranes with metal alkoxides. The subject membranes find use in a variety of applications, such as the separation of constituents of gaseous streams, as catalysts and catalyst supports, and the like.
Amplification of curvature perturbations in cyclic cosmology
NASA Astrophysics Data System (ADS)
Zhang, Jun; Liu, Zhi-Guo; Piao, Yun-Song
2010-12-01
We analytically and numerically show that through the cycles with nonsingular bounce, the amplitude of curvature perturbation on a large scale will be amplified and the power spectrum will redden. In some sense, this amplification will eventually destroy the homogeneity of the background, which will lead to the ultimate end of cycles of the global universe. We argue that for the model with increasing cycles, it might be possible that a fissiparous multiverse will emerge after one or several cycles, in which the cycles will continue only at corresponding local regions.
Solitons in curved space of constant curvature
Batz, Sascha; Peschel, Ulf
2010-05-15
We consider spatial solitons as, for example, self-confined optical beams in spaces of constant curvature, which are a natural generalization of flat space. Due to the symmetries of these spaces we are able to define respective dynamical parameters, for example, velocity and position. For positively curved space we find stable multiple-hump solitons as a continuation from the linear modes. In the case of negatively curved space we show that no localized solution exists and a bright soliton will always decay through a nonlinear tunneling process.
Zero curvature-surface driven small objects
NASA Astrophysics Data System (ADS)
Dou, Xiaoxiao; Li, Shanpeng; Liu, Jianlin
2017-08-01
In this study, we investigate the spontaneous migration of small objects driven by surface tension on a catenoid, formed by a layer of soap constrained by two rings. Although the average curvature of the catenoid is zero at each point, the small objects always migrate to the position near the ring. The force and energy analyses have been performed to uncover the mechanism, and it is found that the small objects distort the local shape of the liquid film, thus making the whole system energetically favorable. These findings provide some inspiration to design microfluidics, aquatic robotics, and miniature boats.
Double curvature mirrors for linear concentrators
NASA Astrophysics Data System (ADS)
Lance, Tamir; Ackler, Harold; Finot, Marc
2012-10-01
Skyline Solar's medium concentration photovoltaic system uses quasi-parabolic mirrors and one axis tracking. Improvements in levelized cost of energy can be achieved by effective management of non-uniformity of the flux line on the panels. To reduce non uniformity of the flux line due to mirror to mirror gaps, Skyline developed a dual curvature mirror that stretches the flux line along the panel. Extensive modeling and experiments have been conducted to analyze the impact of this new design and to optimize the design.
Steering electromagnetic beams with conical curvature singularities.
Zhang, Yong-Liang; Dong, Xian-Zi; Zheng, Mei-Ling; Zhao, Zhen-Sheng; Duan, Xuan-Ming
2015-10-15
We describe how the transformation-optics technique can be used to design an effective medium mimicking the conical curvature singularity. Anholonomic coordinate transformation gives rise to linear topological defects that break the rotational symmetry. The bending and splitting of the optical beams are found analytically and numerically, depending on the incident direction and the topological charge. Beyond their practical applications to omnidirectional beam steering for photonics, our findings set forth an attractive realm to simulate the relevant physical phenomena in the optical laboratory.
Amplification of curvature perturbations in cyclic cosmology
Zhang Jun; Liu Zhiguo; Piao Yunsong
2010-12-15
We analytically and numerically show that through the cycles with nonsingular bounce, the amplitude of curvature perturbation on a large scale will be amplified and the power spectrum will redden. In some sense, this amplification will eventually destroy the homogeneity of the background, which will lead to the ultimate end of cycles of the global universe. We argue that for the model with increasing cycles, it might be possible that a fissiparous multiverse will emerge after one or several cycles, in which the cycles will continue only at corresponding local regions.
Curvature sensor for ocular wavefront measurement.
Díaz-Doutón, Fernando; Pujol, Jaume; Arjona, Montserrat; Luque, Sergio O
2006-08-01
We describe a new wavefront sensor for ocular aberration determination, based on the curvature sensing principle, which adapts the classical system used in astronomy for the living eye's measurements. The actual experimental setup is presented and designed following a process guided by computer simulations to adjust the design parameters for optimal performance. We present results for artificial and real young eyes, compared with the Hartmann-Shack estimations. Both methods show a similar performance for these cases. This system will allow for the measurement of higher order aberrations than the currently used wavefront sensors in situations in which they are supposed to be significant, such as postsurgery eyes.
Spacetime Curvature and Higgs Stability after Inflation.
Herranen, M; Markkanen, T; Nurmi, S; Rajantie, A
2015-12-11
We investigate the dynamics of the Higgs field at the end of inflation in the minimal scenario consisting of an inflaton field coupled to the standard model only through the nonminimal gravitational coupling ξ of the Higgs field. Such a coupling is required by renormalization of the standard model in curved space, and in the current scenario also by vacuum stability during high-scale inflation. We find that for ξ≳1, rapidly changing spacetime curvature at the end of inflation leads to significant production of Higgs particles, potentially triggering a transition to a negative-energy Planck scale vacuum state and causing an immediate collapse of the Universe.
Mechanical model for fiber-laden membranes
NASA Astrophysics Data System (ADS)
Rey, Alejandro D.; Murugesan, Yogesh K.
2011-01-01
An integrated mechanical model for fiber-laden membranes is presented and representative predictions of relevance to cellulose ordering and orientation in the plant cell wall are presented. The model describes nematic liquid crystalline self-assembly of rigid fibers on an arbitrarily curved fluid membrane. The mechanics of the fluid membrane is described by the Helfrich bending-torsion model, the fiber self-assembly is described by the 2D Landau-de Gennes quadrupolar Q-tensor order parameter model, and the fiber-membrane interactions (inspired by an extension of the 2D Maier-Saupe model to curved surfaces) include competing curvo-philic (curvature-seeking) and curvo-phobic (curvature-avoiding) effects. Analysis of the free energy reveals three fiber orientation regimes: (a) along the major curvature, (b) along the minor curvature, (c) away from the principal curvatures, according to the competing curvo-philic and curvo-phobic interactions. The derived shape equation (normal stress balance) now includes curvature-nematic ordering contributions, with both bending and torsion renormalizations. Integration of the shape and nematic order equations gives a complete model whose solution describes the coupled membrane shape/fiber order state. Applications to cylindrical membranes, relevant to the plant cell wall, shows how growth decreases the fiber order parameter and moves the fibers' director from the axial direction towards the azimuthal orientation, eventually leading to a state of stress predicted by pure membranes. The ubiquitous 54.7° cellulose fibril orientation with respect to the long axis in a cylindrical plant cell wall is shown to be predicted by the preset model when the ratio of curvo-phobic and curvo-philic interactions is in the range of the cylinder radius.
Pearling instabilities of membrane tubes with anchored polymers.
Tsafrir, I; Sagi, D; Arzi, T; Guedeau-Boudeville, M A; Frette, V; Kandel, D; Stavans, J
2001-02-05
We have studied the pearling instability induced on hollow tubular lipid vesicles by hydrophilic polymers with hydrophobic side groups along the backbone. The results show that the polymer concentration is coupled to local membrane curvature. The relaxation of a pearled tube is characterized by two different well-separated time scales, indicating two physical mechanisms. We present a model, which explains the observed phenomena and predicts polymer segregation according to local membrane curvature at late stages.
Interaction between bending and tension forces in bilayer membranes.
Secomb, T W
1988-01-01
A theoretical analysis is presented of the bending mechanics of a membrane consisting of two tightly-coupled leaflets, each of which shears and bends readily but strongly resists area changes. Structures of this type have been proposed to model biological membranes such as red blood cell membrane. It is shown that when such a membrane is bent, anisotropic components of resultant membrane tension (shear stresses) are induced, even when the tension in each leaflet is isotropic. The induced shear stresses increase as the square of the membrane curvature, and become significant for moderate curvatures (when the radius of curvature is much larger than the distance between the leaflets). This effect has implications for the analysis of shape and deformation of freely suspended and flowing red blood cells. PMID:3224154
The effect of a small initial curvature on the free vibration of clamped, rectangular plates
NASA Technical Reports Server (NTRS)
Adeniji-Fashola, A. A.; Oyediran, A. A.
1986-01-01
An analytical method of obtaining the natural frequencies and mode shapes of clamped, rectangular plates having a small initial curvature is presented. Specifically, the singular perturbation technique is used to reduce the fourth-order plate vibration problem to the simpler membrane problem with modified boundary conditions that account for the bending effects. The eigenfrequencies for plates with inverse aspect ratios varying between 0.1 and 1.0 and for the dimensionless normal prestress between 0.1 and 1.0 have been presented for values of epsilon, the normalized bending rigidity, ranging between 0.0010 and 0.2500. It is established that a small initial curvature has no effect on the frequency of vibration of the plate. However, its effect is manifested in the eigenmodes.
Isogrid Membranes for Precise, Singly Curved Reflectors
NASA Technical Reports Server (NTRS)
Fang, Houfei; Lou, Michael
2005-01-01
A new type of composite material has been proposed for membranes that would constitute the reflective surfaces of planned lightweight, single-curvature (e.g., parabolic cylindrical) reflectors for some radar and radio-communication systems. The proposed composite materials would consist of polyimide membranes containing embedded grids of highstrength (e.g., carbon) fibers. The purpose of the fiber reinforcements, as explained in more detail below, is to prevent wrinkling or rippling of the membrane.
NASA Astrophysics Data System (ADS)
Iori, F.; Grechy, L.; Corbett, R. W.; Gedroyc, W.; Duncan, N.; Caro, C. G.; Vincent, P. E.
2015-03-01
Arterio-Venous Fistulae (AVF) are the preferred method of vascular access for patients with end stage renal disease who need hemodialysis. In this study, simulations of blood flow and oxygen transport were undertaken in various idealized AVF configurations. The objective of the study was to understand how arterial curvature affects blood flow and oxygen transport patterns within AVF, with a focus on how curvature alters metrics known to correlate with vascular pathology such as Intimal Hyperplasia (IH). If one subscribes to the hypothesis that unsteady flow causes IH within AVF, then the results suggest that in order to avoid IH, AVF should be formed via a vein graft onto the outer-curvature of a curved artery. However, if one subscribes to the hypothesis that low wall shear stress and/or low lumen-to-wall oxygen flux (leading to wall hypoxia) cause IH within AVF, then the results suggest that in order to avoid IH, AVF should be formed via a vein graft onto a straight artery, or the inner-curvature of a curved artery. We note that the recommendations are incompatible—highlighting the importance of ascertaining the exact mechanisms underlying development of IH in AVF. Nonetheless, the results clearly illustrate the important role played by arterial curvature in determining AVF hemodynamics, which to our knowledge has been overlooked in all previous studies.
ODE/PDE analysis of corneal curvature.
Płociniczak, Lukasz; Griffiths, Graham W; Schiesser, William E
2014-10-01
The starting point for this paper is a nonlinear, two-point boundary value ordinary differential equation (BVODE) that defines corneal curvature according to a static force balance. A numerical solution to the BVODE is computed by first converting the BVODE to a parabolic partial differential equation (PDE) by adding an initial value (t, pseudo-time) derivative to the BVODE. A numerical solution to the PDE is then computed by the method of lines (MOL) with the calculation proceeding to a sufficiently large value of t such that the derivative in t reduces to essentially zero. The PDE solution at this point is also the solution for the BVODE. This procedure is implemented in R (an open source scientific programming system) and the programming is discussed in some detail. A series approximation to the solution is derived from which an estimate for the rate of convergence is obtained. This is compared to a fitted exponential model. Also, two linear approximations are derived, one of which leads to a closed form solution. Both provide solutions very close to that obtained from the full nonlinear model. An estimate for the cornea radius of curvature is also derived. The paper concludes with a discussion of the features of the solution to the ODE/PDE system.
Brane Localized Curvature for Warped Gravitons
Rizzo, Thomas G.
2003-06-26
We study the effects of including brane localized curvature terms in the Randall-Sundrum (RS) model of the hierarchy. This leads to the existence of brane localized kinetic terms for the graviton. Such terms can be induced by brane and bulk quantum effects as well as Higgs-curvature mixing on the brane. We derive the modified spectrum of Kaluza-Klein (KK) gravitons and their couplings to 4-dimensional fields in the presence of these terms. We find that the masses and couplings of the KK gravitons have considerable dependence on the size of the brane localized terms; the weak-scale phenomenology of the model is consequently modified . In particular, the weak-scale spin-2 graviton resonances which generically appear in the RS model may be significantly lighter than previously assumed. However, they may avoid detection as their widths may be too narrow to be observable at colliders. In the contact interaction limit, for a certain range of parameters, the experimental reach for the scale of the theory is independent of the size of the boundary terms.
Kinetic information from detonation front curvature
Souers, P. C., LLNL
1998-06-15
The time constants for time-dependent modeling may be estimated from reaction zone lengths, which are obtained from two sources One is detonation front curvature, where the edge lag is close to being a direct measure The other is the Size Effect, where the detonation velocity decreases with decreasing radius as energy is lost to the cylinder edge A simple theory that interlocks the two effects is given A differential equation for energy flow in the front is used, the front is described by quadratic and sixth-power radius terms The quadratic curvature comes from a constant power source of energy moving sideways to the walls Near the walls, the this energy rises to the total energy of detonation and produces the sixth-power term The presence of defects acting on a short reaction zone can eliminate the quadratic part while leaving the wall portion of the cuvature A collection of TNT data shows that the reaction zone increases with both the radius and the void fraction
Effects of streamline curvature on separation prediction
NASA Astrophysics Data System (ADS)
Arolla, Sunil K.; Durbin, Paul A.
2009-11-01
In this study, the effects of streamline curvature on prediction of flow separation are investigated. The geometry is a circulation control airfoil, a high-lift configuration that has been under extensive research for more than two decades. A tangential jet is blown over a thick, rounded trailing edge, using the Coanda effect to delay separation. An attempt is made to understand, through numerical simulations, the dynamics of turbulent separation and reattachment on the Coanda surface. Highly curved, attached recirculation regions are seen to form. A physics based curvature correction proposed by Pettersson-Reif et al. (1999) is used in conjunction with ζ-f turbulence model. The chord-based Reynolds number is Re = 10^6. Two jet momentum coefficients of Cμ=0.03 and 0.1 are computed. In this paper, comparisons between the computed and experimental pressure distributions, velocity profiles and the position of flow detachment are presented. Comparisons with other closures such as Menter's SST model are also discussed.
Detonation Front Curvatures and Detonation Rates
NASA Astrophysics Data System (ADS)
Lauderbach, Lisa M.; Lorenz, K. Thomas; Lee, Edward L.; Souers, P. Clark
2015-06-01
We have normalized the LLNL library of detonation front curvatures by dividing lags by the edge lag and radii by the edge radius. We then fit the normalized data to the equation L = AR2 + BR8, where L is the normalized lag and R is the normalized radius. We attribute the quadratic term to thermal processes and the 8th-power term to shock processes. We compare the % of the quadratic term J at the edge with detonation rates obtained from the size effect. One class of results is made up of fine-grained, uniform explosives with large lags, where a low detonation rate leads to a high J and vice versa. This provides a rough way of estimating unknown rates if the unknown explosive is of high quality. The other, equally-large class contains rough-grained materials, often with small lags and small radii. These have curves that do not fit the equation but superfically often look quadratic. Some HMX and PETN curvatures even show a ``sombrero'' effect. Code models show that density differences of 0.03 g/cc in ram-pressed parts can cause pseudo-quadratic curves and even sombreros. Modeling is used to illustrate J at the lowest and highest possible detonation rates. This work performed under the auspices of the U. S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Vortex motion on surfaces of small curvature
Dorigoni, Daniele Dunajski, Maciej Manton, Nicholas S.
2013-12-15
We consider a single Abelian Higgs vortex on a surface Σ whose Gaussian curvature K is small relative to the size of the vortex, and analyse vortex motion by using geodesics on the moduli space of static solutions. The moduli space is Σ with a modified metric, and we propose that this metric has a universal expansion, in terms of K and its derivatives, around the initial metric on Σ. Using an integral expression for the Kähler potential on the moduli space, we calculate the leading coefficients of this expansion numerically, and find some evidence for their universality. The expansion agrees to first order with the metric resulting from the Ricci flow starting from the initial metric on Σ, but differs at higher order. We compare the vortex motion with the motion of a point particle along geodesics of Σ. Relative to a particle geodesic, the vortex experiences an additional force, which to leading order is proportional to the gradient of K. This force is analogous to the self-force on bodies of finite size that occurs in gravitational motion. -- Highlights: •We study an Abelian Higgs vortex on a surface with small curvature. •A universal expansion for the moduli space metric is proposed. •We numerically check the universality at low orders. •Vortex motion differs from point particle motion because a vortex has a finite size. •Moduli space geometry has similarities with the geometry arising from Ricci flow.
Emergent gravity in spaces of constant curvature
NASA Astrophysics Data System (ADS)
Alvarez, Orlando; Haddad, Matthew
2017-03-01
In physical theories where the energy (action) is localized near a submanifold of a constant curvature space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite number of terms, and depends on intrinsic geometric invariants of the submanifold and extrinsic invariants of the embedding of the submanifold. This is the second of a pair of articles in which we try to develop a theory of emergent gravity arising from the embedding of a submanifold into an ambient space equipped with a quantum field theory. Our theoretical method requires a generalization of a formula due to by Hermann Weyl. While the first paper discussed the framework in Euclidean (Minkowski) space, here we discuss how this framework generalizes to spaces of constant sectional curvature. We focus primarily on anti de Sitter space. We then discuss how such a theory can give rise to a cosmological constant and Planck mass that are within reasonable bounds of the experimental values.
Curvature Filters Efficiently Reduce Certain Variational Energies.
Gong, Yuanhao; Sbalzarini, Ivo F
2017-04-01
In image processing, the rapid approximate solution of variational problems involving generic data-fitting terms is often of practical relevance, for example in real-time applications. Variational solvers based on diffusion schemes or the Euler-Lagrange equations are too slow and restricted in the types of data-fitting terms. Here, we present a filter-based approach to reduce variational energies that contain generic data-fitting terms, but are restricted to specific regularizations. Our approach is based on reducing the regularization part of the variational energy, while guaranteeing non-increasing total energy. This is applicable to regularization-dominated models, where the data-fitting energy initially increases, while the regularization energy initially decreases. We present fast discrete filters for regularizers based on Gaussian curvature, mean curvature, and total variation. These pixel-local filters can be used to rapidly reduce the energy of the full model. We prove the convergence of the resulting iterative scheme in a greedy sense, and we show several experiments to demonstrate applications in image-processing problems involving regularization-dominated variational models.
Brokaw, C J
1985-01-01
Computer simulation is used to examine a simple flagellar model that will initiate and propagate bending waves in the absence of viscous resistances. The model contains only an elastic bending resistance and an active sliding mechanism that generates reduced active shear moment with increasing sliding velocity. Oscillation results from a distributed control mechanism that reverses the direction of operation of the active sliding mechanism when the curvature reaches critical magnitudes in either direction. Bend propagation by curvature-controlled flagellar models therefore does not require interaction with the viscous resistance of an external fluid. An analytical examination of moment balance during bend propagation by this model yields a solution curve giving values of frequency and wavelength that satisfy the moment balance equation and give uniform bend propagation, suggesting that the model is underdetermined. At 0 viscosity, the boundary condition of 0 shear rate at the basal end of the flagellum during the development of new bends selects the particular solution that is obtained by computer simulations. Therefore, the details of the pattern of bend initiation at the basal end of a flagellum can be of major significance in determining the properties of propagated bending waves in the distal portion of a flagellum. At high values of external viscosity, the model oscillates at frequencies and wavelengths that give approximately integral numbers of waves on the flagellum. These operating points are selected because they facilitate the balance of bending moments at the ends of the model, where the external viscous moment approaches 0. These mode preferences can be overridden by forcing the model to operate at a predetermined frequency. The strong mode preferences shown by curvature-controlled flagellar models, in contrast to the weak or absent mode preferences shown by real flagella, therefore do not demonstrate the inapplicability of the moment-balance approach
Crystallizing Membrane Proteins in Lipidic Mesophases. A Host Lipid Screen
Li, Dianfan; Lee, Jean; Caffrey, Martin
2011-01-01
The default lipid for the bulk of the crystallogenesis studies performed to date using the cubic mesophase method is monoolein. There is no good reason however, why this 18-carbon, cis-monounsaturated monoacylglycerol should be the preferred lipid for all target membrane proteins. The latter come from an array of biomembrane types with varying properties that include hydrophobic thickness, intrinsic curvature, lateral pressure profile, lipid and protein makeup, and compositional asymmetry. Thus, it seems reasonable that screening for crystallizability based on the identity of the lipid creating the hosting mesophase would be worthwhile. For this, monoacylglycerols with differing acyl chain characteristics, such as length and olefinic bond position, must be available. A lipid synthesis and purification program is in place in the author's laboratory to serve this need. In the current study with the outer membrane sugar transporter, OprB, we demonstrate the utility of host lipid screening as a means for generating diffraction-quality crystals. Host lipid screening is likely to prove a generally useful strategy for mesophase-based crystallization of membrane proteins. PMID:21743796
Crystallizing Membrane Proteins in Lipidic Mesophases. A Host Lipid Screen
Li, Dianfan; Lee, Jean; Caffrey, Martin
2011-11-30
The default lipid for the bulk of the crystallogenesis studies performed to date using the cubic mesophase method is monoolein. There is no good reason, however, why this 18-carbon, cis-monounsaturated monoacylglycerol should be the preferred lipid for all target membrane proteins. The latter come from an array of biomembrane types with varying properties that include hydrophobic thickness, intrinsic curvature, lateral pressure profile, lipid and protein makeup, and compositional asymmetry. Thus, it seems reasonable that screening for crystallizability based on the identity of the lipid creating the hosting mesophase would be worthwhile. For this, monoacylglycerols with differing acyl chain characteristics, such as length and olefinic bond position, must be available. A lipid synthesis and purification program is in place in the author's laboratory to serve this need. In the current study with the outer membrane sugar transporter, OprB, we demonstrate the utility of host lipid screening as a means for generating diffraction-quality crystals. Host lipid screening is likely to prove a generally useful strategy for mesophase-based crystallization of membrane proteins.
Engineering curvature in graphene ribbons using ultrathin polymer films.
Li, Chunyu; Koslowski, Marisol; Strachan, Alejandro
2014-12-10
We propose a method to induce curvature in graphene nanoribbons in a controlled manner using an ultrathin thermoset polymer in a bimaterial strip setup and test it via molecular dynamics (MD) simulations. Continuum mechanics shows that curvature develops to release the residual stress caused by the chemical and thermal shrinkage of the polymer during processing and that this curvature increases with decreasing film thickness; however, significant deformation is only achieved for ultrathin polymer films. Quite surprisingly, explicit MD simulations of the curing and annealing processes show that the predicted trend not just continues down to film thicknesses of 1-2 nm but that the curvature development is enhanced significantly in such ultrathin films due to surface tension effects. This combination of effects leads to very large curvatures of over 0.14 nm(-1) that can be tuned via film thickness. This provides a new avenue to engineer curvature and, thus, electromagnetic properties of graphene.
Asymptotic behavior of curvature of surface elements in isotropic turbulence
NASA Technical Reports Server (NTRS)
Girimaji, S. S.
1991-01-01
The asymptotic behavior of the curvature of material elements in turbulence is investigated using Lagrangian velocity-gradient time series obtained from direct numerical simulations of isotropic turbulence. Several material-element ensembles of different initial curvatures and shapes are studied. It is found that, at long times, the (first five) moments of the logarithm of characteristic curvature and shape factor asymptote to values that are independent of the initial curvature or shape. This evidence strongly suggests that the asymptotic pdf's of the curvature and shape of material elements are stationary and independent of initial conditions. Irrespective of initial curvature or shape, the asymptotic shape of a material surface is cylindrical with a high probability.
Curvature and Tangency Handles for Control of Convex Cubic Shapes
2000-01-01
looked at A-splines constructed with segments of singular al- gebraic cubics, which are just rational cubics, with new, geometrically more meaningful...contact interpolation , and curvatures at three prescribed points, see Figures 1-4. Curve and Surface Design: Saint-Malo 1999 91 Pierre-Jean Laurent...curvature at one contact point. §2. Barycentric Coordinates and Curvature at the Endpoints The general algebraic cubic in cartesian coordinates x, y is
The curvature measurement of Sagnac loop based on PMF
NASA Astrophysics Data System (ADS)
Zhao, Yu; Jin, Yongxing; Gong, Huaping; Wang, Jianfeng
2010-12-01
An optical fiber curvature sensor is fabricated by using a short section of polarization maintaining fiber (PMF) as the sensing component spliced in an optical fiber Sagnac loop. The length of the sensing element for the curvature sensing is about 142 mm. The sensitivity of the curvature measurement of 0.0344 m-1/pm is achieved experimentally. The propose sensor is more convenient and simply than that of photonic crystal fiber (PCF).
Wrinkles and splay conspire to give positive disclinations negative curvature
Matsumoto, Elisabetta A.; Vega, Daniel A.; Pezzutti, Aldo D.; García, Nicolás A.; Chaikin, Paul M.; Register, Richard A.
2015-01-01
Recently, there has been renewed interest in the coupling between geometry and topological defects in crystalline and striped systems. Standard lore dictates that positive disclinations are associated with positive Gaussian curvature, whereas negative disclinations give rise to negative curvature. Here, we present a diblock copolymer system exhibiting a striped columnar phase that preferentially forms wrinkles perpendicular to the underlying stripes. In free-standing films this wrinkling behavior induces negative Gaussian curvature to form in the vicinity of positive disclinations. PMID:26420873
Radius of Curvature of Off-Axis Paraboloids
NASA Technical Reports Server (NTRS)
Robinson, Brian; Reardon, Patrick; Hadaway, James; Geary, Joseph; Russell, Kevin (Technical Monitor)
2002-01-01
We present several methods for measuring the vertex radius of curvature of off-axis paraboloidal mirrors. One is based on least-squares fitting of interferometer output, one on comparison of sagittal and tangential radii of curvature, and another on measurement of displacement of the nulled test article from the ideal reference wave. Each method defines radius of curvature differently and, as a consequence, produces its own sort of errors.
Membrane fission by protein crowding.
Snead, Wilton T; Hayden, Carl C; Gadok, Avinash K; Zhao, Chi; Lafer, Eileen M; Rangamani, Padmini; Stachowiak, Jeanne C
2017-04-18
Membrane fission, which facilitates compartmentalization of biological processes into discrete, membrane-bound volumes, is essential for cellular life. Proteins with specific structural features including constricting rings, helical scaffolds, and hydrophobic membrane insertions are thought to be the primary drivers of fission. In contrast, here we report a mechanism of fission that is independent of protein structure-steric pressure among membrane-bound proteins. In particular, random collisions among crowded proteins generate substantial pressure, which if unbalanced on the opposite membrane surface can dramatically increase membrane curvature, leading to fission. Using the endocytic protein epsin1 N-terminal homology domain (ENTH), previously thought to drive fission by hydrophobic insertion, our results show that membrane coverage correlates equally with fission regardless of the hydrophobicity of insertions. Specifically, combining FRET-based measurements of membrane coverage with multiple, independent measurements of membrane vesiculation revealed that fission became spontaneous as steric pressure increased. Further, fission efficiency remained equally potent when helices were replaced by synthetic membrane-binding motifs. These data challenge the view that hydrophobic insertions drive membrane fission, suggesting instead that the role of insertions is to anchor proteins strongly to membrane surfaces, amplifying steric pressure. In line with these conclusions, even green fluorescent protein (GFP) was able to drive fission efficiently when bound to the membrane at high coverage. Our conclusions are further strengthened by the finding that intrinsically disordered proteins, which have large hydrodynamic radii yet lack a defined structure, drove fission with substantially greater potency than smaller, structured proteins.
A Direct Estimate of the Spatial Curvature of the Universe
NASA Astrophysics Data System (ADS)
Rosquist, Kjell; Samuelsson, Lars
The main idea of this contribution is to calculate the average spatial curvature directly from the observed mass distribution of the universe. In short, our philosophy is that the curvature of the universe is generated solely by the matter it contains. Although this may seem as self-evident in the context of general relativity, the usual practice in cosmology is rather to use a top-down approach in which the curvature is calculated indirectly using a prescribed matter distribution as a source of the Einstein equations. By contrast, our approach may be seen as part of a bottom-up approach. In practical terms, we first calculate the far field spatial curvature generated by an isolated matter distribution which is in arbitrary motion. At this stage we obtain the result that the sign of the spatial curvature is necessarily positive. For the spatial curvature generated by multiple sources we show that it is sufficient to use linearized theory to compute the leading contributions. In the matter dominated era the spatial curvature is then seen to be generated by local sources at small redshifts. This fact makes it possible to calculate the total spatial curvature just by summing up the contributions from the observed discrete mass distribution. A crude estimate gives a very small value for the curvature.
Fringes of equal tangential inclination by curvature-induced birefringence
NASA Astrophysics Data System (ADS)
Medhat, M.; Hendawy, N. I.; Zaki, A. A.
2003-02-01
A new kind of interference fringes, fringes of equal tangential inclination by curvature-induced birefringence, is presented. These are two-beam interference fringes produced by bending a thin sheet of birefringent material into a part of an exact cylinder such that the curvature is constant. Due to this curvature there is a uniform birefringence being induced. The change in birefringence induced by applying different radii of curvatures to a Fortepan sheet is measured. The stored (fixed) or natural birefringence of this sheet is deduced.
Plane wave gravitons, curvature singularities and string physics
Brooks, R. . Center for Theoretical Physics)
1991-03-21
This paper discusses bounded (compactifying) potentials arising from a conspiracy between plane wave graviton and dilaton condensates. So are string propagation and supersymmetry in spacetimes with curvature singularities.
Evolving extrinsic curvature and the cosmological constant problem
NASA Astrophysics Data System (ADS)
Capistrano, Abraão J. S.; Cabral, Luis A.
2016-10-01
The concept of smooth deformation of Riemannian manifolds associated with the extrinsic curvature is explained and applied to the Friedmann-Lemaître-Robertson-Walker cosmology. We show that such deformation can be derived from the Einstein-Hilbert-like dynamical principle may produce an observable effect in the sense of Noether. As a result, we show how the extrinsic curvature compensates both quantitative and qualitative differences between the cosmological constant Λ and the vacuum energy {ρ }{vac} obtaining the observed upper bound for the cosmological constant problem at electroweak scale. The topological characteristics of the extrinsic curvature are discussed showing that the produced extrinsic scalar curvature is an evolving dynamical quantity.
Evolution of the curvature perturbations during warm inflation
NASA Astrophysics Data System (ADS)
Matsuda, Tomohiro
2009-06-01
This paper considers warm inflation as an interesting application of multi-field inflation. Delta-N formalism is used for the calculation of the evolution of the curvature perturbations during warm inflation. Although the perturbations considered in this paper are decaying after the horizon exit, the corrections to the curvature perturbations sourced by these perturbations can remain and dominate the curvature perturbations at large scales. In addition to the typical evolution of the curvature perturbations, inhomogeneous diffusion rate is considered for warm inflation, which may lead to significant non-Gaussianity of the spectrum.
Inconsistency of scale invariant curvature coupled to gravity
Zoller, D.
1990-01-01
We show that the scale invariant curvature action for paths, the point particle version of Polyakov's extrinsic curvature action for surfaces, does not couple consistently to gravity. Although the curvature action for paths yields a massless representation of the Poincare group with fixed helicity and so potentially provides a description of single photons and gravitons, the inconsistent coupling to gravity apparently suggests such a description is not viable. We present a physical interpretation of the inconsistency in terms of the non-localizability of the photon and point out a conceptual kinship between the local symmetry of the curvature theory and the local supersymmetry of a spinning particle or spinning string. 11 refs.
The curvature index and synchronization of dynamical systems.
Chen, Yen-Sheng; Chang, Chien-Cheng
2012-06-01
We develop a quantity, named the curvature index, for dynamical systems. This index is defined as the limit of the average curvature of the trajectory during evolution, which measures the bending of the curve on an attractor. The curvature index has the ability to differentiate the topological change of an attractor, as its alterations exhibit the structural changes of a dynamical system. Thus, the curvature index may indicate thresholds of some synchronization regimes. The Rössler system and a time-delay system are simulated to demonstrate the effectiveness of the index, respectively.
Multi-scale curvature tensor analysis of machined surfaces
NASA Astrophysics Data System (ADS)
Bartkowiak, Tomasz; Brown, Christopher
2016-12-01
This paper demonstrates the use of multi-scale curvature analysis, an areal new surface characterization technique for better understanding topographies, for analyzing surfaces created by conventional machining and grinding. Curvature, like slope and area, changes with scale of observation, or calculation, on irregular surfaces, therefore it can be used for multi-scale geometric analysis. Curvatures on a surface should be indicative of topographically dependent behavior of a surface and curvatures are, in turn, influenced by the processing and use of the surface. Curvatures have not been well characterized previously. Curvature has been used for calculations in contact mechanics and for the evaluation of cutting edges. In the current work two parts were machined and then one of them was ground. The surface topographies were measured with a scanning laser confocal microscope. Plots of curvatures as a function of position and scale are presented, and the means and standard deviations of principal curvatures are plotted as a function of scale. Statistical analyses show the relations between curvature and these two manufacturing processes at multiple scales.
Evolution of a Rippled Membrane during Phospholipase A2 Hydrolysis Studied by Time-Resolved AFM
Leidy, Chad; Mouritsen, Ole G.; Jørgensen, Kent; Peters, Günther H.
2004-01-01
The sensitivity of phospholipase A2 (PLA2) for lipid membrane curvature is explored by monitoring, through time-resolved atomic force microscopy, the hydrolysis of supported double bilayers in the ripple phase. The ripple phase presents a corrugated morphology. PLA2 is shown to have higher activity toward the ripple phase compared to the gel phase in 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) membranes, indicating its preference for this highly curved membrane morphology. Hydrolysis of the stable and metastable ripple structures is monitored for equimolar DMPC/1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC)-supported double bilayers. As shown by high-performance liquid chromatography results, DSPC is resistant to hydrolysis at this temperature, resulting in a more gradual hydrolysis of the surface that leads to a change in membrane morphology without loss of membrane integrity. This is reflected in an increase in ripple spacing, followed by a sudden flattening of the lipid membrane during hydrolysis. Hydrolysis of the ripple phase results in anisotropic holes running parallel to the ripples, suggesting that the ripple phase has strip regions of higher sensitivity to enzymatic attack. Bulk high-performance liquid chromatography measurements indicate that PLA2 preferentially hydrolyzes DMPC in the DMPC/DSPC ripples. We suggest that this leads to the formation of a flat gel-phase lipid membrane due to enrichment in DSPC. The results point to the ability of PLA2 for inducing a compositional phase transition in multicomponent membranes through preferential hydrolysis while preserving membrane integrity. PMID:15240475
Malinin, Vladimir S.; Lentz, Barry R.
2004-01-01
We reported previously the effects of both osmotic and curvature stress on fusion between poly(ethylene glycol)-aggregated vesicles. In this article, we analyze the energetics of fusion of vesicles of different curvature, paying particular attention to the effects of osmotic stress on small, highly curved vesicles of 26 nm diameter, composed of lipids with negative intrinsic curvature. Our calculations show that high positive curvature of the outer monolayer “charges” these vesicles with excess bending energy, which then releases during stalk expansion (increase of the stalk radius, rs) and thus “drives” fusion. Calculations based on the known mechanical properties of lipid assemblies suggest that the free energy of “void” formation as well as membrane-bending free energy dominate the evolution of a stalk to an extended transmembrane contact. The free-energy profile of stalk expansion (free energy versus rs) clearly shows the presence of two metastable intermediates (intermediate 1 at rs ∼0 − 1.0 nm and intermediate 2 at rs ∼2.5 − 3.0 nm). Applying osmotic gradients of ±5 atm, when assuming a fixed trans-bilayer lipid mass distribution, did not significantly change the free-energy profile. However, inclusion in the model of an additional degree of freedom, the ability of lipids to move into and out of the “void”, made the free-energy profile strongly dependent on the osmotic gradient. Vesicle expansion increased the energy barrier between intermediates by ∼4 kT and the absolute value of the barrier by ∼7 kT, whereas compression decreased it by nearly the same extent. Since these calculations, which are based on the stalk hypothesis, correctly predict the effects of both membrane curvature and osmotic stress, they support the stalk hypothesis for the mechanism of membrane fusion and suggest that both forms of stress alter the final stages, rather than the initial step, of the fusion process, as previously suggested. PMID:15111411
Hair curvature: a natural dialectic and review.
Nissimov, Joseph N; Das Chaudhuri, Asit Baran
2014-08-01
Although hair forms (straight, curly, wavy, etc.) are present in apparently infinite variations, each fibre can be reduced to a finite sequence of tandem segments of just three types: straight, bent/curly, or twisted. Hair forms can thus be regarded as resulting from genetic pathways that induce, reverse or modulate these basic curvature modes. However, physical interconversions between twists and curls demonstrate that strict one-to-one correspondences between them and their genetic causes do not exist. Current hair-curvature theories do not distinguish between bending and twisting mechanisms. We here introduce a multiple papillary centres (MPC) model which is particularly suitable to explain twisting. The model combines previously known features of hair cross-sectional morphology with partially/completely separated dermal papillae within single follicles, and requires such papillae to induce differential growth rates of hair cortical material in their immediate neighbourhoods. The MPC model can further help to explain other, poorly understood, aspects of hair growth and morphology. Separate bending and twisting mechanisms would be preferentially affected at the major or minor ellipsoidal sides of fibres, respectively, and together they exhaust the possibilities for influencing hair-form phenotypes. As such they suggest dialectic for hair-curvature development. We define a natural-dialectic (ND) which could take advantage of speculative aspects of dialectic, but would verify its input data and results by experimental methods. We use this as a top-down approach to first define routes by which hair bending or twisting may be brought about and then review evidence in support of such routes. In particular we consider the wingless (Wnt) and mammalian target of rapamycin (mTOR) pathways as paradigm pathways for molecular hair bending and twisting mechanisms, respectively. In addition to the Wnt canonical pathway, the Wnt/Ca(2+) and planar cell polarity (PCP) pathways
Schell, William J.
1979-01-01
A dry, fabric supported, polymeric gas separation membrane, such as cellulose acetate, is prepared by casting a solution of the polymer onto a shrinkable fabric preferably formed of synthetic polymers such as polyester or polyamide filaments before washing, stretching or calendering (so called griege goods). The supported membrane is then subjected to gelling, annealing, and drying by solvent exchange. During the processing steps, both the fabric support and the membrane shrink a preselected, controlled amount which prevents curling, wrinkling or cracking of the membrane in flat form or when spirally wound into a gas separation element.
Curvature effects in thin magnetic shells.
Gaididei, Yuri; Kravchuk, Volodymyr P; Sheka, Denis D
2014-06-27
A magnetic energy functional is derived for an arbitrary curved thin shell on the assumption that the magnetostatic effects can be reduced to an effective easy-surface anisotropy; it can be used for solving both static and dynamic problems. General static solutions are obtained in the limit of a strong anisotropy of both signs (easy-surface and easy-normal cases). It is shown that the effect of the curvature can be treated as the appearance of an effective magnetic field, which is aligned along the surface normal for the case of easy-surface anisotropy and is tangential to the surface for the case of easy-normal anisotropy. In general, the existence of such a field excludes the solutions that are strictly tangential or strictly normal to the surface. As an example, we consider static equilibrium solutions for a cone surface magnetization.
Hawking temperature of constant curvature black holes
Cai Ronggen; Myung, Yun Soo
2011-05-15
The constant curvature (CC) black holes are higher dimensional generalizations of Banados-Teitelboim-Zanelli black holes. It is known that these black holes have the unusual topology of M{sub D-1}xS{sup 1}, where D is the spacetime dimension and M{sub D-1} stands for a conformal Minkowski spacetime in D-1 dimensions. The unusual topology and time-dependence for the exterior of these black holes cause some difficulties to derive their thermodynamic quantities. In this work, by using a globally embedding approach, we obtain the Hawking temperature of the CC black holes. We find that the Hawking temperature takes the same form when using both the static and global coordinates. Also, it is identical to the Gibbons-Hawking temperature of the boundary de Sitter spaces of these CC black holes.
Band geometry, Berry curvature, and superfluid weight
NASA Astrophysics Data System (ADS)
Liang, Long; Vanhala, Tuomas I.; Peotta, Sebastiano; Siro, Topi; Harju, Ari; Törmä, Päivi
2017-01-01
We present a theory of the superfluid weight in multiband attractive Hubbard models within the Bardeen-Cooper-Schrieffer (BCS) mean-field framework. We show how to separate the geometric contribution to the superfluid weight from the conventional one, and that the geometric contribution is associated with the interband matrix elements of the current operator. Our theory can be applied to systems with or without time-reversal symmetry. In both cases the geometric superfluid weight can be related to the quantum metric of the corresponding noninteracting systems. This leads to a lower bound on the superfluid weight given by the absolute value of the Berry curvature. We apply our theory to the attractive Kane-Mele-Hubbard and Haldane-Hubbard models, which can be realized in ultracold atom gases. Quantitative comparisons are made to state of the art dynamical mean-field theory and exact diagonalization results.
Nonminimal coupling of perfect fluids to curvature
Bertolami, Orfeu; Lobo, Francisco S. N.; Paramos, Jorge
2008-09-15
In this work, we consider different forms of relativistic perfect fluid Lagrangian densities that yield the same gravitational field equations in general relativity (GR). A particularly intriguing example is the case with couplings of the form [1+f{sub 2}(R)]L{sub m}, where R is the scalar curvature, which induces an extra force that depends on the form of the Lagrangian density. It has been found that, considering the Lagrangian density L{sub m}=p, where p is the pressure, the extra-force vanishes. We argue that this is not the unique choice for the matter Lagrangian density, and that more natural forms for L{sub m} do not imply the vanishing of the extra force. Particular attention is paid to the impact on the classical equivalence between different Lagrangian descriptions of a perfect fluid.
Beshears, John; Choi, James J.; Laibson, David; Madrian, Brigitte C.
2009-01-01
Revealed preferences are tastes that rationalize an economic agent’s observed actions. Normative preferences represent the agent’s actual interests. It sometimes makes sense to assume that revealed preferences are identical to normative preferences. But there are many cases where this assumption is violated. We identify five factors that increase the likelihood of a disparity between revealed preferences and normative preferences: passive choice, complexity, limited personal experience, third-party marketing, and intertemporal choice. We then discuss six approaches that jointly contribute to the identification of normative preferences: structural estimation, active decisions, asymptotic choice, aggregated revealed preferences, reported preferences, and informed preferences. Each of these approaches uses consumer behavior to infer some property of normative preferences without equating revealed and normative preferences. We illustrate these issues with evidence from savings and investment outcomes. PMID:24761048
Membrane shape modulates transmembrane protein distribution
Aimon, Sophie; Callan-Jones, Andrew; Berthaud, Alice; Pinot, Mathieu; Toombes, Gilman E. S.; Bassereau, Patricia
2014-01-01
Summary Although membrane shape varies greatly throughout the cell, the contribution of membrane curvature to transmembrane protein targeting is unknown due to the numerous sorting mechanisms taking place concurrently in cells. To isolate the effect of membrane shape, cellsized Giant Unilamellar Vesicles (GUVs) containing either the potassium channel, KvAP, or water channel, AQP0, were used to form membrane nanotubes with controlled radii. While the AQP0 concentrations in flat and curved membranes were indistinguishable, KvAP was enriched in the tubes, with greater enrichment in more highly curved membranes. FRAP measurements showed that both proteins could freely diffuse through the neck between the tube and GUV, and the effect of each protein on membrane shape and stiffness was characterized using a thermodynamic sorting model. This study establishes the importance of membrane shape for targeting transmembrane proteins, and provides a method for determining the effective shape and flexibility of membrane proteins. PMID:24480645
Phospholipase A2: Potential roles in native membrane fusion.
Dabral, Deepti; Coorssen, Jens R
2017-04-01
Membrane fusion is a fundamental molecular mechanism by which two apposed membrane bilayers coalesce in rapid, transient steps that enable the successive merging of the outer and inner leaflets allowing lipid intermixing and subsequent mixing of the two previously separate compartments. The actual membrane merger mechanism - fusion, by definition - is conceptualized to be protein- or lipid-centric. According to the widely vetted stalk-pore hypothesis, membrane fusion proceeds via high curvature lipid intermediates. By cleaving membrane phospholipids at the sn-2 position, Phospholipase A2 generates metabolites that exert spontaneous curvature stress (both negative and positive) on the membrane, thus influencing local membrane bending by altering the packing and conformation of lipids and proteins, respectively. Such changes could potentially modulate priming and attachment/docking steps that precede fusion, as well as the membrane merger steps per se. Copyright © 2017 Elsevier Ltd. All rights reserved.
Coherent gradient sensing method and system for measuring surface curvature
NASA Technical Reports Server (NTRS)
Rosakis, Ares J. (Inventor); Singh, Ramen P. (Inventor); Kolawa, Elizabeth (Inventor); Moore, Jr., Nicholas R. (Inventor)
2000-01-01
A system and method for determining a curvature of a specularly reflective surface based on optical interference. Two optical gratings are used to produce a spatial displacement in an interference field of two different diffraction components produced by one grating from different diffraction components produced by another grating. Thus, the curvature of the surface can be determined.
Gaussian and mean curvatures for discrete asymptotic nets
NASA Astrophysics Data System (ADS)
Schief, W. K.
2017-04-01
We propose discretisations of Gaussian and mean curvatures of surfaces parametrised in terms of asymptotic coordinates and examine their relevance in the context of integrable discretisations of classical classes of surfaces and their underlying integrable systems. We also record discrete analogues of the classical relation between the Gaussian curvature of hyperbolic surfaces and the torsion of their asymptotic lines.
Effects of curvature on asymmetric steady states in catalyst particles
Lucier, B J
1981-02-01
The effects of curvature on steady states of chemical catalytic reactions are investigated by studying the cases of the catalytic particle being a spherical or cylindrical shell. Existence and stability of solutions are studied. It is shown that the solutions converge to the solutions for the catalytic slab when the curvature goes to 0 in each case.
An analytical approach to estimate curvature effect of coseismic deformations
NASA Astrophysics Data System (ADS)
Dong, Jie; Sun, Wenke; Zhou, Xin; Wang, Rongjiang
2016-08-01
We present an analytical approach to compute the curvature effect by the new analytical solutions of coseismic deformation derived for the homogeneous sphere model. We consider two spheres with different radii: one is the same as earth and the other with a larger radius can approximate a half-space model. Then, we calculate the coseismic displacements for the two spheres and define the relative percentage of the displacements as the curvature effect. The near-field curvature effect is defined relative to the maximum coseismic displacement. The results show that the maximum curvature effect is about 4 per cent for source depths of less than 100 km, and about 30 per cent for source depths of less than 600 km. For the far-field curvature effect, we define it relative to the observing point. The curvature effect is extremely large and sometimes exceeds 100 per cent. Moreover, this new approach can be used to estimate any planet's curvature effect quantitatively. For a smaller sphere, such as the Moon, the curvature effect is much larger than that of the Earth, with an inverse ratio to the earth's radius.
The development of curvature in the porcine radioulna.
Pantinople, Jess; McCabe, Kyle; Henderson, Keith; Richards, Hazel L; Milne, Nick
2017-01-01
Long bone curvature in animal limbs has long been a subject of interest and much work has explored why long bones should be curved. However, the 'when' and 'how' of curvature development is poorly understood. It has been shown that the rat tibia fails to attain its normal curvature if the action of muscles is removed early in life, but it is not clear if this is because the curvature fails to develop or if the bone becomes straighter without the action of muscles. No studies have examined the development of bone curvature in a normally developing quadruped, so this study tracks the course of curvature formation in the radioulna in a series of growing pigs. We also histologically examined the epiphyseal growth plates of these bones to determine if they contribute to the formation of curvature. In all three epiphyseal plates examined, the proliferative zone is thicker and more densely populated with chondrocytes on the cranial (convex) side than the caudal (concave) side. Frost's chondral modelling theory would suggest that the cranial side of the bone is under more compression than the caudal side, and we conclude that this is due to the action of triceps extending the elbow by pulling on the olecranon process. These results support the idea that bone curvature is an adaptation to habitual loading, where longitudinal loads acting on the curved bone cause bending strains that counter the bending resulting from the habitual muscle action.
Curvature-processing network in macaque visual cortex.
Yue, Xiaomin; Pourladian, Irene S; Tootell, Roger B H; Ungerleider, Leslie G
2014-08-19
Our visual environment abounds with curved features. Thus, the goal of understanding visual processing should include the processing of curved features. Using functional magnetic resonance imaging in behaving monkeys, we demonstrated a network of cortical areas selective for the processing of curved features. This network includes three distinct hierarchically organized regions within the ventral visual pathway: a posterior curvature-biased patch (PCP) located in the near-foveal representation of dorsal V4, a middle curvature-biased patch (MCP) located on the ventral lip of the posterior superior temporal sulcus (STS) in area TEO, and an anterior curvature-biased patch (ACP) located just below the STS in anterior area TE. Our results further indicate that the processing of curvature becomes increasingly complex from PCP to ACP. The proximity of the curvature-processing network to the well-known face-processing network suggests a possible functional link between them.
Curvature sensor based on a Fabry-Perot interferometer
NASA Astrophysics Data System (ADS)
Monteiro, Catarina; Ferreira, Marta S.; Kobelke, Jens; Schuster, Kay; Bierlich, Jörg; Frazão, Orlando
2016-05-01
A curvature sensor based on a Fabry-Perot interferometer is proposed. A capillary tube of silica is fusion spliced between two single mode fibers, producing a Fabry-Perot cavity. The light propagates in air, when passing through the capillary tube. Two different cavities are subjected to curvature and temperature. The cavity with shorter length shows insensitivity to both measurands. The larger cavity shows two operating regions for curvature measurement, where a linear response is shown, with a maximum sensitivity of 18.77pm/m-1 for the high curvature radius range. When subjected to temperature, the sensing head produces a similar response for different curvature radius, with a sensitivity of 0.87pm/°C.
Robust pupil center detection using a curvature algorithm
NASA Technical Reports Server (NTRS)
Zhu, D.; Moore, S. T.; Raphan, T.; Wall, C. C. (Principal Investigator)
1999-01-01
Determining the pupil center is fundamental for calculating eye orientation in video-based systems. Existing techniques are error prone and not robust because eyelids, eyelashes, corneal reflections or shadows in many instances occlude the pupil. We have developed a new algorithm which utilizes curvature characteristics of the pupil boundary to eliminate these artifacts. Pupil center is computed based solely on points related to the pupil boundary. For each boundary point, a curvature value is computed. Occlusion of the boundary induces characteristic peaks in the curvature function. Curvature values for normal pupil sizes were determined and a threshold was found which together with heuristics discriminated normal from abnormal curvature. Remaining boundary points were fit with an ellipse using a least squares error criterion. The center of the ellipse is an estimate of the pupil center. This technique is robust and accurately estimates pupil center with less than 40% of the pupil boundary points visible.
Curvature-processing network in macaque visual cortex
Yue, Xiaomin; Pourladian, Irene S.; Tootell, Roger B. H.; Ungerleider, Leslie G.
2014-01-01
Our visual environment abounds with curved features. Thus, the goal of understanding visual processing should include the processing of curved features. Using functional magnetic resonance imaging in behaving monkeys, we demonstrated a network of cortical areas selective for the processing of curved features. This network includes three distinct hierarchically organized regions within the ventral visual pathway: a posterior curvature-biased patch (PCP) located in the near-foveal representation of dorsal V4, a middle curvature-biased patch (MCP) located on the ventral lip of the posterior superior temporal sulcus (STS) in area TEO, and an anterior curvature-biased patch (ACP) located just below the STS in anterior area TE. Our results further indicate that the processing of curvature becomes increasingly complex from PCP to ACP. The proximity of the curvature-processing network to the well-known face-processing network suggests a possible functional link between them. PMID:25092328
Nastic curvatures of wheat coleoptiles that develop in true microgravity.
Heathcote, D G; Chapman, D K; Brown, A H
1995-07-01
Dark-grown wheat coleoptiles developed strong curvatures within 5 h of being transferred in orbit from a 1 g centrifuge to microgravity during an experiment flown on the IML-1 shuttle mission. The curving tendency was strongest in seedlings that were immature, with coleoptiles shorter than 10 mm at the time of transfer. The curvature direction was non-random, and directed away from the caryopsis (the coleptile face adjacent to the caryopsis becoming convex). The curvatures were most marked in the basal third of the coleoptiles, contrasting with phototropic responses, which occur in the apical third. We interpret these curvatures as being nastic, and related to the curvatures commonly reported to occur during clinostat rotation treatments.
Curvature dependence of the interfacial heat and mass transfer coefficients
NASA Astrophysics Data System (ADS)
Glavatskiy, K. S.; Bedeaux, D.
2014-03-01
Nucleation is often accompanied by heat transfer between the surroundings and a nucleus of a new phase. The interface between two phases gives an additional resistance to this transfer. For small nuclei the interfacial curvature is high, which affects not only equilibrium quantities such as surface tension, but also the transport properties. In particular, high curvature affects the interfacial resistance to heat and mass transfer. We develop a framework for determining the curvature dependence of the interfacial heat and mass transfer resistances. We determine the interfacial resistances as a function of a curvature. The analysis is performed for a bubble of a one-component fluid and may be extended to various nuclei of multicomponent systems. The curvature dependence of the interfacial resistances is important in modeling transport processes in multiphase systems.
Effects of Iris Surface Curvature on Iris Recognition
Thompson, Joseph T; Flynn, Patrick J; Bowyer, Kevin W; Santos-Villalobos, Hector J
2013-01-01
To focus on objects at various distances, the lens of the eye must change shape to adjust its refractive power. This change in lens shape causes a change in the shape of the iris surface which can be measured by examining the curvature of the iris. This work isolates the variable of iris curvature in the recognition process and shows that differences in iris curvature degrade matching ability. To our knowledge, no other work has examined the effects of varying iris curvature on matching ability. To examine this degradation, we conduct a matching experiment across pairs of images with varying degrees of iris curvature differences. The results show a statistically signi cant degradation in matching ability. Finally, the real world impact of these ndings is discussed
Nastic curvatures of wheat coleoptiles that develop in true microgravity
NASA Technical Reports Server (NTRS)
Heathcote, D. G.; Chapman, D. K.; Brown, A. H.
1995-01-01
Dark-grown wheat coleoptiles developed strong curvatures within 5 h of being transferred in orbit from a 1 g centrifuge to microgravity during an experiment flown on the IML-1 shuttle mission. The curving tendency was strongest in seedlings that were immature, with coleoptiles shorter than 10 mm at the time of transfer. The curvature direction was non-random, and directed away from the caryopsis (the coleptile face adjacent to the caryopsis becoming convex). The curvatures were most marked in the basal third of the coleoptiles, contrasting with phototropic responses, which occur in the apical third. We interpret these curvatures as being nastic, and related to the curvatures commonly reported to occur during clinostat rotation treatments.
Effect of curvature on cholesteric liquid crystals in toroidal geometries
NASA Astrophysics Data System (ADS)
Fialho, Ana R.; Bernardino, Nelson R.; Silvestre, Nuno M.; Telo da Gama, Margarida M.
2017-01-01
The confinement of liquid crystals inside curved geometries leads to exotic structures, with applications ranging from biosensors to optical switches and privacy windows. Here we study how curvature affects the alignment of a cholesteric liquid crystal. We model the system on the mesoscale using the Landau-de Gennes model. Our study was performed in three stages, analyzing different curved geometries from cylindrical walls and pores, to toroidal domains, in order to isolate the curvature effects. Our results show that the stresses introduced by the curvature influence the orientation of the liquid crystal molecules, and cause distortions in the natural periodicity of the cholesteric that depend on the radius of curvature, on the pitch, and on the dimensions of the system. In particular, the cholesteric layers of toroidal droplets exhibit a symmetry breaking not seen in cylindrical pores and that is driven by the additional curvature.
Nastic curvatures of wheat coleoptiles that develop in true microgravity
NASA Technical Reports Server (NTRS)
Heathcote, D. G.; Chapman, D. K.; Brown, A. H.
1995-01-01
Dark-grown wheat coleoptiles developed strong curvatures within 5 h of being transferred in orbit from a 1 g centrifuge to microgravity during an experiment flown on the IML-1 shuttle mission. The curving tendency was strongest in seedlings that were immature, with coleoptiles shorter than 10 mm at the time of transfer. The curvature direction was non-random, and directed away from the caryopsis (the coleptile face adjacent to the caryopsis becoming convex). The curvatures were most marked in the basal third of the coleoptiles, contrasting with phototropic responses, which occur in the apical third. We interpret these curvatures as being nastic, and related to the curvatures commonly reported to occur during clinostat rotation treatments.
Robust pupil center detection using a curvature algorithm
NASA Technical Reports Server (NTRS)
Zhu, D.; Moore, S. T.; Raphan, T.; Wall, C. C. (Principal Investigator)
1999-01-01
Determining the pupil center is fundamental for calculating eye orientation in video-based systems. Existing techniques are error prone and not robust because eyelids, eyelashes, corneal reflections or shadows in many instances occlude the pupil. We have developed a new algorithm which utilizes curvature characteristics of the pupil boundary to eliminate these artifacts. Pupil center is computed based solely on points related to the pupil boundary. For each boundary point, a curvature value is computed. Occlusion of the boundary induces characteristic peaks in the curvature function. Curvature values for normal pupil sizes were determined and a threshold was found which together with heuristics discriminated normal from abnormal curvature. Remaining boundary points were fit with an ellipse using a least squares error criterion. The center of the ellipse is an estimate of the pupil center. This technique is robust and accurately estimates pupil center with less than 40% of the pupil boundary points visible.
Use of autologous grafts in the treatment of acquired penile curvature: An experience of 33 cases
Khawaja, Abdul Rouf; Dar, Tanveer Iqbal; Zahur, Suhael; Tariq, Sheikh; Hamid, Arf; Wani, M. S.; Wazir, B. S.; Iqbal, Arsheed
2016-01-01
Aim: The objective was to compare the use of autologous dermal and temporalis fascia grafts in the treatment of acquired penile curvatures. Materials and Methods: It was a prospective observational study of 33 cases, conducted in Sher-i-Kashmir Institute of Medical Sciences, Srinagar from March 2007 to September 2013. All the patients had stable Peyronies disease (PD). Dorsal, dorsolateral and vental curvatures with good preoperative erections were included. PD index with visual analog scales for curvature was used preoperatively. An informed written consent was taken from all the patients with main emphasis on erectile dysfunction. Results: After an average follow up of 2 years, complete straightening of penis was observed in all patients with satisfactory sexual intercourse in 30 patients (90%). Three patients (10%) required frequent use of type 5 phosphodiesterase inhibitors for adequate erections. Overall 91% of patients and partners were satisfied with the procedure and cosmetically donor site was better in temporalis fascia graft site. No rejection of any graft was noted and glans hypoesthesia was noticed in 4 patients (12%). None of the patients required penile prosthesis. Total operative time for harvesting and application of the graft was more in dermal grafts (>3 hrs) than for temporalis fascia graft (2 hrs). Conclusion: Tunical lengthening procedures by autologous free grafts represents a safe and reproducible technique. A good preoperative erectile function is required for tunical lengthening procedure. Temporalis fascia graft is thin, tough membrane and effective graft for PD with good cosmetic and functional results. PMID:27141196
Use of autologous grafts in the treatment of acquired penile curvature: An experience of 33 cases.
Khawaja, Abdul Rouf; Dar, Tanveer Iqbal; Zahur, Suhael; Tariq, Sheikh; Hamid, Arf; Wani, M S; Wazir, B S; Iqbal, Arsheed
2016-01-01
The objective was to compare the use of autologous dermal and temporalis fascia grafts in the treatment of acquired penile curvatures. It was a prospective observational study of 33 cases, conducted in Sher-i-Kashmir Institute of Medical Sciences, Srinagar from March 2007 to September 2013. All the patients had stable Peyronies disease (PD). Dorsal, dorsolateral and vental curvatures with good preoperative erections were included. PD index with visual analog scales for curvature was used preoperatively. An informed written consent was taken from all the patients with main emphasis on erectile dysfunction. After an average follow up of 2 years, complete straightening of penis was observed in all patients with satisfactory sexual intercourse in 30 patients (90%). Three patients (10%) required frequent use of type 5 phosphodiesterase inhibitors for adequate erections. Overall 91% of patients and partners were satisfied with the procedure and cosmetically donor site was better in temporalis fascia graft site. No rejection of any graft was noted and glans hypoesthesia was noticed in 4 patients (12%). None of the patients required penile prosthesis. Total operative time for harvesting and application of the graft was more in dermal grafts (>3 hrs) than for temporalis fascia graft (2 hrs). Tunical lengthening procedures by autologous free grafts represents a safe and reproducible technique. A good preoperative erectile function is required for tunical lengthening procedure. Temporalis fascia graft is thin, tough membrane and effective graft for PD with good cosmetic and functional results.
Tests and evaluation of a variable focus liquid lens for curvature wavefront sensors in astronomy.
Fuentes-Fernández, Jorge; Cuevas, Salvador; Álvarez-Nuñez, Luis C; Watson, Alan
2013-10-20
Curvature wavefront sensors (WFSs), which obtain the wavefront aberrations from two defocused intensity images at each side of the pupil plane, have shown to be highly efficient for astronomical applications. We propose here an alternative defocusing mechanism for curvature sensors, based on an electrowetting-based variable focus liquid lens. Typically, the sampling rates of a WFS for active optics are of the order of 0.01 Hz, and the focus modulation can be done by simply moving the detector back and forth. On the other hand, adaptive optics may require speeds of up to several hundred hertz, and the modulation is then done by using a fast vibrating membrane mirror. We believe variable focus liquid lenses may be able to perform this focus modulation, reducing the overall size of the system and without the need of extra moving parts. We have done a full characterization of the Varioptic Arctic 416 liquid lens, and we have evaluated its potential performance in different curvature configurations.
Membrane stiffness is modified by integral membrane proteins.
Fowler, Philip W; Hélie, Jean; Duncan, Anna; Chavent, Matthieu; Koldsø, Heidi; Sansom, Mark S P
2016-09-20
The ease with which a cell membrane can bend and deform is important for a wide range of biological functions. Peripheral proteins that induce curvature in membranes (e.g. BAR domains) have been studied for a number of years. Little is known, however, about the effect of integral membrane proteins on the stiffness of a membrane (characterised by the bending rigidity, Kc). We demonstrate by computer simulation that adding integral membrane proteins at physiological densities alters the stiffness of the membrane. First we establish that the coarse-grained MARTINI forcefield is able to accurately reproduce the bending rigidity of a small patch of 1500 phosphatidyl choline lipids by comparing the calculated value to both experiment and an atomistic simulation of the same system. This enables us to simulate the dynamics of large (ca. 50 000 lipids) patches of membrane using the MARTINI coarse-grained description. We find that altering the lipid composition changes the bending rigidity. Adding integral membrane proteins to lipid bilayers also changes the bending rigidity, whilst adding a simple peripheral membrane protein has no effect. Our results suggest that integral membrane proteins can have different effects, and in the case of the bacterial outer membrane protein, BtuB, the greater the density of protein, the larger the reduction in stiffness.
Nagi, Sana Ehsen; Khan, Farhan Raza
2017-01-01
With root canal treatment, the organic debris and micro-organisms from pulp space is removed and an ideal canal preparation is achieved that is conducive of hermetic obturation. The purpose of this study was to correlate the pre-operative canal curvature with the postoperative curvature in human extracted teeth prepared with K-3 rotary systems. The root canal preparation was carried out on extracted human molars and premolars using K-3 endodontic rotary files. A pre and post-operative image of the teeth using digital radiograph were taken in order to compare pre and post-operative canal curvature. The images were saved in an images retrieval system (Gendex software, USA). Change in the canal curvature was measured using the software measuring tool (Vixwin software, USA). Student paired t-test and Pearson correlation test was applied at 0.05 level of significance. There is a statistically significant difference between pre-operative and post-operative canal curvature (p-value <0.001) and a strong positive correlation (91% correlation) between pre-operative and post-operative canal curvature in teeth prepared with the K-3 rotary files. A significant difference between pre and post instrumentation curvature was found. Degree of canal curvature was not correlated with time taken for canal preparation.
Substituted polyacetylene separation membrane
Pinnau, I.; Morisato, Atsushi
1998-01-13
A separation membrane is described which is useful for gas separation, particularly separation of C{sub 2+} hydrocarbons from natural gas. The invention encompasses the membrane itself, methods of making it and processes for using it. The membrane comprises a polymer having repeating units of a hydrocarbon-based, disubstituted polyacetylene, having the general formula shown in the accompanying diagram, wherein R{sub 1} is chosen from the group consisting of C{sub 1}-C{sub 4} alkyl and phenyl, and wherein R{sub 2} is chosen from the group consisting of hydrogen and phenyl. In the most preferred embodiment, the membrane comprises poly(4-methyl-2-pentyne) [PMP]. The membrane exhibits good chemical resistance and has super-glassy properties with regard to separating certain large, condensable permeant species from smaller, less-condensable permeant species. The membranes may also be useful in other fluid separations. 4 figs.
Substituted polyacetylene separation membrane
Pinnau, Ingo; Morisato, Atsushi
1998-01-13
A separation membrane useful for gas separation, particularly separation of C.sub.2+ hydrocarbons from natural gas. The invention encompasses the membrane itself, methods of making it and processes for using it. The membrane comprises a polymer having repeating units of a hydrocarbon-based, disubstituted polyacetylene, having the general formula: ##STR1## wherein R.sub.1 is chosen from the group consisting of C.sub.1 -C.sub.4 alkyl and phenyl, and wherein R.sub.2 is chosen from the group consisting of hydrogen and phenyl. In the most preferred embodiment, the membrane comprises poly(4-methyl-2-pentyne) ›PMP!. The membrane exhibits good chemical resistance and has super-glassy properties with regard to separating certain large, condensable permeant species from smaller, less-condensable permeant species. The membranes may also be useful in other fluid separations.
ERIC Educational Resources Information Center
Regenwetter, Michel; Dana, Jason; Davis-Stober, Clintin P.
2011-01-01
Transitivity of preferences is a fundamental principle shared by most major contemporary rational, prescriptive, and descriptive models of decision making. To have transitive preferences, a person, group, or society that prefers choice option "x" to "y" and "y" to "z" must prefer "x" to…
ERIC Educational Resources Information Center
Regenwetter, Michel; Dana, Jason; Davis-Stober, Clintin P.
2011-01-01
Transitivity of preferences is a fundamental principle shared by most major contemporary rational, prescriptive, and descriptive models of decision making. To have transitive preferences, a person, group, or society that prefers choice option "x" to "y" and "y" to "z" must prefer "x" to…
Tourdot, Richard W.; Ramakrishnan, N.; Baumgart, Tobias; Radhakrishnan, Ravi
2016-01-01
We investigate the phenomenon of protein-induced tubulation of lipid bilayer membranes within a continuum framework using Monte Carlo simulations coupled with the Widom insertion technique to compute excess chemical potentials. Tubular morphologies are spontaneously formed when the density and the curvature-field strength of the membrane-bound proteins exceed their respective thresholds and this transition is marked by a sharp drop in the excess chemical potential. We find that the planar to tubular transition can be described by a micellar model and that the corresponding free-energy barrier increases with an increase in the curvature-field strength (i.e., of protein-membrane interactions) and also with an increase in membrane tension. PMID:26565280
NASA Astrophysics Data System (ADS)
Tourdot, Richard W.; Ramakrishnan, N.; Baumgart, Tobias; Radhakrishnan, Ravi
2015-10-01
We investigate the phenomenon of protein-induced tubulation of lipid bilayer membranes within a continuum framework using Monte Carlo simulations coupled with the Widom insertion technique to compute excess chemical potentials. Tubular morphologies are spontaneously formed when the density and the curvature-field strength of the membrane-bound proteins exceed their respective thresholds and this transition is marked by a sharp drop in the excess chemical potential. We find that the planar to tubular transition can be described by a micellar model and that the corresponding free-energy barrier increases with an increase in the curvature-field strength (i.e., of protein-membrane interactions) and also with an increase in membrane tension.
Programming curvature using origami tessellations.
Dudte, Levi H; Vouga, Etienne; Tachi, Tomohiro; Mahadevan, L
2016-05-01
Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one-degree-of-freedom collapsible structures-we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the difficulty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-off between the accuracy to which the pattern conforms to the target surface, and the effort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, as well as the quantification of the energetic and material cost of doing so.
Characterizing repulsive gravity with curvature eigenvalues
NASA Astrophysics Data System (ADS)
Luongo, Orlando; Quevedo, Hernando
2014-10-01
Repulsive gravity has been investigated in several scenarios near compact objects by using different intuitive approaches. Here, we propose an invariant method to characterize regions of repulsive gravity, associated to black holes and naked singularities. Our method is based upon the behavior of the curvature tensor eigenvalues, and leads to an invariant definition of a repulsion radius. The repulsion radius determines a physical region, which can be interpreted as a repulsion sphere, where the effects due to repulsive gravity naturally arise. Further, we show that the use of effective masses to characterize repulsion regions can lead to coordinate-dependent results whereas, in our approach, repulsion emerges as a consequence of the spacetime geometry in a completely invariant way. Our definition is tested in the spacetime of an electrically charged Kerr naked singularity and in all its limiting cases. We show that a positive mass can generate repulsive gravity if it is equipped with an electric charge or an angular momentum. We obtain reasonable results for the spacetime regions contained inside the repulsion sphere whose size and shape depend on the value of the mass, charge and angular momentum. Consequently, we define repulsive gravity as a classical relativistic effect by using the geometry of spacetime only.
Cosmological spatial curvature probed by microwave polarization
Matzner, R.A.; Tolman, B.W.
1982-11-15
If there is a large-scale anisotropy in the expansion of the universe, the microwave background radiation is expected to be linearly polarized. This communication shows that spatial curvature is capable of rotating the polarization of the microwaves relative to its direction at last scattering, which is directly correlated with the expansion anisotropy (and so also the observed intensity anisotropy). In Friedmann-Robertson-Walker models of the universe with additional small expansion anisotropy, the observed rotation relative to the intensity anisotropy would be appreciable and constant over the celestial sphere in the closed (type IX) model, but in the flat and open models, it must either vanish (types I and V) or vary ina complicated way over the celestial sphere (type VII/sub h/). These facts suggest a clear observational test of the closure of the universe. Also, an ambiguity inherent in the homogeneity of the universe does not allow prediction of the direction of rotation; thus homogeneous universes possess a property which might be called ''handedness.''
Actin filament curvature biases branching direction
NASA Astrophysics Data System (ADS)
Wang, Evan; Risca, Viviana; Chaudhuri, Ovijit; Chia, Jia-Jun; Geissler, Phillip; Fletcher, Daniel
2012-02-01
Actin filaments are key components of the cellular machinery, vital for a wide range of processes ranging from cell motility to endocytosis. Actin filaments can branch, and essential in this process is a protein complex known as the Arp2/3 complex, which nucleate new ``daughter'' filaments from pre-existing ``mother'' filaments by attaching itself to the mother filament. Though much progress has been made in understanding the Arp2/3-actin junction, some very interesting questions remain. In particular, F-actin is a dynamic polymer that undergoes a wide range of fluctuations. Prior studies of the Arp2/3-actin junction provides a very static notion of Arp2/3 binding. The question we ask is how differently does the Arp2/3 complex interact with a straight filament compared to a bent filament? In this study, we used Monte Carlo simulations of a surface-tethered worm-like chain to explore possible mechanisms underlying the experimental observation that there exists preferential branch formation by the Arp2/3 complex on the convex face of a curved filament. We show that a fluctuation gating model in which Arp2/3 binding to the actin filament is dependent upon a rare high-local-curvature shape fluctuation of the filament is consistent with the experimental data.
Mean curvature flow of a hyperbolic surface
Ovchinnikov, Yu. N.; Sigal, I. M.
2011-12-15
A four-parameter family of self-similar solutions is obtained to the mean curvature flow equation for a surface. This family is shown to be stable with respect to a small deformation of a hyperbolic surface. At time instant t*, a singular point is formed within a finite time interval, that is accompanied by a change in the topology of the surface. The solution is continued beyond the singular point. A relationship between the parameters describing the hyperbolic surface before and after the change in the surface topology is obtained. A particular case is analyzed when the unperturbed surface is a cylinder. A cylindrical surface is weakly unstable with respect to a perturbation in the form of a 'wide neck.' At the final stage of the development of the neck when its transverse size becomes much less than the cylinder radius at large distances from the neck, the surface flow in a wide region in the neighborhood of the neck is described by a universal two-parameter family of self-similar solutions. These solutions are stable with respect to small perturbations of the surface.
BICEP2, the curvature perturbation and supersymmetry
Lyth, David H.
2014-11-01
The tensor fraction r ≅ 0.16 found by BICEP2 corresponds to a Hubble parameter H ≅ 1.0 × 10{sup 14} GeV during inflation. This has two implications for the (single-field) slow-roll inflation hypothesis. First, the inflaton perturbation must account for much more than 10% of the curvature perturbation ζ, which barring fine-tuning means that it accounts for practically all of it. It follows that a curvaton-like mechanism for generating ζ requires an alternative to slow roll such as k-inflation. Second, accepting slow-roll inflation, the excursion of the inflaton field is at least of order Planck scale. As a result, the flatness of the inflaton presumably requires a shift symmetry. I point out that if such is the case, the resulting potential is likely to have at least approximately the quadratic form suggested in 1983 by Linde, which is known to be compatible with the observed r as well as the observed spectral index n{sub s}. The shift symmetry does not require supersymmetry. Also, the big H may rule out a GUT by restoring the symmetry and producing fatal cosmic strings. The absence of a GUT would correspond to the absence of superpartners for the Standard Model particles, which indeed have yet to be found at the LHC.
Nonlinear diffusion filtering influenced by mean curvature
NASA Astrophysics Data System (ADS)
Kollár, Michal; Mikula, Karol; Čunderlík, Róbert
2016-04-01
The presentation introduces a new nonlinear diffusion filtering method on closed surfaces such as a sphere, ellipsoid or the Earth's surface. Our new model extends the regularized surface Perona-Malik model by including a local extrema detector based on a mean curvature of processed data. The model is thus represented by a nonlinear diffusion equation which filters noise while preserves main edges, local extrema and details important for a correct interpretation of data. We define a surface finite-volume method to approximate numerically the nonlinear parabolic partial differential equation on a closed surface. The closed surface is approximated by a polyhedral surface created by planar triangles representing subdivision of an initial icosahedron grid and we use a piece-wise linear approximation of a solution in space and the backward Euler time discretization. Numerical experiments present nonlinear diffusion filtering of artificial data and real measurements, namely the GOCE satellite observations. They aim to point out a main advantage of the new nonlinear model which, on the contrary of Perona-Malik model, preserves local extremal values of filtered data.
Cosmic acceleration from matter-curvature coupling
NASA Astrophysics Data System (ADS)
Zaregonbadi, Raziyeh; Farhoudi, Mehrdad
2016-10-01
We consider f( {R,T} ) modified theory of gravity in which, in general, the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor. We indicate that in this type of the theory, the coupling energy-momentum tensor is not conserved. However, we mainly focus on a particular model that matter is minimally coupled to the geometry in the metric formalism and wherein, its coupling energy-momentum tensor is also conserved. We obtain the corresponding Raychaudhuri dynamical equation that presents the evolution of the kinematic quantities. Then for the chosen model, we derive the behavior of the deceleration parameter, and show that the coupling term can lead to an acceleration phase after the matter dominated phase. On the other hand, the curvature of the universe corresponds with the deviation from parallelism in the geodesic motion. Thus, we also scrutinize the motion of the free test particles on their geodesics, and derive the geodesic deviation equation in this modified theory to study the accelerating universe within the spatially flat FLRW background. Actually, this equation gives the relative accelerations of adjacent particles as a measurable physical quantity, and provides an elegant tool to investigate the timelike and the null structures of spacetime geometries. Then, through the null deviation vector, we find the observer area-distance as a function of the redshift for the chosen model, and compare the results with the corresponding results obtained in the literature.
Gradient expansion, curvature perturbations, and magnetized plasmas
Giovannini, Massimo; Rezaei, Zahra
2011-04-15
The properties of magnetized plasmas are always investigated under the hypothesis that the relativistic inhomogeneities stemming from the fluid sources and from the geometry itself are sufficiently small to allow for a perturbative description prior to photon decoupling. The latter assumption is hereby relaxed and predecoupling plasmas are described within a suitable expansion where the inhomogeneities are treated to a given order in the spatial gradients. It is argued that the (general relativistic) gradient expansion shares the same features of the drift approximation, customarily employed in the description of cold plasmas, so that the two schemes are physically complementary in the large-scale limit and for the low-frequency branch of the spectrum of plasma modes. The two-fluid description, as well as the magnetohydrodynamical reduction, is derived and studied in the presence of the spatial gradients of the geometry. Various solutions of the coupled system of evolution equations in the anti-Newtonian regime and in the quasi-isotropic approximation are presented. The relation of this analysis to the so-called separate universe paradigm is outlined. The evolution of the magnetized curvature perturbations in the nonlinear regime is addressed for the magnetized adiabatic mode in the plasma frame.
Budding of domains in mixed bilayer membranes
NASA Astrophysics Data System (ADS)
Wolff, Jean; Komura, Shigeyuki; Andelman, David
2015-01-01
We propose a model that accounts for the budding behavior of domains in lipid bilayers, where each of the bilayer leaflets has a coupling between its local curvature and the local lipid composition. The compositional asymmetry between the two monolayers leads to an overall spontaneous curvature. The membrane free energy contains three contributions: the bending energy, the line tension, and a Landau free energy for a lateral phase separation. Within a mean-field treatment, we obtain various phase diagrams which contain fully budded, dimpled, and flat states. In particular, for some range of membrane parameters, the phase diagrams exhibit a tricritical behavior as well as a three-phase coexistence region. The global phase diagrams can be divided into three types and are analyzed in terms of the curvature-composition coupling parameter and domain size.
Zhang, Zhongwei; Chen, Jie; Li, Baowen
2017-09-28
From the mathematic category of surface Gaussian curvature, carbon allotropes can be classified into three types: zero curvature, positive curvature, and negative curvature. By performing Green-Kubo equilibrium molecular dynamics simulations, we found that surface curvature has a significant impact on the phonon vibration and thermal conductivity (κ) of carbon crystals. When curving from zero curvature to negative or positive curvature structures, κ is reduced by several orders of magnitude. Interestingly, we found that κ of negatively curved carbon crystals exhibits a monotonic dependence on curvature. Through phonon mode analysis, we show that curvature induces remarkable phonon softening in phonon dispersion, which results in the reduction of phonon group velocity and flattening of phonon band structure. Furthermore, the curvature was found to induce phonon mode hybridization, leading to the suppression of phonon relaxation time. Our study provides physical insight into thermal transport in curvature materials, and will be valuable in the modulation of phonon activity through surface curvature.
Controllable curvature from planar polymer sheets in response to light.
Hubbard, Amber M; Mailen, Russell W; Zikry, Mohammed A; Dickey, Michael D; Genzer, Jan
2017-02-24
The ability to change shape and control curvature in 3D structures starting from planar sheets can aid in assembly and add functionality to an object. Herein, we convert planar sheets of shape memory polymers (SMPs) into 3D objects with controllable curvature by dictating where the sheets shrink. Ink patterned on the surface of the sheet absorbs infrared (IR) light, resulting in localized heating, and the material shrinks locally wherever the temperature exceeds the activation temperature, Ta. We introduce two different mechanisms for controlling curvature within SMP sheets. The 'direct' mechanism uses localized shrinkage to induce curvature only in regions patterned with ink. The 'indirect' mechanism uses localized shrinkage in regions patterned with ink to induce curvature in neighboring regions without ink through a balance of internal stresses. Finite element analysis predicts the final shape of the polymer sheets with excellent qualitative agreement with experimental studies. Results from this study show that curvature can be controlled by the distribution and darkness of the ink pattern on the polymer sheet. Additionally, we utilize the direct and indirect curvature mechanisms to demonstrate the formation and actuation of gripper devices, which represent the potential utility of this approach.
Effect of curvature on domain wall motion in elliptical nanorings
NASA Astrophysics Data System (ADS)
Kaya, Fikriye Idil; Bickel, Jessica; Aidala, Katherine
2014-03-01
Understanding domain wall (DW) motion in ferromagnetic nanostructures is important to realize proposed magnetic data storage and logic devices. We investigate the effect of curvature on DW pinning and motion by studying elliptical rings using micromagnetic simulations. Elliptical rings with constant width have varying curvature, with the lowest curvature at the minor axis, and the greatest curvature at the major axis. DWs can be created at any angular position within the ellipse by the application of an appropriate uniform magnetic field. However, only some of these positions are stable when the field is removed. We study the stability and depinning of the DWs by applying a slowly increasing elliptical magnetic field to determine the magnitude of the field at which the DWs begin to move. By varying the major to minor axis ratio, we examine the effect of curvature on DW pinning. A larger field is required to move DWs in regions of higher curvature (near the major axis) than lower curvature (near the minor axis). Overall, we see that increasing the major to minor axis ratio of elliptical nanorings requires increasing field strength to depin the DWs along the major axis. Work supported in part by NSF DMR-1207924 and NSF CMMI-1025020. Simulations performed at the CNS computational facilities at Harvard University, a member of the NNIN supported by NSF Award No. ECS-0335765.
On 3-gauge transformations, 3-curvatures, and Gray-categories
Wang, Wei
2014-04-15
In the 3-gauge theory, a 3-connection is given by a 1-form A valued in the Lie algebra g, a 2-form B valued in the Lie algebra h, and a 3-form C valued in the Lie algebra l, where (g,h,l) constitutes a differential 2-crossed module. We give the 3-gauge transformations from one 3-connection to another, and show the transformation formulae of the 1-curvature 2-form, the 2-curvature 3-form, and the 3-curvature 4-form. The gauge configurations can be interpreted as smooth Gray-functors between two Gray 3-groupoids: the path 3-groupoid P{sub 3}(X) and the 3-gauge group G{sup L} associated to the 2-crossed module L, whose differential is (g,h,l). The derivatives of Gray-functors are 3-connections, and the derivatives of lax-natural transformations between two such Gray-functors are 3-gauge transformations. We give the 3-dimensional holonomy, the lattice version of the 3-curvature, whose derivative gives the 3-curvature 4-form. The covariance of 3-curvatures easily follows from this construction. This Gray-categorical construction explains why 3-gauge transformations and 3-curvatures have the given forms. The interchanging 3-arrows are responsible for the appearance of terms with the Peiffer commutator (, )
Curvature modulates the self-assembly of amphiphilic molecules.
Tian, Falin; Luo, Yu; Zhang, Xianren
2010-10-14
In this work, we used lattice Monte Carlo simulations and theoretical model calculations to show how the self-assembly of adsorbed amphiphilic molecules is affected by the local curvature of solid surfaces. It is found that, beyond a critical curvature value, solid surface geometry governs the spatial ordering of aggregates and may induce the morphological transitions. The simulation results show how the curvature of solid surfaces modulates the distribution of aggregates: the anisotropy in local curvature along and perpendicular to the cylindrical surfaces tends to generate orientationally ordered cylindrical micelles. To account for the morphological transitions induced by the local curvature of solid surfaces, we constructed a theoretical model which includes the Helfrich bending energy, the deformation energy of aggregates induced by solid surfaces, and the adsorption energy. The model calculations indicate that on highly curved solid surfaces the bending energy for bilayer structure sharply increases with surface curvature, which in turn induces the morphological transition from bilayer to cylindrical structure. Our results suggest that the local curvature provides a means of controlling the spatial organization of amphiphilic molecules.
3D curvature of muscle fascicles in triceps surae.
Rana, Manku; Hamarneh, Ghassan; Wakeling, James M
2014-12-01
Muscle fascicles curve along their length, with the curvatures occurring around regions of high intramuscular pressure, and are necessary for mechanical stability. Fascicles are typically considered to lie in fascicle planes that are the planes visualized during dissection or two-dimensional (2D) ultrasound scans. However, it has previously been predicted that fascicles must curve in three-dimensional (3D) and thus the fascicle planes may actually exist as 3D sheets. 3D fascicle curvatures have not been explored in human musculature. Furthermore, if the fascicles do not lie in 2D planes, then this has implications for architectural measures that are derived from 2D ultrasound scans. The purpose of this study was to quantify the 3D curvatures of the muscle fascicles and fascicle sheets within the triceps surae muscles and to test whether these curvatures varied among different contraction levels, muscle length, and regions within the muscle. Six male subjects were tested for three torque levels (0, 30, and 60% maximal voluntary contraction) and four ankle angles (-15, 0, 15, and 30° plantar flexion), and fascicles were imaged using 3D ultrasound techniques. The fascicle curvatures significantly increased at higher ankle torques and shorter muscle lengths. The fascicle sheet curvatures were of similar magnitude to the fascicle curvatures but did not vary between contractions. Fascicle curvatures were regionalized within each muscle with the curvature facing the deeper aponeuroses, and this indicates a greater intramuscular pressure in the deeper layers of muscles. Muscle architectural measures may be in error when using 2D images for complex geometries such as the soleus.
Influence of Coanda surface curvature on performance of bladeless fan
NASA Astrophysics Data System (ADS)
Li, Guoqi; Hu, Yongjun; Jin, Yingzi; Setoguchi, Toshiaki; Kim, Heuy Dong
2014-10-01
The unique Coanda surface has a great influence on the performance of bladeless fan. However, there is few studies to explain the relationship between the performance and Coanda surface curvature at present. In order to gain a qualitative understanding of effect of the curvature on the performance of bladeless fan, numerical studies are performed in this paper. Firstly, three-dimensional numerical simulation is done by Fluent software. For the purpose to obtain detailed information of the flow field around the Coanda surface, two-dimensional numerical simulation is also conducted. Five types of Coanda surfaces with different curvature are designed, and the flow behaviour and the performance of them are analyzed and compared with those of the prototype. The analysis indicates that the curvature of Coanda surface is strongly related to blowing performance, It is found that there is an optimal curvature of Coanda surfaces among the studied models. Simulation result shows that there is a special low pressure region. With increasing curvature in Y direction, several low pressure regions gradually enlarged, then begin to merge slowly, and finally form a large area of low pressure. From the analyses of streamlines and velocity angle, it is found that the magnitude of the curvature affects the flow direction and reasonable curvature can induce fluid flow close to the wall. Thus, it leads to that the curvature of the streamlines is consistent with that of Coanda surface. Meanwhile, it also causes the fluid movement towards the most suitable direction. This study will provide useful information to performance improvements of bladeless fans.
Curvature of the localized surface plasmon resonance peak.
Chen, Peng; Liedberg, Bo
2014-08-05
Localized surface plasmon resonance (LSPR) occurring in noble metal nanoparticles (e.g., Au) is a widely used phenomenon to report molecular interactions. Traditional LSPR sensors typically monitor shifts in the peak position or extinction in response to local refractive index changes in the close vicinity of the nanoparticle surface. The ability to resolve minute shifts/extinction changes is to a large extent limited by instrumental noise. A new strategy to evaluate LSPR responses utilizing changes in the shape of the extinction spectrum (the curvature) is proposed. The response of curvature to refractive index changes is investigated theoretically using Mie theory and an analytical expression relating the curvature to the refractive index is presented. The experimentally derived curvatures for 13 nm spherical gold nanoparticles (AuNPs) exposed to solvents with different bulk refractive indices confirm the theoretical predictions. Moreover, both the calculated and experimental findings suggest that the curvature is approximately a linear function of refractive index in regimes relevant to bio and chemical sensing. We demonstrate that curvature is superior over peak shift and extinction both in terms of signal-to-noise (S/N) ratio and reliability of LSPR sensors. With a curvature, one could readily monitor submonolayer adsorption of a low molecular weight thiol molecule (M(w) = 458.6) onto 13 nm AuNPs. It is also worthwhile mentioning that curvature is virtually insensitive to instrumental instabilities and artifacts occurring during measurement. Instabilities such as baseline tilt and shift, shift in peak position as well as sharp spikes/steps in the extinction spectra do not induce artifacts in the sensorgrams of curvature.
Holomorphic bisectional curvatures, supersymmetry breaking, and Affleck-Dine baryogenesis
NASA Astrophysics Data System (ADS)
Dutta, Bhaskar; Sinha, Kuver
2012-11-01
Working in D=4, N=1 supergravity, we utilize relations between holomorphic sectional and bisectional curvatures of Kahler manifolds to constrain Affleck-Dine baryogenesis. We show the following no-go result: Affleck-Dine baryogenesis cannot be performed if the holomorphic sectional curvature at the origin is isotropic in tangent space; as a special case, this rules out spaces of constant holomorphic sectional curvature (defined in the above sense) and in particular maximally symmetric coset spaces. We also investigate scenarios where inflationary supersymmetry breaking is identified with the supersymmetry breaking responsible for mass splitting in the visible sector, using conditions of sequestering to constrain manifolds where inflation can be performed.
Dynamic Curvature Steering Control for Autonomous Vehicle: Performance Analysis
NASA Astrophysics Data System (ADS)
Aizzat Zakaria, Muhammad; Zamzuri, Hairi; Amri Mazlan, Saiful
2016-02-01
This paper discusses the design of dynamic curvature steering control for autonomous vehicle. The lateral control and longitudinal control are discussed in this paper. The controller is designed based on the dynamic curvature calculation to estimate the path condition and modify the vehicle speed and steering wheel angle accordingly. In this paper, the simulation results are presented to show the capability of the controller to track the reference path. The controller is able to predict the path and modify the vehicle speed to suit the path condition. The effectiveness of the controller is shown in this paper whereby identical performance is achieved with the benchmark but with extra curvature adaptation capabilites.
Engineering Curvature-Induced Anisotropy in Thin Ferromagnetic Films
NASA Astrophysics Data System (ADS)
Tretiakov, Oleg A.; Morini, Massimiliano; Vasylkevych, Sergiy; Slastikov, Valeriy
2017-08-01
We investigate the effect of large curvature and dipolar energy in thin ferromagnetic films with periodically modulated top and bottom surfaces on magnetization behavior. We predict that the dipolar interaction and surface curvature can produce perpendicular anisotropy which can be controlled by engineering special types of periodic surface structures. Similar effects can be achieved by a significant surface roughness in the film. We demonstrate that, in general, the anisotropy can point in an arbitrary direction depending on the surface curvature. Furthermore, we provide simple examples of these periodic surface structures to show how to engineer particular anisotropies in thin films.
LPG-based sensor for curvature and vibration
NASA Astrophysics Data System (ADS)
Nascimento, I. M.; Chesini, G.; Baptista, J. M.; Cordeiro, Cristiano M. B.; Jorge, P. A. S.
2016-05-01
A long-period grating (LPG) written on a standard single mode fiber is investigated as a curvature and vibration sensor. It is demonstrated a high sensitivity to applied curvature and the possibility to monitor vibration in a wide range of frequencies from 30 Hz to 2000 Hz. The system was tested using an intensity based interrogation scheme with the LPG sensor operating in the curvature regime. Results have shown a reproducible frequency discrimination in the 30 Hz to 2000 Hz, with resolutions between 11 mHz and 913 mHz. Frequency retrieval could be performed independent of temperature up to 86 °C.
Measurement of the gravity-field curvature by atom interferometry.
Rosi, G; Cacciapuoti, L; Sorrentino, F; Menchetti, M; Prevedelli, M; Tino, G M
2015-01-09
We present the first direct measurement of the gravity-field curvature based on three conjugated atom interferometers. Three atomic clouds launched in the vertical direction are simultaneously interrogated by the same atom interferometry sequence and used to probe the gravity field at three equally spaced positions. The vertical component of the gravity-field curvature generated by nearby source masses is measured from the difference between adjacent gravity gradient values. Curvature measurements are of interest in geodesy studies and for the validation of gravitational models of the surrounding environment. The possibility of using such a scheme for a new determination of the Newtonian constant of gravity is also discussed.
Inconsistency of scale-invariant curvature coupled to gravity
Zoller, D. )
1990-10-29
We show that the scale-invariant curvature action for paths, the point-particle version of Polyakov's extrinsic-curvature action for surfaces, does not couple consistently to gravity. The curvature action for paths yields a massless representation of the Poincare group with fixed helicity and so potentially provides a description of single photons and gravitons. We present a physical interpretation of the inconsistency in terms of the nonlocalizability of the photon and point out a conceptual kinship with the local supersymmetry of a spinning particle.
Inconsistency of scale-invariant curvature coupled to gravity
NASA Astrophysics Data System (ADS)
Zoller, D.
1990-10-01
We show that the scale-invariant curvature action for paths, the point-particle version of Polyakov's extrinsic-curvature action for surfaces, does not couple consistently to gravity. The curvature action for paths yields a massless representation of the Poincaré group with fixed helicity and so potentially provides a description of single photons and gravitons. We present a physical interpretation of the inconsistency in terms of the nonlocalizability of the photon and point out a conceptual kinship with the local supersymmetry of a spinning particle.
Motion on constant curvature spaces and quantization using Noether symmetries.
Bracken, Paul
2014-12-01
A general approach is presented for quantizing a metric nonlinear system on a manifold of constant curvature. It makes use of a curvature dependent procedure which relies on determining Noether symmetries from the metric. The curvature of the space functions as a constant parameter. For a specific metric which defines the manifold, Lie differentiation of the metric gives these symmetries. A metric is used such that the resulting Schrödinger equation can be solved in terms of hypergeometric functions. This permits the investigation of both the energy spectrum and wave functions exactly for this system.
Enhancing magnetoelectric effect via the curvature of composite cylinder
NASA Astrophysics Data System (ADS)
Wang, H. M.; Pan, E.; Chen, W. Q.
2010-05-01
We solved analytically the magnetoelectric (ME) effect in a bilayered piezoelectric/piezomagnetic cylinder under harmonic excitation. We revealed that at a fixed thickness ratio of the layers, the static or low-frequency ME effect can be substantially enhanced by increasing the curvature of the cylinder. In the megahertz frequency domain, on the other hand, we observed that the peak ME effect can be considerably increased by decreasing the curvature. We further showed that at a fixed curvature, the ME effect can be tuned to be around the resonant frequency for giant output by varying the boundary condition and thickness ratio.
Characterizing the curvature and its first derivative for imperfect fluids
NASA Astrophysics Data System (ADS)
Machado Ramos, Maria da Piedade
2017-04-01
The curvature tensor and its derivatives up to any order can be covariantly characterized by a minimal set of spinor quantities. On the other hand it might be useful, particularly in cosmology, to describe the geometry of a spacetime in a (1+3) formalism, based on an invariantly defined fluid velocity. In this work, we consider an imperfect fluid possessing both isotropic and anisotropic pressure. For these fluids, we determine the (1+3) matter terms of the curvature as well as the parts of the first order covariant derivative of the curvature (\
Radius of curvature changes in spontaneous improvement of foveoschisis in highly myopic eyes.
Hoang, Quan V; Chen, Ching-Lung; Garcia-Arumi, Jose; Sherwood, Pamela R; Chang, Stanley
2016-02-01
Myopic foveoschisis is the splitting of retinal layers overlying staphyloma in highly myopic patients that can lead to vision loss. We assess possible contributing mechanisms to the formation of foveoschisis by examining two cases of spontaneous improvement of myopic foveoschisis and employ a radius of curvature (ROC) measure to track posterior scleral curvature over time. A retrospective, non-comparative case series was performed and optical coherence tomography images were analysed. Retinal pigment epithelial layer ROC was calculated from manually segmented images through the posterior scleral curvature apex. Two cases of myopic foveoschisis with foveal detachments in the left eye (OS) were studied. Both patients had high myopia (either <-10 D or >30 mm in axial length). One case occurred in a treatment-naive patient who improved after 4 months of observation. On initial presentation, OS posterior scleral ROC was 12.35 mm and decreased to 12.15 mm at the time of resolution. The other case occurred in a patient who was followed for 7 years, had previously underwent pars plana vitrectomy and removal of epiretinal membrane, experienced recurrence of foveoschisis and then spontaneously improved without further posterior segment surgery. There was an uncomplicated cataract extraction in the interim. Posterior scleral ROC was 4.05 mm on presentation, 4.10 during recurrence, 3.55 mm after cataract extraction and 3.75 mm at resolution. Spontaneous improvement of myopic foveoschisis may be due to changes in tractional forces from the internal limiting membrane, cortical vitreous or staphyloma or, alternatively, from a delayed or fluctuant recovery course after intervention. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/
Einstein Gravity and Beyond: Aspects of Higher-Curvature Gravity and Black Holes
NASA Astrophysics Data System (ADS)
Chatterjee, Saugata
This thesis explores the different aspects of higher curvature gravity. The "membrane paradigm" of black holes in Einstein gravity is extended to black holes in f(R) gravity and it is shown that the higher curvature effects of f( R) gravity causes the membrane fluid to become non-Newtonian. Next a modification of the null energy condition in gravity is provided. The purpose of the null energy condition is to filter out ill-behaved theories containing ghosts. Conformal transformations, which are simple redefinitions of the spacetime, introduces serious violations of the null energy condition. This violation is shown to be spurious and a prescription for obtaining a modified null energy condition, based on the universality of the second law of thermodynamics, is provided. The thermodynamic properties of the black holes are further explored using merger of extremal black holes whose horizon entropy has topological contributions coming from the higher curvature Gauss-Bonnet term. The analysis refutes the prevalent belief in the literature that the second law of black hole thermodynamics is violated in the presence of the Gauss-Bonnet term in four dimensions. Subsequently a specific class of higher derivative scalar field theories called the galileons are obtained from a Kaluza-Klein reduction of Gauss-Bonnet gravity. Galileons are null energy condition violating theories which lead to violations of the second law of thermodynamics of black holes. These higher derivative scalar field theories which are non-minimally coupled to gravity required the development of a generalized method for obtaining the equations of motion. Utilizing this generalized method, it is shown that the inclusion of the Gauss-Bonnet term made the theory of gravity to become higher derivative, which makes it difficult to make any statements about the connection between the violation of the second law of thermodynamics and the galileon fields.
Interaction of peptides with cell membranes: insights from molecular modeling
NASA Astrophysics Data System (ADS)
Li, Zhen-lu; Ding, Hong-ming; Ma, Yu-qiang
2016-03-01
The investigation of the interaction of peptides with cell membranes is the focus of active research. It can enhance the understanding of basic membrane functions such as membrane transport, fusion, and signaling processes, and it may shed light on potential applications of peptides in biomedicine. In this review, we will present current advances in computational studies on the interaction of different types of peptides with the cell membrane. Depending on the properties of the peptide, membrane, and external environment, the peptide-membrane interaction shows a variety of different forms. Here, on the basis of recent computational progress, we will discuss how different peptides could initiate membrane pores, translocate across the membrane, induce membrane endocytosis, produce membrane curvature, form fibrils on the membrane surface, as well as interact with functional membrane proteins. Finally, we will present a conclusion summarizing recent progress and providing some specific insights into future developments in this field.
NASA Astrophysics Data System (ADS)
Ma, Shuang; Yi, Shengzhen; Chen, Shenghao; Wang, Zhanshan
2014-11-01
Monochromatic energy multilayer Kirkpatrick-Baez microscope is one of key diagnostic tools for researches on inertial confinement fusion. It is composed by two orthogonal concave spherical mirrors with small curvature and aperture, and produce the image of an object by collecting X-rays in each orthogonal direction, independently. Accurate measurement of radius of curvature of concave spherical mirrors is very important to achieve its design optical properties including imaging quality, optical throughput and energy resolution. However, it is difficult to measure the radius of curvature of spherical optical surfaces with small curvature and aperture by conventional methods, for the produced reflective intensity of glass is too low to correctly test. In this paper, we propose an improved measuring method of optical profiler to accomplish accurate measurement of radius of curvature of spherical optical surfaces with small curvature and aperture used in the monochromatic energy multilayer Kirkpatrick-Baez microscope. Firstly, we use a standard super-smooth optical flat to calibrate reference mirror before each experiment. Following, deviation of central position between measurement area and interference pattern is corrected by the theory of Newton's rings, and the zero-order fringe position is derived from the principle of interference in which surface roughness has minimum values in the position of zero light path difference. Measured results by optical profiler show the low relative errors and high repeatability. Eventually, an imaging experiment of monochromatic energy multilayer Kirkpatrick-Baez microscope determines the measurement accuracy of radius of curvature.
Magnetization in narrow ribbons: curvature effects
NASA Astrophysics Data System (ADS)
Gaididei, Yuri; Goussev, Arseni; Kravchuk, Volodymyr P.; Pylypovskyi, Oleksandr V.; Robbins, J. M.; Sheka, Denis D.; Slastikov, Valeriy; Vasylkevych, Sergiy
2017-09-01
A ribbon is a surface swept out by a line segment turning as it moves along a central curve. For narrow magnetic ribbons, for which the length of the line segment is much less than the length of the curve, the anisotropy induced by the magnetostatic interaction is biaxial, with a hard axis normal to the ribbon and an easy axis along the central curve. The micromagnetic energy of a narrow ribbon reduces to that of a one-dimensional ferromagnetic wire, but with curvature, torsion and local anisotropy modified by the rate of turning. These gene