Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

NASA Astrophysics Data System (ADS)

Herath, Narmada; Del Vecchio, Domitilla

2018-03-01

Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

Topological and kinetic determinants of the modal matrices of dynamic models of metabolism

PubMed Central

2017-01-01

Large-scale kinetic models of metabolism are becoming increasingly comprehensive and accurate. A key challenge is to understand the biochemical basis of the dynamic properties of these models. Linear analysis methods are well-established as useful tools for characterizing the dynamic response of metabolic networks. Central to linear analysis methods are two key matrices: the Jacobian matrix (J) and the modal matrix (M-1) arising from its eigendecomposition. The modal matrix M-1 contains dynamically independent motions of the kinetic model near a reference state, and it is sparse in practice for metabolic networks. However, connecting the structure of M-1 to the kinetic properties of the underlying reactions is non-trivial. In this study, we analyze the relationship between J, M-1, and the kinetic properties of the underlying network for kinetic models of metabolism. Specifically, we describe the origin of mode sparsity structure based on features of the network stoichiometric matrix S and the reaction kinetic gradient matrix G. First, we show that due to the scaling of kinetic parameters in real networks, diagonal dominance occurs in a substantial fraction of the rows of J, resulting in simple modal structures with clear biological interpretations. Then, we show that more complicated modes originate from topologically-connected reactions that have similar reaction elasticities in G. These elasticities represent dynamic equilibrium balances within reactions and are key determinants of modal structure. The work presented should prove useful towards obtaining an understanding of the dynamics of kinetic models of metabolism, which are rooted in the network structure and the kinetic properties of reactions. PMID:29267329

Qualitative dynamics semantics for SBGN process description.

PubMed

Rougny, Adrien; Froidevaux, Christine; Calzone, Laurence; Paulevé, Loïc

2016-06-16

Qualitative dynamics semantics provide a coarse-grain modeling of networks dynamics by abstracting away kinetic parameters. They allow to capture general features of systems dynamics, such as attractors or reachability properties, for which scalable analyses exist. The Systems Biology Graphical Notation Process Description language (SBGN-PD) has become a standard to represent reaction networks. However, no qualitative dynamics semantics taking into account all the main features available in SBGN-PD had been proposed so far. We propose two qualitative dynamics semantics for SBGN-PD reaction networks, namely the general semantics and the stories semantics, that we formalize using asynchronous automata networks. While the general semantics extends standard Boolean semantics of reaction networks by taking into account all the main features of SBGN-PD, the stories semantics allows to model several molecules of a network by a unique variable. The obtained qualitative models can be checked against dynamical properties and therefore validated with respect to biological knowledge. We apply our framework to reason on the qualitative dynamics of a large network (more than 200 nodes) modeling the regulation of the cell cycle by RB/E2F. The proposed semantics provide a direct formalization of SBGN-PD networks in dynamical qualitative models that can be further analyzed using standard tools for discrete models. The dynamics in stories semantics have a lower dimension than the general one and prune multiple behaviors (which can be considered as spurious) by enforcing the mutual exclusiveness between the activity of different nodes of a same story. Overall, the qualitative semantics for SBGN-PD allow to capture efficiently important dynamical features of reaction network models and can be exploited to further refine them.

Thermodynamics of random reaction networks.

PubMed

Fischer, Jakob; Kleidon, Axel; Dittrich, Peter

2015-01-01

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa -1.5 for linear and -1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.

Thermodynamics of Random Reaction Networks

PubMed Central

Fischer, Jakob; Kleidon, Axel; Dittrich, Peter

2015-01-01

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa −1.5 for linear and −1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks. PMID:25723751

Simulation of large-scale rule-based models

PubMed Central

Colvin, Joshua; Monine, Michael I.; Faeder, James R.; Hlavacek, William S.; Von Hoff, Daniel D.; Posner, Richard G.

2009-01-01

Motivation: Interactions of molecules, such as signaling proteins, with multiple binding sites and/or multiple sites of post-translational covalent modification can be modeled using reaction rules. Rules comprehensively, but implicitly, define the individual chemical species and reactions that molecular interactions can potentially generate. Although rules can be automatically processed to define a biochemical reaction network, the network implied by a set of rules is often too large to generate completely or to simulate using conventional procedures. To address this problem, we present DYNSTOC, a general-purpose tool for simulating rule-based models. Results: DYNSTOC implements a null-event algorithm for simulating chemical reactions in a homogenous reaction compartment. The simulation method does not require that a reaction network be specified explicitly in advance, but rather takes advantage of the availability of the reaction rules in a rule-based specification of a network to determine if a randomly selected set of molecular components participates in a reaction during a time step. DYNSTOC reads reaction rules written in the BioNetGen language which is useful for modeling protein–protein interactions involved in signal transduction. The method of DYNSTOC is closely related to that of StochSim. DYNSTOC differs from StochSim by allowing for model specification in terms of BNGL, which extends the range of protein complexes that can be considered in a model. DYNSTOC enables the simulation of rule-based models that cannot be simulated by conventional methods. We demonstrate the ability of DYNSTOC to simulate models accounting for multisite phosphorylation and multivalent binding processes that are characterized by large numbers of reactions. Availability: DYNSTOC is free for non-commercial use. The C source code, supporting documentation and example input files are available at http://public.tgen.org/dynstoc/. Contact: dynstoc@tgen.org Supplementary information: Supplementary data are available at Bioinformatics online. PMID:19213740

Microalgal Metabolic Network Model Refinement through High-Throughput Functional Metabolic Profiling

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

Chaiboonchoe, Amphun; Dohai, Bushra Saeed; Cai, Hong

2014-12-10

Metabolic modeling provides the means to define metabolic processes at a systems level; however, genome-scale metabolic models often remain incomplete in their description of metabolic networks and may include reactions that are experimentally unverified. This shortcoming is exacerbated in reconstructed models of newly isolated algal species, as there may be little to no biochemical evidence available for the metabolism of such isolates. The phenotype microarray (PM) technology (Biolog, Hayward, CA, USA) provides an efficient, high-throughput method to functionally define cellular metabolic activities in response to a large array of entry metabolites. The platform can experimentally verify many of the unverifiedmore » reactions in a network model as well as identify missing or new reactions in the reconstructed metabolic model. The PM technology has been used for metabolic phenotyping of non-photosynthetic bacteria and fungi, but it has not been reported for the phenotyping of microalgae. Here, we introduce the use of PM assays in a systematic way to the study of microalgae, applying it specifically to the green microalgal model species Chlamydomonas reinhardtii. The results obtained in this study validate a number of existing annotated metabolic reactions and identify a number of novel and unexpected metabolites. The obtained information was used to expand and refine the existing COBRA-based C. reinhardtii metabolic network model iRC1080. Over 254 reactions were added to the network, and the effects of these additions on flux distribution within the network are described. The novel reactions include the support of metabolism by a number of d-amino acids, l-dipeptides, and l-tripeptides as nitrogen sources, as well as support of cellular respiration by cysteamine-S-phosphate as a phosphorus source. The protocol developed here can be used as a foundation to functionally profile other microalgae such as known microalgae mutants and novel isolates.« less

Microalgal Metabolic Network Model Refinement through High-Throughput Functional Metabolic Profiling

PubMed Central

Chaiboonchoe, Amphun; Dohai, Bushra Saeed; Cai, Hong; Nelson, David R.; Jijakli, Kenan; Salehi-Ashtiani, Kourosh

2014-01-01

Metabolic modeling provides the means to define metabolic processes at a systems level; however, genome-scale metabolic models often remain incomplete in their description of metabolic networks and may include reactions that are experimentally unverified. This shortcoming is exacerbated in reconstructed models of newly isolated algal species, as there may be little to no biochemical evidence available for the metabolism of such isolates. The phenotype microarray (PM) technology (Biolog, Hayward, CA, USA) provides an efficient, high-throughput method to functionally define cellular metabolic activities in response to a large array of entry metabolites. The platform can experimentally verify many of the unverified reactions in a network model as well as identify missing or new reactions in the reconstructed metabolic model. The PM technology has been used for metabolic phenotyping of non-photosynthetic bacteria and fungi, but it has not been reported for the phenotyping of microalgae. Here, we introduce the use of PM assays in a systematic way to the study of microalgae, applying it specifically to the green microalgal model species Chlamydomonas reinhardtii. The results obtained in this study validate a number of existing annotated metabolic reactions and identify a number of novel and unexpected metabolites. The obtained information was used to expand and refine the existing COBRA-based C. reinhardtii metabolic network model iRC1080. Over 254 reactions were added to the network, and the effects of these additions on flux distribution within the network are described. The novel reactions include the support of metabolism by a number of d-amino acids, l-dipeptides, and l-tripeptides as nitrogen sources, as well as support of cellular respiration by cysteamine-S-phosphate as a phosphorus source. The protocol developed here can be used as a foundation to functionally profile other microalgae such as known microalgae mutants and novel isolates. PMID:25540776

Microalgal Metabolic Network Model Refinement through High-Throughput Functional Metabolic Profiling.

PubMed

Chaiboonchoe, Amphun; Dohai, Bushra Saeed; Cai, Hong; Nelson, David R; Jijakli, Kenan; Salehi-Ashtiani, Kourosh

2014-01-01

Metabolic modeling provides the means to define metabolic processes at a systems level; however, genome-scale metabolic models often remain incomplete in their description of metabolic networks and may include reactions that are experimentally unverified. This shortcoming is exacerbated in reconstructed models of newly isolated algal species, as there may be little to no biochemical evidence available for the metabolism of such isolates. The phenotype microarray (PM) technology (Biolog, Hayward, CA, USA) provides an efficient, high-throughput method to functionally define cellular metabolic activities in response to a large array of entry metabolites. The platform can experimentally verify many of the unverified reactions in a network model as well as identify missing or new reactions in the reconstructed metabolic model. The PM technology has been used for metabolic phenotyping of non-photosynthetic bacteria and fungi, but it has not been reported for the phenotyping of microalgae. Here, we introduce the use of PM assays in a systematic way to the study of microalgae, applying it specifically to the green microalgal model species Chlamydomonas reinhardtii. The results obtained in this study validate a number of existing annotated metabolic reactions and identify a number of novel and unexpected metabolites. The obtained information was used to expand and refine the existing COBRA-based C. reinhardtii metabolic network model iRC1080. Over 254 reactions were added to the network, and the effects of these additions on flux distribution within the network are described. The novel reactions include the support of metabolism by a number of d-amino acids, l-dipeptides, and l-tripeptides as nitrogen sources, as well as support of cellular respiration by cysteamine-S-phosphate as a phosphorus source. The protocol developed here can be used as a foundation to functionally profile other microalgae such as known microalgae mutants and novel isolates.

Exhaustive analysis of the modular structure of the spliceosomal assembly network: a petri net approach.

PubMed

Bortfeldt, Ralf H; Schuster, Stefan; Koch, Ina

2011-01-01

Spliceosomes are macro-complexes involving hundreds of proteins with many functional interactions. Spliceosome assembly belongs to the key processes that enable splicing of mRNA and modulate alternative splicing. A detailed list of factors involved in spliceosomal reactions has been assorted over the past decade, but, their functional interplay is often unknown and most of the present biological models cover only parts of the complete assembly process. It is a challenging task to build a computational model that integrates dispersed knowledge and combines a multitude of reaction schemes proposed earlier. Because for most reactions involved in spliceosome assembly kinetic parameters are not available, we propose a discrete modeling using Petri nets, through which we are enabled to get insights into the system's behavior via computation of structural and dynamic properties. In this paper, we compile and examine reactions from experimental reports that contribute to a functional spliceosome. All these reactions form a network, which describes the inventory and conditions necessary to perform the splicing process. The analysis is mainly based on system invariants. Transition invariants (T-invariants) can be interpreted as signaling routes through the network. Due to the huge number of T-invariants that arise with increasing network size and complexity, maximal common transition sets (MCTS) and T-clusters were used for further analysis. Additionally, we introduce a false color map representation, which allows a quick survey of network modules and the visual detection of single reactions or reaction sequences, which participate in more than one signaling route. We designed a structured model of spliceosome assembly, which combines the demands on a platform that i) can display involved factors and concurrent processes, ii) offers the possibility to run computational methods for knowledge extraction, and iii) is successively extendable as new insights into spliceosome function are reported by experimental reports. The network consists of 161 transitions (reactions) and 140 places (reactants). All reactions are part of at least one of the 71 T-invariants. These T-invariants define pathways, which are in good agreement with the current knowledge and known hypotheses on reaction sequences during spliceosome assembly, hence contributing to a functional spliceosome. We demonstrate that present knowledge, in particular of the initial part of the assembly process, describes parallelism and interaction of signaling routes, which indicate functional redundancy and reflect the dependency of spliceosome assembly initiation on different cellular conditions. The complexity of the network is further increased by two switches, which introduce alternative routes during A-complex formation in early spliceosome assembly and upon transition from the B-complex to the C-complex. By compiling known reactions into a complete network, the combinatorial nature of invariant computation leads to pathways that have previously not been described as connected routes, although their constituents were known. T-clusters divide the network into modules, which we interpret as building blocks in spliceosome maturation. We conclude that Petri net representations of large biological networks and system invariants, are well-suited as a means for validating the integration of experimental knowledge into a consistent model. Based on this network model, the design of further experiments is facilitated.

Exhaustive analysis of the modular structure of the spliceosomal assembly network: a Petri net approach.

PubMed

Bortfeldt, Ralf H; Schuster, Stefan; Koch, Ina

2010-01-01

Spliceosomes are macro-complexes involving hundreds of proteins with many functional interactions. Spliceosome assembly belongs to the key processes that enable splicing of mRNA and modulate alternative splicing. A detailed list of factors involved in spliceosomal reactions has been assorted over the past decade, but, their functional interplay is often unknown and most of the present biological models cover only parts of the complete assembly process. It is a challenging task to build a computational model that integrates dispersed knowledge and combines a multitude of reaction schemes proposed earlier.Because for most reactions involved in spliceosome assembly kinetic parameters are not available, we propose a discrete modeling using Petri nets, through which we are enabled to get insights into the system's behavior via computation of structural and dynamic properties. In this paper, we compile and examine reactions from experimental reports that contribute to a functional spliceosome. All these reactions form a network, which describes the inventory and conditions necessary to perform the splicing process. The analysis is mainly based on system invariants. Transition invariants (T-invariants) can be interpreted as signaling routes through the network. Due to the huge number of T-invariants that arise with increasing network size and complexity, maximal common transition sets (MCTS) and T-clusters were used for further analysis. Additionally, we introduce a false color map representation, which allows a quick survey of network modules and the visual detection of single reactions or reaction sequences, which participate in more than one signaling route. We designed a structured model of spliceosome assembly, which combines the demands on a platform that i) can display involved factors and concurrent processes, ii) offers the possibility to run computational methods for knowledge extraction, and iii) is successively extendable as new insights into spliceosome function are reported by experimental reports. The network consists of 161 transitions (reactions) and 140 places (reactants). All reactions are part of at least one of the 71 T-invariants. These T-invariants define pathways, which are in good agreement with the current knowledge and known hypotheses on reaction sequences during spliceosome assembly, hence contributing to a functional spliceosome. We demonstrate that present knowledge, in particular of the initial part of the assembly process, describes parallelism and interaction of signaling routes, which indicate functional redundancy and reflect the dependency of spliceosome assembly initiation on different cellular conditions. The complexity of the network is further increased by two switches, which introduce alternative routes during A-complex formation in early spliceosome assembly and upon transition from the B-complex to the C-complex. By compiling known reactions into a complete network, the combinatorial nature of invariant computation leads to pathways that have previously not been described as connected routes, although their constituents were known. T-clusters divide the network into modules, which we interpret as building blocks in spliceosome maturation. We conclude that Petri net representations of large biological networks and system invariants, are well-suited as a means for validating the integration of experimental knowledge into a consistent model. Based on this network model, the design of further experiments is facilitated.

Toward the automated generation of genome-scale metabolic networks in the SEED.

PubMed

DeJongh, Matthew; Formsma, Kevin; Boillot, Paul; Gould, John; Rycenga, Matthew; Best, Aaron

2007-04-26

Current methods for the automated generation of genome-scale metabolic networks focus on genome annotation and preliminary biochemical reaction network assembly, but do not adequately address the process of identifying and filling gaps in the reaction network, and verifying that the network is suitable for systems level analysis. Thus, current methods are only sufficient for generating draft-quality networks, and refinement of the reaction network is still largely a manual, labor-intensive process. We have developed a method for generating genome-scale metabolic networks that produces substantially complete reaction networks, suitable for systems level analysis. Our method partitions the reaction space of central and intermediary metabolism into discrete, interconnected components that can be assembled and verified in isolation from each other, and then integrated and verified at the level of their interconnectivity. We have developed a database of components that are common across organisms, and have created tools for automatically assembling appropriate components for a particular organism based on the metabolic pathways encoded in the organism's genome. This focuses manual efforts on that portion of an organism's metabolism that is not yet represented in the database. We have demonstrated the efficacy of our method by reverse-engineering and automatically regenerating the reaction network from a published genome-scale metabolic model for Staphylococcus aureus. Additionally, we have verified that our method capitalizes on the database of common reaction network components created for S. aureus, by using these components to generate substantially complete reconstructions of the reaction networks from three other published metabolic models (Escherichia coli, Helicobacter pylori, and Lactococcus lactis). We have implemented our tools and database within the SEED, an open-source software environment for comparative genome annotation and analysis. Our method sets the stage for the automated generation of substantially complete metabolic networks for over 400 complete genome sequences currently in the SEED. With each genome that is processed using our tools, the database of common components grows to cover more of the diversity of metabolic pathways. This increases the likelihood that components of reaction networks for subsequently processed genomes can be retrieved from the database, rather than assembled and verified manually.

A toolbox model of evolution of metabolic pathways on networks of arbitrary topology.

PubMed

Pang, Tin Yau; Maslov, Sergei

2011-05-01

In prokaryotic genomes the number of transcriptional regulators is known to be proportional to the square of the total number of protein-coding genes. A toolbox model of evolution was recently proposed to explain this empirical scaling for metabolic enzymes and their regulators. According to its rules, the metabolic network of an organism evolves by horizontal transfer of pathways from other species. These pathways are part of a larger "universal" network formed by the union of all species-specific networks. It remained to be understood, however, how the topological properties of this universal network influence the scaling law of functional content of genomes in the toolbox model. Here we answer this question by first analyzing the scaling properties of the toolbox model on arbitrary tree-like universal networks. We prove that critical branching topology, in which the average number of upstream neighbors of a node is equal to one, is both necessary and sufficient for quadratic scaling. We further generalize the rules of the model to incorporate reactions with multiple substrates/products as well as branched and cyclic metabolic pathways. To achieve its metabolic tasks, the new model employs evolutionary optimized pathways with minimal number of reactions. Numerical simulations of this realistic model on the universal network of all reactions in the KEGG database produced approximately quadratic scaling between the number of regulated pathways and the size of the metabolic network. To quantify the geometrical structure of individual pathways, we investigated the relationship between their number of reactions, byproducts, intermediate, and feedback metabolites. Our results validate and explain the ubiquitous appearance of the quadratic scaling for a broad spectrum of topologies of underlying universal metabolic networks. They also demonstrate why, in spite of "small-world" topology, real-life metabolic networks are characterized by a broad distribution of pathway lengths and sizes of metabolic regulons in regulatory networks.

Biogeochemical metabolic modeling of methanogenesis by Methanosarcina barkeri

NASA Astrophysics Data System (ADS)

Jensvold, Z. D.; Jin, Q.

2015-12-01

Methanogenesis, the biological process of methane production, is the final step of natural organic matter degradation. In studying natural methanogenesis, important questions include how fast methanogenesis proceeds and how methanogens adapt to the environment. To address these questions, we propose a new approach - biogeochemical reaction modeling - by simulating the metabolic networks of methanogens. Biogeochemical reaction modeling combines geochemical reaction modeling and genome-scale metabolic modeling. Geochemical reaction modeling focuses on the speciation of electron donors and acceptors in the environment, and therefore the energy available to methanogens. Genome-scale metabolic modeling predicts microbial rates and metabolic strategies. Specifically, this approach describes methanogenesis using an enzyme network model, and computes enzyme rates by accounting for both the kinetics and thermodynamics. The network model is simulated numerically to predict enzyme abundances and rates of methanogen metabolism. We applied this new approach to Methanosarcina barkeri strain fusaro, a model methanogen that makes methane by reducing carbon dioxide and oxidizing dihydrogen. The simulation results match well with the results of previous laboratory experiments, including the magnitude of proton motive force and the kinetic parameters of Methanosarcina barkeri. The results also predict that in natural environments, the configuration of methanogenesis network, including the concentrations of enzymes and metabolites, differs significantly from that under laboratory settings.

Exploration of cellular reaction systems.

PubMed

Kirkilionis, Markus

2010-01-01

We discuss and review different ways to map cellular components and their temporal interaction with other such components to different non-spatially explicit mathematical models. The essential choices made in the literature are between discrete and continuous state spaces, between rule and event-based state updates and between deterministic and stochastic series of such updates. The temporal modelling of cellular regulatory networks (dynamic network theory) is compared with static network approaches in two first introductory sections on general network modelling. We concentrate next on deterministic rate-based dynamic regulatory networks and their derivation. In the derivation, we include methods from multiscale analysis and also look at structured large particles, here called macromolecular machines. It is clear that mass-action systems and their derivatives, i.e. networks based on enzyme kinetics, play the most dominant role in the literature. The tools to analyse cellular reaction networks are without doubt most complete for mass-action systems. We devote a long section at the end of the review to make a comprehensive review of related tools and mathematical methods. The emphasis is to show how cellular reaction networks can be analysed with the help of different associated graphs and the dissection into modules, i.e. sub-networks.

SSER: Species specific essential reactions database.

PubMed

Labena, Abraham A; Ye, Yuan-Nong; Dong, Chuan; Zhang, Fa-Z; Guo, Feng-Biao

2017-04-19

Essential reactions are vital components of cellular networks. They are the foundations of synthetic biology and are potential candidate targets for antimetabolic drug design. Especially if a single reaction is catalyzed by multiple enzymes, then inhibiting the reaction would be a better option than targeting the enzymes or the corresponding enzyme-encoding gene. The existing databases such as BRENDA, BiGG, KEGG, Bio-models, Biosilico, and many others offer useful and comprehensive information on biochemical reactions. But none of these databases especially focus on essential reactions. Therefore, building a centralized repository for this class of reactions would be of great value. Here, we present a species-specific essential reactions database (SSER). The current version comprises essential biochemical and transport reactions of twenty-six organisms which are identified via flux balance analysis (FBA) combined with manual curation on experimentally validated metabolic network models. Quantitative data on the number of essential reactions, number of the essential reactions associated with their respective enzyme-encoding genes and shared essential reactions across organisms are the main contents of the database. SSER would be a prime source to obtain essential reactions data and related gene and metabolite information and it can significantly facilitate the metabolic network models reconstruction and analysis, and drug target discovery studies. Users can browse, search, compare and download the essential reactions of organisms of their interest through the website http://cefg.uestc.edu.cn/sser .

Efficiency of reactant site sampling in network-free simulation of rule-based models for biochemical systems

PubMed Central

Yang, Jin; Hlavacek, William S.

2011-01-01

Rule-based models, which are typically formulated to represent cell signaling systems, can now be simulated via various network-free simulation methods. In a network-free method, reaction rates are calculated for rules that characterize molecular interactions, and these rule rates, which each correspond to the cumulative rate of all reactions implied by a rule, are used to perform a stochastic simulation of reaction kinetics. Network-free methods, which can be viewed as generalizations of Gillespie’s method, are so named because these methods do not require that a list of individual reactions implied by a set of rules be explicitly generated, which is a requirement of other methods for simulating rule-based models. This requirement is impractical for rule sets that imply large reaction networks (i.e., long lists of individual reactions), as reaction network generation is expensive. Here, we compare the network-free simulation methods implemented in RuleMonkey and NFsim, general-purpose software tools for simulating rule-based models encoded in the BioNetGen language. The method implemented in NFsim uses rejection sampling to correct overestimates of rule rates, which introduces null events (i.e., time steps that do not change the state of the system being simulated). The method implemented in RuleMonkey uses iterative updates to track rule rates exactly, which avoids null events. To ensure a fair comparison of the two methods, we developed implementations of the rejection and rejection-free methods specific to a particular class of kinetic models for multivalent ligand-receptor interactions. These implementations were written with the intention of making them as much alike as possible, minimizing the contribution of irrelevant coding differences to efficiency differences. Simulation results show that performance of the rejection method is equal to or better than that of the rejection-free method over wide parameter ranges. However, when parameter values are such that ligand-induced aggregation of receptors yields a large connected receptor cluster, the rejection-free method is more efficient. PMID:21832806

Efficient Constant-Time Complexity Algorithm for Stochastic Simulation of Large Reaction Networks.

PubMed

Thanh, Vo Hong; Zunino, Roberto; Priami, Corrado

2017-01-01

Exact stochastic simulation is an indispensable tool for a quantitative study of biochemical reaction networks. The simulation realizes the time evolution of the model by randomly choosing a reaction to fire and update the system state according to a probability that is proportional to the reaction propensity. Two computationally expensive tasks in simulating large biochemical networks are the selection of next reaction firings and the update of reaction propensities due to state changes. We present in this work a new exact algorithm to optimize both of these simulation bottlenecks. Our algorithm employs the composition-rejection on the propensity bounds of reactions to select the next reaction firing. The selection of next reaction firings is independent of the number reactions while the update of propensities is skipped and performed only when necessary. It therefore provides a favorable scaling for the computational complexity in simulating large reaction networks. We benchmark our new algorithm with the state of the art algorithms available in literature to demonstrate its applicability and efficiency.

General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks.

PubMed

Reis, Matthias; Kromer, Justus A; Klipp, Edda

2018-01-20

Multimodality is a phenomenon which complicates the analysis of statistical data based exclusively on mean and variance. Here, we present criteria for multimodality in hierarchic first-order reaction networks, consisting of catalytic and splitting reactions. Those networks are characterized by independent and dependent subnetworks. First, we prove the general solvability of the Chemical Master Equation (CME) for this type of reaction network and thereby extend the class of solvable CME's. Our general solution is analytical in the sense that it allows for a detailed analysis of its statistical properties. Given Poisson/deterministic initial conditions, we then prove the independent species to be Poisson/binomially distributed, while the dependent species exhibit generalized Poisson/Khatri Type B distributions. Generalized Poisson/Khatri Type B distributions are multimodal for an appropriate choice of parameters. We illustrate our criteria for multimodality by several basic models, as well as the well-known two-stage transcription-translation network and Bateman's model from nuclear physics. For both examples, multimodality was previously not reported.

A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks

PubMed Central

Khammash, Mustafa

2014-01-01

Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed. PMID:24968191

Automatic network coupling analysis for dynamical systems based on detailed kinetic models.

PubMed

Lebiedz, Dirk; Kammerer, Julia; Brandt-Pollmann, Ulrich

2005-10-01

We introduce a numerical complexity reduction method for the automatic identification and analysis of dynamic network decompositions in (bio)chemical kinetics based on error-controlled computation of a minimal model dimension represented by the number of (locally) active dynamical modes. Our algorithm exploits a generalized sensitivity analysis along state trajectories and subsequent singular value decomposition of sensitivity matrices for the identification of these dominant dynamical modes. It allows for a dynamic coupling analysis of (bio)chemical species in kinetic models that can be exploited for the piecewise computation of a minimal model on small time intervals and offers valuable functional insight into highly nonlinear reaction mechanisms and network dynamics. We present results for the identification of network decompositions in a simple oscillatory chemical reaction, time scale separation based model reduction in a Michaelis-Menten enzyme system and network decomposition of a detailed model for the oscillatory peroxidase-oxidase enzyme system.

A Petri net approach to the study of persistence in chemical reaction networks.

PubMed

Angeli, David; De Leenheer, Patrick; Sontag, Eduardo D

2007-12-01

Persistence is the property, for differential equations in R(n), that solutions starting in the positive orthant do not approach the boundary of the orthant. For chemical reactions and population models, this translates into the non-extinction property: provided that every species is present at the start of the reaction, no species will tend to be eliminated in the course of the reaction. This paper provides checkable conditions for persistence of chemical species in reaction networks, using concepts and tools from Petri net theory, and verifies these conditions on various systems which arise in the modeling of cell signaling pathways.

Reaction-diffusion processes and metapopulation models on duplex networks

NASA Astrophysics Data System (ADS)

Xuan, Qi; Du, Fang; Yu, Li; Chen, Guanrong

2013-03-01

Reaction-diffusion processes, used to model various spatially distributed dynamics such as epidemics, have been studied mostly on regular lattices or complex networks with simplex links that are identical and invariant in transferring different kinds of particles. However, in many self-organized systems, different particles may have their own private channels to keep their purities. Such division of links often significantly influences the underlying reaction-diffusion dynamics and thus needs to be carefully investigated. This article studies a special reaction-diffusion process, named susceptible-infected-susceptible (SIS) dynamics, given by the reaction steps β→α and α+β→2β, on duplex networks where links are classified into two groups: α and β links used to transfer α and β particles, which, along with the corresponding nodes, consist of an α subnetwork and a β subnetwork, respectively. It is found that the critical point of particle density to sustain reaction activity is independent of the network topology if there is no correlation between the degree sequences of the two subnetworks, and this critical value is suppressed or extended if the two degree sequences are positively or negatively correlated, respectively. Based on the obtained results, it is predicted that epidemic spreading may be promoted on positive correlated traffic networks but may be suppressed on networks with modules composed of different types of diffusion links.

Synchronization criteria for generalized reaction-diffusion neural networks via periodically intermittent control.

PubMed

Gan, Qintao; Lv, Tianshi; Fu, Zhenhua

2016-04-01

In this paper, the synchronization problem for a class of generalized neural networks with time-varying delays and reaction-diffusion terms is investigated concerning Neumann boundary conditions in terms of p-norm. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. By establishing a new inequality, some simple and useful conditions are obtained analytically to guarantee the global exponential synchronization of the addressed neural networks under the periodically intermittent control. According to the theoretical results, the influences of diffusion coefficients, diffusion space, and control rate on synchronization are analyzed. Finally, the feasibility and effectiveness of the proposed methods are shown by simulation examples, and by choosing different diffusion coefficients, diffusion spaces, and control rates, different controlled synchronization states can be obtained.

Genome scale metabolic reconstruction of Chlorella variabilis for exploring its metabolic potential for biofuels.

PubMed

Juneja, Ankita; Chaplen, Frank W R; Murthy, Ganti S

2016-08-01

A compartmentalized genome scale metabolic network was reconstructed for Chlorella variabilis to offer insight into various metabolic potentials from this alga. The model, iAJ526, was reconstructed with 1455 reactions, 1236 metabolites and 526 genes. 21% of the reactions were transport reactions and about 81% of the total reactions were associated with enzymes. Along with gap filling reactions, 2 major sub-pathways were added to the model, chitosan synthesis and rhamnose metabolism. The reconstructed model had reaction participation of 4.3 metabolites per reaction and average lethality fraction of 0.21. The model was effective in capturing the growth of C. variabilis under three light conditions (white, red and red+blue light) with fair agreement. This reconstructed metabolic network will serve an important role in systems biology for further exploration of metabolism for specific target metabolites and enable improved characteristics in the strain through metabolic engineering. Copyright © 2016 Elsevier Ltd. All rights reserved.

Mimoza: web-based semantic zooming and navigation in metabolic networks.

PubMed

Zhukova, Anna; Sherman, David J

2015-02-26

The complexity of genome-scale metabolic models makes them quite difficult for human users to read, since they contain thousands of reactions that must be included for accurate computer simulation. Interestingly, hidden similarities between groups of reactions can be discovered, and generalized to reveal higher-level patterns. The web-based navigation system Mimoza allows a human expert to explore metabolic network models in a semantically zoomable manner: The most general view represents the compartments of the model; the next view shows the generalized versions of reactions and metabolites in each compartment; and the most detailed view represents the initial network with the generalization-based layout (where similar metabolites and reactions are placed next to each other). It allows a human expert to grasp the general structure of the network and analyze it in a top-down manner Mimoza can be installed standalone, or used on-line at http://mimoza.bordeaux.inria.fr/ , or installed in a Galaxy server for use in workflows. Mimoza views can be embedded in web pages, or downloaded as COMBINE archives.

The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions

PubMed Central

2012-01-01

Background It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption). In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA). The validity of this heuristic SSA method is a priori doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions. Results We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA), as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations. Conclusions A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions. The ssLNA provides a simple and accurate means of performing stochastic model reduction and hence it is expected to be of widespread utility in studying the dynamics of large noisy reaction networks, as is common in computational and systems biology. PMID:22583770

Atmospheric reaction systems as null-models to identify structural traces of evolution in metabolism.

PubMed

Holme, Petter; Huss, Mikael; Lee, Sang Hoon

2011-05-06

The metabolism is the motor behind the biological complexity of an organism. One problem of characterizing its large-scale structure is that it is hard to know what to compare it to. All chemical reaction systems are shaped by the same physics that gives molecules their stability and affinity to react. These fundamental factors cannot be captured by standard null-models based on randomization. The unique property of organismal metabolism is that it is controlled, to some extent, by an enzymatic machinery that is subject to evolution. In this paper, we explore the possibility that reaction systems of planetary atmospheres can serve as a null-model against which we can define metabolic structure and trace the influence of evolution. We find that the two types of data can be distinguished by their respective degree distributions. This is especially clear when looking at the degree distribution of the reaction network (of reaction connected to each other if they involve the same molecular species). For the Earth's atmospheric network and the human metabolic network, we look into more detail for an underlying explanation of this deviation. However, we cannot pinpoint a single cause of the difference, rather there are several concurrent factors. By examining quantities relating to the modular-functional organization of the metabolism, we confirm that metabolic networks have a more complex modular organization than the atmospheric networks, but not much more. We interpret the more variegated modular arrangement of metabolism as a trace of evolved functionality. On the other hand, it is quite remarkable how similar the structures of these two types of networks are, which emphasizes that the constraints from the chemical properties of the molecules has a larger influence in shaping the reaction system than does natural selection.

A scalable moment-closure approximation for large-scale biochemical reaction networks

PubMed Central

Kazeroonian, Atefeh; Theis, Fabian J.; Hasenauer, Jan

2017-01-01

Abstract Motivation: Stochastic molecular processes are a leading cause of cell-to-cell variability. Their dynamics are often described by continuous-time discrete-state Markov chains and simulated using stochastic simulation algorithms. As these stochastic simulations are computationally demanding, ordinary differential equation models for the dynamics of the statistical moments have been developed. The number of state variables of these approximating models, however, grows at least quadratically with the number of biochemical species. This limits their application to small- and medium-sized processes. Results: In this article, we present a scalable moment-closure approximation (sMA) for the simulation of statistical moments of large-scale stochastic processes. The sMA exploits the structure of the biochemical reaction network to reduce the covariance matrix. We prove that sMA yields approximating models whose number of state variables depends predominantly on local properties, i.e. the average node degree of the reaction network, instead of the overall network size. The resulting complexity reduction is assessed by studying a range of medium- and large-scale biochemical reaction networks. To evaluate the approximation accuracy and the improvement in computational efficiency, we study models for JAK2/STAT5 signalling and NFκB signalling. Our method is applicable to generic biochemical reaction networks and we provide an implementation, including an SBML interface, which renders the sMA easily accessible. Availability and implementation: The sMA is implemented in the open-source MATLAB toolbox CERENA and is available from https://github.com/CERENADevelopers/CERENA. Contact: jan.hasenauer@helmholtz-muenchen.de or atefeh.kazeroonian@tum.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:28881983

Scalable Parameter Estimation for Genome-Scale Biochemical Reaction Networks

PubMed Central

Kaltenbacher, Barbara; Hasenauer, Jan

2017-01-01

Mechanistic mathematical modeling of biochemical reaction networks using ordinary differential equation (ODE) models has improved our understanding of small- and medium-scale biological processes. While the same should in principle hold for large- and genome-scale processes, the computational methods for the analysis of ODE models which describe hundreds or thousands of biochemical species and reactions are missing so far. While individual simulations are feasible, the inference of the model parameters from experimental data is computationally too intensive. In this manuscript, we evaluate adjoint sensitivity analysis for parameter estimation in large scale biochemical reaction networks. We present the approach for time-discrete measurement and compare it to state-of-the-art methods used in systems and computational biology. Our comparison reveals a significantly improved computational efficiency and a superior scalability of adjoint sensitivity analysis. The computational complexity is effectively independent of the number of parameters, enabling the analysis of large- and genome-scale models. Our study of a comprehensive kinetic model of ErbB signaling shows that parameter estimation using adjoint sensitivity analysis requires a fraction of the computation time of established methods. The proposed method will facilitate mechanistic modeling of genome-scale cellular processes, as required in the age of omics. PMID:28114351

Functional Alignment of Metabolic Networks.

PubMed

Mazza, Arnon; Wagner, Allon; Ruppin, Eytan; Sharan, Roded

2016-05-01

Network alignment has become a standard tool in comparative biology, allowing the inference of protein function, interaction, and orthology. However, current alignment techniques are based on topological properties of networks and do not take into account their functional implications. Here we propose, for the first time, an algorithm to align two metabolic networks by taking advantage of their coupled metabolic models. These models allow us to assess the functional implications of genes or reactions, captured by the metabolic fluxes that are altered following their deletion from the network. Such implications may spread far beyond the region of the network where the gene or reaction lies. We apply our algorithm to align metabolic networks from various organisms, ranging from bacteria to humans, showing that our alignment can reveal functional orthology relations that are missed by conventional topological alignments.

The US nuclear reaction data network. Summary of the first meeting, March 13 & 14 1996

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

NONE

1996-03-01

The first meeting of the US Nuclear Reaction Data Network (USNRDN) was held at the Colorado School of Mines, March 13-14, 1996 chaired by F. Edward Cecil. The Agenda of the meeting is attached. The Network, its mission, products and services; related nuclear data and data networks, members, and organization are described in Attachment 1. The following progress reports from the members of the USNRDN were distributed prior to the meeting and are given as Attachment 2. (1) Measurements and Development of Analytic Techniques for Basic Nuclear Physics and Nuclear Applications; (2) Nuclear Reaction Data Activities at the National Nuclearmore » Data Center; (3) Studies of nuclear reactions at very low energies; (4) Nuclear Reaction Data Activities, Nuclear Data Group; (5) Progress in Neutron Physics at Los Alamos - Experiments; (6) Nuclear Reaction Data Activities in Group T2; (7) Progress Report for the US Nuclear Reaction Data Network Meeting; (8) Nuclear Astrophysics Research Group (ORNL); (9) Progress Report from Ohio University; (10) Exciton Model Phenomenology; and (11) Progress Report for Coordination Meeting USNRDN.« less

Network Thermodynamic Curation of Human and Yeast Genome-Scale Metabolic Models

PubMed Central

Martínez, Verónica S.; Quek, Lake-Ee; Nielsen, Lars K.

2014-01-01

Genome-scale models are used for an ever-widening range of applications. Although there has been much focus on specifying the stoichiometric matrix, the predictive power of genome-scale models equally depends on reaction directions. Two-thirds of reactions in the two eukaryotic reconstructions Homo sapiens Recon 1 and Yeast 5 are specified as irreversible. However, these specifications are mainly based on biochemical textbooks or on their similarity to other organisms and are rarely underpinned by detailed thermodynamic analysis. In this study, a to our knowledge new workflow combining network-embedded thermodynamic and flux variability analysis was used to evaluate existing irreversibility constraints in Recon 1 and Yeast 5 and to identify new ones. A total of 27 and 16 new irreversible reactions were identified in Recon 1 and Yeast 5, respectively, whereas only four reactions were found with directions incorrectly specified against thermodynamics (three in Yeast 5 and one in Recon 1). The workflow further identified for both models several isolated internal loops that require further curation. The framework also highlighted the need for substrate channeling (in human) and ATP hydrolysis (in yeast) for the essential reaction catalyzed by phosphoribosylaminoimidazole carboxylase in purine metabolism. Finally, the framework highlighted differences in proline metabolism between yeast (cytosolic anabolism and mitochondrial catabolism) and humans (exclusively mitochondrial metabolism). We conclude that network-embedded thermodynamics facilitates the specification and validation of irreversibility constraints in compartmentalized metabolic models, at the same time providing further insight into network properties. PMID:25028891

A Hybrid of the Chemical Master Equation and the Gillespie Algorithm for Efficient Stochastic Simulations of Sub-Networks.

PubMed

Albert, Jaroslav

2016-01-01

Modeling stochastic behavior of chemical reaction networks is an important endeavor in many aspects of chemistry and systems biology. The chemical master equation (CME) and the Gillespie algorithm (GA) are the two most fundamental approaches to such modeling; however, each of them has its own limitations: the GA may require long computing times, while the CME may demand unrealistic memory storage capacity. We propose a method that combines the CME and the GA that allows one to simulate stochastically a part of a reaction network. First, a reaction network is divided into two parts. The first part is simulated via the GA, while the solution of the CME for the second part is fed into the GA in order to update its propensities. The advantage of this method is that it avoids the need to solve the CME or stochastically simulate the entire network, which makes it highly efficient. One of its drawbacks, however, is that most of the information about the second part of the network is lost in the process. Therefore, this method is most useful when only partial information about a reaction network is needed. We tested this method against the GA on two systems of interest in biology--the gene switch and the Griffith model of a genetic oscillator--and have shown it to be highly accurate. Comparing this method to four different stochastic algorithms revealed it to be at least an order of magnitude faster than the fastest among them.

Estimation of parameters in rational reaction rates of molecular biological systems via weighted least squares

NASA Astrophysics Data System (ADS)

Wu, Fang-Xiang; Mu, Lei; Shi, Zhong-Ke

2010-01-01

The models of gene regulatory networks are often derived from statistical thermodynamics principle or Michaelis-Menten kinetics equation. As a result, the models contain rational reaction rates which are nonlinear in both parameters and states. It is challenging to estimate parameters nonlinear in a model although there have been many traditional nonlinear parameter estimation methods such as Gauss-Newton iteration method and its variants. In this article, we develop a two-step method to estimate the parameters in rational reaction rates of gene regulatory networks via weighted linear least squares. This method takes the special structure of rational reaction rates into consideration. That is, in the rational reaction rates, the numerator and the denominator are linear in parameters. By designing a special weight matrix for the linear least squares, parameters in the numerator and the denominator can be estimated by solving two linear least squares problems. The main advantage of the developed method is that it can produce the analytical solutions to the estimation of parameters in rational reaction rates which originally is nonlinear parameter estimation problem. The developed method is applied to a couple of gene regulatory networks. The simulation results show the superior performance over Gauss-Newton method.

Exact Hybrid Particle/Population Simulation of Rule-Based Models of Biochemical Systems

PubMed Central

Stover, Lori J.; Nair, Niketh S.; Faeder, James R.

2014-01-01

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This “network-free” approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of “partial network expansion” into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility. PMID:24699269

Exact hybrid particle/population simulation of rule-based models of biochemical systems.

PubMed

Hogg, Justin S; Harris, Leonard A; Stover, Lori J; Nair, Niketh S; Faeder, James R

2014-04-01

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This "network-free" approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of "partial network expansion" into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility.

Sparse Regression Based Structure Learning of Stochastic Reaction Networks from Single Cell Snapshot Time Series.

PubMed

Klimovskaia, Anna; Ganscha, Stefan; Claassen, Manfred

2016-12-01

Stochastic chemical reaction networks constitute a model class to quantitatively describe dynamics and cell-to-cell variability in biological systems. The topology of these networks typically is only partially characterized due to experimental limitations. Current approaches for refining network topology are based on the explicit enumeration of alternative topologies and are therefore restricted to small problem instances with almost complete knowledge. We propose the reactionet lasso, a computational procedure that derives a stepwise sparse regression approach on the basis of the Chemical Master Equation, enabling large-scale structure learning for reaction networks by implicitly accounting for billions of topology variants. We have assessed the structure learning capabilities of the reactionet lasso on synthetic data for the complete TRAIL induced apoptosis signaling cascade comprising 70 reactions. We find that the reactionet lasso is able to efficiently recover the structure of these reaction systems, ab initio, with high sensitivity and specificity. With only < 1% false discoveries, the reactionet lasso is able to recover 45% of all true reactions ab initio among > 6000 possible reactions and over 102000 network topologies. In conjunction with information rich single cell technologies such as single cell RNA sequencing or mass cytometry, the reactionet lasso will enable large-scale structure learning, particularly in areas with partial network structure knowledge, such as cancer biology, and thereby enable the detection of pathological alterations of reaction networks. We provide software to allow for wide applicability of the reactionet lasso.

Minimum reaction network necessary to describe Ar/CF4 plasma etch

NASA Astrophysics Data System (ADS)

Helpert, Sofia; Chopra, Meghali; Bonnecaze, Roger T.

2018-03-01

Predicting the etch and deposition profiles created using plasma processes is challenging due to the complexity of plasma discharges and plasma-surface interactions. Volume-averaged global models allow for efficient prediction of important processing parameters and provide a means to quickly determine the effect of a variety of process inputs on the plasma discharge. However, global models are limited based on simplifying assumptions to describe the chemical reaction network. Here a database of 128 reactions is compiled and their corresponding rate constants collected from 24 sources for an Ar/CF4 plasma using the platform RODEo (Recipe Optimization for Deposition and Etching). Six different reaction sets were tested which employed anywhere from 12 to all 128 reactions to evaluate the impact of the reaction database on particle species densities and electron temperature. Because many the reactions used in our database had conflicting rate constants as reported in literature, we also present a method to deal with those uncertainties when constructing the model which includes weighting each reaction rate and filtering outliers. By analyzing the link between a reaction's rate constant and its impact on the predicted plasma densities and electron temperatures, we determine the conditions at which a reaction is deemed necessary to the plasma model. The results of this study provide a foundation for determining which minimal set of reactions must be included in the reaction set of the plasma model.

Neurocomputation by Reaction Diffusion

NASA Astrophysics Data System (ADS)

Liang, Ping

1995-08-01

This Letter demonstrates the possible role nonsynaptic diffusion neurotransmission may play in neurocomputation using an artificial neural network model. A reaction-diffusion neural network model with field-based information-processing mechanisms is proposed. The advantages of nonsynaptic field neurotransmission from a computational viewpoint demonstrated in this Letter include long-range inhibition using only local interaction, nonhardwired and changeable (target specific) long-range communication pathways, and multiple simultaneous spatiotemporal organization processes in the same medium.

Meneco, a Topology-Based Gap-Filling Tool Applicable to Degraded Genome-Wide Metabolic Networks

PubMed Central

Prigent, Sylvain; Frioux, Clémence; Dittami, Simon M.; Larhlimi, Abdelhalim; Collet, Guillaume; Gutknecht, Fabien; Got, Jeanne; Eveillard, Damien; Bourdon, Jérémie; Plewniak, Frédéric; Tonon, Thierry; Siegel, Anne

2017-01-01

Increasing amounts of sequence data are becoming available for a wide range of non-model organisms. Investigating and modelling the metabolic behaviour of those organisms is highly relevant to understand their biology and ecology. As sequences are often incomplete and poorly annotated, draft networks of their metabolism largely suffer from incompleteness. Appropriate gap-filling methods to identify and add missing reactions are therefore required to address this issue. However, current tools rely on phenotypic or taxonomic information, or are very sensitive to the stoichiometric balance of metabolic reactions, especially concerning the co-factors. This type of information is often not available or at least prone to errors for newly-explored organisms. Here we introduce Meneco, a tool dedicated to the topological gap-filling of genome-scale draft metabolic networks. Meneco reformulates gap-filling as a qualitative combinatorial optimization problem, omitting constraints raised by the stoichiometry of a metabolic network considered in other methods, and solves this problem using Answer Set Programming. Run on several artificial test sets gathering 10,800 degraded Escherichia coli networks Meneco was able to efficiently identify essential reactions missing in networks at high degradation rates, outperforming the stoichiometry-based tools in scalability. To demonstrate the utility of Meneco we applied it to two case studies. Its application to recent metabolic networks reconstructed for the brown algal model Ectocarpus siliculosus and an associated bacterium Candidatus Phaeomarinobacter ectocarpi revealed several candidate metabolic pathways for algal-bacterial interactions. Then Meneco was used to reconstruct, from transcriptomic and metabolomic data, the first metabolic network for the microalga Euglena mutabilis. These two case studies show that Meneco is a versatile tool to complete draft genome-scale metabolic networks produced from heterogeneous data, and to suggest relevant reactions that explain the metabolic capacity of a biological system. PMID:28129330

Meneco, a Topology-Based Gap-Filling Tool Applicable to Degraded Genome-Wide Metabolic Networks.

PubMed

Prigent, Sylvain; Frioux, Clémence; Dittami, Simon M; Thiele, Sven; Larhlimi, Abdelhalim; Collet, Guillaume; Gutknecht, Fabien; Got, Jeanne; Eveillard, Damien; Bourdon, Jérémie; Plewniak, Frédéric; Tonon, Thierry; Siegel, Anne

2017-01-01

Increasing amounts of sequence data are becoming available for a wide range of non-model organisms. Investigating and modelling the metabolic behaviour of those organisms is highly relevant to understand their biology and ecology. As sequences are often incomplete and poorly annotated, draft networks of their metabolism largely suffer from incompleteness. Appropriate gap-filling methods to identify and add missing reactions are therefore required to address this issue. However, current tools rely on phenotypic or taxonomic information, or are very sensitive to the stoichiometric balance of metabolic reactions, especially concerning the co-factors. This type of information is often not available or at least prone to errors for newly-explored organisms. Here we introduce Meneco, a tool dedicated to the topological gap-filling of genome-scale draft metabolic networks. Meneco reformulates gap-filling as a qualitative combinatorial optimization problem, omitting constraints raised by the stoichiometry of a metabolic network considered in other methods, and solves this problem using Answer Set Programming. Run on several artificial test sets gathering 10,800 degraded Escherichia coli networks Meneco was able to efficiently identify essential reactions missing in networks at high degradation rates, outperforming the stoichiometry-based tools in scalability. To demonstrate the utility of Meneco we applied it to two case studies. Its application to recent metabolic networks reconstructed for the brown algal model Ectocarpus siliculosus and an associated bacterium Candidatus Phaeomarinobacter ectocarpi revealed several candidate metabolic pathways for algal-bacterial interactions. Then Meneco was used to reconstruct, from transcriptomic and metabolomic data, the first metabolic network for the microalga Euglena mutabilis. These two case studies show that Meneco is a versatile tool to complete draft genome-scale metabolic networks produced from heterogeneous data, and to suggest relevant reactions that explain the metabolic capacity of a biological system.

BioMOL: a computer-assisted biological modeling tool for complex chemical mixtures and biological processes at the molecular level.

PubMed Central

Klein, Michael T; Hou, Gang; Quann, Richard J; Wei, Wei; Liao, Kai H; Yang, Raymond S H; Campain, Julie A; Mazurek, Monica A; Broadbelt, Linda J

2002-01-01

A chemical engineering approach for the rigorous construction, solution, and optimization of detailed kinetic models for biological processes is described. This modeling capability addresses the required technical components of detailed kinetic modeling, namely, the modeling of reactant structure and composition, the building of the reaction network, the organization of model parameters, the solution of the kinetic model, and the optimization of the model. Even though this modeling approach has enjoyed successful application in the petroleum industry, its application to biomedical research has just begun. We propose to expand the horizons on classic pharmacokinetics and physiologically based pharmacokinetics (PBPK), where human or animal bodies were often described by a few compartments, by integrating PBPK with reaction network modeling described in this article. If one draws a parallel between an oil refinery, where the application of this modeling approach has been very successful, and a human body, the individual processing units in the oil refinery may be considered equivalent to the vital organs of the human body. Even though the cell or organ may be much more complicated, the complex biochemical reaction networks in each organ may be similarly modeled and linked in much the same way as the modeling of the entire oil refinery through linkage of the individual processing units. The integrated chemical engineering software package described in this article, BioMOL, denotes the biological application of molecular-oriented lumping. BioMOL can build a detailed model in 1-1,000 CPU sec using standard desktop hardware. The models solve and optimize using standard and widely available hardware and software and can be presented in the context of a user-friendly interface. We believe this is an engineering tool with great promise in its application to complex biological reaction networks. PMID:12634134

Version 6 of the consensus yeast metabolic network refines biochemical coverage and improves model performance

PubMed Central

Heavner, Benjamin D.; Smallbone, Kieran; Price, Nathan D.; Walker, Larry P.

2013-01-01

Updates to maintain a state-of-the art reconstruction of the yeast metabolic network are essential to reflect our understanding of yeast metabolism and functional organization, to eliminate any inaccuracies identified in earlier iterations, to improve predictive accuracy and to continue to expand into novel subsystems to extend the comprehensiveness of the model. Here, we present version 6 of the consensus yeast metabolic network (Yeast 6) as an update to the community effort to computationally reconstruct the genome-scale metabolic network of Saccharomyces cerevisiae S288c. Yeast 6 comprises 1458 metabolites participating in 1888 reactions, which are annotated with 900 yeast genes encoding the catalyzing enzymes. Compared with Yeast 5, Yeast 6 demonstrates improved sensitivity, specificity and positive and negative predictive values for predicting gene essentiality in glucose-limited aerobic conditions when analyzed with flux balance analysis. Additionally, Yeast 6 improves the accuracy of predicting the likelihood that a mutation will cause auxotrophy. The network reconstruction is available as a Systems Biology Markup Language (SBML) file enriched with Minimium Information Requested in the Annotation of Biochemical Models (MIRIAM)-compliant annotations. Small- and macromolecules in the network are referenced to authoritative databases such as Uniprot or ChEBI. Molecules and reactions are also annotated with appropriate publications that contain supporting evidence. Yeast 6 is freely available at http://yeast.sf.net/ as three separate SBML files: a model using the SBML level 3 Flux Balance Constraint package, a model compatible with the MATLAB® COBRA Toolbox for backward compatibility and a reconstruction containing only reactions for which there is experimental evidence (without the non-biological reactions necessary for simulating growth). Database URL: http://yeast.sf.net/ PMID:23935056

A reaction-based paradigm to model reactive chemical transport in groundwater with general kinetic and equilibrium reactions.

PubMed

Zhang, Fan; Yeh, Gour-Tsyh; Parker, Jack C; Brooks, Scott C; Pace, Molly N; Kim, Young-Jin; Jardine, Philip M; Watson, David B

2007-06-16

This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing N(E) equilibrium reactions and a set of reactive transport equations of M-N(E) kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.

Preprogramming Complex Hydrogel Responses using Enzymatic Reaction Networks.

PubMed

Postma, Sjoerd G J; Vialshin, Ilia N; Gerritsen, Casper Y; Bao, Min; Huck, Wilhelm T S

2017-02-06

The creation of adaptive matter is heavily inspired by biological systems. However, it remains challenging to design complex material responses that are governed by reaction networks, which lie at the heart of cellular complexity. The main reason for this slow progress is the lack of a general strategy to integrate reaction networks with materials. Herein we use a systematic approach to preprogram the response of a hydrogel to a trigger, in this case the enzyme trypsin, which activates a reaction network embedded within the hydrogel. A full characterization of all the kinetic rate constants in the system enabled the construction of a computational model, which predicted different hydrogel responses depending on the input concentration of the trigger. The results of the simulation are in good agreement with experimental findings. Our methodology can be used to design new, adaptive materials of which the properties are governed by reaction networks of arbitrary complexity. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics.

PubMed

Hanel, Rudolf; Pöchacker, Manfred; Thurner, Stefan

2010-12-28

Linearized catalytic reaction equations (modelling, for example, the dynamics of genetic regulatory networks), under the constraint that expression levels, i.e. molecular concentrations of nucleic material, are positive, exhibit non-trivial dynamical properties, which depend on the average connectivity of the reaction network. In these systems, an inflation of the edge of chaos and multi-stability have been demonstrated to exist. The positivity constraint introduces a nonlinearity, which makes chaotic dynamics possible. Despite the simplicity of such minimally nonlinear systems, their basic properties allow us to understand the fundamental dynamical properties of complex biological reaction networks. We analyse the Lyapunov spectrum, determine the probability of finding stationary oscillating solutions, demonstrate the effect of the nonlinearity on the effective in- and out-degree of the active interaction network, and study how the frequency distributions of oscillatory modes of such a system depend on the average connectivity.

Cumulative Significance of Hyporheic Exchange and Biogeochemical Processing in River Networks

NASA Astrophysics Data System (ADS)

Harvey, J. W.; Gomez-Velez, J. D.

2014-12-01

Biogeochemical reactions in rivers that decrease excessive loads of nutrients, metals, organic compounds, etc. are enhanced by hydrologic interactions with microbially and geochemically active sediments of the hyporheic zone. The significance of reactions in individual hyporheic flow paths has been shown to be controlled by the contact time between river water and sediment and the intrinsic reaction rate in the sediment. However, little is known about how the cumulative effects of hyporheic processing in large river basins. We used the river network model NEXSS (Gomez-Velez and Harvey, submitted) to simulate hyporheic exchange through synthetic river networks based on the best available models of network topology, hydraulic geometry and scaling of geomorphic features, grain size, hydraulic conductivity, and intrinsic reaction rates of nutrients and metals in river sediment. The dimensionless reaction significance factor, RSF (Harvey et al., 2013) was used to quantify the cumulative removal fraction of a reactive solute by hyporheic processing. SF scales reaction progress in a single pass through the hyporheic zone with the proportion of stream discharge passing through the hyporheic zone for a specified distance. Reaction progress is optimal where the intrinsic reaction timescale in sediment matches the residence time of hyporheic flow and is less efficient in longer residence time hyporheic flow as a result of the decreasing proportion of river flow that is processed by longer residence time hyporheic flow paths. In contrast, higher fluxes through short residence time hyporheic flow paths may be inefficient because of the repeated surface-subsurface exchanges required to complete the reaction. Using NEXSS we found that reaction efficiency may be high in both small streams and large rivers, although for different reasons. In small streams reaction progress generally is dominated by faster pathways of vertical exchange beneath submerged bedforms. Slower exchange beneath meandering river banks mainly has importance only in large rivers. For solutes entering networks in proportion to water inputs it is the lower order streams that tend to dominate cumulative reaction progress.

Path finding methods accounting for stoichiometry in metabolic networks

PubMed Central

2011-01-01

Graph-based methods have been widely used for the analysis of biological networks. Their application to metabolic networks has been much discussed, in particular noting that an important weakness in such methods is that reaction stoichiometry is neglected. In this study, we show that reaction stoichiometry can be incorporated into path-finding approaches via mixed-integer linear programming. This major advance at the modeling level results in improved prediction of topological and functional properties in metabolic networks. PMID:21619601

Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks.

PubMed

Meng, X Flora; Baetica, Ania-Ariadna; Singhal, Vipul; Murray, Richard M

2017-05-01

Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterize state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing the stationary behaviour of stochastic biochemical reaction networks. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and biochemical reactions with two-dimensional state spaces. © 2017 The Author(s).

Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks

PubMed Central

Baetica, Ania-Ariadna; Singhal, Vipul; Murray, Richard M.

2017-01-01

Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterize state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing the stationary behaviour of stochastic biochemical reaction networks. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and biochemical reactions with two-dimensional state spaces. PMID:28566513

A network dynamics approach to chemical reaction networks

NASA Astrophysics Data System (ADS)

van der Schaft, A. J.; Rao, S.; Jayawardhana, B.

2016-04-01

A treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics, in particular of consensus dynamics. By starting from the complex-balanced assumption, the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in the chemical reaction network theory, and which directly relates to the thermodynamics and port-Hamiltonian formulation of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This immediately leads to the characterisation of the set of equilibria and their stability. Furthermore, the assumption of complex balancedness is revisited from the point of view of Kirchhoff's matrix tree theorem. Both the form of the dynamics and the deduced behaviour are very similar to consensus dynamics, and provide additional perspectives to the latter. Finally, using the classical idea of extending the graph of chemical complexes by a 'zero' complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action kinetics outflows is given, and a unified framework is provided for structure-preserving model reduction of this important class of open reaction networks.

A new network representation of the metabolism to detect chemical transformation modules.

PubMed

Sorokina, Maria; Medigue, Claudine; Vallenet, David

2015-11-14

Metabolism is generally modeled by directed networks where nodes represent reactions and/or metabolites. In order to explore metabolic pathway conservation and divergence among organisms, previous studies were based on graph alignment to find similar pathways. Few years ago, the concept of chemical transformation modules, also called reaction modules, was introduced and correspond to sequences of chemical transformations which are conserved in metabolism. We propose here a novel graph representation of the metabolic network where reactions sharing a same chemical transformation type are grouped in Reaction Molecular Signatures (RMS). RMS were automatically computed for all reactions and encode changes in atoms and bonds. A reaction network containing all available metabolic knowledge was then reduced by an aggregation of reaction nodes and edges to obtain a RMS network. Paths in this network were explored and a substantial number of conserved chemical transformation modules was detected. Furthermore, this graph-based formalism allows us to define several path scores reflecting different biological conservation meanings. These scores are significantly higher for paths corresponding to known metabolic pathways and were used conjointly to build association rules that should predict metabolic pathway types like biosynthesis or degradation. This representation of metabolism in a RMS network offers new insights to capture relevant metabolic contexts. Furthermore, along with genomic context methods, it should improve the detection of gene clusters corresponding to new metabolic pathways.

Network thermodynamic curation of human and yeast genome-scale metabolic models.

PubMed

Martínez, Verónica S; Quek, Lake-Ee; Nielsen, Lars K

2014-07-15

Genome-scale models are used for an ever-widening range of applications. Although there has been much focus on specifying the stoichiometric matrix, the predictive power of genome-scale models equally depends on reaction directions. Two-thirds of reactions in the two eukaryotic reconstructions Homo sapiens Recon 1 and Yeast 5 are specified as irreversible. However, these specifications are mainly based on biochemical textbooks or on their similarity to other organisms and are rarely underpinned by detailed thermodynamic analysis. In this study, a to our knowledge new workflow combining network-embedded thermodynamic and flux variability analysis was used to evaluate existing irreversibility constraints in Recon 1 and Yeast 5 and to identify new ones. A total of 27 and 16 new irreversible reactions were identified in Recon 1 and Yeast 5, respectively, whereas only four reactions were found with directions incorrectly specified against thermodynamics (three in Yeast 5 and one in Recon 1). The workflow further identified for both models several isolated internal loops that require further curation. The framework also highlighted the need for substrate channeling (in human) and ATP hydrolysis (in yeast) for the essential reaction catalyzed by phosphoribosylaminoimidazole carboxylase in purine metabolism. Finally, the framework highlighted differences in proline metabolism between yeast (cytosolic anabolism and mitochondrial catabolism) and humans (exclusively mitochondrial metabolism). We conclude that network-embedded thermodynamics facilitates the specification and validation of irreversibility constraints in compartmentalized metabolic models, at the same time providing further insight into network properties. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Chemical reaction networks as a model to describe UVC- and radiolytically-induced reactions of simple compounds.

PubMed

Dondi, Daniele; Merli, Daniele; Albini, Angelo; Zeffiro, Alberto; Serpone, Nick

2012-05-01

When a chemical system is submitted to high energy sources (UV, ionizing radiation, plasma sparks, etc.), as is expected to be the case of prebiotic chemistry studies, a plethora of reactive intermediates could form. If oxygen is present in excess, carbon dioxide and water are the major products. More interesting is the case of reducing conditions where synthetic pathways are also possible. This article examines the theoretical modeling of such systems with random-generated chemical networks. Four types of random-generated chemical networks were considered that originated from a combination of two connection topologies (viz., Poisson and scale-free) with reversible and irreversible chemical reactions. The results were analyzed taking into account the number of the most abundant products required for reaching 50% of the total number of moles of compounds at equilibrium, as this may be related to an actual problem of complex mixture analysis. The model accounts for multi-component reaction systems with no a priori knowledge of reacting species and the intermediates involved if system components are sufficiently interconnected. The approach taken is relevant to an earlier study on reactions that may have occurred in prebiotic systems where only a few compounds were detected. A validation of the model was attained on the basis of results of UVC and radiolytic reactions of prebiotic mixtures of low molecular weight compounds likely present on the primeval Earth.

An Analytical Framework for Studying Small-Number Effects in Catalytic Reaction Networks: A Probability Generating Function Approach to Chemical Master Equations

PubMed Central

Nakagawa, Masaki; Togashi, Yuichi

2016-01-01

Cell activities primarily depend on chemical reactions, especially those mediated by enzymes, and this has led to these activities being modeled as catalytic reaction networks. Although deterministic ordinary differential equations of concentrations (rate equations) have been widely used for modeling purposes in the field of systems biology, it has been pointed out that these catalytic reaction networks may behave in a way that is qualitatively different from such deterministic representation when the number of molecules for certain chemical species in the system is small. Apart from this, representing these phenomena by simple binary (on/off) systems that omit the quantities would also not be feasible. As recent experiments have revealed the existence of rare chemical species in cells, the importance of being able to model potential small-number phenomena is being recognized. However, most preceding studies were based on numerical simulations, and theoretical frameworks to analyze these phenomena have not been sufficiently developed. Motivated by the small-number issue, this work aimed to develop an analytical framework for the chemical master equation describing the distributional behavior of catalytic reaction networks. For simplicity, we considered networks consisting of two-body catalytic reactions. We used the probability generating function method to obtain the steady-state solutions of the chemical master equation without specifying the parameters. We obtained the time evolution equations of the first- and second-order moments of concentrations, and the steady-state analytical solution of the chemical master equation under certain conditions. These results led to the rank conservation law, the connecting state to the winner-takes-all state, and analysis of 2-molecules M-species systems. A possible interpretation of the theoretical conclusion for actual biochemical pathways is also discussed. PMID:27047384

Rapid neutral-neutral reactions at low temperatures: a new network and first results for TMC-1

NASA Astrophysics Data System (ADS)

Smith, Ian W. M.; Herbst, Eric; Chang, Qiang

2004-05-01

There is now ample evidence from an assortment of experiments, especially those involving the CRESU (Cinétique de Réaction en Ecoulement Supersonique Uniforme) technique, that a variety of neutral-neutral reactions possess no activation energy barrier and are quite rapid at very low temperatures. These reactions include both radical-radical systems and, more surprisingly, systems involving an atom or a radical and one `stable' species. Generalizing from the small but growing number of systems studied in the laboratory, we estimate reaction rate coefficients for a larger number of such reactions and include these estimates in a new network of gas-phase reactions for use in low-temperature interstellar chemistry. Designated osu.2003, the new network is available on the World Wide Web and will be continually updated. A table of new results for molecular abundances in the dark cloud TMC-1 (CP) is provided and compared with results from an older (new standard model; nsm) network.

Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models

NASA Astrophysics Data System (ADS)

Thomas, Philipp; Straube, Arthur V.; Grima, Ramon

2010-11-01

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved by applying a mesoscopic version of the quasisteady-state assumption to the exact Fokker-Planck equation associated with the Poisson representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing subcellular volume, decreasing Michaelis-Menten constants, and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.

Impulsive synchronization of stochastic reaction-diffusion neural networks with mixed time delays.

PubMed

Sheng, Yin; Zeng, Zhigang

2018-07-01

This paper discusses impulsive synchronization of stochastic reaction-diffusion neural networks with Dirichlet boundary conditions and hybrid time delays. By virtue of inequality techniques, theories of stochastic analysis, linear matrix inequalities, and the contradiction method, sufficient criteria are proposed to ensure exponential synchronization of the addressed stochastic reaction-diffusion neural networks with mixed time delays via a designed impulsive controller. Compared with some recent studies, the neural network models herein are more general, some restrictions are relaxed, and the obtained conditions enhance and generalize some published ones. Finally, two numerical simulations are performed to substantiate the validity and merits of the developed theoretical analysis. Copyright © 2018 Elsevier Ltd. All rights reserved.

Reconstruction of metabolic pathways by combining probabilistic graphical model-based and knowledge-based methods

PubMed Central

2014-01-01

Automatic reconstruction of metabolic pathways for an organism from genomics and transcriptomics data has been a challenging and important problem in bioinformatics. Traditionally, known reference pathways can be mapped into an organism-specific ones based on its genome annotation and protein homology. However, this simple knowledge-based mapping method might produce incomplete pathways and generally cannot predict unknown new relations and reactions. In contrast, ab initio metabolic network construction methods can predict novel reactions and interactions, but its accuracy tends to be low leading to a lot of false positives. Here we combine existing pathway knowledge and a new ab initio Bayesian probabilistic graphical model together in a novel fashion to improve automatic reconstruction of metabolic networks. Specifically, we built a knowledge database containing known, individual gene / protein interactions and metabolic reactions extracted from existing reference pathways. Known reactions and interactions were then used as constraints for Bayesian network learning methods to predict metabolic pathways. Using individual reactions and interactions extracted from different pathways of many organisms to guide pathway construction is new and improves both the coverage and accuracy of metabolic pathway construction. We applied this probabilistic knowledge-based approach to construct the metabolic networks from yeast gene expression data and compared its results with 62 known metabolic networks in the KEGG database. The experiment showed that the method improved the coverage of metabolic network construction over the traditional reference pathway mapping method and was more accurate than pure ab initio methods. PMID:25374614

Eliminating fast reactions in stochastic simulations of biochemical networks: A bistable genetic switch

NASA Astrophysics Data System (ADS)

Morelli, Marco J.; Allen, Rosalind J.; Tǎnase-Nicola, Sorin; ten Wolde, Pieter Rein

2008-01-01

In many stochastic simulations of biochemical reaction networks, it is desirable to "coarse grain" the reaction set, removing fast reactions while retaining the correct system dynamics. Various coarse-graining methods have been proposed, but it remains unclear which methods are reliable and which reactions can safely be eliminated. We address these issues for a model gene regulatory network that is particularly sensitive to dynamical fluctuations: a bistable genetic switch. We remove protein-DNA and/or protein-protein association-dissociation reactions from the reaction set using various coarse-graining strategies. We determine the effects on the steady-state probability distribution function and on the rate of fluctuation-driven switch flipping transitions. We find that protein-protein interactions may be safely eliminated from the reaction set, but protein-DNA interactions may not. We also find that it is important to use the chemical master equation rather than macroscopic rate equations to compute effective propensity functions for the coarse-grained reactions.

Identification of lethal reactions in the Esherichia coli metabolic network: Graph theory approach

NASA Astrophysics Data System (ADS)

Ghim, C.-M.; Goh, K.-I.; Kahng, B.; Kim, D.

2004-03-01

As a first step toward holistic modeling of cells, we analyze the biochemical reactions occurring in the genome-scale metabolism of Esherichia coli. To this end, we construct a directed bipartite graph by assigning metabolite or reaction to each node. We apply various measures of centrality, a well-known concept in the graph theory, and their modifications to the metabolic network, finding that there exist lethal reactions involved in the central metabolism. Such lethal reactions or associated enzymes under diverse environments in silico are identified and compared with earlier results obtained from flux balance analysis.

Signalling Network Construction for Modelling Plant Defence Response

PubMed Central

Miljkovic, Dragana; Stare, Tjaša; Mozetič, Igor; Podpečan, Vid; Petek, Marko; Witek, Kamil; Dermastia, Marina; Lavrač, Nada; Gruden, Kristina

2012-01-01

Plant defence signalling response against various pathogens, including viruses, is a complex phenomenon. In resistant interaction a plant cell perceives the pathogen signal, transduces it within the cell and performs a reprogramming of the cell metabolism leading to the pathogen replication arrest. This work focuses on signalling pathways crucial for the plant defence response, i.e., the salicylic acid, jasmonic acid and ethylene signal transduction pathways, in the Arabidopsis thaliana model plant. The initial signalling network topology was constructed manually by defining the representation formalism, encoding the information from public databases and literature, and composing a pathway diagram. The manually constructed network structure consists of 175 components and 387 reactions. In order to complement the network topology with possibly missing relations, a new approach to automated information extraction from biological literature was developed. This approach, named Bio3graph, allows for automated extraction of biological relations from the literature, resulting in a set of (component1, reaction, component2) triplets and composing a graph structure which can be visualised, compared to the manually constructed topology and examined by the experts. Using a plant defence response vocabulary of components and reaction types, Bio3graph was applied to a set of 9,586 relevant full text articles, resulting in 137 newly detected reactions between the components. Finally, the manually constructed topology and the new reactions were merged to form a network structure consisting of 175 components and 524 reactions. The resulting pathway diagram of plant defence signalling represents a valuable source for further computational modelling and interpretation of omics data. The developed Bio3graph approach, implemented as an executable language processing and graph visualisation workflow, is publically available at http://ropot.ijs.si/bio3graph/and can be utilised for modelling other biological systems, given that an adequate vocabulary is provided. PMID:23272172

Generalizing Gillespie’s Direct Method to Enable Network-Free Simulations

DOE PAGES

Suderman, Ryan T.; Mitra, Eshan David; Lin, Yen Ting; ...

2018-03-28

Gillespie’s direct method for stochastic simulation of chemical kinetics is a staple of computational systems biology research. However, the algorithm requires explicit enumeration of all reactions and all chemical species that may arise in the system. In many cases, this is not feasible due to the combinatorial explosion of reactions and species in biological networks. Rule-based modeling frameworks provide a way to exactly represent networks containing such combinatorial complexity, and generalizations of Gillespie’s direct method have been developed as simulation engines for rule-based modeling languages. Here, we provide both a high-level description of the algorithms underlying the simulation engines, termedmore » network-free simulation algorithms, and how they have been applied in systems biology research. We also define a generic rule-based modeling framework and describe a number of technical details required for adapting Gillespie’s direct method for network-free simulation. Lastly, we briefly discuss potential avenues for advancing network-free simulation and the role they continue to play in modeling dynamical systems in biology.« less

Generalizing Gillespie’s Direct Method to Enable Network-Free Simulations

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

Suderman, Ryan T.; Mitra, Eshan David; Lin, Yen Ting

Gillespie’s direct method for stochastic simulation of chemical kinetics is a staple of computational systems biology research. However, the algorithm requires explicit enumeration of all reactions and all chemical species that may arise in the system. In many cases, this is not feasible due to the combinatorial explosion of reactions and species in biological networks. Rule-based modeling frameworks provide a way to exactly represent networks containing such combinatorial complexity, and generalizations of Gillespie’s direct method have been developed as simulation engines for rule-based modeling languages. Here, we provide both a high-level description of the algorithms underlying the simulation engines, termedmore » network-free simulation algorithms, and how they have been applied in systems biology research. We also define a generic rule-based modeling framework and describe a number of technical details required for adapting Gillespie’s direct method for network-free simulation. Lastly, we briefly discuss potential avenues for advancing network-free simulation and the role they continue to play in modeling dynamical systems in biology.« less

Modeling CH 4 and CO 2 cycling using porewater stable isotopes in a thermokarst bog in Interior Alaska: results from three conceptual reaction networks

DOE PAGES

Neumann, Rebecca B.; Blazewicz, Steven J.; Conaway, Christopher H.; ...

2015-12-16

Quantifying rates of microbial carbon transformation in peatlands is essential for gaining mechanistic understanding of the factors that influence methane emissions from these systems, and for predicting how emissions will respond to climate change and other disturbances. In this study, we used porewater stable isotopes collected from both the edge and center of a thermokarst bog in Interior Alaska to estimate in situ microbial reaction rates. We expected that near the edge of the thaw feature, actively thawing permafrost and greater abundance of sedges would increase carbon, oxygen and nutrient availability, enabling faster microbial rates relative to the center ofmore » the thaw feature. We developed three different conceptual reaction networks that explained the temporal change in porewater CO2, CH4, δ13C-CO2 and δ13C-CH4. All three reaction-network models included methane production, methane oxidation and CO2 production, and two of the models included homoacetogenesis — a reaction not previously included in isotope-based porewater models. All three models fit the data equally well, but rates resulting from the models differed. Most notably, inclusion of homoacetogenesis altered the modeled pathways of methane production when the reaction was directly coupled to methanogenesis, and it decreased gross methane production rates by up to a factor of five when it remained decoupled from methanogenesis. The ability of all three conceptual reaction networks to successfully match the measured data indicate that this technique for estimating in-situ reaction rates requires other data and information from the site to confirm the considered set of microbial reactions. Despite these differences, all models indicated that, as expected, rates were greater at the edge than in the center of the thaw bog, that rates at the edge increased more during the growing season than did rates in the center, and that the ratio of acetoclastic to hydrogenotrophic methanogenesis was greater at the edge than in the center. In both locations, modeled rates (excluding methane oxidation) increased with depth. A puzzling outcome from the effort was that none of the models could fit the porewater dataset without generating “fugitive” carbon (i.e., methane or acetate generated by the models but not detected at the field site), indicating that either our conceptualization of the reactions occurring at the site remains incomplete or our site measurements are missing important carbon transformations and/or carbon fluxes. This model–data discrepancy will motivate and inform future research efforts focused on improving our understanding of carbon cycling in permafrost wetlands.« less

Reaction dynamics analysis of a reconstituted Escherichia coli protein translation system by computational modeling

PubMed Central

Matsuura, Tomoaki; Tanimura, Naoki; Hosoda, Kazufumi; Yomo, Tetsuya; Shimizu, Yoshihiro

2017-01-01

To elucidate the dynamic features of a biologically relevant large-scale reaction network, we constructed a computational model of minimal protein synthesis consisting of 241 components and 968 reactions that synthesize the Met-Gly-Gly (MGG) peptide based on an Escherichia coli-based reconstituted in vitro protein synthesis system. We performed a simulation using parameters collected primarily from the literature and found that the rate of MGG peptide synthesis becomes nearly constant in minutes, thus achieving a steady state similar to experimental observations. In addition, concentration changes to 70% of the components, including intermediates, reached a plateau in a few minutes. However, the concentration change of each component exhibits several temporal plateaus, or a quasi-stationary state (QSS), before reaching the final plateau. To understand these complex dynamics, we focused on whether the components reached a QSS, mapped the arrangement of components in a QSS in the entire reaction network structure, and investigated time-dependent changes. We found that components in a QSS form clusters that grow over time but not in a linear fashion, and that this process involves the collapse and regrowth of clusters before the formation of a final large single cluster. These observations might commonly occur in other large-scale biological reaction networks. This developed analysis might be useful for understanding large-scale biological reactions by visualizing complex dynamics, thereby extracting the characteristics of the reaction network, including phase transitions. PMID:28167777

MODELING CHLORINE RESIDUALS IN DRINKING-WATER DISTRIBUTION SYSTEMS

EPA Science Inventory

A mass-transfer-based model is developed for predicting chlorine decay in drinking-water distribution networks. The model considers first-order reactions of chlorine to occur both in the bulk flow and at the pipe wall. The overall rate of the wall reaction is a function of the ...

MODELING CHLORINE RESIDUALS IN DRINKING-WATER DISTRIBUTION SYSTEMS

EPA Science Inventory

A mass transfer-based model is developed for predicting chlorine decay in drinking water distribution networks. he model considers first order reactions of chlorine to occur both in the bulk flow and at the pipe wall. he overall rate of the wall reaction is a function of the rate...

Time-ordered product expansions for computational stochastic system biology.

PubMed

Mjolsness, Eric

2013-06-01

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems.

Chemical networks with inflows and outflows: a positive linear differential inclusions approach.

PubMed

Angeli, David; De Leenheer, Patrick; Sontag, Eduardo D

2009-01-01

Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. 2009 American Institute of Chemical Engineers

Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers.

PubMed

Stamova, Ivanka; Stamov, Gani

2017-12-01

In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.

DISCRETE VOLUME-ELEMENT METHOD FOR NETWORK WATER- QUALITY MODELS

EPA Science Inventory

An explicit dynamic water-quality modeling algorithm is developed for tracking dissolved substances in water-distribution networks. The algorithm is based on a mass-balance relation within pipes that considers both advective transport and reaction kinetics. Complete mixing of m...

Computing chemical organizations in biological networks.

PubMed

Centler, Florian; Kaleta, Christoph; di Fenizio, Pietro Speroni; Dittrich, Peter

2008-07-15

Novel techniques are required to analyze computational models of intracellular processes as they increase steadily in size and complexity. The theory of chemical organizations has recently been introduced as such a technique that links the topology of biochemical reaction network models to their dynamical repertoire. The network is decomposed into algebraically closed and self-maintaining subnetworks called organizations. They form a hierarchy representing all feasible system states including all steady states. We present three algorithms to compute the hierarchy of organizations for network models provided in SBML format. Two of them compute the complete organization hierarchy, while the third one uses heuristics to obtain a subset of all organizations for large models. While the constructive approach computes the hierarchy starting from the smallest organization in a bottom-up fashion, the flux-based approach employs self-maintaining flux distributions to determine organizations. A runtime comparison on 16 different network models of natural systems showed that none of the two exhaustive algorithms is superior in all cases. Studying a 'genome-scale' network model with 762 species and 1193 reactions, we demonstrate how the organization hierarchy helps to uncover the model structure and allows to evaluate the model's quality, for example by detecting components and subsystems of the model whose maintenance is not explained by the model. All data and a Java implementation that plugs into the Systems Biology Workbench is available from http://www.minet.uni-jena.de/csb/prj/ot/tools.

The Validity of Quasi-Steady-State Approximations in Discrete Stochastic Simulations

PubMed Central

Kim, Jae Kyoung; Josić, Krešimir; Bennett, Matthew R.

2014-01-01

In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales. PMID:25099817

Computational neural networks in chemistry: Model free mapping devices for predicting chemical reactivity from molecular structure

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

Elrod, D.W.

1992-01-01

Computational neural networks (CNNs) are a computational paradigm inspired by the brain's massively parallel network of highly interconnected neurons. The power of computational neural networks derives not so much from their ability to model the brain as from their ability to learn by example and to map highly complex, nonlinear functions, without the need to explicitly specify the functional relationship. Two central questions about CNNs were investigated in the context of predicting chemical reactions: (1) the mapping properties of neural networks and (2) the representation of chemical information for use in CNNs. Chemical reactivity is here considered an example ofmore » a complex, nonlinear function of molecular structure. CNN's were trained using modifications of the back propagation learning rule to map a three dimensional response surface similar to those typically observed in quantitative structure-activity and structure-property relationships. The computational neural network's mapping of the response surface was found to be robust to the effects of training sample size, noisy data and intercorrelated input variables. The investigation of chemical structure representation led to the development of a molecular structure-based connection-table representation suitable for neural network training. An extension of this work led to a BE-matrix structure representation that was found to be general for several classes of reactions. The CNN prediction of chemical reactivity and regiochemistry was investigated for electrophilic aromatic substitution reactions, Markovnikov addition to alkenes, Saytzeff elimination from haloalkanes, Diels-Alder cycloaddition, and retro Diels-Alder ring opening reactions using these connectivity-matrix derived representations. The reaction predictions made by the CNNs were more accurate than those of an expert system and were comparable to predictions made by chemists.« less

Development and testing of a compartmentalized reaction network model for redox zones in contaminated aquifers

USGS Publications Warehouse

Abrams , Robert H.; Loague, Keith; Kent, Douglas B.

1998-01-01

The work reported here is the first part of a larger effort focused on efficient numerical simulation of redox zone development in contaminated aquifers. The sequential use of various electron acceptors, which is governed by the energy yield of each reaction, gives rise to redox zones. The large difference in energy yields between the various redox reactions leads to systems of equations that are extremely ill-conditioned. These equations are very difficult to solve, especially in the context of coupled fluid flow, solute transport, and geochemical simulations. We have developed a general, rational method to solve such systems where we focus on the dominant reactions, compartmentalizing them in a manner that is analogous to the redox zones that are often observed in the field. The compartmentalized approach allows us to easily solve a complex geochemical system as a function of time and energy yield, laying the foundation for our ongoing work in which we couple the reaction network, for the development of redox zones, to a model of subsurface fluid flow and solute transport. Our method (1) solves the numerical system without evoking a redox parameter, (2) improves the numerical stability of redox systems by choosing which compartment and thus which reaction network to use based upon the concentration ratios of key constituents, (3) simulates the development of redox zones as a function of time without the use of inhibition factors or switching functions, and (4) can reduce the number of transport equations that need to be solved in space and time. We show through the use of various model performance evaluation statistics that the appropriate compartment choice under different geochemical conditions leads to numerical solutions without significant error. The compartmentalized approach described here facilitates the next phase of this effort where we couple the redox zone reaction network to models of fluid flow and solute transport.

Complex Chemical Reaction Networks from Heuristics-Aided Quantum Chemistry.

PubMed

Rappoport, Dmitrij; Galvin, Cooper J; Zubarev, Dmitry Yu; Aspuru-Guzik, Alán

2014-03-11

While structures and reactivities of many small molecules can be computed efficiently and accurately using quantum chemical methods, heuristic approaches remain essential for modeling complex structures and large-scale chemical systems. Here, we present a heuristics-aided quantum chemical methodology applicable to complex chemical reaction networks such as those arising in cell metabolism and prebiotic chemistry. Chemical heuristics offer an expedient way of traversing high-dimensional reactive potential energy surfaces and are combined here with quantum chemical structure optimizations, which yield the structures and energies of the reaction intermediates and products. Application of heuristics-aided quantum chemical methodology to the formose reaction reproduces the experimentally observed reaction products, major reaction pathways, and autocatalytic cycles.

Automation of route identification and optimisation based on data-mining and chemical intuition.

PubMed

Lapkin, A A; Heer, P K; Jacob, P-M; Hutchby, M; Cunningham, W; Bull, S D; Davidson, M G

2017-09-21

Data-mining of Reaxys and network analysis of the combined literature and in-house reactions set were used to generate multiple possible reaction routes to convert a bio-waste feedstock, limonene, into a pharmaceutical API, paracetamol. The network analysis of data provides a rich knowledge-base for generation of the initial reaction screening and development programme. Based on the literature and the in-house data, an overall flowsheet for the conversion of limonene to paracetamol was proposed. Each individual reaction-separation step in the sequence was simulated as a combination of the continuous flow and batch steps. The linear model generation methodology allowed us to identify the reaction steps requiring further chemical optimisation. The generated model can be used for global optimisation and generation of environmental and other performance indicators, such as cost indicators. However, the identified further challenge is to automate model generation to evolve optimal multi-step chemical routes and optimal process configurations.

Predicting effects of structural stress in a genome-reduced model bacterial metabolism

NASA Astrophysics Data System (ADS)

Güell, Oriol; Sagués, Francesc; Serrano, M. Ángeles

2012-08-01

Mycoplasma pneumoniae is a human pathogen recently proposed as a genome-reduced model for bacterial systems biology. Here, we study the response of its metabolic network to different forms of structural stress, including removal of individual and pairs of reactions and knockout of genes and clusters of co-expressed genes. Our results reveal a network architecture as robust as that of other model bacteria regarding multiple failures, although less robust against individual reaction inactivation. Interestingly, metabolite motifs associated to reactions can predict the propagation of inactivation cascades and damage amplification effects arising in double knockouts. We also detect a significant correlation between gene essentiality and damages produced by single gene knockouts, and find that genes controlling high-damage reactions tend to be expressed independently of each other, a functional switch mechanism that, simultaneously, acts as a genetic firewall to protect metabolism. Prediction of failure propagation is crucial for metabolic engineering or disease treatment.

Hybrid discrete/continuum algorithms for stochastic reaction networks

DOE PAGES

Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; ...

2014-10-22

Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discretemore » and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.« less

XML Encoding of Features Describing Rule-Based Modeling of Reaction Networks with Multi-Component Molecular Complexes

PubMed Central

Blinov, Michael L.; Moraru, Ion I.

2011-01-01

Multi-state molecules and multi-component complexes are commonly involved in cellular signaling. Accounting for molecules that have multiple potential states, such as a protein that may be phosphorylated on multiple residues, and molecules that combine to form heterogeneous complexes located among multiple compartments, generates an effect of combinatorial complexity. Models involving relatively few signaling molecules can include thousands of distinct chemical species. Several software tools (StochSim, BioNetGen) are already available to deal with combinatorial complexity. Such tools need information standards if models are to be shared, jointly evaluated and developed. Here we discuss XML conventions that can be adopted for modeling biochemical reaction networks described by user-specified reaction rules. These could form a basis for possible future extensions of the Systems Biology Markup Language (SBML). PMID:21464833

Solving gap metabolites and blocked reactions in genome-scale models: application to the metabolic network of Blattabacterium cuenoti.

PubMed

Ponce-de-León, Miguel; Montero, Francisco; Peretó, Juli

2013-10-31

Metabolic reconstruction is the computational-based process that aims to elucidate the network of metabolites interconnected through reactions catalyzed by activities assigned to one or more genes. Reconstructed models may contain inconsistencies that appear as gap metabolites and blocked reactions. Although automatic methods for solving this problem have been previously developed, there are many situations where manual curation is still needed. We introduce a general definition of gap metabolite that allows its detection in a straightforward manner. Moreover, a method for the detection of Unconnected Modules, defined as isolated sets of blocked reactions connected through gap metabolites, is proposed. The method has been successfully applied to the curation of iCG238, the genome-scale metabolic model for the bacterium Blattabacterium cuenoti, obligate endosymbiont of cockroaches. We found the proposed approach to be a valuable tool for the curation of genome-scale metabolic models. The outcome of its application to the genome-scale model B. cuenoti iCG238 is a more accurate model version named as B. cuenoti iMP240.

Approaching mathematical model of the immune network based DNA Strand Displacement system.

PubMed

Mardian, Rizki; Sekiyama, Kosuke; Fukuda, Toshio

2013-12-01

One biggest obstacle in molecular programming is that there is still no direct method to compile any existed mathematical model into biochemical reaction in order to solve a computational problem. In this paper, the implementation of DNA Strand Displacement system based on nature-inspired computation is observed. By using the Immune Network Theory and Chemical Reaction Network, the compilation of DNA-based operation is defined and the formulation of its mathematical model is derived. Furthermore, the implementation on this system is compared with the conventional implementation by using silicon-based programming. From the obtained results, we can see a positive correlation between both. One possible application from this DNA-based model is for a decision making scheme of intelligent computer or molecular robot. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

A mixed-integer linear programming approach to the reduction of genome-scale metabolic networks.

PubMed

Röhl, Annika; Bockmayr, Alexander

2017-01-03

Constraint-based analysis has become a widely used method to study metabolic networks. While some of the associated algorithms can be applied to genome-scale network reconstructions with several thousands of reactions, others are limited to small or medium-sized models. In 2015, Erdrich et al. introduced a method called NetworkReducer, which reduces large metabolic networks to smaller subnetworks, while preserving a set of biological requirements that can be specified by the user. Already in 2001, Burgard et al. developed a mixed-integer linear programming (MILP) approach for computing minimal reaction sets under a given growth requirement. Here we present an MILP approach for computing minimum subnetworks with the given properties. The minimality (with respect to the number of active reactions) is not guaranteed by NetworkReducer, while the method by Burgard et al. does not allow specifying the different biological requirements. Our procedure is about 5-10 times faster than NetworkReducer and can enumerate all minimum subnetworks in case there exist several ones. This allows identifying common reactions that are present in all subnetworks, and reactions appearing in alternative pathways. Applying complex analysis methods to genome-scale metabolic networks is often not possible in practice. Thus it may become necessary to reduce the size of the network while keeping important functionalities. We propose a MILP solution to this problem. Compared to previous work, our approach is more efficient and allows computing not only one, but even all minimum subnetworks satisfying the required properties.

Oral insulin delivery using P(MAA-g-EG) hydrogels: effects of network morphology on insulin delivery characteristics.

PubMed

Nakamura, Koji; Murray, Robert J; Joseph, Jeffrey I; Peppas, Nicholas A; Morishita, Mariko; Lowman, Anthony M

2004-03-24

Hydrogels of poly(methacrylic acid-g-ethylene glycol) were prepared using different reaction water contents in order to vary the network mesh size, swelling behavior and insulin loading/release kinetics. Gels prepared with greater reaction solvent contents swelled to a greater degree and had a larger network mesh size. All of the hydrogels were able to incorporate insulin and protected it from release in acidic media. At higher pH (7.4), the release rates increased with reaction solvent content. Using a closed loop animal model, all of the insulin loaded formulations produced significant insulin absorption in the upper small intestine combined with hypoglycemic effects. In these studies, bioavailabilities ranged from 4.6% to 7.2% and were dependent on reaction solvent content.

Modeling integrated cellular machinery using hybrid Petri-Boolean networks.

PubMed

Berestovsky, Natalie; Zhou, Wanding; Nagrath, Deepak; Nakhleh, Luay

2013-01-01

The behavior and phenotypic changes of cells are governed by a cellular circuitry that represents a set of biochemical reactions. Based on biological functions, this circuitry is divided into three types of networks, each encoding for a major biological process: signal transduction, transcription regulation, and metabolism. This division has generally enabled taming computational complexity dealing with the entire system, allowed for using modeling techniques that are specific to each of the components, and achieved separation of the different time scales at which reactions in each of the three networks occur. Nonetheless, with this division comes loss of information and power needed to elucidate certain cellular phenomena. Within the cell, these three types of networks work in tandem, and each produces signals and/or substances that are used by the others to process information and operate normally. Therefore, computational techniques for modeling integrated cellular machinery are needed. In this work, we propose an integrated hybrid model (IHM) that combines Petri nets and Boolean networks to model integrated cellular networks. Coupled with a stochastic simulation mechanism, the model simulates the dynamics of the integrated network, and can be perturbed to generate testable hypotheses. Our model is qualitative and is mostly built upon knowledge from the literature and requires fine-tuning of very few parameters. We validated our model on two systems: the transcriptional regulation of glucose metabolism in human cells, and cellular osmoregulation in S. cerevisiae. The model produced results that are in very good agreement with experimental data, and produces valid hypotheses. The abstract nature of our model and the ease of its construction makes it a very good candidate for modeling integrated networks from qualitative data. The results it produces can guide the practitioner to zoom into components and interconnections and investigate them using such more detailed mathematical models.

Modeling Integrated Cellular Machinery Using Hybrid Petri-Boolean Networks

PubMed Central

Berestovsky, Natalie; Zhou, Wanding; Nagrath, Deepak; Nakhleh, Luay

2013-01-01

The behavior and phenotypic changes of cells are governed by a cellular circuitry that represents a set of biochemical reactions. Based on biological functions, this circuitry is divided into three types of networks, each encoding for a major biological process: signal transduction, transcription regulation, and metabolism. This division has generally enabled taming computational complexity dealing with the entire system, allowed for using modeling techniques that are specific to each of the components, and achieved separation of the different time scales at which reactions in each of the three networks occur. Nonetheless, with this division comes loss of information and power needed to elucidate certain cellular phenomena. Within the cell, these three types of networks work in tandem, and each produces signals and/or substances that are used by the others to process information and operate normally. Therefore, computational techniques for modeling integrated cellular machinery are needed. In this work, we propose an integrated hybrid model (IHM) that combines Petri nets and Boolean networks to model integrated cellular networks. Coupled with a stochastic simulation mechanism, the model simulates the dynamics of the integrated network, and can be perturbed to generate testable hypotheses. Our model is qualitative and is mostly built upon knowledge from the literature and requires fine-tuning of very few parameters. We validated our model on two systems: the transcriptional regulation of glucose metabolism in human cells, and cellular osmoregulation in S. cerevisiae. The model produced results that are in very good agreement with experimental data, and produces valid hypotheses. The abstract nature of our model and the ease of its construction makes it a very good candidate for modeling integrated networks from qualitative data. The results it produces can guide the practitioner to zoom into components and interconnections and investigate them using such more detailed mathematical models. PMID:24244124

Petri Nets - A Mathematical Formalism to Analyze Chemical Reaction Networks.

PubMed

Koch, Ina

2010-12-17

In this review we introduce and discuss Petri nets - a mathematical formalism to describe and analyze chemical reaction networks. Petri nets were developed to describe concurrency in general systems. We find most applications to technical and financial systems, but since about twenty years also in systems biology to model biochemical systems. This review aims to give a short informal introduction to the basic formalism illustrated by a chemical example, and to discuss possible applications to the analysis of chemical reaction networks, including cheminformatics. We give a short overview about qualitative as well as quantitative modeling Petri net techniques useful in systems biology, summarizing the state-of-the-art in that field and providing the main literature references. Finally, we discuss advantages and limitations of Petri nets and give an outlook to further development. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A reaction-diffusion-based coding rate control mechanism for camera sensor networks.

PubMed

Yamamoto, Hiroshi; Hyodo, Katsuya; Wakamiya, Naoki; Murata, Masayuki

2010-01-01

A wireless camera sensor network is useful for surveillance and monitoring for its visibility and easy deployment. However, it suffers from the limited capacity of wireless communication and a network is easily overflown with a considerable amount of video traffic. In this paper, we propose an autonomous video coding rate control mechanism where each camera sensor node can autonomously determine its coding rate in accordance with the location and velocity of target objects. For this purpose, we adopted a biological model, i.e., reaction-diffusion model, inspired by the similarity of biological spatial patterns and the spatial distribution of video coding rate. Through simulation and practical experiments, we verify the effectiveness of our proposal.

Time-Frequency Cross Mutual Information Analysis of the Brain Functional Networks Underlying Multiclass Motor Imagery.

PubMed

Gong, Anmin; Liu, Jianping; Chen, Si; Fu, Yunfa

2018-01-01

To study the physiologic mechanism of the brain during different motor imagery (MI) tasks, the authors employed a method of brain-network modeling based on time-frequency cross mutual information obtained from 4-class (left hand, right hand, feet, and tongue) MI tasks recorded as brain-computer interface (BCI) electroencephalography data. The authors explored the brain network revealed by these MI tasks using statistical analysis and the analysis of topologic characteristics, and observed significant differences in the reaction level, reaction time, and activated target during 4-class MI tasks. There was a great difference in the reaction level between the execution and resting states during different tasks: the reaction level of the left-hand MI task was the greatest, followed by that of the right-hand, feet, and tongue MI tasks. The reaction time required to perform the tasks also differed: during the left-hand and right-hand MI tasks, the brain networks of subjects reacted promptly and strongly, but there was a delay during the feet and tongue MI task. Statistical analysis and the analysis of network topology revealed the target regions of the brain network during different MI processes. In conclusion, our findings suggest a new way to explain the neural mechanism behind MI.

ReMatch: a web-based tool to construct, store and share stoichiometric metabolic models with carbon maps for metabolic flux analysis.

PubMed

Pitkänen, Esa; Akerlund, Arto; Rantanen, Ari; Jouhten, Paula; Ukkonen, Esko

2008-08-25

ReMatch is a web-based, user-friendly tool that constructs stoichiometric network models for metabolic flux analysis, integrating user-developed models into a database collected from several comprehensive metabolic data resources, including KEGG, MetaCyc and CheBI. Particularly, ReMatch augments the metabolic reactions of the model with carbon mappings to facilitate (13)C metabolic flux analysis. The construction of a network model consisting of biochemical reactions is the first step in most metabolic modelling tasks. This model construction can be a tedious task as the required information is usually scattered to many separate databases whose interoperability is suboptimal, due to the heterogeneous naming conventions of metabolites in different databases. Another, particularly severe data integration problem is faced in (13)C metabolic flux analysis, where the mappings of carbon atoms from substrates into products in the model are required. ReMatch has been developed to solve the above data integration problems. First, ReMatch matches the imported user-developed model against the internal ReMatch database while considering a comprehensive metabolite name thesaurus. This, together with wild card support, allows the user to specify the model quickly without having to look the names up manually. Second, ReMatch is able to augment reactions of the model with carbon mappings, obtained either from the internal database or given by the user with an easy-touse tool. The constructed models can be exported into 13C-FLUX and SBML file formats. Further, a stoichiometric matrix and visualizations of the network model can be generated. The constructed models of metabolic networks can be optionally made available to the other users of ReMatch. Thus, ReMatch provides a common repository for metabolic network models with carbon mappings for the needs of metabolic flux analysis community. ReMatch is freely available for academic use at http://www.cs.helsinki.fi/group/sysfys/software/rematch/.

Pre-supernova models for massive stars produced with large nuclear reaction network by MESA

NASA Astrophysics Data System (ADS)

Park, Byeongchan; Kwak, Kyujin

2018-04-01

Core-collapsed Supernova (CCSN) is one of violent phenomena in the universe. CCSN generates heavy elements and leaves a neutron star behind. It has been known that the physical properties of CCSN depend on those of pre-supernova such as mass, metallicities including distribution of elements, and the density and temperature profile which are obtained from the stellar evolution calculation. In particular, the production of heavy elements in CCSN is sensitive to the abundance profiles in the pre-supernova models. In this study, we evolve a massive main sequence star with 15Msun and solar metallicity to the pre-supernova stage by using two different networks, small and large. The large nuclear reaction network includes more than four times isotopes than the small network. Our calculations were done by MESA (Modules for Experiments in Stellar Astrophysics) which allowed us to use the large network containing about a hundred isotopes. We compare the results obtained with two networks.

Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis

NASA Astrophysics Data System (ADS)

Wang, Ting; Plecháč, Petr

2017-12-01

Stochastic reaction networks that exhibit bistable behavior are common in systems biology, materials science, and catalysis. Sampling of stationary distributions is crucial for understanding and characterizing the long-time dynamics of bistable stochastic dynamical systems. However, simulations are often hindered by the insufficient sampling of rare transitions between the two metastable regions. In this paper, we apply the parallel replica method for a continuous time Markov chain in order to improve sampling of the stationary distribution in bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate the sampling of rare transitions. Furthermore, it can be combined with the path-space information bounds for parametric sensitivity analysis. With the proposed methodology, we study three bistable biological networks: the Schlögl model, the genetic switch network, and the enzymatic futile cycle network. We demonstrate the algorithmic speedup achieved in these numerical benchmarks. More significant acceleration is expected when multi-core or graphics processing unit computer architectures and programming tools such as CUDA are employed.

Multiscale Simulations of Reactive Transport

NASA Astrophysics Data System (ADS)

Tartakovsky, D. M.; Bakarji, J.

2014-12-01

Discrete, particle-based simulations offer distinct advantages when modeling solute transport and chemical reactions. For example, Brownian motion is often used to model diffusion in complex pore networks, and Gillespie-type algorithms allow one to handle multicomponent chemical reactions with uncertain reaction pathways. Yet such models can be computationally more intensive than their continuum-scale counterparts, e.g., advection-dispersion-reaction equations. Combining the discrete and continuum models has a potential to resolve the quantity of interest with a required degree of physicochemical granularity at acceptable computational cost. We present computational examples of such "hybrid models" and discuss the challenges associated with coupling these two levels of description.

Neural network modelling of the influence of channelopathies on reflex visual attention.

PubMed

Gravier, Alexandre; Quek, Chai; Duch, Włodzisław; Wahab, Abdul; Gravier-Rymaszewska, Joanna

2016-02-01

This paper introduces a model of Emergent Visual Attention in presence of calcium channelopathy (EVAC). By modelling channelopathy, EVAC constitutes an effort towards identifying the possible causes of autism. The network structure embodies the dual pathways model of cortical processing of visual input, with reflex attention as an emergent property of neural interactions. EVAC extends existing work by introducing attention shift in a larger-scale network and applying a phenomenological model of channelopathy. In presence of a distractor, the channelopathic network's rate of failure to shift attention is lower than the control network's, but overall, the control network exhibits a lower classification error rate. The simulation results also show differences in task-relative reaction times between control and channelopathic networks. The attention shift timings inferred from the model are consistent with studies of attention shift in autistic children.

Metabolic networks in motion: 13C-based flux analysis

PubMed Central

Sauer, Uwe

2006-01-01

Many properties of complex networks cannot be understood from monitoring the components—not even when comprehensively monitoring all protein or metabolite concentrations—unless such information is connected and integrated through mathematical models. The reason is that static component concentrations, albeit extremely informative, do not contain functional information per se. The functional behavior of a network emerges only through the nonlinear gene, protein, and metabolite interactions across multiple metabolic and regulatory layers. I argue here that intracellular reaction rates are the functional end points of these interactions in metabolic networks, hence are highly relevant for systems biology. Methods for experimental determination of metabolic fluxes differ fundamentally from component concentration measurements; that is, intracellular reaction rates cannot be detected directly, but must be estimated through computer model-based interpretation of stable isotope patterns in products of metabolism. PMID:17102807

Methods of Model Reduction for Large-Scale Biological Systems: A Survey of Current Methods and Trends.

PubMed

Snowden, Thomas J; van der Graaf, Piet H; Tindall, Marcus J

2017-07-01

Complex models of biochemical reaction systems have become increasingly common in the systems biology literature. The complexity of such models can present a number of obstacles for their practical use, often making problems difficult to intuit or computationally intractable. Methods of model reduction can be employed to alleviate the issue of complexity by seeking to eliminate those portions of a reaction network that have little or no effect upon the outcomes of interest, hence yielding simplified systems that retain an accurate predictive capacity. This review paper seeks to provide a brief overview of a range of such methods and their application in the context of biochemical reaction network models. To achieve this, we provide a brief mathematical account of the main methods including timescale exploitation approaches, reduction via sensitivity analysis, optimisation methods, lumping, and singular value decomposition-based approaches. Methods are reviewed in the context of large-scale systems biology type models, and future areas of research are briefly discussed.

An exact arithmetic toolbox for a consistent and reproducible structural analysis of metabolic network models

PubMed Central

Chindelevitch, Leonid; Trigg, Jason; Regev, Aviv; Berger, Bonnie

2014-01-01

Constraint-based models are currently the only methodology that allows the study of metabolism at the whole-genome scale. Flux balance analysis is commonly used to analyse constraint-based models. Curiously, the results of this analysis vary with the software being run, a situation that we show can be remedied by using exact rather than floating-point arithmetic. Here we introduce MONGOOSE, a toolbox for analysing the structure of constraint-based metabolic models in exact arithmetic. We apply MONGOOSE to the analysis of 98 existing metabolic network models and find that the biomass reaction is surprisingly blocked (unable to sustain non-zero flux) in nearly half of them. We propose a principled approach for unblocking these reactions and extend it to the problems of identifying essential and synthetic lethal reactions and minimal media. Our structural insights enable a systematic study of constraint-based metabolic models, yielding a deeper understanding of their possibilities and limitations. PMID:25291352

Delay-induced Turing-like waves for one-species reaction-diffusion model on a network

NASA Astrophysics Data System (ADS)

Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio

2015-09-01

A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turing-like waves that materialize in a single-species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time-delayed differential equations. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz network and with the inclusion of the delay.

Conditions for duality between fluxes and concentrations in biochemical networks

PubMed Central

Fleming, Ronan M.T.; Vlassis, Nikos; Thiele, Ines; Saunders, Michael A.

2016-01-01

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner. We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We also provide a combinatorial characterisation that is sufficient to ensure flux-concentration duality. The condition prescribes that, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes. PMID:27345817

Conditions for duality between fluxes and concentrations in biochemical networks

DOE PAGES

Fleming, Ronan M. T.; Vlassis, Nikos; Thiele, Ines; ...

2016-06-23

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner. We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We alsomore » provide a combinatorial characterisation that is sufficient to ensure flux-concentration duality.The condition prescribes that, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes« less

Conditions for duality between fluxes and concentrations in biochemical networks

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

Fleming, Ronan M. T.; Vlassis, Nikos; Thiele, Ines

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner. We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We alsomore » provide a combinatorial characterisation that is sufficient to ensure flux-concentration duality.The condition prescribes that, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes« less

Identification of Conserved Moieties in Metabolic Networks by Graph Theoretical Analysis of Atom Transition Networks

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

Haraldsdóttir, Hulda S.; Fleming, Ronan M. T.

Conserved moieties are groups of atoms that remain intact in all reactions of a metabolic network. Identification of conserved moieties gives insight into the structure and function of metabolic networks and facilitates metabolic modelling. All moiety conservation relations can be represented as nonnegative integer vectors in the left null space of the stoichiometric matrix corresponding to a biochemical network. Algorithms exist to compute such vectors based only on reaction stoichiometry but their computational complexity has limited their application to relatively small metabolic networks. Moreover, the vectors returned by existing algorithms do not, in general, represent conservation of a specific moietymore » with a defined atomic structure. Here, we show that identification of conserved moieties requires data on reaction atom mappings in addition to stoichiometry. We present a novel method to identify conserved moieties in metabolic networks by graph theoretical analysis of their underlying atom transition networks. Our method returns the exact group of atoms belonging to each conserved moiety as well as the corresponding vector in the left null space of the stoichiometric matrix. It can be implemented as a pipeline of polynomial time algorithms. Our implementation completes in under five minutes on a metabolic network with more than 4,000 mass balanced reactions. The scalability of the method enables extension of existing applications for moiety conservation relations to genome-scale metabolic networks. Finally, we also give examples of new applications made possible by elucidating the atomic structure of conserved moieties.« less

Identification of Conserved Moieties in Metabolic Networks by Graph Theoretical Analysis of Atom Transition Networks

PubMed Central

Haraldsdóttir, Hulda S.; Fleming, Ronan M. T.

2016-01-01

Conserved moieties are groups of atoms that remain intact in all reactions of a metabolic network. Identification of conserved moieties gives insight into the structure and function of metabolic networks and facilitates metabolic modelling. All moiety conservation relations can be represented as nonnegative integer vectors in the left null space of the stoichiometric matrix corresponding to a biochemical network. Algorithms exist to compute such vectors based only on reaction stoichiometry but their computational complexity has limited their application to relatively small metabolic networks. Moreover, the vectors returned by existing algorithms do not, in general, represent conservation of a specific moiety with a defined atomic structure. Here, we show that identification of conserved moieties requires data on reaction atom mappings in addition to stoichiometry. We present a novel method to identify conserved moieties in metabolic networks by graph theoretical analysis of their underlying atom transition networks. Our method returns the exact group of atoms belonging to each conserved moiety as well as the corresponding vector in the left null space of the stoichiometric matrix. It can be implemented as a pipeline of polynomial time algorithms. Our implementation completes in under five minutes on a metabolic network with more than 4,000 mass balanced reactions. The scalability of the method enables extension of existing applications for moiety conservation relations to genome-scale metabolic networks. We also give examples of new applications made possible by elucidating the atomic structure of conserved moieties. PMID:27870845

Identification of Conserved Moieties in Metabolic Networks by Graph Theoretical Analysis of Atom Transition Networks

DOE PAGES

Haraldsdóttir, Hulda S.; Fleming, Ronan M. T.

2016-11-21

Conserved moieties are groups of atoms that remain intact in all reactions of a metabolic network. Identification of conserved moieties gives insight into the structure and function of metabolic networks and facilitates metabolic modelling. All moiety conservation relations can be represented as nonnegative integer vectors in the left null space of the stoichiometric matrix corresponding to a biochemical network. Algorithms exist to compute such vectors based only on reaction stoichiometry but their computational complexity has limited their application to relatively small metabolic networks. Moreover, the vectors returned by existing algorithms do not, in general, represent conservation of a specific moietymore » with a defined atomic structure. Here, we show that identification of conserved moieties requires data on reaction atom mappings in addition to stoichiometry. We present a novel method to identify conserved moieties in metabolic networks by graph theoretical analysis of their underlying atom transition networks. Our method returns the exact group of atoms belonging to each conserved moiety as well as the corresponding vector in the left null space of the stoichiometric matrix. It can be implemented as a pipeline of polynomial time algorithms. Our implementation completes in under five minutes on a metabolic network with more than 4,000 mass balanced reactions. The scalability of the method enables extension of existing applications for moiety conservation relations to genome-scale metabolic networks. Finally, we also give examples of new applications made possible by elucidating the atomic structure of conserved moieties.« less

Identification of Conserved Moieties in Metabolic Networks by Graph Theoretical Analysis of Atom Transition Networks.

PubMed

Haraldsdóttir, Hulda S; Fleming, Ronan M T

2016-11-01

Conserved moieties are groups of atoms that remain intact in all reactions of a metabolic network. Identification of conserved moieties gives insight into the structure and function of metabolic networks and facilitates metabolic modelling. All moiety conservation relations can be represented as nonnegative integer vectors in the left null space of the stoichiometric matrix corresponding to a biochemical network. Algorithms exist to compute such vectors based only on reaction stoichiometry but their computational complexity has limited their application to relatively small metabolic networks. Moreover, the vectors returned by existing algorithms do not, in general, represent conservation of a specific moiety with a defined atomic structure. Here, we show that identification of conserved moieties requires data on reaction atom mappings in addition to stoichiometry. We present a novel method to identify conserved moieties in metabolic networks by graph theoretical analysis of their underlying atom transition networks. Our method returns the exact group of atoms belonging to each conserved moiety as well as the corresponding vector in the left null space of the stoichiometric matrix. It can be implemented as a pipeline of polynomial time algorithms. Our implementation completes in under five minutes on a metabolic network with more than 4,000 mass balanced reactions. The scalability of the method enables extension of existing applications for moiety conservation relations to genome-scale metabolic networks. We also give examples of new applications made possible by elucidating the atomic structure of conserved moieties.

DEF: an automated dead-end filling approach based on quasi-endosymbiosis.

PubMed

Liu, Lili; Zhang, Zijun; Sheng, Taotao; Chen, Ming

2017-02-01

Gap filling for the reconstruction of metabolic networks is to restore the connectivity of metabolites via finding high-confidence reactions that could be missed in target organism. Current methods for gap filling either fall into the network topology or have limited capability in finding missing reactions that are indirectly related to dead-end metabolites but of biological importance to the target model. We present an automated dead-end filling (DEF) approach, which is derived from the wisdom of endosymbiosis theory, to fill gaps by finding the most efficient dead-end utilization paths in a constructed quasi-endosymbiosis model. The recalls of reactions and dead ends of DEF reach around 73% and 86%, respectively. This method is capable of finding indirectly dead-end-related reactions with biological importance for the target organism and is applicable to any given metabolic model. In the E. coli iJR904 model, for instance, about 42% of the dead-end metabolites were fixed by our proposed method. DEF is publicly available at http://bis.zju.edu.cn/DEF/. mchen@zju.edu.cn Supplementary data are available at Bioinformatics online.

Global investigation of potential energy surfaces for the pyrolysis of C(1)-C(3) hydrocarbons: toward the development of detailed kinetic models from first principles.

PubMed

Ryazantsev, Mikhail N; Jamal, Adeel; Maeda, Satoshi; Morokuma, Keiji

2015-11-07

Detailed kinetic models (DKMs) are the most fundamental "bottom-up" approaches to computational investigation of the pyrolysis and oxidation of fuels. The weakest points of existing DKMs are incomplete information about the reaction types that can be involved in the potential energy surfaces (PESs) in pyrolysis and oxidation processes. Also, the computational thermodynamic parameters available in the literature vary widely with the level of theory employed. More sophisticated models require improvement both in our knowledge of the type of the reactions involved and the consistency of thermodynamic and kinetic parameters. In this paper, we aim to address these issues by developing ab initio models that can be used to describe early stages of pyrolysis of C1-C3 hydrocarbons. We applied a recently developed global reaction route mapping (GRRM) strategy to systematically investigate the PES of the pyrolysis of C1-C3 hydrocarbons at a consistent level of theory. The reactions are classified into 14 reaction types. The critical points on the PES for all reactions in the network are calculated at the highly accurate UCCSD(T)-F12b/cc-pVTZ//UM06-2X/cc-pVTZ level of theory. The data reported in this paper can be used for first principle calculations of kinetic constants and for a subsequent study on modeling the evolution of the species from the reaction network of the pyrolysis and oxidation of C1-C3 hydrocarbons.

Rule-based modeling and simulations of the inner kinetochore structure.

PubMed

Tschernyschkow, Sergej; Herda, Sabine; Gruenert, Gerd; Döring, Volker; Görlich, Dennis; Hofmeister, Antje; Hoischen, Christian; Dittrich, Peter; Diekmann, Stephan; Ibrahim, Bashar

2013-09-01

Combinatorial complexity is a central problem when modeling biochemical reaction networks, since the association of a few components can give rise to a large variation of protein complexes. Available classical modeling approaches are often insufficient for the analysis of very large and complex networks in detail. Recently, we developed a new rule-based modeling approach that facilitates the analysis of spatial and combinatorially complex problems. Here, we explore for the first time how this approach can be applied to a specific biological system, the human kinetochore, which is a multi-protein complex involving over 100 proteins. Applying our freely available SRSim software to a large data set on kinetochore proteins in human cells, we construct a spatial rule-based simulation model of the human inner kinetochore. The model generates an estimation of the probability distribution of the inner kinetochore 3D architecture and we show how to analyze this distribution using information theory. In our model, the formation of a bridge between CenpA and an H3 containing nucleosome only occurs efficiently for higher protein concentration realized during S-phase but may be not in G1. Above a certain nucleosome distance the protein bridge barely formed pointing towards the importance of chromatin structure for kinetochore complex formation. We define a metric for the distance between structures that allow us to identify structural clusters. Using this modeling technique, we explore different hypothetical chromatin layouts. Applying a rule-based network analysis to the spatial kinetochore complex geometry allowed us to integrate experimental data on kinetochore proteins, suggesting a 3D model of the human inner kinetochore architecture that is governed by a combinatorial algebraic reaction network. This reaction network can serve as bridge between multiple scales of modeling. Our approach can be applied to other systems beyond kinetochores. Copyright © 2013 Elsevier Ltd. All rights reserved.

Stochastic simulation and analysis of biomolecular reaction networks

PubMed Central

Frazier, John M; Chushak, Yaroslav; Foy, Brent

2009-01-01

Background In recent years, several stochastic simulation algorithms have been developed to generate Monte Carlo trajectories that describe the time evolution of the behavior of biomolecular reaction networks. However, the effects of various stochastic simulation and data analysis conditions on the observed dynamics of complex biomolecular reaction networks have not recieved much attention. In order to investigate these issues, we employed a a software package developed in out group, called Biomolecular Network Simulator (BNS), to simulate and analyze the behavior of such systems. The behavior of a hypothetical two gene in vitro transcription-translation reaction network is investigated using the Gillespie exact stochastic algorithm to illustrate some of the factors that influence the analysis and interpretation of these data. Results Specific issues affecting the analysis and interpretation of simulation data are investigated, including: (1) the effect of time interval on data presentation and time-weighted averaging of molecule numbers, (2) effect of time averaging interval on reaction rate analysis, (3) effect of number of simulations on precision of model predictions, and (4) implications of stochastic simulations on optimization procedures. Conclusion The two main factors affecting the analysis of stochastic simulations are: (1) the selection of time intervals to compute or average state variables and (2) the number of simulations generated to evaluate the system behavior. PMID:19534796

Generic strategies for chemical space exploration.

PubMed

Andersen, Jakob L; Flamm, Christoph; Merkle, Daniel; Stadler, Peter F

2014-01-01

The chemical universe of molecules reachable from a set of start compounds by iterative application of a finite number of reactions is usually so vast, that sophisticated and efficient exploration strategies are required to cope with the combinatorial complexity. A stringent analysis of (bio)chemical reaction networks, as approximations of these complex chemical spaces, forms the foundation for the understanding of functional relations in Chemistry and Biology. Graphs and graph rewriting are natural models for molecules and reactions. Borrowing the idea of partial evaluation from functional programming, we introduce partial applications of rewrite rules. A framework for the specification of exploration strategies in graph-rewriting systems is presented. Using key examples of complex reaction networks from carbohydrate chemistry we demonstrate the feasibility of this high-level strategy framework. While being designed for chemical applications, the framework can also be used to emulate higher-level transformation models such as illustrated in a small puzzle game.

Bootstrapping Least Squares Estimates in Biochemical Reaction Networks

PubMed Central

Linder, Daniel F.

2015-01-01

The paper proposes new computational methods of computing confidence bounds for the least squares estimates (LSEs) of rate constants in mass-action biochemical reaction network and stochastic epidemic models. Such LSEs are obtained by fitting the set of deterministic ordinary differential equations (ODEs), corresponding to the large volume limit of a reaction network, to network’s partially observed trajectory treated as a continuous-time, pure jump Markov process. In the large volume limit the LSEs are asymptotically Gaussian, but their limiting covariance structure is complicated since it is described by a set of nonlinear ODEs which are often ill-conditioned and numerically unstable. The current paper considers two bootstrap Monte-Carlo procedures, based on the diffusion and linear noise approximations for pure jump processes, which allow one to avoid solving the limiting covariance ODEs. The results are illustrated with both in-silico and real data examples from the LINE 1 gene retrotranscription model and compared with those obtained using other methods. PMID:25898769

Behavior of silica aerogel networks as highly porous solid solvent media for lipases in a model transesterification reaction.

PubMed

El Rassy, H; Perrard, A; Pierre, A C

2003-03-03

Highly porous silica aerogels with differing balances of hydrophobic and hydrophilic functionalities were studied as a new immobilization medium for enzymes. Two types of lipases from Candida rugosa and Burkholderia cepacia were homogeneously dispersed in wet gel precursors before gelation. The materials obtained were compared in a simple model reaction: transesterification of vinyl laurate by 1-octanol. To allow a better comparison of the hydrophobic/hydrophilic action of the solid, very open aerogel networks with traditional organic hydrophobic/hydrophilic liquid solvents, this reaction was studied in mixtures containing different proportions of 2-methyl-2-butanol, isooctane, and water. The results are discussed in relation to the porous and hydrophobic nature of aerogels, characterized by nitrogen adsorption. It was found that silica aerogels can be considered as "solid" solvents for the enzymes, able to provide hydrophobic/hydrophilic characteristics different from those prevailing in the liquid surrounding the aerogels. A simple mechanism of action for these aerogel networks is proposed.

Synthesis and materialization of a reaction-diffusion French flag pattern

NASA Astrophysics Data System (ADS)

Zadorin, Anton S.; Rondelez, Yannick; Gines, Guillaume; Dilhas, Vadim; Urtel, Georg; Zambrano, Adrian; Galas, Jean-Christophe; Estevez-Torres, André

2017-10-01

During embryo development, patterns of protein concentration appear in response to morphogen gradients. These patterns provide spatial and chemical information that directs the fate of the underlying cells. Here, we emulate this process within non-living matter and demonstrate the autonomous structuration of a synthetic material. First, we use DNA-based reaction networks to synthesize a French flag, an archetypal pattern composed of three chemically distinct zones with sharp borders whose synthetic analogue has remained elusive. A bistable network within a shallow concentration gradient creates an immobile, sharp and long-lasting concentration front through a reaction-diffusion mechanism. The combination of two bistable circuits generates a French flag pattern whose 'phenotype' can be reprogrammed by network mutation. Second, these concentration patterns control the macroscopic organization of DNA-decorated particles, inducing a French flag pattern of colloidal aggregation. This experimental framework could be used to test reaction-diffusion models and fabricate soft materials following an autonomous developmental programme.

optGpSampler: an improved tool for uniformly sampling the solution-space of genome-scale metabolic networks.

PubMed

Megchelenbrink, Wout; Huynen, Martijn; Marchiori, Elena

2014-01-01

Constraint-based models of metabolic networks are typically underdetermined, because they contain more reactions than metabolites. Therefore the solutions to this system do not consist of unique flux rates for each reaction, but rather a space of possible flux rates. By uniformly sampling this space, an estimated probability distribution for each reaction's flux in the network can be obtained. However, sampling a high dimensional network is time-consuming. Furthermore, the constraints imposed on the network give rise to an irregularly shaped solution space. Therefore more tailored, efficient sampling methods are needed. We propose an efficient sampling algorithm (called optGpSampler), which implements the Artificial Centering Hit-and-Run algorithm in a different manner than the sampling algorithm implemented in the COBRA Toolbox for metabolic network analysis, here called gpSampler. Results of extensive experiments on different genome-scale metabolic networks show that optGpSampler is up to 40 times faster than gpSampler. Application of existing convergence diagnostics on small network reconstructions indicate that optGpSampler converges roughly ten times faster than gpSampler towards similar sampling distributions. For networks of higher dimension (i.e. containing more than 500 reactions), we observed significantly better convergence of optGpSampler and a large deviation between the samples generated by the two algorithms. optGpSampler for Matlab and Python is available for non-commercial use at: http://cs.ru.nl/~wmegchel/optGpSampler/.

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

Hay, J.; Schwender, J.

Computational simulation of large-scale biochemical networks can be used to analyze and predict the metabolic behavior of an organism, such as a developing seed. Based on the biochemical literature, pathways databases and decision rules defining reaction directionality we reconstructed bna572, a stoichiometric metabolic network model representing Brassica napus seed storage metabolism. In the highly compartmentalized network about 25% of the 572 reactions are transport reactions interconnecting nine subcellular compartments and the environment. According to known physiological capabilities of developing B. napus embryos, four nutritional conditions were defined to simulate heterotrophy or photoheterotrophy, each in combination with the availability of inorganicmore » nitrogen (ammonia, nitrate) or amino acids as nitrogen sources. Based on mathematical linear optimization the optimal solution space was comprehensively explored by flux variability analysis, thereby identifying for each reaction the range of flux values allowable under optimality. The range and variability of flux values was then categorized into flux variability types. Across the four nutritional conditions, approximately 13% of the reactions have variable flux values and 10-11% are substitutable (can be inactive), both indicating metabolic redundancy given, for example, by isoenzymes, subcellular compartmentalization or the presence of alternative pathways. About one-third of the reactions are never used and are associated with pathways that are suboptimal for storage synthesis. Fifty-seven reactions change flux variability type among the different nutritional conditions, indicating their function in metabolic adjustments. This predictive modeling framework allows analysis and quantitative exploration of storage metabolism of a developing B. napus oilseed.« less

Reachability bounds for chemical reaction networks and strand displacement systems.

PubMed

Condon, Anne; Kirkpatrick, Bonnie; Maňuch, Ján

2014-01-01

Chemical reaction networks (CRNs) and DNA strand displacement systems (DSDs) are widely-studied and useful models of molecular programming. However, in order for some DSDs in the literature to behave in an expected manner, the initial number of copies of some reagents is required to be fixed. In this paper we show that, when multiple copies of all initial molecules are present, general types of CRNs and DSDs fail to work correctly if the length of the shortest sequence of reactions needed to produce any given molecule exceeds a threshold that grows polynomially with attributes of the system.

Compendium of Anomaly Detection and Reaction Tools and Projects

DTIC Science & Technology

2000-05-17

identify changes to the risk levels of business network functions based on proposed modifications. Expert can model networks as well (see special...can easily scale to support any size network from departmental systems to enterprise-wide environments. ACX is scaled with the use of a Policy Model ...Defender is a host-based intrusion detector designed for use on home or small business systems. It scans all inbound and outbound Internet traffic for

Learning reduced kinetic Monte Carlo models of complex chemistry from molecular dynamics.

PubMed

Yang, Qian; Sing-Long, Carlos A; Reed, Evan J

2017-08-01

We propose a novel statistical learning framework for automatically and efficiently building reduced kinetic Monte Carlo (KMC) models of large-scale elementary reaction networks from data generated by a single or few molecular dynamics simulations (MD). Existing approaches for identifying species and reactions from molecular dynamics typically use bond length and duration criteria, where bond duration is a fixed parameter motivated by an understanding of bond vibrational frequencies. In contrast, we show that for highly reactive systems, bond duration should be a model parameter that is chosen to maximize the predictive power of the resulting statistical model. We demonstrate our method on a high temperature, high pressure system of reacting liquid methane, and show that the learned KMC model is able to extrapolate more than an order of magnitude in time for key molecules. Additionally, our KMC model of elementary reactions enables us to isolate the most important set of reactions governing the behavior of key molecules found in the MD simulation. We develop a new data-driven algorithm to reduce the chemical reaction network which can be solved either as an integer program or efficiently using L1 regularization, and compare our results with simple count-based reduction. For our liquid methane system, we discover that rare reactions do not play a significant role in the system, and find that less than 7% of the approximately 2000 reactions observed from molecular dynamics are necessary to reproduce the molecular concentration over time of methane. The framework described in this work paves the way towards a genomic approach to studying complex chemical systems, where expensive MD simulation data can be reused to contribute to an increasingly large and accurate genome of elementary reactions and rates.

Learning reduced kinetic Monte Carlo models of complex chemistry from molecular dynamics

PubMed Central

Sing-Long, Carlos A.

2017-01-01

We propose a novel statistical learning framework for automatically and efficiently building reduced kinetic Monte Carlo (KMC) models of large-scale elementary reaction networks from data generated by a single or few molecular dynamics simulations (MD). Existing approaches for identifying species and reactions from molecular dynamics typically use bond length and duration criteria, where bond duration is a fixed parameter motivated by an understanding of bond vibrational frequencies. In contrast, we show that for highly reactive systems, bond duration should be a model parameter that is chosen to maximize the predictive power of the resulting statistical model. We demonstrate our method on a high temperature, high pressure system of reacting liquid methane, and show that the learned KMC model is able to extrapolate more than an order of magnitude in time for key molecules. Additionally, our KMC model of elementary reactions enables us to isolate the most important set of reactions governing the behavior of key molecules found in the MD simulation. We develop a new data-driven algorithm to reduce the chemical reaction network which can be solved either as an integer program or efficiently using L1 regularization, and compare our results with simple count-based reduction. For our liquid methane system, we discover that rare reactions do not play a significant role in the system, and find that less than 7% of the approximately 2000 reactions observed from molecular dynamics are necessary to reproduce the molecular concentration over time of methane. The framework described in this work paves the way towards a genomic approach to studying complex chemical systems, where expensive MD simulation data can be reused to contribute to an increasingly large and accurate genome of elementary reactions and rates. PMID:28989618

Learning reduced kinetic Monte Carlo models of complex chemistry from molecular dynamics

DOE PAGES

Yang, Qian; Sing-Long, Carlos A.; Reed, Evan J.

2017-06-19

Here, we propose a novel statistical learning framework for automatically and efficiently building reduced kinetic Monte Carlo (KMC) models of large-scale elementary reaction networks from data generated by a single or few molecular dynamics simulations (MD). Existing approaches for identifying species and reactions from molecular dynamics typically use bond length and duration criteria, where bond duration is a fixed parameter motivated by an understanding of bond vibrational frequencies. Conversely, we show that for highly reactive systems, bond duration should be a model parameter that is chosen to maximize the predictive power of the resulting statistical model. We demonstrate our methodmore » on a high temperature, high pressure system of reacting liquid methane, and show that the learned KMC model is able to extrapolate more than an order of magnitude in time for key molecules. Additionally, our KMC model of elementary reactions enables us to isolate the most important set of reactions governing the behavior of key molecules found in the MD simulation. We develop a new data-driven algorithm to reduce the chemical reaction network which can be solved either as an integer program or efficiently using L1 regularization, and compare our results with simple count-based reduction. For our liquid methane system, we discover that rare reactions do not play a significant role in the system, and find that less than 7% of the approximately 2000 reactions observed from molecular dynamics are necessary to reproduce the molecular concentration over time of methane. Furthermore, we describe a framework in this work that paves the way towards a genomic approach to studying complex chemical systems, where expensive MD simulation data can be reused to contribute to an increasingly large and accurate genome of elementary reactions and rates.« less

A multiscale, model-based analysis of the multi-tissue interplay underlying blood glucose regulation in type I diabetes.

PubMed

Wadehn, Federico; Schaller, Stephan; Eissing, Thomas; Krauss, Markus; Kupfer, Lars

2016-08-01

A multiscale model for blood glucose regulation in diabetes type I patients is constructed by integrating detailed metabolic network models for fat, liver and muscle cells into a whole body physiologically-based pharmacokinetic/pharmacodynamic (pBPK/PD) model. The blood glucose regulation PBPK/PD model simulates the distribution and metabolization of glucose, insulin and glucagon on an organ and whole body level. The genome-scale metabolic networks in contrast describe intracellular reactions. The developed multiscale model is fitted to insulin, glucagon and glucose measurements of a 48h clinical trial featuring 6 subjects and is subsequently used to simulate (in silico) the influence of geneknockouts and drug-induced enzyme inhibitions on whole body blood glucose levels. Simulations of diabetes associated gene knockouts and impaired cellular glucose metabolism, resulted in elevated whole body blood-glucose levels, but also in a metabolic shift within the cell's reaction network. Such multiscale models have the potential to be employed in the exploration of novel drug-targets or to be integrated into control algorithms for artificial pancreas systems.

FindPrimaryPairs: An efficient algorithm for predicting element-transferring reactant/product pairs in metabolic networks.

PubMed

Steffensen, Jon Lund; Dufault-Thompson, Keith; Zhang, Ying

2018-01-01

The metabolism of individual organisms and biological communities can be viewed as a network of metabolites connected to each other through chemical reactions. In metabolic networks, chemical reactions transform reactants into products, thereby transferring elements between these metabolites. Knowledge of how elements are transferred through reactant/product pairs allows for the identification of primary compound connections through a metabolic network. However, such information is not readily available and is often challenging to obtain for large reaction databases or genome-scale metabolic models. In this study, a new algorithm was developed for automatically predicting the element-transferring reactant/product pairs using the limited information available in the standard representation of metabolic networks. The algorithm demonstrated high efficiency in analyzing large datasets and provided accurate predictions when benchmarked with manually curated data. Applying the algorithm to the visualization of metabolic networks highlighted pathways of primary reactant/product connections and provided an organized view of element-transferring biochemical transformations. The algorithm was implemented as a new function in the open source software package PSAMM in the release v0.30 (https://zhanglab.github.io/psamm/).

Computing molecular fluctuations in biochemical reaction systems based on a mechanistic, statistical theory of irreversible processes.

PubMed

Kulasiri, Don

2011-01-01

We discuss the quantification of molecular fluctuations in the biochemical reaction systems within the context of intracellular processes associated with gene expression. We take the molecular reactions pertaining to circadian rhythms to develop models of molecular fluctuations in this chapter. There are a significant number of studies on stochastic fluctuations in intracellular genetic regulatory networks based on single cell-level experiments. In order to understand the fluctuations associated with the gene expression in circadian rhythm networks, it is important to model the interactions of transcriptional factors with the E-boxes in the promoter regions of some of the genes. The pertinent aspects of a near-equilibrium theory that would integrate the thermodynamical and particle dynamic characteristics of intracellular molecular fluctuations would be discussed, and the theory is extended by using the theory of stochastic differential equations. We then model the fluctuations associated with the promoter regions using general mathematical settings. We implemented ubiquitous Gillespie's algorithms, which are used to simulate stochasticity in biochemical networks, for each of the motifs. Both the theory and the Gillespie's algorithms gave the same results in terms of the time evolution of means and variances of molecular numbers. As biochemical reactions occur far away from equilibrium-hence the use of the Gillespie algorithm-these results suggest that the near-equilibrium theory should be a good approximation for some of the biochemical reactions. © 2011 Elsevier Inc. All rights reserved.

A General Map of Iron Metabolism and Tissue-specific Subnetworks

PubMed Central

Hower, Valerie; Mendes, Pedro; Torti, Frank M.; Laubenbacher, Reinhard; Akman, Steven; Shulaev, Vladmir; Torti, Suzy V.

2009-01-01

Iron is required for survival of mammalian cells. Recently, understanding of iron metabolism and trafficking has increased dramatically, revealing a complex, interacting network largely unknown just a few years ago. This provides an excellent model for systems biology development and analysis. The first step in such an analysis is the construction of a structural network of iron metabolism, which we present here. This network was created using CellDesigner version 3.5.2 and includes reactions occurring in mammalian cells of numerous tissue types. The iron metabolic network contains 151 chemical species and 107 reactions and transport steps. Starting from this general model, we construct iron networks for specific tissues and cells that are fundamental to maintaining body iron homeostasis. We include subnetworks for cells of the intestine and liver, tissues important in iron uptake and storage, respectively; as well as the reticulocyte and macrophage, key cells in iron utilization and recycling. The addition of kinetic information to our structural network will permit the simulation of iron metabolism in different tissues as well as in health and disease. PMID:19381358

Modelling and prediction for chaotic fir laser attractor using rational function neural network.

PubMed

Cho, S

2001-02-01

Many real-world systems such as irregular ECG signal, volatility of currency exchange rate and heated fluid reaction exhibit highly complex nonlinear characteristic known as chaos. These chaotic systems cannot be retreated satisfactorily using linear system theory due to its high dimensionality and irregularity. This research focuses on prediction and modelling of chaotic FIR (Far InfraRed) laser system for which the underlying equations are not given. This paper proposed a method for prediction and modelling a chaotic FIR laser time series using rational function neural network. Three network architectures, TDNN (Time Delayed Neural Network), RBF (radial basis function) network and the RF (rational function) network, are also presented. Comparisons between these networks performance show the improvements introduced by the RF network in terms of a decrement in network complexity and better ability of predictability.

From sparse to dense and from assortative to disassortative in online social networks

PubMed Central

Li, Menghui; Guan, Shuguang; Wu, Chensheng; Gong, Xiaofeng; Li, Kun; Wu, Jinshan; Di, Zengru; Lai, Choy-Heng

2014-01-01

Inspired by the analysis of several empirical online social networks, we propose a simple reaction-diffusion-like coevolving model, in which individuals are activated to create links based on their states, influenced by local dynamics and their own intention. It is shown that the model can reproduce the remarkable properties observed in empirical online social networks; in particular, the assortative coefficients are neutral or negative, and the power law exponents γ are smaller than 2. Moreover, we demonstrate that, under appropriate conditions, the model network naturally makes transition(s) from assortative to disassortative, and from sparse to dense in their characteristics. The model is useful in understanding the formation and evolution of online social networks. PMID:24798703

From sparse to dense and from assortative to disassortative in online social networks.

PubMed

Li, Menghui; Guan, Shuguang; Wu, Chensheng; Gong, Xiaofeng; Li, Kun; Wu, Jinshan; Di, Zengru; Lai, Choy-Heng

2014-05-06

Inspired by the analysis of several empirical online social networks, we propose a simple reaction-diffusion-like coevolving model, in which individuals are activated to create links based on their states, influenced by local dynamics and their own intention. It is shown that the model can reproduce the remarkable properties observed in empirical online social networks; in particular, the assortative coefficients are neutral or negative, and the power law exponents γ are smaller than 2. Moreover, we demonstrate that, under appropriate conditions, the model network naturally makes transition(s) from assortative to disassortative, and from sparse to dense in their characteristics. The model is useful in understanding the formation and evolution of online social networks.

A systems biology approach to reconcile metabolic network models with application to Synechocystis sp. PCC 6803 for biofuel production.

PubMed

Mohammadi, Reza; Fallah-Mehrabadi, Jalil; Bidkhori, Gholamreza; Zahiri, Javad; Javad Niroomand, Mohammad; Masoudi-Nejad, Ali

2016-07-19

Production of biofuels has been one of the promising efforts in biotechnology in the past few decades. The perspective of these efforts can be reduction of increasing demands for fossil fuels and consequently reducing environmental pollution. Nonetheless, most previous approaches did not succeed in obviating many big challenges in this way. In recent years systems biology with the help of microorganisms has been trying to overcome these challenges. Unicellular cyanobacteria are widespread phototrophic microorganisms that have capabilities such as consuming solar energy and atmospheric carbon dioxide for growth and thus can be a suitable chassis for the production of valuable organic materials such as biofuels. For the ultimate use of metabolic potential of cyanobacteria, it is necessary to understand the reactions that are taking place inside the metabolic network of these microorganisms. In this study, we developed a Java tool to reconstruct an integrated metabolic network of a cyanobacterium (Synechocystis sp. PCC 6803). We merged three existing reconstructed metabolic networks of this microorganism. Then, after modeling for biofuel production, the results from flux balance analysis (FBA) disclosed an increased yield in biofuel production for ethanol, isobutanol, 3-methyl-1-butanol, 2-methyl-1-butanol, and propanol. The numbers of blocked reactions were also decreased for 2-methyl-1-butanol production. In addition, coverage of the metabolic network in terms of the number of metabolites and reactions was increased in the new obtained model.

Computationally-efficient stochastic cluster dynamics method for modeling damage accumulation in irradiated materials

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

Hoang, Tuan L.; Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, CA 94550; Marian, Jaime, E-mail: jmarian@ucla.edu

2015-11-01

An improved version of a recently developed stochastic cluster dynamics (SCD) method (Marian and Bulatov, 2012) [6] is introduced as an alternative to rate theory (RT) methods for solving coupled ordinary differential equation (ODE) systems for irradiation damage simulations. SCD circumvents by design the curse of dimensionality of the variable space that renders traditional ODE-based RT approaches inefficient when handling complex defect population comprised of multiple (more than two) defect species. Several improvements introduced here enable efficient and accurate simulations of irradiated materials up to realistic (high) damage doses characteristic of next-generation nuclear systems. The first improvement is a proceduremore » for efficiently updating the defect reaction-network and event selection in the context of a dynamically expanding reaction-network. Next is a novel implementation of the τ-leaping method that speeds up SCD simulations by advancing the state of the reaction network in large time increments when appropriate. Lastly, a volume rescaling procedure is introduced to control the computational complexity of the expanding reaction-network through occasional reductions of the defect population while maintaining accurate statistics. The enhanced SCD method is then applied to model defect cluster accumulation in iron thin films subjected to triple ion-beam (Fe{sup 3+}, He{sup +} and H{sup +}) irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo simulations are prohibitively expensive.« less

Computationally-efficient stochastic cluster dynamics method for modeling damage accumulation in irradiated materials

NASA Astrophysics Data System (ADS)

Hoang, Tuan L.; Marian, Jaime; Bulatov, Vasily V.; Hosemann, Peter

2015-11-01

An improved version of a recently developed stochastic cluster dynamics (SCD) method (Marian and Bulatov, 2012) [6] is introduced as an alternative to rate theory (RT) methods for solving coupled ordinary differential equation (ODE) systems for irradiation damage simulations. SCD circumvents by design the curse of dimensionality of the variable space that renders traditional ODE-based RT approaches inefficient when handling complex defect population comprised of multiple (more than two) defect species. Several improvements introduced here enable efficient and accurate simulations of irradiated materials up to realistic (high) damage doses characteristic of next-generation nuclear systems. The first improvement is a procedure for efficiently updating the defect reaction-network and event selection in the context of a dynamically expanding reaction-network. Next is a novel implementation of the τ-leaping method that speeds up SCD simulations by advancing the state of the reaction network in large time increments when appropriate. Lastly, a volume rescaling procedure is introduced to control the computational complexity of the expanding reaction-network through occasional reductions of the defect population while maintaining accurate statistics. The enhanced SCD method is then applied to model defect cluster accumulation in iron thin films subjected to triple ion-beam (Fe3+, He+ and H+) irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo simulations are prohibitively expensive.

Reply to 'Comments on upscaling geochemical reaction rates usingpore-scale network modeling' by Peter C. Lichtner and Qinjun Kang

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

Li, Li; Peters, Catherine A.; Celia, Michael A.

2006-05-03

Our paper "Upscaling geochemical reaction rates usingpore-scale network modeling" presents a novel application of pore-scalenetwork modeling to upscale mineral dissolution and precipitationreaction rates from the pore scale to the continuum scale, anddemonstrates the methodology by analyzing the scaling behavior ofanorthite and kaolinite reaction kinetics under conditions related to CO2sequestration. We conclude that under highly acidic conditions relevantto CO2 sequestration, the traditional continuum-based methodology may notcapture the spatial variation in concentrations from pore to pore, andscaling tools may be important in correctly modeling reactive transportprocesses in such systems. This work addresses the important butdifficult question of scaling mineral dissolution and precipitationreactionmore » kinetics, which is often ignored in fields such as geochemistry,water resources, and contaminant hydrology. Although scaling of physicalprocesses has been studied for almost three decades, very few studieshave examined the scaling issues related to chemical processes, despitetheir importance in governing the transport and fate of contaminants insubsurface systems.« less

A Digitally Programmable Cytomorphic Chip for Simulation of Arbitrary Biochemical Reaction Networks.

PubMed

Woo, Sung Sik; Kim, Jaewook; Sarpeshkar, Rahul

2018-04-01

Prior work has shown that compact analog circuits can faithfully represent and model fundamental biomolecular circuits via efficient log-domain cytomorphic transistor equivalents. Such circuits have emphasized basis functions that are dominant in genetic transcription and translation networks and deoxyribonucleic acid (DNA)-protein binding. Here, we report a system featuring digitally programmable 0.35 μm BiCMOS analog cytomorphic chips that enable arbitrary biochemical reaction networks to be exactly represented thus enabling compact and easy composition of protein networks as well. Since all biomolecular networks can be represented as chemical reaction networks, our protein networks also include the former genetic network circuits as a special case. The cytomorphic analog protein circuits use one fundamental association-dissociation-degradation building-block circuit that can be configured digitally to exactly represent any zeroth-, first-, and second-order reaction including loading, dynamics, nonlinearity, and interactions with other building-block circuits. To address a divergence issue caused by random variations in chip fabrication processes, we propose a unique way of performing computation based on total variables and conservation laws, which we instantiate at both the circuit and network levels. Thus, scalable systems that operate with finite error over infinite time can be built. We show how the building-block circuits can be composed to form various network topologies, such as cascade, fan-out, fan-in, loop, dimerization, or arbitrary networks using total variables. We demonstrate results from a system that combines interacting cytomorphic chips to simulate a cancer pathway and a glycolysis pathway. Both simulations are consistent with conventional software simulations. Our highly parallel digitally programmable analog cytomorphic systems can lead to a useful design, analysis, and simulation tool for studying arbitrary large-scale biological networks in systems and synthetic biology.

Pyrolysis reaction networks for lignin model compounds: unraveling thermal deconstruction of β-O-4 and α-O-4 compounds

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

Choi, Yong S.; Singh, Rahul; Zhang, Jing

2016-01-01

Although lignin is one of the main components of biomass, its pyrolysis chemistry is not well understood due to complex heterogeneity. To gain insights into this chemistry, the pyrolysis of seven lignin model compounds (five ..beta..-O-4 and two ..alpha..-O-4 linked molecules) was investigated in a micropyrolyzer connected to GC-MS/FID. According to quantitative product mole balance for the reaction networks, concerted retro-ene fragmentation and homolytic dissociation were strongly suggested as the initial reaction step for ..beta..-O-4 compounds and ..alpha..-O-4 compounds, respectively. The difference in reaction pathway between compounds with different linkages was believed to result from thermodynamics of the radical initiation.more » The rate constants for the different reaction pathways were predicted from ab initio density functional theory calculations and pre-exponential literature values. The computational findings were consistent with the experiment results, further supporting the different pyrolysis mechanisms for the ..beta..-ether linked and ..alpha..-ether linked compounds. A combination of the two pathways from the dimeric model compounds was able to describe qualitatively the pyrolysis of a trimeric lignin model compound containing both ..beta..-O-4 and ..alpha..-O-4 linkages.« less

Rule-based modeling with Virtual Cell

PubMed Central

Schaff, James C.; Vasilescu, Dan; Moraru, Ion I.; Loew, Leslie M.; Blinov, Michael L.

2016-01-01

Summary: Rule-based modeling is invaluable when the number of possible species and reactions in a model become too large to allow convenient manual specification. The popular rule-based software tools BioNetGen and NFSim provide powerful modeling and simulation capabilities at the cost of learning a complex scripting language which is used to specify these models. Here, we introduce a modeling tool that combines new graphical rule-based model specification with existing simulation engines in a seamless way within the familiar Virtual Cell (VCell) modeling environment. A mathematical model can be built integrating explicit reaction networks with reaction rules. In addition to offering a large choice of ODE and stochastic solvers, a model can be simulated using a network free approach through the NFSim simulation engine. Availability and implementation: Available as VCell (versions 6.0 and later) at the Virtual Cell web site (http://vcell.org/). The application installs and runs on all major platforms and does not require registration for use on the user’s computer. Tutorials are available at the Virtual Cell website and Help is provided within the software. Source code is available at Sourceforge. Contact: vcell_support@uchc.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:27497444

FCDECOMP: decomposition of metabolic networks based on flux coupling relations.

PubMed

Rezvan, Abolfazl; Marashi, Sayed-Amir; Eslahchi, Changiz

2014-10-01

A metabolic network model provides a computational framework to study the metabolism of a cell at the system level. Due to their large sizes and complexity, rational decomposition of these networks into subsystems is a strategy to obtain better insight into the metabolic functions. Additionally, decomposing metabolic networks paves the way to use computational methods that will be otherwise very slow when run on the original genome-scale network. In the present study, we propose FCDECOMP decomposition method based on flux coupling relations (FCRs) between pairs of reaction fluxes. This approach utilizes a genetic algorithm (GA) to obtain subsystems that can be analyzed in isolation, i.e. without considering the reactions of the original network in the analysis. Therefore, we propose that our method is useful for discovering biologically meaningful modules in metabolic networks. As a case study, we show that when this method is applied to the metabolic networks of barley seeds and yeast, the modules are in good agreement with the biological compartments of these networks.

Acceleration and sensitivity analysis of lattice kinetic Monte Carlo simulations using parallel processing and rate constant rescaling

NASA Astrophysics Data System (ADS)

Núñez, M.; Robie, T.; Vlachos, D. G.

2017-10-01

Kinetic Monte Carlo (KMC) simulation provides insights into catalytic reactions unobtainable with either experiments or mean-field microkinetic models. Sensitivity analysis of KMC models assesses the robustness of the predictions to parametric perturbations and identifies rate determining steps in a chemical reaction network. Stiffness in the chemical reaction network, a ubiquitous feature, demands lengthy run times for KMC models and renders efficient sensitivity analysis based on the likelihood ratio method unusable. We address the challenge of efficiently conducting KMC simulations and performing accurate sensitivity analysis in systems with unknown time scales by employing two acceleration techniques: rate constant rescaling and parallel processing. We develop statistical criteria that ensure sufficient sampling of non-equilibrium steady state conditions. Our approach provides the twofold benefit of accelerating the simulation itself and enabling likelihood ratio sensitivity analysis, which provides further speedup relative to finite difference sensitivity analysis. As a result, the likelihood ratio method can be applied to real chemistry. We apply our methodology to the water-gas shift reaction on Pt(111).

Rule-based spatial modeling with diffusing, geometrically constrained molecules.

PubMed

Gruenert, Gerd; Ibrahim, Bashar; Lenser, Thorsten; Lohel, Maiko; Hinze, Thomas; Dittrich, Peter

2010-06-07

We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly.

Rule-based spatial modeling with diffusing, geometrically constrained molecules

PubMed Central

2010-01-01

Background We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Results Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. Conclusions We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly. PMID:20529264

The Impact of Nuclear Reaction Rate Uncertainties on the Evolution of Core-collapse Supernova Progenitors

NASA Astrophysics Data System (ADS)

Fields, C. E.; Timmes, F. X.; Farmer, R.; Petermann, I.; Wolf, William M.; Couch, S. M.

2018-02-01

We explore properties of core-collapse supernova progenitors with respect to the composite uncertainties in the thermonuclear reaction rates by coupling the probability density functions of the reaction rates provided by the STARLIB reaction rate library with MESA stellar models. We evolve 1000 models of 15{M}ȯ from the pre-main sequence to core O-depletion at solar and subsolar metallicities for a total of 2000 Monte Carlo stellar models. For each stellar model, we independently and simultaneously sample 665 thermonuclear reaction rates and use them in a MESA in situ reaction network that follows 127 isotopes from 1H to 64Zn. With this framework we survey the core mass, burning lifetime, composition, and structural properties at five different evolutionary epochs. At each epoch we measure the probability distribution function of the variations of each property and calculate Spearman rank-order correlation coefficients for each sampled reaction rate to identify which reaction rate has the largest impact on the variations on each property. We find that uncertainties in the reaction rates of {}14{{N}}{({{p}},γ )}15{{O}}, triple-α, {}12{{C}}{(α ,γ )}16{{O}}, 12C(12C,p)23Na, 12C(16O, p)27Al, 16O(16O,n)31S, 16O(16O, p)31P, and 16O(16O,α)28Si dominate the variations of the properties surveyed. We find that variations induced by uncertainties in nuclear reaction rates grow with each passing phase of evolution, and at core H-, He-depletion they are of comparable magnitude to the variations induced by choices of mass resolution and network resolution. However, at core C-, Ne-, and O-depletion, the reaction rate uncertainties can dominate the variation, causing uncertainty in various properties of the stellar model in the evolution toward iron core-collapse.

Genome-Scale Reconstruction of the Human Astrocyte Metabolic Network

PubMed Central

Martín-Jiménez, Cynthia A.; Salazar-Barreto, Diego; Barreto, George E.; González, Janneth

2017-01-01

Astrocytes are the most abundant cells of the central nervous system; they have a predominant role in maintaining brain metabolism. In this sense, abnormal metabolic states have been found in different neuropathological diseases. Determination of metabolic states of astrocytes is difficult to model using current experimental approaches given the high number of reactions and metabolites present. Thus, genome-scale metabolic networks derived from transcriptomic data can be used as a framework to elucidate how astrocytes modulate human brain metabolic states during normal conditions and in neurodegenerative diseases. We performed a Genome-Scale Reconstruction of the Human Astrocyte Metabolic Network with the purpose of elucidating a significant portion of the metabolic map of the astrocyte. This is the first global high-quality, manually curated metabolic reconstruction network of a human astrocyte. It includes 5,007 metabolites and 5,659 reactions distributed among 8 cell compartments, (extracellular, cytoplasm, mitochondria, endoplasmic reticle, Golgi apparatus, lysosome, peroxisome and nucleus). Using the reconstructed network, the metabolic capabilities of human astrocytes were calculated and compared both in normal and ischemic conditions. We identified reactions activated in these two states, which can be useful for understanding the astrocytic pathways that are affected during brain disease. Additionally, we also showed that the obtained flux distributions in the model, are in accordance with literature-based findings. Up to date, this is the most complete representation of the human astrocyte in terms of inclusion of genes, proteins, reactions and metabolic pathways, being a useful guide for in-silico analysis of several metabolic behaviors of the astrocyte during normal and pathologic states. PMID:28243200

Adaptively biased sequential importance sampling for rare events in reaction networks with comparison to exact solutions from finite buffer dCME method

PubMed Central

Cao, Youfang; Liang, Jie

2013-01-01

Critical events that occur rarely in biological processes are of great importance, but are challenging to study using Monte Carlo simulation. By introducing biases to reaction selection and reaction rates, weighted stochastic simulation algorithms based on importance sampling allow rare events to be sampled more effectively. However, existing methods do not address the important issue of barrier crossing, which often arises from multistable networks and systems with complex probability landscape. In addition, the proliferation of parameters and the associated computing cost pose significant problems. Here we introduce a general theoretical framework for obtaining optimized biases in sampling individual reactions for estimating probabilities of rare events. We further describe a practical algorithm called adaptively biased sequential importance sampling (ABSIS) method for efficient probability estimation. By adopting a look-ahead strategy and by enumerating short paths from the current state, we estimate the reaction-specific and state-specific forward and backward moving probabilities of the system, which are then used to bias reaction selections. The ABSIS algorithm can automatically detect barrier-crossing regions, and can adjust bias adaptively at different steps of the sampling process, with bias determined by the outcome of exhaustively generated short paths. In addition, there are only two bias parameters to be determined, regardless of the number of the reactions and the complexity of the network. We have applied the ABSIS method to four biochemical networks: the birth-death process, the reversible isomerization, the bistable Schlögl model, and the enzymatic futile cycle model. For comparison, we have also applied the finite buffer discrete chemical master equation (dCME) method recently developed to obtain exact numerical solutions of the underlying discrete chemical master equations of these problems. This allows us to assess sampling results objectively by comparing simulation results with true answers. Overall, ABSIS can accurately and efficiently estimate rare event probabilities for all examples, often with smaller variance than other importance sampling algorithms. The ABSIS method is general and can be applied to study rare events of other stochastic networks with complex probability landscape. PMID:23862966

Adaptively biased sequential importance sampling for rare events in reaction networks with comparison to exact solutions from finite buffer dCME method

NASA Astrophysics Data System (ADS)

Cao, Youfang; Liang, Jie

2013-07-01

Critical events that occur rarely in biological processes are of great importance, but are challenging to study using Monte Carlo simulation. By introducing biases to reaction selection and reaction rates, weighted stochastic simulation algorithms based on importance sampling allow rare events to be sampled more effectively. However, existing methods do not address the important issue of barrier crossing, which often arises from multistable networks and systems with complex probability landscape. In addition, the proliferation of parameters and the associated computing cost pose significant problems. Here we introduce a general theoretical framework for obtaining optimized biases in sampling individual reactions for estimating probabilities of rare events. We further describe a practical algorithm called adaptively biased sequential importance sampling (ABSIS) method for efficient probability estimation. By adopting a look-ahead strategy and by enumerating short paths from the current state, we estimate the reaction-specific and state-specific forward and backward moving probabilities of the system, which are then used to bias reaction selections. The ABSIS algorithm can automatically detect barrier-crossing regions, and can adjust bias adaptively at different steps of the sampling process, with bias determined by the outcome of exhaustively generated short paths. In addition, there are only two bias parameters to be determined, regardless of the number of the reactions and the complexity of the network. We have applied the ABSIS method to four biochemical networks: the birth-death process, the reversible isomerization, the bistable Schlögl model, and the enzymatic futile cycle model. For comparison, we have also applied the finite buffer discrete chemical master equation (dCME) method recently developed to obtain exact numerical solutions of the underlying discrete chemical master equations of these problems. This allows us to assess sampling results objectively by comparing simulation results with true answers. Overall, ABSIS can accurately and efficiently estimate rare event probabilities for all examples, often with smaller variance than other importance sampling algorithms. The ABSIS method is general and can be applied to study rare events of other stochastic networks with complex probability landscape.

Adaptively biased sequential importance sampling for rare events in reaction networks with comparison to exact solutions from finite buffer dCME method.

PubMed

Cao, Youfang; Liang, Jie

2013-07-14

Critical events that occur rarely in biological processes are of great importance, but are challenging to study using Monte Carlo simulation. By introducing biases to reaction selection and reaction rates, weighted stochastic simulation algorithms based on importance sampling allow rare events to be sampled more effectively. However, existing methods do not address the important issue of barrier crossing, which often arises from multistable networks and systems with complex probability landscape. In addition, the proliferation of parameters and the associated computing cost pose significant problems. Here we introduce a general theoretical framework for obtaining optimized biases in sampling individual reactions for estimating probabilities of rare events. We further describe a practical algorithm called adaptively biased sequential importance sampling (ABSIS) method for efficient probability estimation. By adopting a look-ahead strategy and by enumerating short paths from the current state, we estimate the reaction-specific and state-specific forward and backward moving probabilities of the system, which are then used to bias reaction selections. The ABSIS algorithm can automatically detect barrier-crossing regions, and can adjust bias adaptively at different steps of the sampling process, with bias determined by the outcome of exhaustively generated short paths. In addition, there are only two bias parameters to be determined, regardless of the number of the reactions and the complexity of the network. We have applied the ABSIS method to four biochemical networks: the birth-death process, the reversible isomerization, the bistable Schlögl model, and the enzymatic futile cycle model. For comparison, we have also applied the finite buffer discrete chemical master equation (dCME) method recently developed to obtain exact numerical solutions of the underlying discrete chemical master equations of these problems. This allows us to assess sampling results objectively by comparing simulation results with true answers. Overall, ABSIS can accurately and efficiently estimate rare event probabilities for all examples, often with smaller variance than other importance sampling algorithms. The ABSIS method is general and can be applied to study rare events of other stochastic networks with complex probability landscape.

Role of nuclear reactions on stellar evolution of intermediate-mass stars

NASA Astrophysics Data System (ADS)

Möller, H.; Jones, S.; Fischer, T.; Martínez-Pinedo, G.

2018-01-01

The evolution of intermediate-mass stars (8 - 12 solar masses) represents one of the most challenging subjects in nuclear astrophysics. Their final fate is highly uncertain and strongly model dependent. They can become white dwarfs, they can undergo electron-capture or core-collapse supernovae or they might even proceed towards explosive oxygen burning and a subsequent thermonuclear explosion. We believe that an accurate description of nuclear reactions is crucial for the determination of the pre-supernova structure of these stars. We argue that due to the possible development of an oxygen-deflagration, a hydrodynamic description has to be used. We implement a nuclear reaction network with ∼200 nuclear species into the implicit hydrodynamic code AGILE. The reaction network considers all relevant nuclear electron captures and beta-decays. For selected relevant nuclear species, we include a set of updated reaction rates, for which we discuss the role for the evolution of the stellar core, at the example of selected stellar models. We find that the final fate of these intermediate-mass stars depends sensitively on the density threshold for weak processes that deleptonize the core.

Non-steady state mass action dynamics without rate constants: dynamics of coupled reactions using chemical potentials

NASA Astrophysics Data System (ADS)

Cannon, William R.; Baker, Scott E.

2017-10-01

Comprehensive and predictive simulation of coupled reaction networks has long been a goal of biology and other fields. Currently, metabolic network models that utilize enzyme mass action kinetics have predictive power but are limited in scope and application by the fact that the determination of enzyme rate constants is laborious and low throughput. We present a statistical thermodynamic formulation of the law of mass action for coupled reactions at both steady states and non-stationary states. The formulation uses chemical potentials instead of rate constants. When used to model deterministic systems, the method corresponds to a rescaling of the time dependent reactions in such a way that steady states can be reached on the same time scale but with significantly fewer computational steps. The relationships between reaction affinities, free energy changes and generalized detailed balance are central to the discussion. The significance for applications in systems biology are discussed as is the concept and assumption of maximum entropy production rate as a biological principle that links thermodynamics to natural selection.

Toward efficiency in heterogeneous multispecies reactive transport modeling: A particle-tracking solution for first-order network reactions

NASA Astrophysics Data System (ADS)

Henri, Christopher; Fernàndez-Garcia, Daniel

2015-04-01

Modeling multi-species reactive transport in natural systems with strong heterogeneities and complex biochemical reactions is a major challenge for assessing groundwater polluted sites with organic and inorganic contaminants. A large variety of these contaminants react according to serial-parallel reaction networks commonly simplified by a combination of first-order kinetic reactions. In this context, a random-walk particle tracking method is presented. This method is capable of efficiently simulating the motion of particles affected by first-order network reactions in three-dimensional systems, which are represented by spatially variable physical and biochemical coefficients described at high resolution. The approach is based on the development of transition probabilities that describe the likelihood that particles belonging to a given species and location at a given time will be transformed into and moved to another species and location afterwards. These probabilities are derived from the solution matrix of the spatial moments governing equations. The method is fully coupled with reactions, free of numerical dispersion and overcomes the inherent numerical problems stemming from the incorporation of heterogeneities to reactive transport codes. In doing this, we demonstrate that the motion of particles follows a standard random walk with time-dependent effective retardation and dispersion parameters that depend on the initial and final chemical state of the particle. The behavior of effective parameters develops as a result of differential retardation effects among species. Moreover, explicit analytic solutions of the transition probability matrix and related particle motions are provided for serial reactions. An example of the effect of heterogeneity on the dechlorination of organic solvents in a three-dimensional random porous media shows that the power-law behavior typically observed in conservative tracers breakthrough curves can be largely compromised by the effect of biochemical reactions.

Toward efficiency in heterogeneous multispecies reactive transport modeling: A particle-tracking solution for first-order network reactions

NASA Astrophysics Data System (ADS)

Henri, Christopher V.; Fernàndez-Garcia, Daniel

2014-09-01

Modeling multispecies reactive transport in natural systems with strong heterogeneities and complex biochemical reactions is a major challenge for assessing groundwater polluted sites with organic and inorganic contaminants. A large variety of these contaminants react according to serial-parallel reaction networks commonly simplified by a combination of first-order kinetic reactions. In this context, a random-walk particle tracking method is presented. This method is capable of efficiently simulating the motion of particles affected by first-order network reactions in three-dimensional systems, which are represented by spatially variable physical and biochemical coefficients described at high resolution. The approach is based on the development of transition probabilities that describe the likelihood that particles belonging to a given species and location at a given time will be transformed into and moved to another species and location afterward. These probabilities are derived from the solution matrix of the spatial moments governing equations. The method is fully coupled with reactions, free of numerical dispersion and overcomes the inherent numerical problems stemming from the incorporation of heterogeneities to reactive transport codes. In doing this, we demonstrate that the motion of particles follows a standard random walk with time-dependent effective retardation and dispersion parameters that depend on the initial and final chemical state of the particle. The behavior of effective parameters develops as a result of differential retardation effects among species. Moreover, explicit analytic solutions of the transition probability matrix and related particle motions are provided for serial reactions. An example of the effect of heterogeneity on the dechlorination of organic solvents in a three-dimensional random porous media shows that the power-law behavior typically observed in conservative tracers breakthrough curves can be largely compromised by the effect of biochemical reactions.

DRUM: A New Framework for Metabolic Modeling under Non-Balanced Growth. Application to the Carbon Metabolism of Unicellular Microalgae

PubMed Central

Baroukh, Caroline; Muñoz-Tamayo, Rafael; Steyer, Jean-Philippe; Bernard, Olivier

2014-01-01

Metabolic modeling is a powerful tool to understand, predict and optimize bioprocesses, particularly when they imply intracellular molecules of interest. Unfortunately, the use of metabolic models for time varying metabolic fluxes is hampered by the lack of experimental data required to define and calibrate the kinetic reaction rates of the metabolic pathways. For this reason, metabolic models are often used under the balanced growth hypothesis. However, for some processes such as the photoautotrophic metabolism of microalgae, the balanced-growth assumption appears to be unreasonable because of the synchronization of their circadian cycle on the daily light. Yet, understanding microalgae metabolism is necessary to optimize the production yield of bioprocesses based on this microorganism, as for example production of third-generation biofuels. In this paper, we propose DRUM, a new dynamic metabolic modeling framework that handles the non-balanced growth condition and hence accumulation of intracellular metabolites. The first stage of the approach consists in splitting the metabolic network into sub-networks describing reactions which are spatially close, and which are assumed to satisfy balanced growth condition. The left metabolites interconnecting the sub-networks behave dynamically. Then, thanks to Elementary Flux Mode analysis, each sub-network is reduced to macroscopic reactions, for which simple kinetics are assumed. Finally, an Ordinary Differential Equation system is obtained to describe substrate consumption, biomass production, products excretion and accumulation of some internal metabolites. DRUM was applied to the accumulation of lipids and carbohydrates of the microalgae Tisochrysis lutea under day/night cycles. The resulting model describes accurately experimental data obtained in day/night conditions. It efficiently predicts the accumulation and consumption of lipids and carbohydrates. PMID:25105494

High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals.

PubMed

Marcon, Luciano; Diego, Xavier; Sharpe, James; Müller, Patrick

2016-04-08

The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software (available at http://www.RDNets.com) to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study offers a new theoretical framework to understand multicellular pattern formation and enables the wide-spread use of mathematical biology to engineer synthetic patterning systems.

High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals

PubMed Central

Marcon, Luciano; Diego, Xavier; Sharpe, James; Müller, Patrick

2016-01-01

The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software (available at http://www.RDNets.com) to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study offers a new theoretical framework to understand multicellular pattern formation and enables the wide-spread use of mathematical biology to engineer synthetic patterning systems. DOI: http://dx.doi.org/10.7554/eLife.14022.001 PMID:27058171

Model-based analysis of keratin intermediate filament assembly

NASA Astrophysics Data System (ADS)

Martin, Ines; Leitner, Anke; Walther, Paul; Herrmann, Harald; Marti, Othmar

2015-09-01

The cytoskeleton of epithelial cells consists of three types of filament systems: microtubules, actin filaments and intermediate filaments (IFs). Here, we took a closer look at type I and type II IF proteins, i.e. keratins. They are hallmark constituents of epithelial cells and are responsible for the generation of stiffness, the cellular response to mechanical stimuli and the integrity of entire cell layers. Thereby, keratin networks constitute an important instrument for cells to adapt to their environment. In particular, we applied models to characterize the assembly of keratin K8 and K18 into elongated filaments as a means for network formation. For this purpose, we measured the length of in vitro assembled keratin K8/K18 filaments by transmission electron microscopy at different time points. We evaluated the experimental data of the longitudinal annealing reaction using two models from polymer chemistry: the Schulz-Zimm model and the condensation polymerization model. In both scenarios one has to make assumptions about the reaction process. We compare how well the models fit the measured data and thus determine which assumptions fit best. Based on mathematical modelling of experimental filament assembly data we define basic mechanistic properties of the elongation reaction process.

Modeling languages for biochemical network simulation: reaction vs equation based approaches.

PubMed

Wiechert, Wolfgang; Noack, Stephan; Elsheikh, Atya

2010-01-01

Biochemical network modeling and simulation is an essential task in any systems biology project. The systems biology markup language (SBML) was established as a standardized model exchange language for mechanistic models. A specific strength of SBML is that numerous tools for formulating, processing, simulation and analysis of models are freely available. Interestingly, in the field of multidisciplinary simulation, the problem of model exchange between different simulation tools occurred much earlier. Several general modeling languages like Modelica have been developed in the 1990s. Modelica enables an equation based modular specification of arbitrary hierarchical differential algebraic equation models. Moreover, libraries for special application domains can be rapidly developed. This contribution compares the reaction based approach of SBML with the equation based approach of Modelica and explains the specific strengths of both tools. Several biological examples illustrating essential SBML and Modelica concepts are given. The chosen criteria for tool comparison are flexibility for constraint specification, different modeling flavors, hierarchical, modular and multidisciplinary modeling. Additionally, support for spatially distributed systems, event handling and network analysis features is discussed. As a major result it is shown that the choice of the modeling tool has a strong impact on the expressivity of the specified models but also strongly depends on the requirements of the application context.

Metabolic design of macroscopic bioreaction models: application to Chinese hamster ovary cells.

PubMed

Provost, A; Bastin, G; Agathos, S N; Schneider, Y-J

2006-12-01

The aim of this paper is to present a systematic methodology to design macroscopic bioreaction models for cell cultures based upon metabolic networks. The cell culture is seen as a succession of phases. During each phase, a metabolic network represents the set of reactions occurring in the cell. Then, through the use of the elementary flux modes, these metabolic networks are used to derive macroscopic bioreactions linking the extracellular substrates and products. On this basis, as many separate models are obtained as there are phases. Then, a complete model is obtained by smoothly switching from model to model. This is illustrated with batch cultures of Chinese hamster ovary cells.

Effects of correlated parameters and uncertainty in electronic-structure-based chemical kinetic modelling

NASA Astrophysics Data System (ADS)

Sutton, Jonathan E.; Guo, Wei; Katsoulakis, Markos A.; Vlachos, Dionisios G.

2016-04-01

Kinetic models based on first principles are becoming common place in heterogeneous catalysis because of their ability to interpret experimental data, identify the rate-controlling step, guide experiments and predict novel materials. To overcome the tremendous computational cost of estimating parameters of complex networks on metal catalysts, approximate quantum mechanical calculations are employed that render models potentially inaccurate. Here, by introducing correlative global sensitivity analysis and uncertainty quantification, we show that neglecting correlations in the energies of species and reactions can lead to an incorrect identification of influential parameters and key reaction intermediates and reactions. We rationalize why models often underpredict reaction rates and show that, despite the uncertainty being large, the method can, in conjunction with experimental data, identify influential missing reaction pathways and provide insights into the catalyst active site and the kinetic reliability of a model. The method is demonstrated in ethanol steam reforming for hydrogen production for fuel cells.

Evaluation of rate law approximations in bottom-up kinetic models of metabolism.

PubMed

Du, Bin; Zielinski, Daniel C; Kavvas, Erol S; Dräger, Andreas; Tan, Justin; Zhang, Zhen; Ruggiero, Kayla E; Arzumanyan, Garri A; Palsson, Bernhard O

2016-06-06

The mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question. In this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations. Overall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches.

Optimal design of stimulus experiments for robust discrimination of biochemical reaction networks.

PubMed

Flassig, R J; Sundmacher, K

2012-12-01

Biochemical reaction networks in the form of coupled ordinary differential equations (ODEs) provide a powerful modeling tool for understanding the dynamics of biochemical processes. During the early phase of modeling, scientists have to deal with a large pool of competing nonlinear models. At this point, discrimination experiments can be designed and conducted to obtain optimal data for selecting the most plausible model. Since biological ODE models have widely distributed parameters due to, e.g. biologic variability or experimental variations, model responses become distributed. Therefore, a robust optimal experimental design (OED) for model discrimination can be used to discriminate models based on their response probability distribution functions (PDFs). In this work, we present an optimal control-based methodology for designing optimal stimulus experiments aimed at robust model discrimination. For estimating the time-varying model response PDF, which results from the nonlinear propagation of the parameter PDF under the ODE dynamics, we suggest using the sigma-point approach. Using the model overlap (expected likelihood) as a robust discrimination criterion to measure dissimilarities between expected model response PDFs, we benchmark the proposed nonlinear design approach against linearization with respect to prediction accuracy and design quality for two nonlinear biological reaction networks. As shown, the sigma-point outperforms the linearization approach in the case of widely distributed parameter sets and/or existing multiple steady states. Since the sigma-point approach scales linearly with the number of model parameter, it can be applied to large systems for robust experimental planning. An implementation of the method in MATLAB/AMPL is available at http://www.uni-magdeburg.de/ivt/svt/person/rf/roed.html. flassig@mpi-magdeburg.mpg.de Supplementary data are are available at Bioinformatics online.

Conditions for extinction events in chemical reaction networks with discrete state spaces.

PubMed

Johnston, Matthew D; Anderson, David F; Craciun, Gheorghe; Brijder, Robert

2018-05-01

We study chemical reaction networks with discrete state spaces and present sufficient conditions on the structure of the network that guarantee the system exhibits an extinction event. The conditions we derive involve creating a modified chemical reaction network called a domination-expanded reaction network and then checking properties of this network. Unlike previous results, our analysis allows algorithmic implementation via systems of equalities and inequalities and suggests sequences of reactions which may lead to extinction events. We apply the results to several networks including an EnvZ-OmpR signaling pathway in Escherichia coli.

Leveraging Modeling Approaches: Reaction Networks and Rules

PubMed Central

Blinov, Michael L.; Moraru, Ion I.

2012-01-01

We have witnessed an explosive growth in research involving mathematical models and computer simulations of intracellular molecular interactions, ranging from metabolic pathways to signaling and gene regulatory networks. Many software tools have been developed to aid in the study of such biological systems, some of which have a wealth of features for model building and visualization, and powerful capabilities for simulation and data analysis. Novel high resolution and/or high throughput experimental techniques have led to an abundance of qualitative and quantitative data related to the spatio-temporal distribution of molecules and complexes, their interactions kinetics, and functional modifications. Based on this information, computational biology researchers are attempting to build larger and more detailed models. However, this has proved to be a major challenge. Traditionally, modeling tools require the explicit specification of all molecular species and interactions in a model, which can quickly become a major limitation in the case of complex networks – the number of ways biomolecules can combine to form multimolecular complexes can be combinatorially large. Recently, a new breed of software tools has been created to address the problems faced when building models marked by combinatorial complexity. These have a different approach for model specification, using reaction rules and species patterns. Here we compare the traditional modeling approach with the new rule-based methods. We make a case for combining the capabilities of conventional simulation software with the unique features and flexibility of a rule-based approach in a single software platform for building models of molecular interaction networks. PMID:22161349

Leveraging modeling approaches: reaction networks and rules.

PubMed

Blinov, Michael L; Moraru, Ion I

2012-01-01

We have witnessed an explosive growth in research involving mathematical models and computer simulations of intracellular molecular interactions, ranging from metabolic pathways to signaling and gene regulatory networks. Many software tools have been developed to aid in the study of such biological systems, some of which have a wealth of features for model building and visualization, and powerful capabilities for simulation and data analysis. Novel high-resolution and/or high-throughput experimental techniques have led to an abundance of qualitative and quantitative data related to the spatiotemporal distribution of molecules and complexes, their interactions kinetics, and functional modifications. Based on this information, computational biology researchers are attempting to build larger and more detailed models. However, this has proved to be a major challenge. Traditionally, modeling tools require the explicit specification of all molecular species and interactions in a model, which can quickly become a major limitation in the case of complex networks - the number of ways biomolecules can combine to form multimolecular complexes can be combinatorially large. Recently, a new breed of software tools has been created to address the problems faced when building models marked by combinatorial complexity. These have a different approach for model specification, using reaction rules and species patterns. Here we compare the traditional modeling approach with the new rule-based methods. We make a case for combining the capabilities of conventional simulation software with the unique features and flexibility of a rule-based approach in a single software platform for building models of molecular interaction networks.

Hybrid deterministic/stochastic simulation of complex biochemical systems.

PubMed

Lecca, Paola; Bagagiolo, Fabio; Scarpa, Marina

2017-11-21

In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by complex networks of chemical reactions involving genes, proteins, and enzymes. Accurate computational models are indispensable means for understanding the mechanisms behind the evolution of a complex system, not always explored with wet lab experiments. To serve their purpose, computational models, however, should be able to describe and simulate the complexity of a biological system in many of its aspects. Moreover, it should be implemented by efficient algorithms requiring the shortest possible execution time, to avoid enlarging excessively the time elapsing between data analysis and any subsequent experiment. Besides the features of their topological structure, the complexity of biological networks also refers to their dynamics, that is often non-linear and stiff. The stiffness is due to the presence of molecular species whose abundance fluctuates by many orders of magnitude. A fully stochastic simulation of a stiff system is computationally time-expensive. On the other hand, continuous models are less costly, but they fail to capture the stochastic behaviour of small populations of molecular species. We introduce a new efficient hybrid stochastic-deterministic computational model and the software tool MoBioS (MOlecular Biology Simulator) implementing it. The mathematical model of MoBioS uses continuous differential equations to describe the deterministic reactions and a Gillespie-like algorithm to describe the stochastic ones. Unlike the majority of current hybrid methods, the MoBioS algorithm divides the reactions' set into fast reactions, moderate reactions, and slow reactions and implements a hysteresis switching between the stochastic model and the deterministic model. Fast reactions are approximated as continuous-deterministic processes and modelled by deterministic rate equations. Moderate reactions are those whose reaction waiting time is greater than the fast reaction waiting time but smaller than the slow reaction waiting time. A moderate reaction is approximated as a stochastic (deterministic) process if it was classified as a stochastic (deterministic) process at the time at which it crosses the threshold of low (high) waiting time. A Gillespie First Reaction Method is implemented to select and execute the slow reactions. The performances of MoBios were tested on a typical example of hybrid dynamics: that is the DNA transcription regulation. The simulated dynamic profile of the reagents' abundance and the estimate of the error introduced by the fully deterministic approach were used to evaluate the consistency of the computational model and that of the software tool.

Validation of a metabolic network for Saccharomyces cerevisiae using mixed substrate studies.

PubMed

Vanrolleghem, P A; de Jong-Gubbels, P; van Gulik, W M; Pronk, J T; van Dijken, J P; Heijnen, S

1996-01-01

Setting up a metabolic network model for respiratory growth of Saccharomyces cerevisiae requires the estimation of only two (energetic) stoichiometric parameters: (1) the operational PO ratio and (2) a growth-related maintenance factor k. It is shown, both theoretically and practically, how chemostat cultivations with different mixtures of two substrates allow unique values to be given to these unknowns of the proposed metabolic model. For the yeast and model considered, an effective PO ratio of 1.09 mol of ATP/mol of O (95% confidence interval 1.07-1.11) and a k factor of 0.415 mol of ATP/C-mol of biomass (0.385-0.445) were obtained from biomass substrate yield data on glucose/ethanol mixtures. Symbolic manipulation software proved very valuable in this study as it supported the proof of theoretical identifiability and significantly reduced the necessary computations for parameter estimation. In the transition from 100% glucose to 100% ethanol in the feed, four metabolic regimes occur. Switching between these regimes is determined by cessation of an irreversible reaction and initiation of an alternative reaction. Metabolic network predictions of these metabolic switches compared well with activity measurements of key enzymes. As a second validation of the network, the biomass yield of S. cerevisiae on acetate was also compared to the network prediction. An excellent agreement was found for a network in which acetate transport was modeled with a proton symport, while passive diffusion of acetate gave significantly higher yield predictions.

The subtle business of model reduction for stochastic chemical kinetics

NASA Astrophysics Data System (ADS)

Gillespie, Dan T.; Cao, Yang; Sanft, Kevin R.; Petzold, Linda R.

2009-02-01

This paper addresses the problem of simplifying chemical reaction networks by adroitly reducing the number of reaction channels and chemical species. The analysis adopts a discrete-stochastic point of view and focuses on the model reaction set S1⇌S2→S3, whose simplicity allows all the mathematics to be done exactly. The advantages and disadvantages of replacing this reaction set with a single S3-producing reaction are analyzed quantitatively using novel criteria for measuring simulation accuracy and simulation efficiency. It is shown that in all cases in which such a model reduction can be accomplished accurately and with a significant gain in simulation efficiency, a procedure called the slow-scale stochastic simulation algorithm provides a robust and theoretically transparent way of implementing the reduction.

The subtle business of model reduction for stochastic chemical kinetics.

PubMed

Gillespie, Dan T; Cao, Yang; Sanft, Kevin R; Petzold, Linda R

2009-02-14

This paper addresses the problem of simplifying chemical reaction networks by adroitly reducing the number of reaction channels and chemical species. The analysis adopts a discrete-stochastic point of view and focuses on the model reaction set S(1)<=>S(2)-->S(3), whose simplicity allows all the mathematics to be done exactly. The advantages and disadvantages of replacing this reaction set with a single S(3)-producing reaction are analyzed quantitatively using novel criteria for measuring simulation accuracy and simulation efficiency. It is shown that in all cases in which such a model reduction can be accomplished accurately and with a significant gain in simulation efficiency, a procedure called the slow-scale stochastic simulation algorithm provides a robust and theoretically transparent way of implementing the reduction.

A mathematical model for foreign body reactions in 2D.

PubMed

Su, Jianzhong; Gonzales, Humberto Perez; Todorov, Michail; Kojouharov, Hristo; Tang, Liping

2011-02-01

The foreign body reactions are commonly referred to the network of immune and inflammatory reactions of human or animals to foreign objects placed in tissues. They are basic biological processes, and are also highly relevant to bioengineering applications in implants, as fibrotic tissue formations surrounding medical implants have been found to substantially reduce the effectiveness of devices. Despite of intensive research on determining the mechanisms governing such complex responses, few mechanistic mathematical models have been developed to study such foreign body reactions. This study focuses on a kinetics-based predictive tool in order to analyze outcomes of multiple interactive complex reactions of various cells/proteins and biochemical processes and to understand transient behavior during the entire period (up to several months). A computational model in two spatial dimensions is constructed to investigate the time dynamics as well as spatial variation of foreign body reaction kinetics. The simulation results have been consistent with experimental data and the model can facilitate quantitative insights for study of foreign body reaction process in general.

Multiscale simulations of anisotropic particles combining molecular dynamics and Green's function reaction dynamics

NASA Astrophysics Data System (ADS)

Vijaykumar, Adithya; Ouldridge, Thomas E.; ten Wolde, Pieter Rein; Bolhuis, Peter G.

2017-03-01

The modeling of complex reaction-diffusion processes in, for instance, cellular biochemical networks or self-assembling soft matter can be tremendously sped up by employing a multiscale algorithm which combines the mesoscopic Green's Function Reaction Dynamics (GFRD) method with explicit stochastic Brownian, Langevin, or deterministic molecular dynamics to treat reactants at the microscopic scale [A. Vijaykumar, P. G. Bolhuis, and P. R. ten Wolde, J. Chem. Phys. 143, 214102 (2015)]. Here we extend this multiscale MD-GFRD approach to include the orientational dynamics that is crucial to describe the anisotropic interactions often prevalent in biomolecular systems. We present the novel algorithm focusing on Brownian dynamics only, although the methodology is generic. We illustrate the novel algorithm using a simple patchy particle model. After validation of the algorithm, we discuss its performance. The rotational Brownian dynamics MD-GFRD multiscale method will open up the possibility for large scale simulations of protein signalling networks.

Reactive Transport Modeling of Microbe-mediated Fe (II) Oxidation for Enhanced Oil Recovery

NASA Astrophysics Data System (ADS)

Surasani, V.; Li, L.

2011-12-01

Microbially Enhanced Oil Recovery (MEOR) aims to improve the recovery of entrapped heavy oil in depleted reservoirs using microbe-based technology. Reservoir ecosystems often contain diverse microbial communities those can interact with subsurface fluids and minerals through a network of nutrients and energy fluxes. Microbe-mediated reactions products include gases, biosurfactants, biopolymers those can alter the properties of oil and interfacial interactions between oil, brine, and rocks. In addition, the produced biomass and mineral precipitates can change the reservoir permeability profile and increase sweeping efficiency. Under subsurface conditions, the injection of nitrate and Fe (II) as the electron acceptor and donor allows bacteria to grow. The reaction products include minerals such as Fe(OH)3 and nitrogen containing gases. These reaction products can have large impact on oil and reservoir properties and can enhance the recovery of trapped oil. This work aims to understand the Fe(II) oxidation by nitrate under conditions relevant to MEOR. Reactive transport modeling is used to simulate the fluid flow, transport, and reactions involved in this process. Here we developed a complex reactive network for microbial mediated nitrate-dependent Fe (II) oxidation that involves both thermodynamic controlled aqueous reactions and kinetic controlled Fe (II) mineral reaction. Reactive transport modeling is used to understand and quantify the coupling between flow, transport, and reaction processes. Our results identify key parameter controls those are important for the alteration of permeability profile under field conditions.

Modeling of uncertainties in biochemical reactions.

PubMed

Mišković, Ljubiša; Hatzimanikatis, Vassily

2011-02-01

Mathematical modeling is an indispensable tool for research and development in biotechnology and bioengineering. The formulation of kinetic models of biochemical networks depends on knowledge of the kinetic properties of the enzymes of the individual reactions. However, kinetic data acquired from experimental observations bring along uncertainties due to various experimental conditions and measurement methods. In this contribution, we propose a novel way to model the uncertainty in the enzyme kinetics and to predict quantitatively the responses of metabolic reactions to the changes in enzyme activities under uncertainty. The proposed methodology accounts explicitly for mechanistic properties of enzymes and physico-chemical and thermodynamic constraints, and is based on formalism from systems theory and metabolic control analysis. We achieve this by observing that kinetic responses of metabolic reactions depend: (i) on the distribution of the enzymes among their free form and all reactive states; (ii) on the equilibrium displacements of the overall reaction and that of the individual enzymatic steps; and (iii) on the net fluxes through the enzyme. Relying on this observation, we develop a novel, efficient Monte Carlo sampling procedure to generate all states within a metabolic reaction that satisfy imposed constrains. Thus, we derive the statistics of the expected responses of the metabolic reactions to changes in enzyme levels and activities, in the levels of metabolites, and in the values of the kinetic parameters. We present aspects of the proposed framework through an example of the fundamental three-step reversible enzymatic reaction mechanism. We demonstrate that the equilibrium displacements of the individual enzymatic steps have an important influence on kinetic responses of the enzyme. Furthermore, we derive the conditions that must be satisfied by a reversible three-step enzymatic reaction operating far away from the equilibrium in order to respond to changes in metabolite levels according to the irreversible Michelis-Menten kinetics. The efficient sampling procedure allows easy, scalable, implementation of this methodology to modeling of large-scale biochemical networks. © 2010 Wiley Periodicals, Inc.

Retrosynthetic Reaction Prediction Using Neural Sequence-to-Sequence Models

PubMed Central

2017-01-01

We describe a fully data driven model that learns to perform a retrosynthetic reaction prediction task, which is treated as a sequence-to-sequence mapping problem. The end-to-end trained model has an encoder–decoder architecture that consists of two recurrent neural networks, which has previously shown great success in solving other sequence-to-sequence prediction tasks such as machine translation. The model is trained on 50,000 experimental reaction examples from the United States patent literature, which span 10 broad reaction types that are commonly used by medicinal chemists. We find that our model performs comparably with a rule-based expert system baseline model, and also overcomes certain limitations associated with rule-based expert systems and with any machine learning approach that contains a rule-based expert system component. Our model provides an important first step toward solving the challenging problem of computational retrosynthetic analysis. PMID:29104927

Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments.

PubMed

Wiechert, W; de Graaf, A A

1997-07-05

The extension of metabolite balancing with carbon labeling experiments, as described by Marx et al. (Biotechnol. Bioeng. 49: 11-29), results in a much more detailed stationary metabolic flux analysis. As opposed to basic metabolite flux balancing alone, this method enables both flux directions of bidirectional reaction steps to be quantitated. However, the mathematical treatment of carbon labeling systems is much more complicated, because it requires the solution of numerous balance equations that are bilinear with respect to fluxes and fractional labeling. In this study, a universal modeling framework is presented for describing the metabolite and carbon atom flux in a metabolic network. Bidirectional reaction steps are extensively treated and their impact on the system's labeling state is investigated. Various kinds of modeling assumptions, as usually made for metabolic fluxes, are expressed by linear constraint equations. A numerical algorithm for the solution of the resulting linear constrained set of nonlinear equations is developed. The numerical stability problems caused by large bidirectional fluxes are solved by a specially developed transformation method. Finally, the simulation of carbon labeling experiments is facilitated by a flexible software tool for network synthesis. An illustrative simulation study on flux identifiability from available flux and labeling measurements in the cyclic pentose phosphate pathway of a recombinant strain of Zymomonas mobilis concludes this contribution.

Stochastic surface walking reaction sampling for resolving heterogeneous catalytic reaction network: A revisit to the mechanism of water-gas shift reaction on Cu

NASA Astrophysics Data System (ADS)

Zhang, Xiao-Jie; Shang, Cheng; Liu, Zhi-Pan

2017-10-01

Heterogeneous catalytic reactions on surface and interfaces are renowned for ample intermediate adsorbates and complex reaction networks. The common practice to reveal the reaction mechanism is via theoretical computation, which locates all likely transition states based on the pre-guessed reaction mechanism. Here we develop a new theoretical method, namely, stochastic surface walking (SSW)-Cat method, to resolve the lowest energy reaction pathway of heterogeneous catalytic reactions, which combines our recently developed SSW global structure optimization and SSW reaction sampling. The SSW-Cat is automated and massively parallel, taking a rough reaction pattern as input to guide reaction search. We present the detailed algorithm, discuss the key features, and demonstrate the efficiency in a model catalytic reaction, water-gas shift reaction on Cu(111) (CO + H2O → CO2 + H2). The SSW-Cat simulation shows that water dissociation is the rate-determining step and formic acid (HCOOH) is the kinetically favorable product, instead of the observed final products, CO2 and H2. It implies that CO2 and H2 are secondary products from further decomposition of HCOOH at high temperatures. Being a general purpose tool for reaction prediction, the SSW-Cat may be utilized for rational catalyst design via large-scale computations.

Simulating Network Retrieval of Arithmetic Facts.

ERIC Educational Resources Information Center

Ashcraft, Mark H.

This report describes a simulation of adults' retrieval of arithmetic facts from a network-based memory representation. The goals of the simulation project are to: demonstrate in specific form the nature of a spreading activation model of mental arithmetic; account for three important reaction time effects observed in laboratory investigations;…

Nuclear Forensics and Radiochemistry: Reaction Networks

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

Rundberg, Robert S.

In the intense neutron flux of a nuclear explosion the production of isotopes may occur through successive neutron induced reactions. The pathway to these isotopes illustrates both the complexity of the problem and the need for high quality nuclear data. The growth and decay of radioactive isotopes can follow a similarly complex network. The Bateman equation will be described and modified to apply to the transmutation of isotopes in a high flux reactor. A alternative model of growth and decay, the GD code, that can be applied to fission products will also be described.

Theory and Experimental and Chemical Instabilities

DTIC Science & Technology

1989-01-31

Thresholds, Hysteresis, and Neuromodulation of Signal-to-Noise; and Statistical-Mechanical Theory of Many-body Effects in Reaction Rates. T Ic 2 UL3...submitted to the Journal of Physical Chemistry. 6. Noise in Neural Networks: Thresholds, Hysteresis, and Neuromodulation of Signal-to-Noise. We study a...neural-network model including Gaussian noise, higher-order neuronal interactions, and neuromodulation . For a first-order network, there is a

Consistency Analysis of Genome-Scale Models of Bacterial Metabolism: A Metamodel Approach

PubMed Central

Ponce-de-Leon, Miguel; Calle-Espinosa, Jorge; Peretó, Juli; Montero, Francisco

2015-01-01

Genome-scale metabolic models usually contain inconsistencies that manifest as blocked reactions and gap metabolites. With the purpose to detect recurrent inconsistencies in metabolic models, a large-scale analysis was performed using a previously published dataset of 130 genome-scale models. The results showed that a large number of reactions (~22%) are blocked in all the models where they are present. To unravel the nature of such inconsistencies a metamodel was construed by joining the 130 models in a single network. This metamodel was manually curated using the unconnected modules approach, and then, it was used as a reference network to perform a gap-filling on each individual genome-scale model. Finally, a set of 36 models that had not been considered during the construction of the metamodel was used, as a proof of concept, to extend the metamodel with new biochemical information, and to assess its impact on gap-filling results. The analysis performed on the metamodel allowed to conclude: 1) the recurrent inconsistencies found in the models were already present in the metabolic database used during the reconstructions process; 2) the presence of inconsistencies in a metabolic database can be propagated to the reconstructed models; 3) there are reactions not manifested as blocked which are active as a consequence of some classes of artifacts, and; 4) the results of an automatic gap-filling are highly dependent on the consistency and completeness of the metamodel or metabolic database used as the reference network. In conclusion the consistency analysis should be applied to metabolic databases in order to detect and fill gaps as well as to detect and remove artifacts and redundant information. PMID:26629901

Anaerobic oxidation of methane (AOM) in marine sediments from the Skagerrak (Denmark): II. Reaction-transport modeling

NASA Astrophysics Data System (ADS)

Dale, A. W.; Regnier, P.; Knab, N. J.; Jørgensen, B. B.; Van Cappellen, P.

2008-06-01

A steady-state reaction-transport model is applied to sediments retrieved by gravity core from two stations (S10 and S13) in the Skagerrak to determine the main kinetic and thermodynamic controls on anaerobic oxidation of methane (AOM). The model considers an extended biomass-implicit reaction network for organic carbon degradation, which includes extracellular hydrolysis of macromolecular organic matter, fermentation, sulfate reduction, methanogenesis, AOM, acetogenesis and acetotrophy. Catabolic reaction rates are determined using a modified Monod rate expression that explicitly accounts for limitation by the in situ catabolic energy yields. The fraction of total sulfate reduction due to AOM in the sulfate-methane transition zone (SMTZ) at each site is calculated. The model provides an explanation for the methane tailing phenomenon which is observed here and in other marine sediments, whereby methane diffuses up from the SMTZ to the top of the core without being consumed. The tailing is due to bioenergetic limitation of AOM in the sulfate reduction zone, because the methane concentration is too low to engender favorable thermodynamic drive. AOM is also bioenergetically inhibited below the SMTZ at both sites because of high hydrogen concentrations (∼3-6 nM). The model results imply there is no straightforward relationship between pore water concentrations and the minimum catabolic energy needed to support life because of the highly coupled nature of the reaction network. Best model fits are obtained with a minimum energy for AOM of ∼11 kJ mol-1, which is within the range reported in the literature for anaerobic processes.

Reconstruction of extended Petri nets from time series data and its application to signal transduction and to gene regulatory networks

PubMed Central

2011-01-01

Background Network inference methods reconstruct mathematical models of molecular or genetic networks directly from experimental data sets. We have previously reported a mathematical method which is exclusively data-driven, does not involve any heuristic decisions within the reconstruction process, and deliveres all possible alternative minimal networks in terms of simple place/transition Petri nets that are consistent with a given discrete time series data set. Results We fundamentally extended the previously published algorithm to consider catalysis and inhibition of the reactions that occur in the underlying network. The results of the reconstruction algorithm are encoded in the form of an extended Petri net involving control arcs. This allows the consideration of processes involving mass flow and/or regulatory interactions. As a non-trivial test case, the phosphate regulatory network of enterobacteria was reconstructed using in silico-generated time-series data sets on wild-type and in silico mutants. Conclusions The new exact algorithm reconstructs extended Petri nets from time series data sets by finding all alternative minimal networks that are consistent with the data. It suggested alternative molecular mechanisms for certain reactions in the network. The algorithm is useful to combine data from wild-type and mutant cells and may potentially integrate physiological, biochemical, pharmacological, and genetic data in the form of a single model. PMID:21762503

Catalysis by Metallic Nanoparticles in Solution: Thermosensitive Microgels as Nanoreactors

NASA Astrophysics Data System (ADS)

Roa, Rafael; Angioletti-Uberti, Stefano; Lu, Yan; Dzubiella, Joachim; Piazza, Francesco; Ballauff, Matthias

2018-05-01

Metallic nanoparticles have been used as catalysts for various reactions, and the huge literature on the subject is hard to overlook. In many applications, the nanoparticles must be affixed to a colloidal carrier for easy handling during catalysis. These "passive carriers" (e.g. dendrimers) serve for a controlled synthesis of the nanoparticles and prevent coagulation during catalysis. Recently, hybrids from nanoparticles and polymers have been developed that allow us to change the catalytic activity of the nanoparticles by external triggers. In particular, single nanoparticles embedded in a thermosensitive network made from poly(N-isopropylacrylamide) (PNIPAM) have become the most-studied examples of such hybrids: immersed in cold water, the PNIPAM network is hydrophilic and fully swollen. In this state, hydrophilic substrates can diffuse easily through the network, and react at the surface of the nanoparticles. Above the volume transition located at 32°C, the network becomes hydrophobic and shrinks. Now hydrophobic substrates will preferably diffuse through the network and react with other substrates in the reaction catalyzed by the enclosed nanoparticle. Such "active carriers", may thus be viewed as true nanoreactors that open new ways for the use of nanoparticles in catalysis. In this review, we give a survey on recent work done on these hybrids and their application in catalysis. The aim of this review is threefold: we first review hybrid systems composed of nanoparticles and thermosensitive networks and compare these "active carriers" to other colloidal and polymeric carriers (e.g. dendrimers). In a second step we discuss the model reactions used to obtain precise kinetic data on the catalytic activity of nanoparticles in various carriers and environments. These kinetic data allow us to present a fully quantitative comparison of different nanoreactors. In a final section we shall present the salient points of recent efforts in the theoretical modeling of these nanoreactors. By accounting for the presence of a free-energy landscape for the reactants' diffusive approach towards the catalytic nanoparticle, arising from solvent-reactant and polymeric shell-reactant interactions, these models are capable of explaining the emergence of all the important features observed so far in studies of nanoreactors. The present survey also suggests that such models may be used for the design of future carrier systems adapted to a given reaction and solvent.

Temperature-programmed natural convection for micromixing and biochemical reaction in a single microfluidic chamber.

PubMed

Kim, Sung-Jin; Wang, Fang; Burns, Mark A; Kurabayashi, Katsuo

2009-06-01

Micromixing is a crucial step for biochemical reactions in microfluidic networks. A critical challenge is that the system containing micromixers needs numerous pumps, chambers, and channels not only for the micromixing but also for the biochemical reactions and detections. Thus, a simple and compatible design of the micromixer element for the system is essential. Here, we propose a simple, yet effective, scheme that enables micromixing and a biochemical reaction in a single microfluidic chamber without using any pumps. We accomplish this process by using natural convection in conjunction with alternating heating of two heaters for efficient micromixing, and by regulating capillarity for sample transport. As a model application, we demonstrate micromixing and subsequent polymerase chain reaction (PCR) for an influenza viral DNA fragment. This process is achieved in a platform of a microfluidic cartridge and a microfabricated heating-instrument with a fast thermal response. Our results will significantly simplify micromixing and a subsequent biochemical reaction that involves reagent heating in microfluidic networks.

Engineering a Functional Small RNA Negative Autoregulation Network with Model-Guided Design.

PubMed

Hu, Chelsea Y; Takahashi, Melissa K; Zhang, Yan; Lucks, Julius B

2018-05-22

RNA regulators are powerful components of the synthetic biology toolbox. Here, we expand the repertoire of synthetic gene networks built from these regulators by constructing a transcriptional negative autoregulation (NAR) network out of small RNAs (sRNAs). NAR network motifs are core motifs of natural genetic networks, and are known for reducing network response time and steady state signal. Here we use cell-free transcription-translation (TX-TL) reactions and a computational model to design and prototype sRNA NAR constructs. Using parameter sensitivity analysis, we design a simple set of experiments that allow us to accurately predict NAR function in TX-TL. We transfer successful network designs into Escherichia coli and show that our sRNA transcriptional network reduces both network response time and steady-state gene expression. This work broadens our ability to construct increasingly sophisticated RNA genetic networks with predictable function.

Toward a reaction rate model of condensed-phase RDX decomposition under high temperatures

NASA Astrophysics Data System (ADS)

Schweigert, Igor

2014-03-01

Shock ignition of energetic molecular solids is driven by microstructural heterogeneities, at which even moderate stresses can result in sufficiently high temperatures to initiate material decomposition and the release of the chemical energy. Mesoscale modeling of these ``hot spots'' requires a chemical reaction rate model that describes the energy release with a sub-microsecond resolution and under a wide range of temperatures. No such model is available even for well-studied energetic materials such as RDX. In this presentation, I will describe an ongoing effort to develop a reaction rate model of condensed-phase RDX decomposition under high temperatures using first-principles molecular dynamics, transition-state theory, and reaction network analysis. This work was supported by the Naval Research Laboratory, by the Office of Naval Research, and by the DOD High Performance Computing Modernization Program Software Application Institute for Multiscale Reactive Modeling of Insensitive Munitions.

Toward a reaction rate model of condensed-phase RDX decomposition under high temperatures

NASA Astrophysics Data System (ADS)

Schweigert, Igor

2015-06-01

Shock ignition of energetic molecular solids is driven by microstructural heterogeneities, at which even moderate stresses can result in sufficiently high temperatures to initiate material decomposition and chemical energy release. Mesoscale modeling of these ``hot spots'' requires a reaction rate model that describes the energy release with a sub-microsecond resolution and under a wide range of temperatures. No such model is available even for well-studied energetic materials such as RDX. In this presentation, I will describe an ongoing effort to develop a reaction rate model of condensed-phase RDX decomposition under high temperatures using first-principles molecular dynamics, transition-state theory, and reaction network analysis. This work was supported by the Naval Research Laboratory, by the Office of Naval Research, and by the DoD High Performance Computing Modernization Program Software Application Institute for Multiscale Reactive Modeling of Insensitive Munitions.

Sensitivity and network topology in chemical reaction systems

NASA Astrophysics Data System (ADS)

Okada, Takashi; Mochizuki, Atsushi

2017-08-01

In living cells, biochemical reactions are catalyzed by specific enzymes and connect to one another by sharing substrates and products, forming complex networks. In our previous studies, we established a framework determining the responses to enzyme perturbations only from network topology, and then proved a theorem, called the law of localization, explaining response patterns in terms of network topology. In this paper, we generalize these results to reaction networks with conserved concentrations, which allows us to study any reaction system. We also propose network characteristics quantifying robustness. We compare E. coli metabolic network with randomly rewired networks, and find that the robustness of the E. coli network is significantly higher than that of the random networks.

Mathematical Modeling and Dynamic Simulation of Metabolic Reaction Systems Using Metabolome Time Series Data.

PubMed

Sriyudthsak, Kansuporn; Shiraishi, Fumihide; Hirai, Masami Yokota

2016-01-01

The high-throughput acquisition of metabolome data is greatly anticipated for the complete understanding of cellular metabolism in living organisms. A variety of analytical technologies have been developed to acquire large-scale metabolic profiles under different biological or environmental conditions. Time series data are useful for predicting the most likely metabolic pathways because they provide important information regarding the accumulation of metabolites, which implies causal relationships in the metabolic reaction network. Considerable effort has been undertaken to utilize these data for constructing a mathematical model merging system properties and quantitatively characterizing a whole metabolic system in toto. However, there are technical difficulties between benchmarking the provision and utilization of data. Although, hundreds of metabolites can be measured, which provide information on the metabolic reaction system, simultaneous measurement of thousands of metabolites is still challenging. In addition, it is nontrivial to logically predict the dynamic behaviors of unmeasurable metabolite concentrations without sufficient information on the metabolic reaction network. Yet, consolidating the advantages of advancements in both metabolomics and mathematical modeling remain to be accomplished. This review outlines the conceptual basis of and recent advances in technologies in both the research fields. It also highlights the potential for constructing a large-scale mathematical model by estimating model parameters from time series metabolome data in order to comprehensively understand metabolism at the systems level.

Genetic Algorithm Approaches to Prebiobiotic Chemistry Modeling

NASA Technical Reports Server (NTRS)

Lohn, Jason; Colombano, Silvano

1997-01-01

We model an artificial chemistry comprised of interacting polymers by specifying two initial conditions: a distribution of polymers and a fixed set of reversible catalytic reactions. A genetic algorithm is used to find a set of reactions that exhibit a desired dynamical behavior. Such a technique is useful because it allows an investigator to determine whether a specific pattern of dynamics can be produced, and if it can, the reaction network found can be then analyzed. We present our results in the context of studying simplified chemical dynamics in theorized protocells - hypothesized precursors of the first living organisms. Our results show that given a small sample of plausible protocell reaction dynamics, catalytic reaction sets can be found. We present cases where this is not possible and also analyze the evolved reaction sets.

Unraveling reaction pathways and specifying reaction kinetics for complex systems.

PubMed

Vinu, R; Broadbelt, Linda J

2012-01-01

Many natural and industrial processes involve a complex set of competing reactions that include several different species. Detailed kinetic modeling of such systems can shed light on the important pathways involved in various transformations and therefore can be used to optimize the process conditions for the desired product composition and properties. This review focuses on elucidating the various components involved in modeling the kinetics of pyrolysis and oxidation of polymers. The elementary free radical steps that constitute the chain reaction mechanism of gas-phase/nonpolar liquid-phase processes are outlined. Specification of the rate coefficients of the various reaction families, which is central to the theme of kinetics, is described. Construction of the reaction network on the basis of the types of end groups and reactive moieties in a polymer chain is discussed. Modeling frameworks based on the method of moments and kinetic Monte Carlo are evaluated using illustrations. Finally, the prospects and challenges in modeling biomass conversion are addressed.

Transient and sustained elementary flux mode networks on a catalytic string-based chemical evolution model.

PubMed

Pereira, José A

2014-08-01

Theoretical models designed to test the metabolism-first hypothesis for prebiotic evolution have yield strong indications about the hypothesis validity but could sometimes use a more extensive identification between model objects and real objects towards a more meaningful interpretation of results. In an attempt to go in that direction, the string-based model SSE ("steady state evolution") was developed, where abstract molecules (strings) and catalytic interaction rules are based on some of the most important features of carbon compounds in biological chemistry. The system is open with a random inflow and outflow of strings but also with a permanent string food source. Although specific catalysis is a key aspect of the model, used to define reaction rules, the focus is on energetics rather than kinetics. Standard energy change tables were constructed and used with standard formation reactions to track energy flows through the interpretation of equilibrium constant values. Detection of metabolic networks on the reaction system was done with elementary flux mode (EFM) analysis. The combination of these model design and analysis options enabled obtaining metabolic and catalytic networks showing several central features of biological metabolism, some more clearly than in previous models: metabolic networks with stepwise synthesis, energy coupling, catalysts regulation, SN2 coupling, redox coupling, intermediate cycling, coupled inverse pathways (metabolic cycling), autocatalytic cycles and catalytic cascades. The results strongly suggest that the main biological metabolism features, including the genotype-phenotype interpretation, are caused by the principles of catalytic systems and are prior to modern genetic systems principles. It also gives further theoretical support to the thesis that the basic features of biologic metabolism are a consequence of the time evolution of a random catalyst search working on an open system with a permanent food source. The importance of the food source characteristics and evolutionary possibilities are discussed. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Neighbourhood reaction in the evolution of cooperation.

PubMed

Yang, Guoli; Zhang, Weiming; Xiu, Baoxin

2015-05-07

Combining evolutionary games with adaptive networks, an entangled model between strategy evolution and structure adaptation is researched in this paper. We consider a large population of cooperators C and defectors D placed in the networks, playing the repeated prisoner׳s dilemma (PD) games. Because of the conflicts between social welfare and personal rationality, both strategy and structure are allowed to change. In this paper, the dynamics of strategy originates form the partner imitation based on social learning and the dynamics of structure is driven by the active linking and neighbourhood reaction. Notably, the neighbourhood reaction is investigated considering the changes of interfaces between cooperators and defectors, where some neighbours may get away from the interface once the focal agent changes to different strategy. A rich landscape is demonstrated by changing various embedding parameters, which sheds light upon that reacting promptly to the shifted neighbour will promote the prevalence of cooperation. Our model encapsulates the dynamics of strategy, reaction and structure into the evolutionary games, which manifests some intriguing principles in the competition between two groups in natural populations, artificial systems and even human societies. Copyright © 2015 Elsevier Ltd. All rights reserved.

On understanding nuclear reaction network flows with branchings on directed graphs

NASA Astrophysics Data System (ADS)

Meyer, Bradley S.

2018-04-01

Nuclear reaction network flow diagrams are useful for understanding which reactions are governing the abundance changes at a particular time during nucleosynthesis. This is especially true when the flows are largely unidirectional, such as during the s-process of nucleosynthesis. In explosive nucleosynthesis, when reaction flows are large, and when forward reactions are nearly balanced by their reverses, reaction flows no longer give a clear picture of the abundance evolution in the network. This paper presents a way of understanding network evolution in terms of sums of branchings on a directed graph, which extends the concept of reaction flows to allow for multiple reaction pathways.

Propagation of kinetic uncertainties through a canonical topology of the TLR4 signaling network in different regions of biochemical reaction space

PubMed Central

2010-01-01

Background Signal transduction networks represent the information processing systems that dictate which dynamical regimes of biochemical activity can be accessible to a cell under certain circumstances. One of the major concerns in molecular systems biology is centered on the elucidation of the robustness properties and information processing capabilities of signal transduction networks. Achieving this goal requires the establishment of causal relations between the design principle of biochemical reaction systems and their emergent dynamical behaviors. Methods In this study, efforts were focused in the construction of a relatively well informed, deterministic, non-linear dynamic model, accounting for reaction mechanisms grounded on standard mass action and Hill saturation kinetics, of the canonical reaction topology underlying Toll-like receptor 4 (TLR4)-mediated signaling events. This signaling mechanism has been shown to be deployed in macrophages during a relatively short time window in response to lypopolysaccharyde (LPS) stimulation, which leads to a rapidly mounted innate immune response. An extensive computational exploration of the biochemical reaction space inhabited by this signal transduction network was performed via local and global perturbation strategies. Importantly, a broad spectrum of biologically plausible dynamical regimes accessible to the network in widely scattered regions of parameter space was reconstructed computationally. Additionally, experimentally reported transcriptional readouts of target pro-inflammatory genes, which are actively modulated by the network in response to LPS stimulation, were also simulated. This was done with the main goal of carrying out an unbiased statistical assessment of the intrinsic robustness properties of this canonical reaction topology. Results Our simulation results provide convincing numerical evidence supporting the idea that a canonical reaction mechanism of the TLR4 signaling network is capable of performing information processing in a robust manner, a functional property that is independent of the signaling task required to be executed. Nevertheless, it was found that the robust performance of the network is not solely determined by its design principle (topology), but this may be heavily dependent on the network's current position in biochemical reaction space. Ultimately, our results enabled us the identification of key rate limiting steps which most effectively control the performance of the system under diverse dynamical regimes. Conclusions Overall, our in silico study suggests that biologically relevant and non-intuitive aspects on the general behavior of a complex biomolecular network can be elucidated only when taking into account a wide spectrum of dynamical regimes attainable by the system. Most importantly, this strategy provides the means for a suitable assessment of the inherent variational constraints imposed by the structure of the system when systematically probing its parameter space. PMID:20230643

Reframed Genome-Scale Metabolic Model to Facilitate Genetic Design and Integration with Expression Data.

PubMed

Gu, Deqing; Jian, Xingxing; Zhang, Cheng; Hua, Qiang

2017-01-01

Genome-scale metabolic network models (GEMs) have played important roles in the design of genetically engineered strains and helped biologists to decipher metabolism. However, due to the complex gene-reaction relationships that exist in model systems, most algorithms have limited capabilities with respect to directly predicting accurate genetic design for metabolic engineering. In particular, methods that predict reaction knockout strategies leading to overproduction are often impractical in terms of gene manipulations. Recently, we proposed a method named logical transformation of model (LTM) to simplify the gene-reaction associations by introducing intermediate pseudo reactions, which makes it possible to generate genetic design. Here, we propose an alternative method to relieve researchers from deciphering complex gene-reactions by adding pseudo gene controlling reactions. In comparison to LTM, this new method introduces fewer pseudo reactions and generates a much smaller model system named as gModel. We showed that gModel allows two seldom reported applications: identification of minimal genomes and design of minimal cell factories within a modified OptKnock framework. In addition, gModel could be used to integrate expression data directly and improve the performance of the E-Fmin method for predicting fluxes. In conclusion, the model transformation procedure will facilitate genetic research based on GEMs, extending their applications.

Chemical control of the viscoelastic properties of vinylogous urethane vitrimers

PubMed Central

Denissen, Wim; Droesbeke, Martijn; Nicolaÿ, Renaud; Leibler, Ludwik; Winne, Johan M.; Du Prez, Filip E.

2017-01-01

Vinylogous urethane based vitrimers are polymer networks that have the intrinsic property to undergo network rearrangements, stress relaxation and viscoelastic flow, mediated by rapid addition/elimination reactions of free chain end amines. Here we show that the covalent exchange kinetics significantly can be influenced by combination with various simple additives. As anticipated, the exchange reactions on network level can be further accelerated using either Brønsted or Lewis acid additives. Remarkably, however, a strong inhibitory effect is observed when a base is added to the polymer matrix. These effects have been mechanistically rationalized, guided by low-molecular weight kinetic model experiments. Thus, vitrimer elastomer materials can be rationally designed to display a wide range of viscoelastic properties. PMID:28317893

Blueprint for antimicrobial hit discovery targeting metabolic networks.

PubMed

Shen, Y; Liu, J; Estiu, G; Isin, B; Ahn, Y-Y; Lee, D-S; Barabási, A-L; Kapatral, V; Wiest, O; Oltvai, Z N

2010-01-19

Advances in genome analysis, network biology, and computational chemistry have the potential to revolutionize drug discovery by combining system-level identification of drug targets with the atomistic modeling of small molecules capable of modulating their activity. To demonstrate the effectiveness of such a discovery pipeline, we deduced common antibiotic targets in Escherichia coli and Staphylococcus aureus by identifying shared tissue-specific or uniformly essential metabolic reactions in their metabolic networks. We then predicted through virtual screening dozens of potential inhibitors for several enzymes of these reactions and showed experimentally that a subset of these inhibited both enzyme activities in vitro and bacterial cell viability. This blueprint is applicable for any sequenced organism with high-quality metabolic reconstruction and suggests a general strategy for strain-specific antiinfective therapy.

DL-ADR: a novel deep learning model for classifying genomic variants into adverse drug reactions.

PubMed

Liang, Zhaohui; Huang, Jimmy Xiangji; Zeng, Xing; Zhang, Gang

2016-08-10

Genomic variations are associated with the metabolism and the occurrence of adverse reactions of many therapeutic agents. The polymorphisms on over 2000 locations of cytochrome P450 enzymes (CYP) due to many factors such as ethnicity, mutations, and inheritance attribute to the diversity of response and side effects of various drugs. The associations of the single nucleotide polymorphisms (SNPs), the internal pharmacokinetic patterns and the vulnerability of specific adverse reactions become one of the research interests of pharmacogenomics. The conventional genomewide association studies (GWAS) mainly focuses on the relation of single or multiple SNPs to a specific risk factors which are a one-to-many relation. However, there are no robust methods to establish a many-to-many network which can combine the direct and indirect associations between multiple SNPs and a serial of events (e.g. adverse reactions, metabolic patterns, prognostic factors etc.). In this paper, we present a novel deep learning model based on generative stochastic networks and hidden Markov chain to classify the observed samples with SNPs on five loci of two genes (CYP2D6 and CYP1A2) respectively to the vulnerable population of 14 types of adverse reactions. A supervised deep learning model is proposed in this study. The revised generative stochastic networks (GSN) model with transited by the hidden Markov chain is used. The data of the training set are collected from clinical observation. The training set is composed of 83 observations of blood samples with the genotypes respectively on CYP2D6*2, *10, *14 and CYP1A2*1C, *1 F. The samples are genotyped by the polymerase chain reaction (PCR) method. A hidden Markov chain is used as the transition operator to simulate the probabilistic distribution. The model can perform learning at lower cost compared to the conventional maximal likelihood method because the transition distribution is conditional on the previous state of the hidden Markov chain. A least square loss (LASSO) algorithm and a k-Nearest Neighbors (kNN) algorithm are used as the baselines for comparison and to evaluate the performance of our proposed deep learning model. There are 53 adverse reactions reported during the observation. They are assigned to 14 categories. In the comparison of classification accuracy, the deep learning model shows superiority over the LASSO and kNN model with a rate over 80 %. In the comparison of reliability, the deep learning model shows the best stability among the three models. Machine learning provides a new method to explore the complex associations among genomic variations and multiple events in pharmacogenomics studies. The new deep learning algorithm is capable of classifying various SNPs to the corresponding adverse reactions. We expect that as more genomic variations are added as features and more observations are made, the deep learning model can improve its performance and can act as a black-box but reliable verifier for other GWAS studies.

A compositional framework for reaction networks

NASA Astrophysics Data System (ADS)

Baez, John C.; Pollard, Blake S.

Reaction networks, or equivalently Petri nets, are a general framework for describing processes in which entities of various kinds interact and turn into other entities. In chemistry, where the reactions are assigned ‘rate constants’, any reaction network gives rise to a nonlinear dynamical system called its ‘rate equation’. Here we generalize these ideas to ‘open’ reaction networks, which allow entities to flow in and out at certain designated inputs and outputs. We treat open reaction networks as morphisms in a category. Composing two such morphisms connects the outputs of the first to the inputs of the second. We construct a functor sending any open reaction network to its corresponding ‘open dynamical system’. This provides a compositional framework for studying the dynamics of reaction networks. We then turn to statics: that is, steady state solutions of open dynamical systems. We construct a ‘black-boxing’ functor that sends any open dynamical system to the relation that it imposes between input and output variables in steady states. This extends our earlier work on black-boxing for Markov processes.

Network-level architecture and the evolutionary potential of underground metabolism.

PubMed

Notebaart, Richard A; Szappanos, Balázs; Kintses, Bálint; Pál, Ferenc; Györkei, Ádám; Bogos, Balázs; Lázár, Viktória; Spohn, Réka; Csörgő, Bálint; Wagner, Allon; Ruppin, Eytan; Pál, Csaba; Papp, Balázs

2014-08-12

A central unresolved issue in evolutionary biology is how metabolic innovations emerge. Low-level enzymatic side activities are frequent and can potentially be recruited for new biochemical functions. However, the role of such underground reactions in adaptation toward novel environments has remained largely unknown and out of reach of computational predictions, not least because these issues demand analyses at the level of the entire metabolic network. Here, we provide a comprehensive computational model of the underground metabolism in Escherichia coli. Most underground reactions are not isolated and 45% of them can be fully wired into the existing network and form novel pathways that produce key precursors for cell growth. This observation allowed us to conduct an integrated genome-wide in silico and experimental survey to characterize the evolutionary potential of E. coli to adapt to hundreds of nutrient conditions. We revealed that underground reactions allow growth in new environments when their activity is increased. We estimate that at least ∼20% of the underground reactions that can be connected to the existing network confer a fitness advantage under specific environments. Moreover, our results demonstrate that the genetic basis of evolutionary adaptations via underground metabolism is computationally predictable. The approach used here has potential for various application areas from bioengineering to medical genetics.

Why Do Computer Viruses Survive In The Internet?

NASA Astrophysics Data System (ADS)

Ifti, Margarita; Neumann, Paul

2010-01-01

We use the three-species cyclic competition model (Rock-Paper-Scissors), described by reactions A+B→2B, B+C→2C, C+A→2A, for emulating a computer network with e-mail viruses. Different topologies of the network bring about different dynamics of the epidemics. When the parameters of the network are varied, it is observed that very high clustering coefficients are necessary for a pandemics to happen. The differences between the networks of computer users, e-mail networks, and social networks, as well as their role in determining the nature of epidemics are also discussed.

Zipf's Law in Gene Expression

NASA Astrophysics Data System (ADS)

Furusawa, Chikara; Kaneko, Kunihiko

2003-02-01

Using data from gene expression databases on various organisms and tissues, including yeast, nematodes, human normal and cancer tissues, and embryonic stem cells, we found that the abundances of expressed genes exhibit a power-law distribution with an exponent close to -1; i.e., they obey Zipf’s law. Furthermore, by simulations of a simple model with an intracellular reaction network, we found that Zipf’s law of chemical abundance is a universal feature of cells where such a network optimizes the efficiency and faithfulness of self-reproduction. These findings provide novel insights into the nature of the organization of reaction dynamics in living cells.

Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion

DOE PAGES

Cao, Boqiang; Zhang, Qimin; Ye, Ming

2016-11-29

We present a mean-square exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with time-varying delays and reaction-diffusion driven by fractional Brownian motion (fBm). By constructing a Lyapunov functional and using linear matrix inequality for stochastic analysis we derive sufficient conditions to guarantee the exponential stability of the stochastic model of impulsive GRNs in the mean-square sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. Finally, an example is presented to illustrate our results of the mean-square exponential stability analysis.

Mass Conservation and Inference of Metabolic Networks from High-Throughput Mass Spectrometry Data

PubMed Central

Bandaru, Pradeep; Bansal, Mukesh

2011-01-01

Abstract We present a step towards the metabolome-wide computational inference of cellular metabolic reaction networks from metabolic profiling data, such as mass spectrometry. The reconstruction is based on identification of irreducible statistical interactions among the metabolite activities using the ARACNE reverse-engineering algorithm and on constraining possible metabolic transformations to satisfy the conservation of mass. The resulting algorithms are validated on synthetic data from an abridged computational model of Escherichia coli metabolism. Precision rates upwards of 50% are routinely observed for identification of full metabolic reactions, and recalls upwards of 20% are also seen. PMID:21314454

Exact model reduction of combinatorial reaction networks

PubMed Central

Conzelmann, Holger; Fey, Dirk; Gilles, Ernst D

2008-01-01

Background Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models. Results We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs) to a model with 87 ODEs. Conclusion The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks. PMID:18755034

Physiologically Shrinking the Solution Space of a Saccharomyces cerevisiae Genome-Scale Model Suggests the Role of the Metabolic Network in Shaping Gene Expression Noise.

PubMed

Chi, Baofang; Tao, Shiheng; Liu, Yanlin

2015-01-01

Sampling the solution space of genome-scale models is generally conducted to determine the feasible region for metabolic flux distribution. Because the region for actual metabolic states resides only in a small fraction of the entire space, it is necessary to shrink the solution space to improve the predictive power of a model. A common strategy is to constrain models by integrating extra datasets such as high-throughput datasets and C13-labeled flux datasets. However, studies refining these approaches by performing a meta-analysis of massive experimental metabolic flux measurements, which are closely linked to cellular phenotypes, are limited. In the present study, experimentally identified metabolic flux data from 96 published reports were systematically reviewed. Several strong associations among metabolic flux phenotypes were observed. These phenotype-phenotype associations at the flux level were quantified and integrated into a Saccharomyces cerevisiae genome-scale model as extra physiological constraints. By sampling the shrunken solution space of the model, the metabolic flux fluctuation level, which is an intrinsic trait of metabolic reactions determined by the network, was estimated and utilized to explore its relationship to gene expression noise. Although no correlation was observed in all enzyme-coding genes, a relationship between metabolic flux fluctuation and expression noise of genes associated with enzyme-dosage sensitive reactions was detected, suggesting that the metabolic network plays a role in shaping gene expression noise. Such correlation was mainly attributed to the genes corresponding to non-essential reactions, rather than essential ones. This was at least partially, due to regulations underlying the flux phenotype-phenotype associations. Altogether, this study proposes a new approach in shrinking the solution space of a genome-scale model, of which sampling provides new insights into gene expression noise.

Incorporating redox processes improves prediction of carbon and nutrient cycling and greenhouse gas emission

NASA Astrophysics Data System (ADS)

Tang, Guoping; Zheng, Jianqiu; Yang, Ziming; Graham, David; Gu, Baohua; Mayes, Melanie; Painter, Scott; Thornton, Peter

2016-04-01

Among the coupled thermal, hydrological, geochemical, and biological processes, redox processes play major roles in carbon and nutrient cycling and greenhouse gas (GHG) emission. Increasingly, mechanistic representation of redox processes is acknowledged as necessary for accurate prediction of GHG emission in the assessment of land-atmosphere interactions. Simple organic substrates, Fe reduction, microbial reactions, and the Windermere Humic Aqueous Model (WHAM) were added to a reaction network used in the land component of an Earth system model. In conjunction with this amended reaction network, various temperature response functions used in ecosystem models were assessed for their ability to describe experimental observations from incubation tests with arctic soils. Incorporation of Fe reduction reactions improves the prediction of the lag time between CO2 and CH4 accumulation. The inclusion of the WHAM model enables us to approximately simulate the initial pH drop due to organic acid accumulation and then a pH increase due to Fe reduction without parameter adjustment. The CLM4.0, CENTURY, and Ratkowsky temperature response functions better described the observations than the Q10 method, Arrhenius equation, and ROTH-C. As electron acceptors between O2 and CO2 (e.g., Fe(III), SO42-) are often involved, our results support inclusion of these redox reactions for accurate prediction of CH4 production and consumption. Ongoing work includes improving the parameterization of organic matter decomposition to produce simple organic substrates, examining the influence of redox potential on methanogenesis under thermodynamically favorable conditions, and refining temperature response representation near the freezing point by additional model-experiment iterations. We will use the model to describe observed GHG emission at arctic and tropical sites.

Consistent dust and gas models for protoplanetary disks. II. Chemical networks and rates

NASA Astrophysics Data System (ADS)

Kamp, I.; Thi, W.-F.; Woitke, P.; Rab, C.; Bouma, S.; Ménard, F.

2017-11-01

Aims: We aim to define a small and large chemical network which can be used for the quantitative simultaneous analysis of molecular emission from the near-IR to the submm. We also aim to revise reactions of excited molecular hydrogen, which are not included in UMIST, to provide a homogeneous database for future applications. Methods: We have used the thermo-chemical disk modeling code ProDiMo and a standard T Tauri disk model to evaluate the impact of various chemical networks, reaction rate databases and sets of adsorption energies on a large sample of chemical species and emerging line fluxes from the near-IR to the submm wavelength range. Results: We find large differences in the masses and radial distribution of ice reservoirs when considering freeze-out on bare or polar ice coated grains. Most strongly the ammonia ice mass and the location of the snow line (water) change. As a consequence molecules associated to the ice lines such as N2H+ change their emitting region; none of the line fluxes in the sample considered here changes by more than 25% except CO isotopologues, CN and N2H+ lines. The three-body reaction N+H2+M plays a key role in the formation of water in the outer disk. Besides that, differences between the UMIST 2006 and 2012 database change line fluxes in the sample considered here by less than a factor of two (a subset of low excitation CO and fine structure lines stays even within 25%); exceptions are OH, CN, HCN, HCO+ and N2H+ lines. However, different networks such as OSU and KIDA 2011 lead to pronounced differences in the chemistry inside 100 au and thus affect emission lines from high excitation CO, OH and CN lines. H2 is easily excited at the disk surface and state-to-state reactions enhance the abundance of CH+ and to a lesser extent HCO+. For sub-mm lines of HCN, N2H+ and HCO+, a more complex larger network is recommended. Conclusions: More work is required to consolidate data on key reactions leading to the formation of water, molecular ions such as HCO+ and N2H+ as well as the nitrogen chemistry. This affects many of the key lines used in the interpretation of disk observations. Differential analysis of various disk models using the same chemical input data will be more robust than the interpretation of absolute fluxes.

Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions.

PubMed

Semenov, Sergey N; Kraft, Lewis J; Ainla, Alar; Zhao, Mengxia; Baghbanzadeh, Mostafa; Campbell, Victoria E; Kang, Kyungtae; Fox, Jerome M; Whitesides, George M

2016-09-29

Networks of organic chemical reactions are important in life and probably played a central part in its origin. Network dynamics regulate cell division, circadian rhythms, nerve impulses and chemotaxis, and guide the development of organisms. Although out-of-equilibrium networks of chemical reactions have the potential to display emergent network dynamics such as spontaneous pattern formation, bistability and periodic oscillations, the principles that enable networks of organic reactions to develop complex behaviours are incompletely understood. Here we describe a network of biologically relevant organic reactions (amide formation, thiolate-thioester exchange, thiolate-disulfide interchange and conjugate addition) that displays bistability and oscillations in the concentrations of organic thiols and amides. Oscillations arise from the interaction between three subcomponents of the network: an autocatalytic cycle that generates thiols and amides from thioesters and dialkyl disulfides; a trigger that controls autocatalytic growth; and inhibitory processes that remove activating thiol species that are produced during the autocatalytic cycle. In contrast to previous studies that have demonstrated oscillations and bistability using highly evolved biomolecules (enzymes and DNA) or inorganic molecules of questionable biochemical relevance (for example, those used in Belousov-Zhabotinskii-type reactions), the organic molecules we use are relevant to metabolism and similar to those that might have existed on the early Earth. By using small organic molecules to build a network of organic reactions with autocatalytic, bistable and oscillatory behaviour, we identify principles that explain the ways in which dynamic networks relevant to life could have developed. Modifications of this network will clarify the influence of molecular structure on the dynamics of reaction networks, and may enable the design of biomimetic networks and of synthetic self-regulating and evolving chemical systems.

Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions

NASA Astrophysics Data System (ADS)

Semenov, Sergey N.; Kraft, Lewis J.; Ainla, Alar; Zhao, Mengxia; Baghbanzadeh, Mostafa; Campbell, Victoria E.; Kang, Kyungtae; Fox, Jerome M.; Whitesides, George M.

2016-09-01

Networks of organic chemical reactions are important in life and probably played a central part in its origin. Network dynamics regulate cell division, circadian rhythms, nerve impulses and chemotaxis, and guide the development of organisms. Although out-of-equilibrium networks of chemical reactions have the potential to display emergent network dynamics such as spontaneous pattern formation, bistability and periodic oscillations, the principles that enable networks of organic reactions to develop complex behaviours are incompletely understood. Here we describe a network of biologically relevant organic reactions (amide formation, thiolate-thioester exchange, thiolate-disulfide interchange and conjugate addition) that displays bistability and oscillations in the concentrations of organic thiols and amides. Oscillations arise from the interaction between three subcomponents of the network: an autocatalytic cycle that generates thiols and amides from thioesters and dialkyl disulfides; a trigger that controls autocatalytic growth; and inhibitory processes that remove activating thiol species that are produced during the autocatalytic cycle. In contrast to previous studies that have demonstrated oscillations and bistability using highly evolved biomolecules (enzymes and DNA) or inorganic molecules of questionable biochemical relevance (for example, those used in Belousov-Zhabotinskii-type reactions), the organic molecules we use are relevant to metabolism and similar to those that might have existed on the early Earth. By using small organic molecules to build a network of organic reactions with autocatalytic, bistable and oscillatory behaviour, we identify principles that explain the ways in which dynamic networks relevant to life could have developed. Modifications of this network will clarify the influence of molecular structure on the dynamics of reaction networks, and may enable the design of biomimetic networks and of synthetic self-regulating and evolving chemical systems.

The evolution of metabolic networks of E. coli

PubMed Central

2011-01-01

Background Despite the availability of numerous complete genome sequences from E. coli strains, published genome-scale metabolic models exist only for two commensal E. coli strains. These models have proven useful for many applications, such as engineering strains for desired product formation, and we sought to explore how constructing and evaluating additional metabolic models for E. coli strains could enhance these efforts. Results We used the genomic information from 16 E. coli strains to generate an E. coli pangenome metabolic network by evaluating their collective 76,990 ORFs. Each of these ORFs was assigned to one of 17,647 ortholog groups including ORFs associated with reactions in the most recent metabolic model for E. coli K-12. For orthologous groups that contain an ORF already represented in the MG1655 model, the gene to protein to reaction associations represented in this model could then be easily propagated to other E. coli strain models. All remaining orthologous groups were evaluated to see if new metabolic reactions could be added to generate a pangenome-scale metabolic model (iEco1712_pan). The pangenome model included reactions from a metabolic model update for E. coli K-12 MG1655 (iEco1339_MG1655) and enabled development of five additional strain-specific genome-scale metabolic models. These additional models include a second K-12 strain (iEco1335_W3110) and four pathogenic strains (two enterohemorrhagic E. coli O157:H7 and two uropathogens). When compared to the E. coli K-12 models, the metabolic models for the enterohemorrhagic (iEco1344_EDL933 and iEco1345_Sakai) and uropathogenic strains (iEco1288_CFT073 and iEco1301_UTI89) contained numerous lineage-specific gene and reaction differences. All six E. coli models were evaluated by comparing model predictions to carbon source utilization measurements under aerobic and anaerobic conditions, and to batch growth profiles in minimal media with 0.2% (w/v) glucose. An ancestral genome-scale metabolic model based on conserved ortholog groups in all 16 E. coli genomes was also constructed, reflecting the conserved ancestral core of E. coli metabolism (iEco1053_core). Comparative analysis of all six strain-specific E. coli models revealed that some of the pathogenic E. coli strains possess reactions in their metabolic networks enabling higher biomass yields on glucose. Finally the lineage-specific metabolic traits were compared to the ancestral core model predictions to derive new insight into the evolution of metabolism within this species. Conclusion Our findings demonstrate that a pangenome-scale metabolic model can be used to rapidly construct additional E. coli strain-specific models, and that quantitative models of different strains of E. coli can accurately predict strain-specific phenotypes. Such pangenome and strain-specific models can be further used to engineer metabolic phenotypes of interest, such as designing new industrial E. coli strains. PMID:22044664

Enzyme localization, crowding, and buffers collectively modulate diffusion-influenced signal transduction: Insights from continuum diffusion modeling

PubMed Central

Kekenes-Huskey, Peter M.; Eun, Changsun; McCammon, J. A.

2015-01-01

Biochemical reaction networks consisting of coupled enzymes connect substrate signaling events with biological function. Substrates involved in these reactions can be strongly influenced by diffusion “barriers” arising from impenetrable cellular structures and macromolecules, as well as interactions with biomolecules, especially within crowded environments. For diffusion-influenced reactions, the spatial organization of diffusion barriers arising from intracellular structures, non-specific crowders, and specific-binders (buffers) strongly controls the temporal and spatial reaction kinetics. In this study, we use two prototypical biochemical reactions, a Goodwin oscillator, and a reaction with a periodic source/sink term to examine how a diffusion barrier that partitions substrates controls reaction behavior. Namely, we examine how conditions representative of a densely packed cytosol, including reduced accessible volume fraction, non-specific interactions, and buffers, impede diffusion over nanometer length-scales. We find that diffusion barriers can modulate the frequencies and amplitudes of coupled diffusion-influenced reaction networks, as well as give rise to “compartments” of decoupled reactant populations. These effects appear to be intensified in the presence of buffers localized to the diffusion barrier. These findings have strong implications for the role of the cellular environment in tuning the dynamics of signaling pathways. PMID:26342355

State space truncation with quantified errors for accurate solutions to discrete Chemical Master Equation

PubMed Central

Cao, Youfang; Terebus, Anna; Liang, Jie

2016-01-01

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEG), we truncate the state space by limiting the total molecular copy numbers in each MEG. We further describe a theoretical framework for analysis of the truncation error in the steady state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of 1) the birth and death model, 2) the single gene expression model, 3) the genetic toggle switch model, and 4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate out theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks. PMID:27105653

State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation

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

Cao, Youfang; Terebus, Anna; Liang, Jie

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEGs), we truncate the state space by limiting the total molecular copy numbers in each MEG. Wemore » further describe a theoretical framework for analysis of the truncation error in the steady-state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of (1) the birth and death model, (2) the single gene expression model, (3) the genetic toggle switch model, and (4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady-state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate our theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks.« less

State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation

DOE PAGES

Cao, Youfang; Terebus, Anna; Liang, Jie

2016-04-22

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEGs), we truncate the state space by limiting the total molecular copy numbers in each MEG. Wemore » further describe a theoretical framework for analysis of the truncation error in the steady-state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of (1) the birth and death model, (2) the single gene expression model, (3) the genetic toggle switch model, and (4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady-state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate our theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks.« less

Maximal aggregation of polynomial dynamical systems

PubMed Central

Cardelli, Luca; Tschaikowski, Max

2017-01-01

Ordinary differential equations (ODEs) with polynomial derivatives are a fundamental tool for understanding the dynamics of systems across many branches of science, but our ability to gain mechanistic insight and effectively conduct numerical evaluations is critically hindered when dealing with large models. Here we propose an aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion). A key feature of our proposal is to encode a polynomial ODE system into a finitary structure akin to a formal chemical reaction network. This enables the development of a discrete algorithm to efficiently compute the largest equivalence, building on approaches rooted in computer science to minimize basic models of computation through iterative partition refinements. The physical interpretability of the aggregation is shown on polynomial ODE systems for biochemical reaction networks, gene regulatory networks, and evolutionary game theory. PMID:28878023

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

Chen, Hang, E-mail: hangchen@mit.edu; Thill, Peter; Cao, Jianshu

In biochemical systems, intrinsic noise may drive the system switch from one stable state to another. We investigate how kinetic switching between stable states in a bistable network is influenced by dynamic disorder, i.e., fluctuations in the rate coefficients. Using the geometric minimum action method, we first investigate the optimal transition paths and the corresponding minimum actions based on a genetic toggle switch model in which reaction coefficients draw from a discrete probability distribution. For the continuous probability distribution of the rate coefficient, we then consider two models of dynamic disorder in which reaction coefficients undergo different stochastic processes withmore » the same stationary distribution. In one, the kinetic parameters follow a discrete Markov process and in the other they follow continuous Langevin dynamics. We find that regulation of the parameters modulating the dynamic disorder, as has been demonstrated to occur through allosteric control in bistable networks in the immune system, can be crucial in shaping the statistics of optimal transition paths, transition probabilities, and the stationary probability distribution of the network.« less

Linking actin networks and cell membrane via a reaction-diffusion-elastic description of nonlinear filopodia initiation.

PubMed

Ben Isaac, Eyal; Manor, Uri; Kachar, Bechara; Yochelis, Arik; Gov, Nir S

2013-08-01

Reaction-diffusion models have been used to describe pattern formation on the cellular scale, and traditionally do not include feedback between cellular shape changes and biochemical reactions. We introduce here a distinct reaction-diffusion-elasticity approach: The reaction-diffusion part describes bistability between two actin orientations, coupled to the elastic energy of the cell membrane deformations. This coupling supports spatially localized patterns, even when such solutions do not exist in the uncoupled self-inhibited reaction-diffusion system. We apply this concept to describe the nonlinear (threshold driven) initiation mechanism of actin-based cellular protrusions and provide support by several experimental observations.

Interconnectivity of human cellular metabolism and disease prevalence

NASA Astrophysics Data System (ADS)

Lee, Deok-Sun

2010-12-01

Fluctuations of metabolic reaction fluxes may cause abnormal concentrations of toxic or essential metabolites, possibly leading to metabolic diseases. The mutual binding of enzymatic proteins and ones involving common metabolites enforces distinct coupled reactions, by which local perturbations may spread through the cellular network. Such network effects at the molecular interaction level in human cellular metabolism can reappear in the patterns of disease occurrence. Here we construct the enzyme-reaction network and the metabolite-reaction network, capturing the flux coupling of metabolic reactions caused by the interacting enzymes and the shared metabolites, respectively. Diseases potentially caused by the failure of individual metabolic reactions can be identified by using the known disease-gene association, which allows us to derive the probability of an inactivated reaction causing diseases from the disease records at the population level. We find that the greater the number of proteins that catalyze a reaction, the higher the mean prevalence of its associated diseases. Moreover, the number of connected reactions and the mean size of the avalanches in the networks constructed are also shown to be positively correlated with the disease prevalence. These findings illuminate the impact of the cellular network topology on disease development, suggesting that the global organization of the molecular interaction network should be understood to assist in disease diagnosis, treatment, and drug discovery.

How accurate is automated gap filling of metabolic models?

PubMed

Karp, Peter D; Weaver, Daniel; Latendresse, Mario

2018-06-19

Reaction gap filling is a computational technique for proposing the addition of reactions to genome-scale metabolic models to permit those models to run correctly. Gap filling completes what are otherwise incomplete models that lack fully connected metabolic networks. The models are incomplete because they are derived from annotated genomes in which not all enzymes have been identified. Here we compare the results of applying an automated likelihood-based gap filler within the Pathway Tools software with the results of manually gap filling the same metabolic model. Both gap-filling exercises were applied to the same genome-derived qualitative metabolic reconstruction for Bifidobacterium longum subsp. longum JCM 1217, and to the same modeling conditions - anaerobic growth under four nutrients producing 53 biomass metabolites. The solution computed by the gap-filling program GenDev contained 12 reactions, but closer examination showed that solution was not minimal; two of the twelve reactions can be removed to yield a set of ten reactions that enable model growth. The manually curated solution contained 13 reactions, eight of which were shared with the 12-reaction computed solution. Thus, GenDev achieved recall of 61.5% and precision of 66.6%. These results suggest that although computational gap fillers are populating metabolic models with significant numbers of correct reactions, automatically gap-filled metabolic models also contain significant numbers of incorrect reactions. Our conclusion is that manual curation of gap-filler results is needed to obtain high-accuracy models. Many of the differences between the manual and automatic solutions resulted from using expert biological knowledge to direct the choice of reactions within the curated solution, such as reactions specific to the anaerobic lifestyle of B. longum.

IDENTIFICATION OF AN IDEAL REACTOR MODEL IN A SECONDARY COMBUSTION CHAMBER

EPA Science Inventory

Tracer analysis was applied to a secondary combustion chamber of a rotary kiln incinerator simulator to develop a computationally inexpensive networked ideal reactor model and allow for the later incorporation of detailed reaction mechanisms. Tracer data from sulfur dioxide trace...

Decoding Network Structure in On-Chip Integrated Flow Cells with Synchronization of Electrochemical Oscillators

NASA Astrophysics Data System (ADS)

Jia, Yanxin; Kiss, István Z.

2017-04-01

The analysis of network interactions among dynamical units and the impact of the coupling on self-organized structures is a challenging task with implications in many biological and engineered systems. We explore the coupling topology that arises through the potential drops in a flow channel in a lab-on-chip device that accommodates chemical reactions on electrode arrays. The networks are revealed by analysis of the synchronization patterns with the use of an oscillatory chemical reaction (nickel electrodissolution) and are further confirmed by direct decoding using phase model analysis. In dual electrode configuration, a variety coupling schemes, (uni- or bidirectional positive or negative) were identified depending on the relative placement of the reference and counter electrodes (e.g., placed at the same or the opposite ends of the flow channel). With three electrodes, the network consists of a superposition of a localized (upstream) and global (all-to-all) coupling. With six electrodes, the unique, position dependent coupling topology resulted spatially organized partial synchronization such that there was a synchrony gradient along the quasi-one-dimensional spatial coordinate. The networked, electrode potential (current) spike generating electrochemical reactions hold potential for construction of an in-situ information processing unit to be used in electrochemical devices in sensors and batteries.

Blueprint for antimicrobial hit discovery targeting metabolic networks

PubMed Central

Shen, Y.; Liu, J.; Estiu, G.; Isin, B.; Ahn, Y-Y.; Lee, D-S.; Barabási, A-L.; Kapatral, V.; Wiest, O.; Oltvai, Z. N.

2010-01-01

Advances in genome analysis, network biology, and computational chemistry have the potential to revolutionize drug discovery by combining system-level identification of drug targets with the atomistic modeling of small molecules capable of modulating their activity. To demonstrate the effectiveness of such a discovery pipeline, we deduced common antibiotic targets in Escherichia coli and Staphylococcus aureus by identifying shared tissue-specific or uniformly essential metabolic reactions in their metabolic networks. We then predicted through virtual screening dozens of potential inhibitors for several enzymes of these reactions and showed experimentally that a subset of these inhibited both enzyme activities in vitro and bacterial cell viability. This blueprint is applicable for any sequenced organism with high-quality metabolic reconstruction and suggests a general strategy for strain-specific antiinfective therapy. PMID:20080587

FERN - a Java framework for stochastic simulation and evaluation of reaction networks.

PubMed

Erhard, Florian; Friedel, Caroline C; Zimmer, Ralf

2008-08-29

Stochastic simulation can be used to illustrate the development of biological systems over time and the stochastic nature of these processes. Currently available programs for stochastic simulation, however, are limited in that they either a) do not provide the most efficient simulation algorithms and are difficult to extend, b) cannot be easily integrated into other applications or c) do not allow to monitor and intervene during the simulation process in an easy and intuitive way. Thus, in order to use stochastic simulation in innovative high-level modeling and analysis approaches more flexible tools are necessary. In this article, we present FERN (Framework for Evaluation of Reaction Networks), a Java framework for the efficient simulation of chemical reaction networks. FERN is subdivided into three layers for network representation, simulation and visualization of the simulation results each of which can be easily extended. It provides efficient and accurate state-of-the-art stochastic simulation algorithms for well-mixed chemical systems and a powerful observer system, which makes it possible to track and control the simulation progress on every level. To illustrate how FERN can be easily integrated into other systems biology applications, plugins to Cytoscape and CellDesigner are included. These plugins make it possible to run simulations and to observe the simulation progress in a reaction network in real-time from within the Cytoscape or CellDesigner environment. FERN addresses shortcomings of currently available stochastic simulation programs in several ways. First, it provides a broad range of efficient and accurate algorithms both for exact and approximate stochastic simulation and a simple interface for extending to new algorithms. FERN's implementations are considerably faster than the C implementations of gillespie2 or the Java implementations of ISBJava. Second, it can be used in a straightforward way both as a stand-alone program and within new systems biology applications. Finally, complex scenarios requiring intervention during the simulation progress can be modelled easily with FERN.

Modeling biological pathway dynamics with timed automata.

PubMed

Schivo, Stefano; Scholma, Jetse; Wanders, Brend; Urquidi Camacho, Ricardo A; van der Vet, Paul E; Karperien, Marcel; Langerak, Rom; van de Pol, Jaco; Post, Janine N

2014-05-01

Living cells are constantly subjected to a plethora of environmental stimuli that require integration into an appropriate cellular response. This integration takes place through signal transduction events that form tightly interconnected networks. The understanding of these networks requires capturing their dynamics through computational support and models. ANIMO (analysis of Networks with Interactive Modeling) is a tool that enables the construction and exploration of executable models of biological networks, helping to derive hypotheses and to plan wet-lab experiments. The tool is based on the formalism of Timed Automata, which can be analyzed via the UPPAAL model checker. Thanks to Timed Automata, we can provide a formal semantics for the domain-specific language used to represent signaling networks. This enforces precision and uniformity in the definition of signaling pathways, contributing to the integration of isolated signaling events into complex network models. We propose an approach to discretization of reaction kinetics that allows us to efficiently use UPPAAL as the computational engine to explore the dynamic behavior of the network of interest. A user-friendly interface hides the use of Timed Automata from the user, while keeping the expressive power intact. Abstraction to single-parameter kinetics speeds up construction of models that remain faithful enough to provide meaningful insight. The resulting dynamic behavior of the network components is displayed graphically, allowing for an intuitive and interactive modeling experience.

Constraining the astrophysical origin of the p-nuclei through nuclear physics and meteoritic data.

PubMed

Rauscher, T; Dauphas, N; Dillmann, I; Fröhlich, C; Fülöp, Zs; Gyürky, Gy

2013-06-01

A small number of naturally occurring, proton-rich nuclides (the p-nuclei) cannot be made in the s- and r-processes. Their origin is not well understood. Massive stars can produce p-nuclei through photodisintegration of pre-existing intermediate and heavy nuclei. This so-called γ-process requires high stellar plasma temperatures and occurs mainly in explosive O/Ne burning during a core-collapse supernova. Although the γ-process in massive stars has been successful in producing a large range of p-nuclei, significant deficiencies remain. An increasing number of processes and sites has been studied in recent years in search of viable alternatives replacing or supplementing the massive star models. A large number of unstable nuclei, however, with only theoretically predicted reaction rates are included in the reaction network and thus the nuclear input may also bear considerable uncertainties. The current status of astrophysical models, nuclear input and observational constraints is reviewed. After an overview of currently discussed models, the focus is on the possibility to better constrain those models through different means. Meteoritic data not only provide the actual isotopic abundances of the p-nuclei but can also put constraints on the possible contribution of proton-rich nucleosynthesis. The main part of the review focuses on the nuclear uncertainties involved in the determination of the astrophysical reaction rates required for the extended reaction networks used in nucleosynthesis studies. Experimental approaches are discussed together with their necessary connection to theory, which is especially pronounced for reactions with intermediate and heavy nuclei in explosive nuclear burning, even close to stability.

Supercritical water oxidation of quinazoline: Reaction kinetics and modeling.

PubMed

Gong, Yanmeng; Guo, Yang; Wang, Shuzhong; Song, Wenhan; Xu, Donghai

2017-03-01

This paper presents a first quantitative kinetic model for supercritical water oxidation (SCWO) of quinazoline that describes the formation and interconversion of intermediates and final products at 673-873 K. The set of 11 reaction pathways for phenol, pyrimidine, naphthalene, NH 3 , etc, involved in the simplified reaction network proved sufficient for fitting the experimental results satisfactorily. We validated the model prediction ability on CO 2 yields at initial quinazoline loading not used in the parameter estimation. Reaction rate analysis and sensitivity analysis indicate that nearly all reactions reach their thermodynamic equilibrium within 300 s. The pyrimidine yielding from quinazoline is the dominant ring-opening pathway and provides a significant contribution to CO 2 formation. Low sensitivity of NH 3 decomposition rate to concentration confirms its refractory nature in SCWO. Nitrogen content in liquid products decreases whereas that in gaseous phase increases as reaction time prolonged. The nitrogen predicted by the model in gaseous phase combined with the experimental nitrogen in liquid products gives an accurate nitrogen balance of conversion process. Copyright © 2016 Elsevier Ltd. All rights reserved.

Defect reaction network in Si-doped InAs. Numerical predictions.

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

Schultz, Peter A.

This Report characterizes the defects in the def ect reaction network in silicon - doped, n - type InAs predicted with first principles density functional theory. The reaction network is deduced by following exothermic defect reactions starting with the initially mobile interstitial defects reacting with common displacement damage defects in Si - doped InAs , until culminating in immobile reaction p roducts. The defect reactions and reaction energies are tabulated, along with the properties of all the silicon - related defects in the reaction network. This Report serves to extend the results for the properties of intrinsic defects in bulkmore » InAs as colla ted in SAND 2013 - 2477 : Simple intrinsic defects in InAs : Numerical predictions to include Si - containing simple defects likely to be present in a radiation - induced defect reaction sequence . This page intentionally left blank« less

A Hybrid Method of Moment Equations and Rate Equations to Modeling Gas-Grain Chemistry

NASA Astrophysics Data System (ADS)

Pei, Y.; Herbst, E.

2011-05-01

Grain surfaces play a crucial role in catalyzing many important chemical reactions in the interstellar medium (ISM). The deterministic rate equation (RE) method has often been used to simulate the surface chemistry. But this method becomes inaccurate when the number of reacting particles per grain is typically less than one, which can occur in the ISM. In this condition, stochastic approaches such as the master equations are adopted. However, these methods have mostly been constrained to small chemical networks due to the large amounts of processor time and computer power required. In this study, we present a hybrid method consisting of the moment equation approximation to the stochastic master equation approach and deterministic rate equations to treat a gas-grain model of homogeneous cold cloud cores with time-independent physical conditions. In this model, we use the standard OSU gas phase network (version OSU2006V3) which involves 458 gas phase species and more than 4000 reactions, and treat it by deterministic rate equations. A medium-sized surface reaction network which consists of 21 species and 19 reactions accounts for the productions of stable molecules such as H_2O, CO, CO_2, H_2CO, CH_3OH, NH_3 and CH_4. These surface reactions are treated by a hybrid method of moment equations (Barzel & Biham 2007) and rate equations: when the abundance of a surface species is lower than a specific threshold, say one per grain, we use the ``stochastic" moment equations to simulate the evolution; when its abundance goes above this threshold, we use the rate equations. A continuity technique is utilized to secure a smooth transition between these two methods. We have run chemical simulations for a time up to 10^8 yr at three temperatures: 10 K, 15 K, and 20 K. The results will be compared with those generated from (1) a completely deterministic model that uses rate equations for both gas phase and grain surface chemistry, (2) the method of modified rate equations (Garrod 2008), which partially takes into account the stochastic effect for surface reactions, and (3) the master equation approach solved using a Monte Carlo technique. At 10 K and standard grain sizes, our model results agree well with the above three methods, while discrepancies appear at higher temperatures and smaller grain sizes.

Steady states and stability in metabolic networks without regulation.

PubMed

Ivanov, Oleksandr; van der Schaft, Arjan; Weissing, Franz J

2016-07-21

Metabolic networks are often extremely complex. Despite intensive efforts many details of these networks, e.g., exact kinetic rates and parameters of metabolic reactions, are not known, making it difficult to derive their properties. Considerable effort has been made to develop theory about properties of steady states in metabolic networks that are valid for any values of parameters. General results on uniqueness of steady states and their stability have been derived with specific assumptions on reaction kinetics, stoichiometry and network topology. For example, deep results have been obtained under the assumptions of mass-action reaction kinetics, continuous flow stirred tank reactors (CFSTR), concordant reaction networks and others. Nevertheless, a general theory about properties of steady states in metabolic networks is still missing. Here we make a step further in the quest for such a theory. Specifically, we study properties of steady states in metabolic networks with monotonic kinetics in relation to their stoichiometry (simple and general) and the number of metabolites participating in every reaction (single or many). Our approach is based on the investigation of properties of the Jacobian matrix. We show that stoichiometry, network topology, and the number of metabolites that participate in every reaction have a large influence on the number of steady states and their stability in metabolic networks. Specifically, metabolic networks with single-substrate-single-product reactions have disconnected steady states, whereas in metabolic networks with multiple-substrates-multiple-product reactions manifolds of steady states arise. Metabolic networks with simple stoichiometry have either a unique globally asymptotically stable steady state or asymptotically stable manifolds of steady states. In metabolic networks with general stoichiometry the steady states are not always stable and we provide conditions for their stability. In order to demonstrate the biological relevance we illustrate the results on the examples of the TCA cycle, the mevalonate pathway and the Calvin cycle. Copyright © 2016 Elsevier Ltd. All rights reserved.

A neural network model of foraging decisions made under predation risk.

PubMed

Coleman, Scott L; Brown, Vincent R; Levine, Daniel S; Mellgren, Roger L

2005-12-01

This article develops the cognitive-emotional forager (CEF) model, a novel application of a neural network to dynamical processes in foraging behavior. The CEF is based on a neural network known as the gated dipole, introduced by Grossberg, which is capable of representing short-term affective reactions in a manner similar to Solomon and Corbit's (1974) opponent process theory. The model incorporates a trade-off between approach toward food and avoidance of predation under varying levels of motivation induced by hunger. The results of simulations in a simple patch selection paradigm, using a lifetime fitness criterion for comparison, indicate that the CEF model is capable of nearly optimal foraging and outperforms a run-of-luck rule-of-thumb model. Models such as the one presented here can illuminate the underlying cognitive and motivational components of animal decision making.

Formal reasoning about systems biology using theorem proving

PubMed Central

Hasan, Osman; Siddique, Umair; Tahar, Sofiène

2017-01-01

System biology provides the basis to understand the behavioral properties of complex biological organisms at different levels of abstraction. Traditionally, analysing systems biology based models of various diseases have been carried out by paper-and-pencil based proofs and simulations. However, these methods cannot provide an accurate analysis, which is a serious drawback for the safety-critical domain of human medicine. In order to overcome these limitations, we propose a framework to formally analyze biological networks and pathways. In particular, we formalize the notion of reaction kinetics in higher-order logic and formally verify some of the commonly used reaction based models of biological networks using the HOL Light theorem prover. Furthermore, we have ported our earlier formalization of Zsyntax, i.e., a deductive language for reasoning about biological networks and pathways, from HOL4 to the HOL Light theorem prover to make it compatible with the above-mentioned formalization of reaction kinetics. To illustrate the usefulness of the proposed framework, we present the formal analysis of three case studies, i.e., the pathway leading to TP53 Phosphorylation, the pathway leading to the death of cancer stem cells and the tumor growth based on cancer stem cells, which is used for the prognosis and future drug designs to treat cancer patients. PMID:28671950

Mechanistic Representation of Soil C Dynamics: for Arctic Ecosystem

NASA Astrophysics Data System (ADS)

Dwivedi, D.; Riley, W. J.; Bisht, G.

2013-12-01

Arctic and sub-Arctic soils store vast amounts of carbon, approximately 1700 billion metric tones of frozen organic carbon. This carbon is susceptible to release to the atmosphere due to environmental changes (e.g., rapidly evolving landscape, warming); however, the mechanisms responsible for this susceptibility of soil organic matter (SOM) are not well understood, and uncertainties exist in terms of their representation in Earth System models. The representation of SOM dynamics in Earth System Models is critical for future climate prediction. To investigate the impacts of various physical (e.g., multi-phase transport, sorption, desorption, temperature), chemical (e.g., pH), and biological (e.g., microbial activity, enzyme dynamics) factors on SOM stability, we have developed CENTURY-like (describing labile and recalcitrant pools) and complex (describing multiple archetypal polymers and monomers C substrate groups) reaction networks. These reaction networks are integrated in a three-dimensional, multi-phase reactive transport solver (PFLOTRAN) and include representations of bacterial and fungal activity as well as population dynamics, gaseous and aqueous advection, and adsorption and desorption. We test and compare these reaction networks in PFLOTRAN to accurately predict depth-resolved soil organic matter (SOM) in the subsurface. We present results showing impacts of abiotic controls (e.g., surface interactions and temperature) on the long-term stabilization of SOM under permafrost conditions.

A hierarchical model of metabolic machinery based on the kcore decomposition of plant metabolic networks.

PubMed

Filho, Humberto A; Machicao, Jeaneth; Bruno, Odemir M

2018-01-01

Modeling the basic structure of metabolic machinery is a challenge for modern biology. Some models based on complex networks have provided important information regarding this machinery. In this paper, we constructed metabolic networks of 17 plants covering unicellular organisms to more complex dicotyledonous plants. The metabolic networks were built based on the substrate-product model and a topological percolation was performed using the kcore decomposition. The distribution of metabolites across the percolation layers showed correlations between the metabolic integration hierarchy and the network topology. We show that metabolites concentrated in the internal network (maximum kcore) only comprise molecules of the primary basal metabolism. Moreover, we found a high proportion of a set of common metabolites, among the 17 plants, centered at the inner kcore layers. Meanwhile, the metabolites recognized as participants in the secondary metabolism of plants are concentrated in the outermost layers of the network. This data suggests that the metabolites in the central layer form a basic molecular module in which the whole plant metabolism is anchored. The elements from this central core participate in almost all plant metabolic reactions, which suggests that plant metabolic networks follows a centralized topology.

A hierarchical model of metabolic machinery based on the kcore decomposition of plant metabolic networks

PubMed Central

Filho, Humberto A.; Machicao, Jeaneth

2018-01-01

Modeling the basic structure of metabolic machinery is a challenge for modern biology. Some models based on complex networks have provided important information regarding this machinery. In this paper, we constructed metabolic networks of 17 plants covering unicellular organisms to more complex dicotyledonous plants. The metabolic networks were built based on the substrate-product model and a topological percolation was performed using the kcore decomposition. The distribution of metabolites across the percolation layers showed correlations between the metabolic integration hierarchy and the network topology. We show that metabolites concentrated in the internal network (maximum kcore) only comprise molecules of the primary basal metabolism. Moreover, we found a high proportion of a set of common metabolites, among the 17 plants, centered at the inner kcore layers. Meanwhile, the metabolites recognized as participants in the secondary metabolism of plants are concentrated in the outermost layers of the network. This data suggests that the metabolites in the central layer form a basic molecular module in which the whole plant metabolism is anchored. The elements from this central core participate in almost all plant metabolic reactions, which suggests that plant metabolic networks follows a centralized topology. PMID:29734359

Dissolution Front Instabilities in Reacting Porous Media

NASA Astrophysics Data System (ADS)

Raoof, Amir; Spiers, Chris; Hassanizadeh, Majid

2013-04-01

The main objective of this research is to gain a better understanding of the relation between regime of reaction and dissolution front instability, leading to formation of channels or wormholes. Potential applications are geological sequestration of CO2 and acid-gas injection during enhanced oil recovery. The microscopic pore space is modeled using a multi-directional pore network, allowing for a distribution of pore coordination number, together with distribution of pore sizes. In order to simulate transport of multi-component chemical species, mass balance equations are solved within each element of the network (i.e., pore body and pore throat). We have considered advective and diffusive transport processes within the pore spaces together with multi-component chemical reactions, including both equilibrium and kinetic reactions. Using dimensionless scaling groups (such as Damköhler number and Péclet-Damköhler number) we characterized the dissolution front behavior, and by averaging over the network domain we calculated the evolution of porosity and permeability as well as flux-averaged concentration breakthrough curves. We obtain constitutive relations linking porosity and permeability, under conditions relevant to geological storage of CO2. Effect of distribution of reactive minerals is also evaluated and regime of reaction is shown to play a key role.

Functional Characterization of Alternate Optimal Solutions of Escherichia coli's Transcriptional and Translational Machinery

PubMed Central

Thiele, Ines; Fleming, Ronan M.T.; Bordbar, Aarash; Schellenberger, Jan; Palsson, Bernhard Ø.

2010-01-01

Abstract The constraint-based reconstruction and analysis approach has recently been extended to describe Escherichia coli's transcriptional and translational machinery. Here, we introduce the concept of reaction coupling to represent the dependency between protein synthesis and utilization. These coupling constraints lead to a significant contraction of the feasible set of steady-state fluxes. The subset of alternate optimal solutions (AOS) consistent with maximal ribosome production was calculated. The majority of transcriptional and translational reactions were active for all of these AOS, showing that the network has a low degree of redundancy. Furthermore, all calculated AOS contained the qualitative expression of at least 92% of the known essential genes. Principal component analysis of AOS demonstrated that energy currencies (ATP, GTP, and phosphate) dominate the network's capability to produce ribosomes. Additionally, we identified regulatory control points of the network, which include the transcription reactions of σ70 (RpoD) as well as that of a degradosome component (Rne) and of tRNA charging (ValS). These reactions contribute significant variance among AOS. These results show that constraint-based modeling can be applied to gain insight into the systemic properties of E. coli's transcriptional and translational machinery. PMID:20483314

A variational approach to parameter estimation in ordinary differential equations.

PubMed

Kaschek, Daniel; Timmer, Jens

2012-08-14

Ordinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial conditions or steady state concentrations from time-resolved data. In contrast to this countable set of parameters, the estimation of entire courses of network components corresponds to an innumerable set of parameters. The approach presented in this work is able to deal with course estimation for extrinsic system inputs or intrinsic reactants, both not being constrained by the reaction network itself. Our method is based on variational calculus which is carried out analytically to derive an augmented system of differential equations including the unconstrained components as ordinary state variables. Finally, conventional parameter estimation is applied to the augmented system resulting in a combined estimation of courses and parameters. The combined estimation approach takes the uncertainty in input courses correctly into account. This leads to precise parameter estimates and correct confidence intervals. In particular this implies that small motifs of large reaction networks can be analysed independently of the rest. By the use of variational methods, elements from control theory and statistics are combined allowing for future transfer of methods between the two fields.

Programmable chemical reaction networks: emulating regulatory functions in living cells using a bottom-up approach.

PubMed

van Roekel, Hendrik W H; Rosier, Bas J H M; Meijer, Lenny H H; Hilbers, Peter A J; Markvoort, Albert J; Huck, Wilhelm T S; de Greef, Tom F A

2015-11-07

Living cells are able to produce a wide variety of biological responses when subjected to biochemical stimuli. It has become apparent that these biological responses are regulated by complex chemical reaction networks (CRNs). Unravelling the function of these circuits is a key topic of both systems biology and synthetic biology. Recent progress at the interface of chemistry and biology together with the realisation that current experimental tools are insufficient to quantitatively understand the molecular logic of pathways inside living cells has triggered renewed interest in the bottom-up development of CRNs. This builds upon earlier work of physical chemists who extensively studied inorganic CRNs and showed how a system of chemical reactions can give rise to complex spatiotemporal responses such as oscillations and pattern formation. Using purified biochemical components, in vitro synthetic biologists have started to engineer simplified model systems with the goal of mimicking biological responses of intracellular circuits. Emulation and reconstruction of system-level properties of intracellular networks using simplified circuits are able to reveal key design principles and molecular programs that underlie the biological function of interest. In this Tutorial Review, we present an accessible overview of this emerging field starting with key studies on inorganic CRNs followed by a discussion of recent work involving purified biochemical components. Finally, we review recent work showing the versatility of programmable biochemical reaction networks (BRNs) in analytical and diagnostic applications.

Atomic Force Microscopy Nanomechanical Mapping Visualizes Interfacial Broadening between Networks Due to Chemical Exchange Reactions.

PubMed

He, Changfei; Shi, Shaowei; Wu, Xuefei; Russell, Thomas P; Wang, Dong

2018-06-06

The interfacial broadening between two different epoxy networks having different moduli was nanomechanically mapped. The interfacial broadening of the two networks produced an interfacial zone having a gradient in the concentration and, hence, properties of the original two networks. This interfacial broadening of the networks leads to the generation of a new network with a segmental composition corresponding to a mixture of the original two network segments. The intermixing of the two, by nature of the exchange reactions, was on the segmental level. By mapping the time dependence of the variation in the modulus at different temperatures, the kinetics of the exchange reaction was measured and, by varying the temperature, the activation energy of the exchange reaction was determined.

Prediction of contaminant fate and transport in potable water systems using H2OFate

NASA Astrophysics Data System (ADS)

Devarakonda, Venkat; Manickavasagam, Sivakumar; VanBlaricum, Vicki; Ginsberg, Mark

2009-05-01

BlazeTech has recently developed a software called H2OFate to predict the fate and transport of chemical and biological contaminants in water distribution systems. This software includes models for the reactions of these contaminants with residual disinfectant in bulk water and at the pipe wall, and their adhesion/reactions with the pipe walls. This software can be interfaced with sensors through SCADA systems to monitor water distribution networks for contamination events and activate countermeasures, as needed. This paper presents results from parametric calculations carried out using H2OFate for a simulated contaminant release into a sample water distribution network.

Dynamic optimization of metabolic networks coupled with gene expression.

PubMed

Waldherr, Steffen; Oyarzún, Diego A; Bockmayr, Alexander

2015-01-21

The regulation of metabolic activity by tuning enzyme expression levels is crucial to sustain cellular growth in changing environments. Metabolic networks are often studied at steady state using constraint-based models and optimization techniques. However, metabolic adaptations driven by changes in gene expression cannot be analyzed by steady state models, as these do not account for temporal changes in biomass composition. Here we present a dynamic optimization framework that integrates the metabolic network with the dynamics of biomass production and composition. An approximation by a timescale separation leads to a coupled model of quasi-steady state constraints on the metabolic reactions, and differential equations for the substrate concentrations and biomass composition. We propose a dynamic optimization approach to determine reaction fluxes for this model, explicitly taking into account enzyme production costs and enzymatic capacity. In contrast to the established dynamic flux balance analysis, our approach allows predicting dynamic changes in both the metabolic fluxes and the biomass composition during metabolic adaptations. Discretization of the optimization problems leads to a linear program that can be efficiently solved. We applied our algorithm in two case studies: a minimal nutrient uptake network, and an abstraction of core metabolic processes in bacteria. In the minimal model, we show that the optimized uptake rates reproduce the empirical Monod growth for bacterial cultures. For the network of core metabolic processes, the dynamic optimization algorithm predicted commonly observed metabolic adaptations, such as a diauxic switch with a preference ranking for different nutrients, re-utilization of waste products after depletion of the original substrate, and metabolic adaptation to an impending nutrient depletion. These examples illustrate how dynamic adaptations of enzyme expression can be predicted solely from an optimization principle. Copyright © 2014 Elsevier Ltd. All rights reserved.

Thermodynamics-based Metabolite Sensitivity Analysis in metabolic networks.

PubMed

Kiparissides, A; Hatzimanikatis, V

2017-01-01

The increasing availability of large metabolomics datasets enhances the need for computational methodologies that can organize the data in a way that can lead to the inference of meaningful relationships. Knowledge of the metabolic state of a cell and how it responds to various stimuli and extracellular conditions can offer significant insight in the regulatory functions and how to manipulate them. Constraint based methods, such as Flux Balance Analysis (FBA) and Thermodynamics-based flux analysis (TFA), are commonly used to estimate the flow of metabolites through genome-wide metabolic networks, making it possible to identify the ranges of flux values that are consistent with the studied physiological and thermodynamic conditions. However, unless key intracellular fluxes and metabolite concentrations are known, constraint-based models lead to underdetermined problem formulations. This lack of information propagates as uncertainty in the estimation of fluxes and basic reaction properties such as the determination of reaction directionalities. Therefore, knowledge of which metabolites, if measured, would contribute the most to reducing this uncertainty can significantly improve our ability to define the internal state of the cell. In the present work we combine constraint based modeling, Design of Experiments (DoE) and Global Sensitivity Analysis (GSA) into the Thermodynamics-based Metabolite Sensitivity Analysis (TMSA) method. TMSA ranks metabolites comprising a metabolic network based on their ability to constrain the gamut of possible solutions to a limited, thermodynamically consistent set of internal states. TMSA is modular and can be applied to a single reaction, a metabolic pathway or an entire metabolic network. This is, to our knowledge, the first attempt to use metabolic modeling in order to provide a significance ranking of metabolites to guide experimental measurements. Copyright © 2016 International Metabolic Engineering Society. Published by Elsevier Inc. All rights reserved.

Reconstruction of Tissue-Specific Metabolic Networks Using CORDA

PubMed Central

Schultz, André; Qutub, Amina A.

2016-01-01

Human metabolism involves thousands of reactions and metabolites. To interpret this complexity, computational modeling becomes an essential experimental tool. One of the most popular techniques to study human metabolism as a whole is genome scale modeling. A key challenge to applying genome scale modeling is identifying critical metabolic reactions across diverse human tissues. Here we introduce a novel algorithm called Cost Optimization Reaction Dependency Assessment (CORDA) to build genome scale models in a tissue-specific manner. CORDA performs more efficiently computationally, shows better agreement to experimental data, and displays better model functionality and capacity when compared to previous algorithms. CORDA also returns reaction associations that can greatly assist in any manual curation to be performed following the automated reconstruction process. Using CORDA, we developed a library of 76 healthy and 20 cancer tissue-specific reconstructions. These reconstructions identified which metabolic pathways are shared across diverse human tissues. Moreover, we identified changes in reactions and pathways that are differentially included and present different capacity profiles in cancer compared to healthy tissues, including up-regulation of folate metabolism, the down-regulation of thiamine metabolism, and tight regulation of oxidative phosphorylation. PMID:26942765

Pattern Formation on Networks: from Localised Activity to Turing Patterns

PubMed Central

McCullen, Nick; Wagenknecht, Thomas

2016-01-01

Networks of interactions between competing species are used to model many complex systems, such as in genetics, evolutionary biology or sociology and knowledge of the patterns of activity they can exhibit is important for understanding their behaviour. The emergence of patterns on complex networks with reaction-diffusion dynamics is studied here, where node dynamics interact via diffusion via the network edges. Through the application of a generalisation of dynamical systems analysis this work reveals a fundamental connection between small-scale modes of activity on networks and localised pattern formation seen throughout science, such as solitons, breathers and localised buckling. The connection between solutions with a single and small numbers of activated nodes and the fully developed system-scale patterns are investigated computationally using numerical continuation methods. These techniques are also used to help reveal a much larger portion of of the full number of solutions that exist in the system at different parameter values. The importance of network structure is also highlighted, with a key role being played by nodes with a certain so-called optimal degree, on which the interaction between the reaction kinetics and the network structure organise the behaviour of the system. PMID:27273339

Hybrid Multiscale Simulation of Hydrologic and Biogeochemical Processes in the River-Groundwater Interaction Zone

NASA Astrophysics Data System (ADS)

Yang, X.; Scheibe, T. D.; Chen, X.; Hammond, G. E.; Song, X.

2015-12-01

The zone in which river water and groundwater mix plays an important role in natural ecosystems as it regulates the mixing of nutrients that control biogeochemical transformations. Subsurface heterogeneity leads to local hotspots of microbial activity that are important to system function yet difficult to resolve computationally. To address this challenge, we are testing a hybrid multiscale approach that couples models at two distinct scales, based on field research at the U. S. Department of Energy's Hanford Site. The region of interest is a 400 x 400 x 20 m macroscale domain that intersects the aquifer and the river and contains a contaminant plume. However, biogeochemical activity is high in a thin zone (mud layer, <1 m thick) immediately adjacent to the river. This microscale domain is highly heterogeneous and requires fine spatial resolution to adequately represent the effects of local mixing on reactions. It is not computationally feasible to resolve the full macroscale domain at the fine resolution needed in the mud layer, and the reaction network needed in the mud layer is much more complex than that needed in the rest of the macroscale domain. Hence, a hybrid multiscale approach is used to efficiently and accurately predict flow and reactive transport at both scales. In our simulations, models at both scales are simulated using the PFLOTRAN code. Multiple microscale simulations in dynamically defined sub-domains (fine resolution, complex reaction network) are executed and coupled with a macroscale simulation over the entire domain (coarse resolution, simpler reaction network). The objectives of the research include: 1) comparing accuracy and computing cost of the hybrid multiscale simulation with a single-scale simulation; 2) identifying hot spots of microbial activity; and 3) defining macroscopic quantities such as fluxes, residence times and effective reaction rates.

Modeling complex metabolic reactions, ecological systems, and financial and legal networks with MIANN models based on Markov-Wiener node descriptors.

PubMed

Duardo-Sánchez, Aliuska; Munteanu, Cristian R; Riera-Fernández, Pablo; López-Díaz, Antonio; Pazos, Alejandro; González-Díaz, Humberto

2014-01-27

The use of numerical parameters in Complex Network analysis is expanding to new fields of application. At a molecular level, we can use them to describe the molecular structure of chemical entities, protein interactions, or metabolic networks. However, the applications are not restricted to the world of molecules and can be extended to the study of macroscopic nonliving systems, organisms, or even legal or social networks. On the other hand, the development of the field of Artificial Intelligence has led to the formulation of computational algorithms whose design is based on the structure and functioning of networks of biological neurons. These algorithms, called Artificial Neural Networks (ANNs), can be useful for the study of complex networks, since the numerical parameters that encode information of the network (for example centralities/node descriptors) can be used as inputs for the ANNs. The Wiener index (W) is a graph invariant widely used in chemoinformatics to quantify the molecular structure of drugs and to study complex networks. In this work, we explore for the first time the possibility of using Markov chains to calculate analogues of node distance numbers/W to describe complex networks from the point of view of their nodes. These parameters are called Markov-Wiener node descriptors of order k(th) (W(k)). Please, note that these descriptors are not related to Markov-Wiener stochastic processes. Here, we calculated the W(k)(i) values for a very high number of nodes (>100,000) in more than 100 different complex networks using the software MI-NODES. These networks were grouped according to the field of application. Molecular networks include the Metabolic Reaction Networks (MRNs) of 40 different organisms. In addition, we analyzed other biological and legal and social networks. These include the Interaction Web Database Biological Networks (IWDBNs), with 75 food webs or ecological systems and the Spanish Financial Law Network (SFLN). The calculated W(k)(i) values were used as inputs for different ANNs in order to discriminate correct node connectivity patterns from incorrect random patterns. The MIANN models obtained present good values of Sensitivity/Specificity (%): MRNs (78/78), IWDBNs (90/88), and SFLN (86/84). These preliminary results are very promising from the point of view of a first exploratory study and suggest that the use of these models could be extended to the high-throughput re-evaluation of connectivity in known complex networks (collation).

Heterogeneous network promotes species coexistence: metapopulation model for rock-paper-scissors game.

PubMed

Nagatani, Takashi; Ichinose, Genki; Tainaka, Kei-Ichi

2018-05-04

Understanding mechanisms of biodiversity has been a central question in ecology. The coexistence of three species in rock-paper-scissors (RPS) systems are discussed by many authors; however, the relation between coexistence and network structure is rarely discussed. Here we present a metapopulation model for RPS game. The total population is assumed to consist of three subpopulations (nodes). Each individual migrates by random walk; the destination of migration is randomly determined. From reaction-migration equations, we obtain the population dynamics. It is found that the dynamic highly depends on network structures. When a network is homogeneous, the dynamics are neutrally stable: each node has a periodic solution, and the oscillations synchronize in all nodes. However, when a network is heterogeneous, the dynamics approach stable focus and all nodes reach equilibriums with different densities. Hence, the heterogeneity of the network promotes biodiversity.

Impact parameter determination in experimental analysis using a neural network

NASA Astrophysics Data System (ADS)

Haddad, F.; Hagel, K.; Li, J.; Mdeiwayeh, N.; Natowitz, J. B.; Wada, R.; Xiao, B.; David, C.; Freslier, M.; Aichelin, J.

1997-03-01

A neural network is used to determine the impact parameter in 40Ca+40Ca reactions. The effect of the detection efficiency as well as the model dependence of the training procedure has been studied carefully. An overall improvement of the impact parameter determination of 25% is obtained using this technique. The analysis of Amphora 40Ca+40Ca data at 35 MeV per nucleon using a neural network shows two well-separated classes of events among the selected ``complete'' events.

Bifurcation analysis of a delay reaction-diffusion malware propagation model with feedback control

NASA Astrophysics Data System (ADS)

Zhu, Linhe; Zhao, Hongyong; Wang, Xiaoming

2015-05-01

With the rapid development of network information technology, information networks security has become a very critical issue in our work and daily life. This paper attempts to develop a delay reaction-diffusion model with a state feedback controller to describe the process of malware propagation in mobile wireless sensor networks (MWSNs). By analyzing the stability and Hopf bifurcation, we show that the state feedback method can successfully be used to control unstable steady states or periodic oscillations. Moreover, formulas for determining the properties of the bifurcating periodic oscillations are derived by applying the normal form method and center manifold theorem. Finally, we conduct extensive simulations on large-scale MWSNs to evaluate the proposed model. Numerical evidences show that the linear term of the controller is enough to delay the onset of the Hopf bifurcation and the properties of the bifurcation can be regulated to achieve some desirable behaviors by choosing the appropriate higher terms of the controller. Furthermore, we obtain that the spatial-temporal dynamic characteristics of malware propagation are closely related to the rate constant for nodes leaving the infective class for recovered class and the mobile behavior of nodes.

Modular verification of chemical reaction network encodings via serializability analysis

PubMed Central

Lakin, Matthew R.; Stefanovic, Darko; Phillips, Andrew

2015-01-01

Chemical reaction networks are a powerful means of specifying the intended behaviour of synthetic biochemical systems. A high-level formal specification, expressed as a chemical reaction network, may be compiled into a lower-level encoding, which can be directly implemented in wet chemistry and may itself be expressed as a chemical reaction network. Here we present conditions under which a lower-level encoding correctly emulates the sequential dynamics of a high-level chemical reaction network. We require that encodings are transactional, such that their execution is divided by a “commit reaction” that irreversibly separates the reactant-consuming phase of the encoding from the product-generating phase. We also impose restrictions on the sharing of species between reaction encodings, based on a notion of “extra tolerance”, which defines species that may be shared between encodings without enabling unwanted reactions. Our notion of correctness is serializability of interleaved reaction encodings, and if all reaction encodings satisfy our correctness properties then we can infer that the global dynamics of the system are correct. This allows us to infer correctness of any system constructed using verified encodings. As an example, we show how this approach may be used to verify two- and four-domain DNA strand displacement encodings of chemical reaction networks, and we generalize our result to the limit where the populations of helper species are unlimited. PMID:27325906

Modelling the molecular composition and nuclear-spin chemistryof collapsing pre-stellar sources

NASA Astrophysics Data System (ADS)

Hily-Blant, P.; Faure, A.; Rist, C.; Pineau des Forêts, G.; Flower, D. R.

2018-07-01

We study the gravitational collapse of pre-stellar sources and the associated evolution of their chemical composition. We use the University of Grenoble Alpes Astrochemical Network (UGAN), which includes reactions involving the different nuclear-spin states of H2, H_3^+, and of the hydrides of carbon, nitrogen, oxygen, and sulphur, for reactions involving up to seven protons. In addition, species-to-species rate coefficients are provided for the ortho/para interconversion of the H_3^+ + H2 system and isotopic variants. The composition of the medium is followed from an initial steady state through the early phase of isothermal gravitational collapse. Both the freeze-out of the molecules on to grains and the coagulation of the grains were incorporated in the model. The predicted abundances and column densities of the spin isomers of ammonia and its deuterated forms are compared with those measured recently towards the pre-stellar cores H-MM1, L16293E, and Barnard B1. We find that gas-phase processes alone account satisfactorily for the observations, without recourse to grain-surface reactions. In particular, our model reproduces both the isotopologue abundance ratios and the ortho:para ratios of NH2D and NHD2 within observational uncertainties. More accurate observations are necessary to distinguish between full scrambling processes - as assumed in our gas-phase network - and direct nucleus- or atom-exchange reactions.

Genome-scale reconstruction of the Streptococcus pyogenes M49 metabolic network reveals growth requirements and indicates potential drug targets.

PubMed

Levering, Jennifer; Fiedler, Tomas; Sieg, Antje; van Grinsven, Koen W A; Hering, Silvio; Veith, Nadine; Olivier, Brett G; Klett, Lara; Hugenholtz, Jeroen; Teusink, Bas; Kreikemeyer, Bernd; Kummer, Ursula

2016-08-20

Genome-scale metabolic models comprise stoichiometric relations between metabolites, as well as associations between genes and metabolic reactions and facilitate the analysis of metabolism. We computationally reconstructed the metabolic network of the lactic acid bacterium Streptococcus pyogenes M49. Initially, we based the reconstruction on genome annotations and already existing and curated metabolic networks of Bacillus subtilis, Escherichia coli, Lactobacillus plantarum and Lactococcus lactis. This initial draft was manually curated with the final reconstruction accounting for 480 genes associated with 576 reactions and 558 metabolites. In order to constrain the model further, we performed growth experiments of wild type and arcA deletion strains of S. pyogenes M49 in a chemically defined medium and calculated nutrient uptake and production fluxes. We additionally performed amino acid auxotrophy experiments to test the consistency of the model. The established genome-scale model can be used to understand the growth requirements of the human pathogen S. pyogenes and define optimal and suboptimal conditions, but also to describe differences and similarities between S. pyogenes and related lactic acid bacteria such as L. lactis in order to find strategies to reduce the growth of the pathogen and propose drug targets. Copyright © 2016 Elsevier B.V. All rights reserved.

Reaction-diffusion-like formalism for plastic neural networks reveals dissipative solitons at criticality

NASA Astrophysics Data System (ADS)

Grytskyy, Dmytro; Diesmann, Markus; Helias, Moritz

2016-06-01

Self-organized structures in networks with spike-timing dependent synaptic plasticity (STDP) are likely to play a central role for information processing in the brain. In the present study we derive a reaction-diffusion-like formalism for plastic feed-forward networks of nonlinear rate-based model neurons with a correlation sensitive learning rule inspired by and being qualitatively similar to STDP. After obtaining equations that describe the change of the spatial shape of the signal from layer to layer, we derive a criterion for the nonlinearity necessary to obtain stable dynamics for arbitrary input. We classify the possible scenarios of signal evolution and find that close to the transition to the unstable regime metastable solutions appear. The form of these dissipative solitons is determined analytically and the evolution and interaction of several such coexistent objects is investigated.

Genome-scale fluxes predicted under the guidance of enzyme abundance using a novel hyper-cube shrink algorithm.

PubMed

Xie, Zhengwei; Zhang, Tianyu; Ouyang, Qi

2018-02-01

One of the long-expected goals of genome-scale metabolic modelling is to evaluate the influence of the perturbed enzymes on flux distribution. Both ordinary differential equation (ODE) models and constraint-based models, like Flux balance analysis (FBA), lack the capacity to perform metabolic control analysis (MCA) for large-scale networks. In this study, we developed a hyper-cube shrink algorithm (HCSA) to incorporate the enzymatic properties into the FBA model by introducing a pseudo reaction V constrained by enzymatic parameters. Our algorithm uses the enzymatic information quantitatively rather than qualitatively. We first demonstrate the concept by applying HCSA to a simple three-node network, whereby we obtained a good correlation between flux and enzyme abundance. We then validate its prediction by comparison with ODE and with a synthetic network producing voilacein and analogues in Saccharomyces cerevisiae. We show that HCSA can mimic the state-state results of ODE. Finally, we show its capability of predicting the flux distribution in genome-scale networks by applying it to sporulation in yeast. We show the ability of HCSA to operate without biomass flux and perform MCA to determine rate-limiting reactions. Algorithm was implemented by Matlab and C ++. The code is available at https://github.com/kekegg/HCSA. xiezhengwei@hsc.pku.edu.cn or qi@pku.edu.cn. Supplementary data are available at Bioinformatics online. © The Author (2017). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com

A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks.

PubMed

Laomettachit, Teeraphan; Chen, Katherine C; Baumann, William T; Tyson, John J

2016-01-01

To understand the molecular mechanisms that regulate cell cycle progression in eukaryotes, a variety of mathematical modeling approaches have been employed, ranging from Boolean networks and differential equations to stochastic simulations. Each approach has its own characteristic strengths and weaknesses. In this paper, we propose a "standard component" modeling strategy that combines advantageous features of Boolean networks, differential equations and stochastic simulations in a framework that acknowledges the typical sorts of reactions found in protein regulatory networks. Applying this strategy to a comprehensive mechanism of the budding yeast cell cycle, we illustrate the potential value of standard component modeling. The deterministic version of our model reproduces the phenotypic properties of wild-type cells and of 125 mutant strains. The stochastic version of our model reproduces the cell-to-cell variability of wild-type cells and the partial viability of the CLB2-dbΔ clb5Δ mutant strain. Our simulations show that mathematical modeling with "standard components" can capture in quantitative detail many essential properties of cell cycle control in budding yeast.

A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks

PubMed Central

Laomettachit, Teeraphan; Chen, Katherine C.; Baumann, William T.

2016-01-01

To understand the molecular mechanisms that regulate cell cycle progression in eukaryotes, a variety of mathematical modeling approaches have been employed, ranging from Boolean networks and differential equations to stochastic simulations. Each approach has its own characteristic strengths and weaknesses. In this paper, we propose a “standard component” modeling strategy that combines advantageous features of Boolean networks, differential equations and stochastic simulations in a framework that acknowledges the typical sorts of reactions found in protein regulatory networks. Applying this strategy to a comprehensive mechanism of the budding yeast cell cycle, we illustrate the potential value of standard component modeling. The deterministic version of our model reproduces the phenotypic properties of wild-type cells and of 125 mutant strains. The stochastic version of our model reproduces the cell-to-cell variability of wild-type cells and the partial viability of the CLB2-dbΔ clb5Δ mutant strain. Our simulations show that mathematical modeling with “standard components” can capture in quantitative detail many essential properties of cell cycle control in budding yeast. PMID:27187804

TIde: a software for the systematic scanning of drug targets in kinetic network models

PubMed Central

Schulz, Marvin; Bakker, Barbara M; Klipp, Edda

2009-01-01

Background During the stages of the development of a potent drug candidate compounds can fail for several reasons. One of them, the efficacy of a candidate, can be estimated in silico if an appropriate ordinary differential equation model of the affected pathway is available. With such a model at hand it is also possible to detect reactions having a large effect on a certain variable such as a substance concentration. Results We show an algorithm that systematically tests the influence of activators and inhibitors of different type and strength acting at different positions in the network. The effect on a quantity to be selected (e.g. a steady state flux or concentration) is calculated. Moreover, combinations of two inhibitors or one inhibitor and one activator targeting different network positions are analysed. Furthermore, we present TIde (Target Identification), an open source, platform independent tool to investigate ordinary differential equation models in the common systems biology markup language format. It automatically assigns the respectively altered kinetics to the inhibited or activated reactions, performs the necessary calculations, and provides a graphical output of the analysis results. For illustration, TIde is used to detect optimal inhibitor positions in simple branched networks, a signalling pathway, and a well studied model of glycolysis in Trypanosoma brucei. Conclusion Using TIde, we show in the branched models under which conditions inhibitions in a certain pathway can affect a molecule concentrations in a different. In the signalling pathway we illuminate which inhibitions have an effect on the signalling characteristics of the last active kinase. Finally, we compare our set of best targets in the glycolysis model with a similar analysis showing the applicability of our tool. PMID:19840374

Decomposition of metabolic network into functional modules based on the global connectivity structure of reaction graph.

PubMed

Ma, Hong-Wu; Zhao, Xue-Ming; Yuan, Ying-Jin; Zeng, An-Ping

2004-08-12

Metabolic networks are organized in a modular, hierarchical manner. Methods for a rational decomposition of the metabolic network into relatively independent functional subsets are essential to better understand the modularity and organization principle of a large-scale, genome-wide network. Network decomposition is also necessary for functional analysis of metabolism by pathway analysis methods that are often hampered by the problem of combinatorial explosion due to the complexity of metabolic network. Decomposition methods proposed in literature are mainly based on the connection degree of metabolites. To obtain a more reasonable decomposition, the global connectivity structure of metabolic networks should be taken into account. In this work, we use a reaction graph representation of a metabolic network for the identification of its global connectivity structure and for decomposition. A bow-tie connectivity structure similar to that previously discovered for metabolite graph is found also to exist in the reaction graph. Based on this bow-tie structure, a new decomposition method is proposed, which uses a distance definition derived from the path length between two reactions. An hierarchical classification tree is first constructed from the distance matrix among the reactions in the giant strong component of the bow-tie structure. These reactions are then grouped into different subsets based on the hierarchical tree. Reactions in the IN and OUT subsets of the bow-tie structure are subsequently placed in the corresponding subsets according to a 'majority rule'. Compared with the decomposition methods proposed in literature, ours is based on combined properties of the global network structure and local reaction connectivity rather than, primarily, on the connection degree of metabolites. The method is applied to decompose the metabolic network of Escherichia coli. Eleven subsets are obtained. More detailed investigations of the subsets show that reactions in the same subset are really functionally related. The rational decomposition of metabolic networks, and subsequent studies of the subsets, make it more amenable to understand the inherent organization and functionality of metabolic networks at the modular level. http://genome.gbf.de/bioinformatics/

Synthetic Biology for Cell-Free Biosynthesis: Fundamentals of Designing Novel In Vitro Multi-Enzyme Reaction Networks.

PubMed

Morgado, Gaspar; Gerngross, Daniel; Roberts, Tania M; Panke, Sven

Cell-free biosynthesis in the form of in vitro multi-enzyme reaction networks or enzyme cascade reactions emerges as a promising tool to carry out complex catalysis in one-step, one-vessel settings. It combines the advantages of well-established in vitro biocatalysis with the power of multi-step in vivo pathways. Such cascades have been successfully applied to the synthesis of fine and bulk chemicals, monomers and complex polymers of chemical importance, and energy molecules from renewable resources as well as electricity. The scale of these initial attempts remains small, suggesting that more robust control of such systems and more efficient optimization are currently major bottlenecks. To this end, the very nature of enzyme cascade reactions as multi-membered systems requires novel approaches for implementation and optimization, some of which can be obtained from in vivo disciplines (such as pathway refactoring and DNA assembly), and some of which can be built on the unique, cell-free properties of cascade reactions (such as easy analytical access to all system intermediates to facilitate modeling).

Passivity of Directed and Undirected Complex Dynamical Networks With Adaptive Coupling Weights.

PubMed

Wang, Jin-Liang; Wu, Huai-Ning; Huang, Tingwen; Ren, Shun-Yan; Wu, Jigang

2017-08-01

A complex dynamical network consisting of N identical neural networks with reaction-diffusion terms is considered in this paper. First, several passivity definitions for the systems with different dimensions of input and output are given. By utilizing some inequality techniques, several criteria are presented, ensuring the passivity of the complex dynamical network under the designed adaptive law. Then, we discuss the relationship between the synchronization and output strict passivity of the proposed network model. Furthermore, these results are extended to the case when the topological structure of the network is undirected. Finally, two examples with numerical simulations are provided to illustrate the correctness and effectiveness of the proposed results.

Networks in cognitive science.

PubMed

Baronchelli, Andrea; Ferrer-i-Cancho, Ramon; Pastor-Satorras, Romualdo; Chater, Nick; Christiansen, Morten H

2013-07-01

Networks of interconnected nodes have long played a key role in Cognitive Science, from artificial neural networks to spreading activation models of semantic memory. Recently, however, a new Network Science has been developed, providing insights into the emergence of global, system-scale properties in contexts as diverse as the Internet, metabolic reactions, and collaborations among scientists. Today, the inclusion of network theory into Cognitive Sciences, and the expansion of complex-systems science, promises to significantly change the way in which the organization and dynamics of cognitive and behavioral processes are understood. In this paper, we review recent contributions of network theory at different levels and domains within the Cognitive Sciences. Copyright © 2013 Elsevier Ltd. All rights reserved.

Multi-scale modeling of multi-component reactive transport in geothermal aquifers

NASA Astrophysics Data System (ADS)

Nick, Hamidreza M.; Raoof, Amir; Wolf, Karl-Heinz; Bruhn, David

2014-05-01

In deep geothermal systems heat and chemical stresses can cause physical alterations, which may have a significant effect on flow and reaction rates. As a consequence it will lead to changes in permeability and porosity of the formations due to mineral precipitation and dissolution. Large-scale modeling of reactive transport in such systems is still challenging. A large area of uncertainty is the way in which the pore-scale information controlling the flow and reaction will behave at a larger scale. A possible choice is to use constitutive relationships relating, for example the permeability and porosity evolutions to the change in the pore geometry. While determining such relationships through laboratory experiments may be limited, pore-network modeling provides an alternative solution. In this work, we introduce a new workflow in which a hybrid Finite-Element Finite-Volume method [1,2] and a pore network modeling approach [3] are employed. Using the pore-scale model, relevant constitutive relations are developed. These relations are then embedded in the continuum-scale model. This approach enables us to study non-isothermal reactive transport in porous media while accounting for micro-scale features under realistic conditions. The performance and applicability of the proposed model is explored for different flow and reaction regimes. References: 1. Matthäi, S.K., et al.: Simulation of solute transport through fractured rock: a higher-order accurate finite-element finite-volume method permitting large time steps. Transport in porous media 83.2 (2010): 289-318. 2. Nick, H.M., et al.: Reactive dispersive contaminant transport in coastal aquifers: Numerical simulation of a reactive Henry problem. Journal of contaminant hydrology 145 (2012), 90-104. 3. Raoof A., et al.: PoreFlow: A Complex pore-network model for simulation of reactive transport in variably saturated porous media, Computers & Geosciences, 61, (2013), 160-174.

P-adic model of transport in porous disordered media

NASA Astrophysics Data System (ADS)

Khrennikov, Adrei Yu.; Oleschko, Klaudia

2014-05-01

The soil porosity and permeability are the most important quantitative indicators of soil dynamics under the land-use change. The main problema in the modeling of this dynamic is still poor correlation between the real measuring data and the mathematical and computer simulation models. In order to overpassed this deep divorce we have designed a new technique, able to compare the data arised from the multiscale image analices and time series of the basic physical properties dynamics in porous media studied in time and space. We present a model of the diffusion reaction type describing transport in disordered porous media, e.g., water or oil flow in a complex network of pores. Our model is based on p-adic representation of such networks. This is a kind of fractal representation. We explore advantages of p- adic representation, namely, the possibility to endow p-adic trees with an algebraic structure and ultrametric topology and, hence, to apply analysis which have (at least some) similarities with ordinary real analysis on the straight line. We present the system of two diffusion reaction equations describing propagation of particles in networks of pores in disordered media. As an application, one can consider water transport through the soil pore Networks, or oil flow through capillaries nets. Under some restrictions on potentials and rate coefficients we found the stationary regime corresponding to water content or concentration of oil in a cluster of capillaries. Usage of p-adic analysis (in particular, p-adic wavelets) gives a possibility to find the stationary solution in the analytic form which makes possible to present a clear pedological or geological picture of the process. The mathematical model elaborated in this paper (Khrennikov, 2013) can be applied to variety of problems from water concentration in aquifers to the problem of formation of oil reservoirs in disordered media with porous structures. Another possible application may have real practical output. In fact, our system of diffusion-reaction equations can be used to model the process of extraction of water or oil from an extended network of capillaries (Khrennikov et al., 2013). The accomplished analyses show that the time series of water content/pressure dynamics in saturated/unsaturated conditions reflect the fractal structure of pores separated by familias base don the seven geometric descriptors which we used for the soils multiscale images (Oleschko et al., 2012). The similar models were applied to the porous media behind the oil flow from wells. These results motivate usage of the fractal and, in particular, p-adic methods of modeling.

Rational design of functional and tunable oscillating enzymatic networks

NASA Astrophysics Data System (ADS)

Semenov, Sergey N.; Wong, Albert S. Y.; van der Made, R. Martijn; Postma, Sjoerd G. J.; Groen, Joost; van Roekel, Hendrik W. H.; de Greef, Tom F. A.; Huck, Wilhelm T. S.

2015-02-01

Life is sustained by complex systems operating far from equilibrium and consisting of a multitude of enzymatic reaction networks. The operating principles of biology's regulatory networks are known, but the in vitro assembly of out-of-equilibrium enzymatic reaction networks has proved challenging, limiting the development of synthetic systems showing autonomous behaviour. Here, we present a strategy for the rational design of programmable functional reaction networks that exhibit dynamic behaviour. We demonstrate that a network built around autoactivation and delayed negative feedback of the enzyme trypsin is capable of producing sustained oscillating concentrations of active trypsin for over 65 h. Other functions, such as amplification, analog-to-digital conversion and periodic control over equilibrium systems, are obtained by linking multiple network modules in microfluidic flow reactors. The methodology developed here provides a general framework to construct dissipative, tunable and robust (bio)chemical reaction networks.

Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.

PubMed

Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan

2018-05-30

Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.

New types of experimental data shape the use of enzyme kinetics for dynamic network modeling.

PubMed

Tummler, Katja; Lubitz, Timo; Schelker, Max; Klipp, Edda

2014-01-01

Since the publication of Leonor Michaelis and Maude Menten's paper on the reaction kinetics of the enzyme invertase in 1913, molecular biology has evolved tremendously. New measurement techniques allow in vivo characterization of the whole genome, proteome or transcriptome of cells, whereas the classical enzyme essay only allows determination of the two Michaelis-Menten parameters V and K(m). Nevertheless, Michaelis-Menten kinetics are still commonly used, not only in the in vitro context of enzyme characterization but also as a rate law for enzymatic reactions in larger biochemical reaction networks. In this review, we give an overview of the historical development of kinetic rate laws originating from Michaelis-Menten kinetics over the past 100 years. Furthermore, we briefly summarize the experimental techniques used for the characterization of enzymes, and discuss web resources that systematically store kinetic parameters and related information. Finally, describe the novel opportunities that arise from using these data in dynamic mathematical modeling. In this framework, traditional in vitro approaches may be combined with modern genome-scale measurements to foster thorough understanding of the underlying complex mechanisms. © 2013 FEBS.

Computational models of airway branching morphogenesis.

PubMed

Varner, Victor D; Nelson, Celeste M

2017-07-01

The bronchial network of the mammalian lung consists of millions of dichotomous branches arranged in a highly complex, space-filling tree. Recent computational models of branching morphogenesis in the lung have helped uncover the biological mechanisms that construct this ramified architecture. In this review, we focus on three different theoretical approaches - geometric modeling, reaction-diffusion modeling, and continuum mechanical modeling - and discuss how, taken together, these models have identified the geometric principles necessary to build an efficient bronchial network, as well as the patterning mechanisms that specify airway geometry in the developing embryo. We emphasize models that are integrated with biological experiments and suggest how recent progress in computational modeling has advanced our understanding of airway branching morphogenesis. Copyright © 2016 Elsevier Ltd. All rights reserved.

Analytical transport network theory to guide the design of 3-D microstructural networks in energy materials: Part 1. Flow without reactions

NASA Astrophysics Data System (ADS)

Cocco, Alex P.; Nakajo, Arata; Chiu, Wilson K. S.

2017-12-01

We present a fully analytical, heuristic model - the "Analytical Transport Network Model" - for steady-state, diffusive, potential flow through a 3-D network. Employing a combination of graph theory, linear algebra, and geometry, the model explicitly relates a microstructural network's topology and the morphology of its channels to an effective material transport coefficient (a general term meant to encompass, e.g., conductivity or diffusion coefficient). The model's transport coefficient predictions agree well with those from electrochemical fin (ECF) theory and finite element analysis (FEA), but are computed 0.5-1.5 and 5-6 orders of magnitude faster, respectively. In addition, the theory explicitly relates a number of morphological and topological parameters directly to the transport coefficient, whereby the distributions that characterize the structure are readily available for further analysis. Furthermore, ATN's explicit development provides insight into the nature of the tortuosity factor and offers the potential to apply theory from network science and to consider the optimization of a network's effective resistance in a mathematically rigorous manner. The ATN model's speed and relative ease-of-use offer the potential to aid in accelerating the design (with respect to transport), and thus reducing the cost, of energy materials.

PENDISC: a simple method for constructing a mathematical model from time-series data of metabolite concentrations.

PubMed

Sriyudthsak, Kansuporn; Iwata, Michio; Hirai, Masami Yokota; Shiraishi, Fumihide

2014-06-01

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC (Parameter Estimation in a N on- DImensionalized S-system with Constraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.

Modeling reactive transport processes in fractured rock using the time domain random walk approach within a dual-porosity framework

NASA Astrophysics Data System (ADS)

Roubinet, D.; Russian, A.; Dentz, M.; Gouze, P.

2017-12-01

Characterizing and modeling hydrodynamic reactive transport in fractured rock are critical challenges for various research fields and applications including environmental remediation, geological storage, and energy production. To this end, we consider a recently developed time domain random walk (TDRW) approach, which is adapted to reproduce anomalous transport behaviors and capture heterogeneous structural and physical properties. This method is also very well suited to optimize numerical simulations by memory-shared massive parallelization and provide numerical results at various scales. So far, the TDRW approach has been applied for modeling advective-diffusive transport with mass transfer between mobile and immobile regions and simple (theoretical) reactions in heterogeneous porous media represented as single continuum domains. We extend this approach to dual-continuum representations considering a highly permeable fracture network embedded into a poorly permeable rock matrix with heterogeneous geochemical reactions occurring in both geological structures. The resulting numerical model enables us to extend the range of the modeled heterogeneity scales with an accurate representation of solute transport processes and no assumption on the Fickianity of these processes. The proposed model is compared to existing particle-based methods that are usually used to model reactive transport in fractured rocks assuming a homogeneous surrounding matrix, and is used to evaluate the impact of the matrix heterogeneity on the apparent reaction rates for different 2D and 3D simple-to-complex fracture network configurations.

Yeast 5 – an expanded reconstruction of the Saccharomyces cerevisiae metabolic network

PubMed Central

2012-01-01

Background Efforts to improve the computational reconstruction of the Saccharomyces cerevisiae biochemical reaction network and to refine the stoichiometrically constrained metabolic models that can be derived from such a reconstruction have continued since the first stoichiometrically constrained yeast genome scale metabolic model was published in 2003. Continuing this ongoing process, we have constructed an update to the Yeast Consensus Reconstruction, Yeast 5. The Yeast Consensus Reconstruction is a product of efforts to forge a community-based reconstruction emphasizing standards compliance and biochemical accuracy via evidence-based selection of reactions. It draws upon models published by a variety of independent research groups as well as information obtained from biochemical databases and primary literature. Results Yeast 5 refines the biochemical reactions included in the reconstruction, particularly reactions involved in sphingolipid metabolism; updates gene-reaction annotations; and emphasizes the distinction between reconstruction and stoichiometrically constrained model. Although it was not a primary goal, this update also improves the accuracy of model prediction of viability and auxotrophy phenotypes and increases the number of epistatic interactions. This update maintains an emphasis on standards compliance, unambiguous metabolite naming, and computer-readable annotations available through a structured document format. Additionally, we have developed MATLAB scripts to evaluate the model’s predictive accuracy and to demonstrate basic model applications such as simulating aerobic and anaerobic growth. These scripts, which provide an independent tool for evaluating the performance of various stoichiometrically constrained yeast metabolic models using flux balance analysis, are included as Additional files 1, 2 and 3. Conclusions Yeast 5 expands and refines the computational reconstruction of yeast metabolism and improves the predictive accuracy of a stoichiometrically constrained yeast metabolic model. It differs from previous reconstructions and models by emphasizing the distinction between the yeast metabolic reconstruction and the stoichiometrically constrained model, and makes both available as Additional file 4 and Additional file 5 and at http://yeast.sf.net/ as separate systems biology markup language (SBML) files. Through this separation, we intend to make the modeling process more accessible, explicit, transparent, and reproducible. PMID:22663945

SynBioSS designer: a web-based tool for the automated generation of kinetic models for synthetic biological constructs

PubMed Central

Weeding, Emma; Houle, Jason

2010-01-01

Modeling tools can play an important role in synthetic biology the same way modeling helps in other engineering disciplines: simulations can quickly probe mechanisms and provide a clear picture of how different components influence the behavior of the whole. We present a brief review of available tools and present SynBioSS Designer. The Synthetic Biology Software Suite (SynBioSS) is used for the generation, storing, retrieval and quantitative simulation of synthetic biological networks. SynBioSS consists of three distinct components: the Desktop Simulator, the Wiki, and the Designer. SynBioSS Designer takes as input molecular parts involved in gene expression and regulation (e.g. promoters, transcription factors, ribosome binding sites, etc.), and automatically generates complete networks of reactions that represent transcription, translation, regulation, induction and degradation of those parts. Effectively, Designer uses DNA sequences as input and generates networks of biomolecular reactions as output. In this paper we describe how Designer uses universal principles of molecular biology to generate models of any arbitrary synthetic biological system. These models are useful as they explain biological phenotypic complexity in mechanistic terms. In turn, such mechanistic explanations can assist in designing synthetic biological systems. We also discuss, giving practical guidance to users, how Designer interfaces with the Registry of Standard Biological Parts, the de facto compendium of parts used in synthetic biology applications. PMID:20639523

How the contagion at links influences epidemic spreading

NASA Astrophysics Data System (ADS)

Ruan, Zhongyuan; Tang, Ming; Liu, Zonghua

2013-04-01

The reaction-diffusion (RD) model of epidemic spreading generally assume that contagion occurs only at the nodes of network, i.e., the links are used only for migration/diffusion of agents. However, in reality, we observe that contagion occurs also among the travelers staying in the same car, train or plane etc., which consist of the links of network. To reflect the contagious effect of links, we here present a traveling-contagion model where contagion occurs not only at nodes but also at links. Considering that the population density in transportation is generally much larger than that in districts, we introduce different infection rates for the nodes and links, respectively, whose two extreme cases correspond to the type-I and type-II reactions in the RD model [V. Colizza, R. Pastor-Satorras, A. Vespignani, Nat. Phys. 3, 276 (2007)]. Through studying three typical diffusion processes, we reveal both numerically and theoretically that the contagion at links can accelerate significantly the epidemic spreading. This finding is helpful in designing the controlling strategies of epidemic spreading.

Effects of active links on epidemic transmission over social networks

NASA Astrophysics Data System (ADS)

Zhu, Guanghu; Chen, Guanrong; Fu, Xinchu

2017-02-01

A new epidemic model with two infection periods is developed to account for the human behavior in social network, where newly infected individuals gradually restrict most of future contacts or are quarantined, causing infectivity change from a degree-dependent form to a constant. The corresponding dynamics are formulated by a set of ordinary differential equations (ODEs) via mean-field approximation. The effects of diverse infectivity on the epidemic dynamics ​are examined, with a behavioral interpretation of the basic reproduction number. Results show that such simple adaptive reactions largely determine the impact of network structure on epidemics. Particularly, a theorem proposed by Lajmanovich and Yorke in 1976 is generalized, so that it can be applied for the analysis of the epidemic models with multi-compartments especially network-coupled ODE systems.

The QSE-Reduced Nuclear Reaction Network for Silicon Burning

NASA Astrophysics Data System (ADS)

Hix, W. Raphael; Parete-Koon, Suzanne T.; Freiburghaus, Christian; Thielemann, Friedrich-Karl

2007-09-01

Iron and neighboring nuclei are formed in massive stars shortly before core collapse and during their supernova outbursts, as well as during thermonuclear supernovae. Complete and incomplete silicon burning are responsible for the production of a wide range of nuclei with atomic mass numbers from 28 to 64. Because of the large number of nuclei involved, accurate modeling of silicon burning is computationally expensive. However, examination of the physics of silicon burning has revealed that the nuclear evolution is dominated by large groups of nuclei in mutual equilibrium. We present a new hybrid equilibrium-network scheme which takes advantage of this quasi-equilibrium in order to reduce the number of independent variables calculated. This allows accurate prediction of the nuclear abundance evolution, deleptonization, and energy generation at a greatly reduced computational cost when compared to a conventional nuclear reaction network. During silicon burning, the resultant QSE-reduced network is approximately an order of magnitude faster than the full network it replaces and requires the tracking of less than a third as many abundance variables, without significant loss of accuracy. These reductions in computational cost and the number of species evolved make QSE-reduced networks well suited for inclusion within hydrodynamic simulations, particularly in multidimensional applications.

Neuron-Inspired Fe3O4/Conductive Carbon Filament Network for High-Speed and Stable Lithium Storage.

PubMed

Hao, Shu-Meng; Li, Qian-Jie; Qu, Jin; An, Fei; Zhang, Yu-Jiao; Yu, Zhong-Zhen

2018-05-17

Construction of a continuous conductance network with high electron-transfer rate is extremely important for high-performance energy storage. Owing to the highly efficient mass transport and information transmission, neurons are exactly a perfect model for electron transport, inspiring us to design a neuron-like reaction network for high-performance lithium-ion batteries (LIBs) with Fe 3 O 4 as an example. The reactive cores (Fe 3 O 4 ) are protected by carbon shells and linked by carbon filaments, constituting an integrated conductance network. Thus, once the reaction starts, the electrons released from every Fe 3 O 4 cores are capable of being transferred rapidly through the whole network directly to the external circuit, endowing the nanocomposite with tremendous rate performance and ultralong cycle life. After 1000 cycles at current densities as high as 1 and 2 A g -1 , charge capacities of the as-synthesized nanocomposite maintain 971 and 715 mA h g -1 , respectively, much higher than those of reported Fe 3 O 4 -based anode materials. The Fe 3 O 4 -based conductive network provides a new idea for future developments of high-rate-performance LIBs.

Solvated dissipative electro-elastic network model of hydrated proteins

NASA Astrophysics Data System (ADS)

Martin, Daniel

2013-03-01

Elastic network models coarse grain proteins into a network of residue beads connected by springs. We add dissipative dynamics to this mechanical system by applying overdamped Langevin equations of motion to normal-mode vibrations of the network. In addition, the network is made heterogeneous and softened at the protein surface by accounting for hydration of the ionized residues. Solvation changes the network Hessian in two ways. Diagonal solvation terms soften the spring constants and off-diagonal dipole-dipole terms correlate displacements of the ionized residues. The model is used to formulate the response functions of the electrostatic potential and electric field appearing in theories of redox reactions and spectroscopy. We also formulate the dielectric response of the protein and find that solvation of the surface ionized residues leads to a slow relaxation peak in the dielectric loss spectrum, about two orders of magnitude slower than the main peak of protein relaxation. Finally, the solvated network is used to formulate the allosteric response of the protein to ion binding. The global thermodynamics of ion binding is not strongly affected by the network solvation, but it dramatically enhances conformational changes in response to placing a charge at the a the active site.

Solvated dissipative electro-elastic network model of hydrated proteins

NASA Astrophysics Data System (ADS)

Martin, Daniel R.; Matyushov, Dmitry V.

2012-10-01

Elastic network models coarse grain proteins into a network of residue beads connected by springs. We add dissipative dynamics to this mechanical system by applying overdamped Langevin equations of motion to normal-mode vibrations of the network. In addition, the network is made heterogeneous and softened at the protein surface by accounting for hydration of the ionized residues. Solvation changes the network Hessian in two ways. Diagonal solvation terms soften the spring constants and off-diagonal dipole-dipole terms correlate displacements of the ionized residues. The model is used to formulate the response functions of the electrostatic potential and electric field appearing in theories of redox reactions and spectroscopy. We also formulate the dielectric response of the protein and find that solvation of the surface ionized residues leads to a slow relaxation peak in the dielectric loss spectrum, about two orders of magnitude slower than the main peak of protein relaxation. Finally, the solvated network is used to formulate the allosteric response of the protein to ion binding. The global thermodynamics of ion binding is not strongly affected by the network solvation, but it dramatically enhances conformational changes in response to placing a charge at the active site of the protein.

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

Sakai, Osamu, E-mail: sakai.o@e.usp.ac.jp; Nobuto, Kyosuke; Miyagi, Shigeyuki

Chemical reactions of molecular gases like methane are so complicated that a chart of decomposed and/or synthesized species originating from molecules in plasma resembles a weblike network in which we write down species and reactions among them. Here we consider properties of the network structures of chemical reactions in methane plasmas. In the network, atoms/molecules/radical species are assumed to form nodes and chemical reactions correspond to directed edges in the terminology of graph theory. Investigation of the centrality index reveals importance of CH{sub 3} in the global chemical reaction, and difference of an index for each radical species between casesmore » with and without electrons clarifies that the electrons are at an influential position to tighten the network structure.« less

Enumeration of Smallest Intervention Strategies in Genome-Scale Metabolic Networks

PubMed Central

von Kamp, Axel; Klamt, Steffen

2014-01-01

One ultimate goal of metabolic network modeling is the rational redesign of biochemical networks to optimize the production of certain compounds by cellular systems. Although several constraint-based optimization techniques have been developed for this purpose, methods for systematic enumeration of intervention strategies in genome-scale metabolic networks are still lacking. In principle, Minimal Cut Sets (MCSs; inclusion-minimal combinations of reaction or gene deletions that lead to the fulfilment of a given intervention goal) provide an exhaustive enumeration approach. However, their disadvantage is the combinatorial explosion in larger networks and the requirement to compute first the elementary modes (EMs) which itself is impractical in genome-scale networks. We present MCSEnumerator, a new method for effective enumeration of the smallest MCSs (with fewest interventions) in genome-scale metabolic network models. For this we combine two approaches, namely (i) the mapping of MCSs to EMs in a dual network, and (ii) a modified algorithm by which shortest EMs can be effectively determined in large networks. In this way, we can identify the smallest MCSs by calculating the shortest EMs in the dual network. Realistic application examples demonstrate that our algorithm is able to list thousands of the most efficient intervention strategies in genome-scale networks for various intervention problems. For instance, for the first time we could enumerate all synthetic lethals in E.coli with combinations of up to 5 reactions. We also applied the new algorithm exemplarily to compute strain designs for growth-coupled synthesis of different products (ethanol, fumarate, serine) by E.coli. We found numerous new engineering strategies partially requiring less knockouts and guaranteeing higher product yields (even without the assumption of optimal growth) than reported previously. The strength of the presented approach is that smallest intervention strategies can be quickly calculated and screened with neither network size nor the number of required interventions posing major challenges. PMID:24391481

STANDARD BIG BANG NUCLEOSYNTHESIS UP TO CNO WITH AN IMPROVED EXTENDED NUCLEAR NETWORK

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

Coc, Alain; Goriely, Stephane; Xu, Yi

Primordial or big bang nucleosynthesis (BBN) is one of the three strong pieces of evidence for the big bang model together with the expansion of the universe and cosmic microwave background radiation. In this study, we improve the standard BBN calculations taking into account new nuclear physics analyses and enlarge the nuclear network up to sodium. This is, in particular, important to evaluate the primitive value of CNO mass fraction that could affect Population III stellar evolution. For the first time we list the complete network of more than 400 reactions with references to the origin of the rates, includingmore » Almost-Equal-To 270 reaction rates calculated using the TALYS code. Together with the cosmological light elements, we calculate the primordial beryllium, boron, carbon, nitrogen, and oxygen nuclei. We performed a sensitivity study to identify the important reactions for CNO, {sup 9}Be, and boron nucleosynthesis. We re-evaluated those important reaction rates using experimental data and/or theoretical evaluations. The results are compared with precedent calculations: a primordial beryllium abundance increase by a factor of four compared to its previous evaluation, but we note a stability for B/H and for the CNO/H abundance ratio that remains close to its previous value of 0.7 Multiplication-Sign 10{sup -15}. On the other hand, the extension of the nuclear network has not changed the {sup 7}Li value, so its abundance is still 3-4 times greater than its observed spectroscopic value.« less

An efficient graph theory based method to identify every minimal reaction set in a metabolic network

PubMed Central

2014-01-01

Background Development of cells with minimal metabolic functionality is gaining importance due to their efficiency in producing chemicals and fuels. Existing computational methods to identify minimal reaction sets in metabolic networks are computationally expensive. Further, they identify only one of the several possible minimal reaction sets. Results In this paper, we propose an efficient graph theory based recursive optimization approach to identify all minimal reaction sets. Graph theoretical insights offer systematic methods to not only reduce the number of variables in math programming and increase its computational efficiency, but also provide efficient ways to find multiple optimal solutions. The efficacy of the proposed approach is demonstrated using case studies from Escherichia coli and Saccharomyces cerevisiae. In case study 1, the proposed method identified three minimal reaction sets each containing 38 reactions in Escherichia coli central metabolic network with 77 reactions. Analysis of these three minimal reaction sets revealed that one of them is more suitable for developing minimal metabolism cell compared to other two due to practically achievable internal flux distribution. In case study 2, the proposed method identified 256 minimal reaction sets from the Saccharomyces cerevisiae genome scale metabolic network with 620 reactions. The proposed method required only 4.5 hours to identify all the 256 minimal reaction sets and has shown a significant reduction (approximately 80%) in the solution time when compared to the existing methods for finding minimal reaction set. Conclusions Identification of all minimal reactions sets in metabolic networks is essential since different minimal reaction sets have different properties that effect the bioprocess development. The proposed method correctly identified all minimal reaction sets in a both the case studies. The proposed method is computationally efficient compared to other methods for finding minimal reaction sets and useful to employ with genome-scale metabolic networks. PMID:24594118

Model reduction of multiscale chemical langevin equations: a numerical case study.

PubMed

Sotiropoulos, Vassilios; Contou-Carrere, Marie-Nathalie; Daoutidis, Prodromos; Kaznessis, Yiannis N

2009-01-01

Two very important characteristics of biological reaction networks need to be considered carefully when modeling these systems. First, models must account for the inherent probabilistic nature of systems far from the thermodynamic limit. Often, biological systems cannot be modeled with traditional continuous-deterministic models. Second, models must take into consideration the disparate spectrum of time scales observed in biological phenomena, such as slow transcription events and fast dimerization reactions. In the last decade, significant efforts have been expended on the development of stochastic chemical kinetics models to capture the dynamics of biomolecular systems, and on the development of robust multiscale algorithms, able to handle stiffness. In this paper, the focus is on the dynamics of reaction sets governed by stiff chemical Langevin equations, i.e., stiff stochastic differential equations. These are particularly challenging systems to model, requiring prohibitively small integration step sizes. We describe and illustrate the application of a semianalytical reduction framework for chemical Langevin equations that results in significant gains in computational cost.

[Construction of automatic elucidation platform for mechanism of traditional Chinese medicine].

PubMed

Zhang, Bai-xia; Luo, Si-jun; Yan, Jing; Gu, Hao; Luo, Ji; Zhang, Yan-ling; Tao, Ou; Wang, Yun

2015-10-01

Aim at the two problems in the field of traditional Chinese medicine (TCM) mechanism elucidation, one is the lack of detailed biological processes information, next is the low efficient in constructing network models, we constructed an auxiliary elucidation system for the TCM mechanism and realize the automatic establishment of biological network model. This study used the Entity Grammar Systems (EGS) as the theoretical framework, integrated the data of formulae, herbs, chemical components, targets of component, biological reactions, signaling pathways and disease related proteins, established the formal models, wrote the reasoning engine, constructed the auxiliary elucidation system for the TCM mechanism elucidation. The platform provides an automatic modeling method for biological network model of TCM mechanism. It would be benefit to perform the in-depth research on TCM theory of natures and combination and provides the scientific references for R&D of TCM.

A spiking neural integrator model of the adaptive control of action by the medial prefrontal cortex.

PubMed

Bekolay, Trevor; Laubach, Mark; Eliasmith, Chris

2014-01-29

Subjects performing simple reaction-time tasks can improve reaction times by learning the expected timing of action-imperative stimuli and preparing movements in advance. Success or failure on the previous trial is often an important factor for determining whether a subject will attempt to time the stimulus or wait for it to occur before initiating action. The medial prefrontal cortex (mPFC) has been implicated in enabling the top-down control of action depending on the outcome of the previous trial. Analysis of spike activity from the rat mPFC suggests that neural integration is a key mechanism for adaptive control in precisely timed tasks. We show through simulation that a spiking neural network consisting of coupled neural integrators captures the neural dynamics of the experimentally recorded mPFC. Errors lead to deviations in the normal dynamics of the system, a process that could enable learning from past mistakes. We expand on this coupled integrator network to construct a spiking neural network that performs a reaction-time task by following either a cue-response or timing strategy, and show that it performs the task with similar reaction times as experimental subjects while maintaining the same spiking dynamics as the experimentally recorded mPFC.

Observation of oscillatory surface reactions of riboflavin, trolox, and singlet oxygen using single carbon nanotube fluorescence spectroscopy.

PubMed

Sen, Fatih; Boghossian, Ardemis A; Sen, Selda; Ulissi, Zachary W; Zhang, Jingqing; Strano, Michael S

2012-12-21

Single-molecule fluorescent microscopy allows semiconducting single-walled carbon nanotubes (SWCNTs) to detect the adsorption and desorption of single adsorbate molecules as a stochastic modulation of emission intensity. In this study, we identify and assign the signature of the complex decomposition and reaction pathways of riboflavin in the presence of the free radical scavenger Trolox using DNA-wrapped SWCNT sensors dispersed onto an aminopropyltriethoxysilane (APTES) coated surface. SWCNT emission is quenched by riboflavin-induced reactive oxygen species (ROS), but increases upon the adsorption of Trolox, which functions as a reductive brightening agent. Riboflavin has two parallel reaction pathways, a Trolox oxidizer and a photosensitizer for singlet oxygen and superoxide generation. The resulting reaction network can be detected in real time in the vicinity of a single SWCNT and can be completely described using elementary reactions and kinetic rate constants measured independently. The reaction mechanism results in an oscillatory fluorescence response from each SWCNT, allowing for the simultaneous detection of multiple reactants. A series-parallel kinetic model is shown to describe the critical points of these oscillations, with partition coefficients on the order of 10(-6)-10(-4) for the reactive oxygen and excited state species. These results highlight the potential for SWCNTs to characterize complex reaction networks at the nanometer scale.

Synthesis of Biofluidic Microsystems (SYNBIOSYS)

DTIC Science & Technology

2007-10-01

reaction system. 58 FIGURE 41. The micro reactor is represented by a PFR network model. The calculation of reaction and convection is conducted in...one column of PFRs and the calculation of diffusional mixing is conducted between two columns of PFRs. 59 FIGURE 42. Apply the numerical method of...lines to calculate the diffusion in the channel width direction. Here, we take 10 discretized concentration points in the channel: ci1 - ci10. Points

Conditional iron and pH-dependent activity of a non-enzymatic glycolysis and pentose phosphate pathway.

PubMed

Keller, Markus A; Zylstra, Andre; Castro, Cecilia; Turchyn, Alexandra V; Griffin, Julian L; Ralser, Markus

2016-01-01

Little is known about the evolutionary origins of metabolism. However, key biochemical reactions of glycolysis and the pentose phosphate pathway (PPP), ancient metabolic pathways central to the metabolic network, have non-enzymatic pendants that occur in a prebiotically plausible reaction milieu reconstituted to contain Archean sediment metal components. These non-enzymatic reactions could have given rise to the origin of glycolysis and the PPP during early evolution. Using nuclear magnetic resonance spectroscopy and high-content metabolomics that allowed us to measure several thousand reaction mixtures, we experimentally address the chemical logic of a metabolism-like network constituted from these non-enzymatic reactions. Fe(II), the dominant transition metal component of Archean oceanic sediments, has binding affinity toward metabolic sugar phosphates and drives metabolism-like reactivity acting as both catalyst and cosubstrate. Iron and pH dependencies determine a metabolism-like network topology and comediate reaction rates over several orders of magnitude so that the network adopts conditional activity. Alkaline pH triggered the activity of the non-enzymatic PPP pendant, whereas gentle acidic or neutral conditions favored non-enzymatic glycolytic reactions. Fe(II)-sensitive glycolytic and PPP-like reactions thus form a chemical network mimicking structural features of extant carbon metabolism, including topology, pH dependency, and conditional reactivity. Chemical networks that obtain structure and catalysis on the basis of transition metals found in Archean sediments are hence plausible direct precursors of cellular metabolic networks.

Conditional iron and pH-dependent activity of a non-enzymatic glycolysis and pentose phosphate pathway

PubMed Central

Keller, Markus A.; Zylstra, Andre; Castro, Cecilia; Turchyn, Alexandra V.; Griffin, Julian L.; Ralser, Markus

2016-01-01

Little is known about the evolutionary origins of metabolism. However, key biochemical reactions of glycolysis and the pentose phosphate pathway (PPP), ancient metabolic pathways central to the metabolic network, have non-enzymatic pendants that occur in a prebiotically plausible reaction milieu reconstituted to contain Archean sediment metal components. These non-enzymatic reactions could have given rise to the origin of glycolysis and the PPP during early evolution. Using nuclear magnetic resonance spectroscopy and high-content metabolomics that allowed us to measure several thousand reaction mixtures, we experimentally address the chemical logic of a metabolism-like network constituted from these non-enzymatic reactions. Fe(II), the dominant transition metal component of Archean oceanic sediments, has binding affinity toward metabolic sugar phosphates and drives metabolism-like reactivity acting as both catalyst and cosubstrate. Iron and pH dependencies determine a metabolism-like network topology and comediate reaction rates over several orders of magnitude so that the network adopts conditional activity. Alkaline pH triggered the activity of the non-enzymatic PPP pendant, whereas gentle acidic or neutral conditions favored non-enzymatic glycolytic reactions. Fe(II)-sensitive glycolytic and PPP-like reactions thus form a chemical network mimicking structural features of extant carbon metabolism, including topology, pH dependency, and conditional reactivity. Chemical networks that obtain structure and catalysis on the basis of transition metals found in Archean sediments are hence plausible direct precursors of cellular metabolic networks. PMID:26824074

Elementary Reactions and Their Role in Gas-Phase Prebiotic Chemistry

PubMed Central

Balucani, Nadia

2009-01-01

The formation of complex organic molecules in a reactor filled with gaseous mixtures possibly reproducing the primitive terrestrial atmosphere and ocean demonstrated more than 50 years ago that inorganic synthesis of prebiotic molecules is possible, provided that some form of energy is provided to the system. After that groundbreaking experiment, gas-phase prebiotic molecules have been observed in a wide variety of extraterrestrial objects (including interstellar clouds, comets and planetary atmospheres) where the physical conditions vary widely. A thorough characterization of the chemical evolution of those objects relies on a multi-disciplinary approach: 1) observations allow us to identify the molecules and their number densities as they are nowadays; 2) the chemistry which lies behind their formation starting from atoms and simple molecules is accounted for by complex reaction networks; 3) for a realistic modeling of such networks, a number of experimental parameters are needed and, therefore, the relevant molecular processes should be fully characterized in laboratory experiments. A survey of the available literature reveals, however, that much information is still lacking if it is true that only a small percentage of the elementary reactions considered in the models have been characterized in laboratory experiments. New experimental approaches to characterize the relevant elementary reactions in laboratory are presented and the implications of the results are discussed. PMID:19564951

Methane utilization in Methylomicrobium alcaliphilum 20ZR: a systems approach.

PubMed

Akberdin, Ilya R; Thompson, Merlin; Hamilton, Richard; Desai, Nalini; Alexander, Danny; Henard, Calvin A; Guarnieri, Michael T; Kalyuzhnaya, Marina G

2018-02-06

Biological methane utilization, one of the main sinks of the greenhouse gas in nature, represents an attractive platform for production of fuels and value-added chemicals. Despite the progress made in our understanding of the individual parts of methane utilization, our knowledge of how the whole-cell metabolic network is organized and coordinated is limited. Attractive growth and methane-conversion rates, a complete and expert-annotated genome sequence, as well as large enzymatic, 13 C-labeling, and transcriptomic datasets make Methylomicrobium alcaliphilum 20Z R an exceptional model system for investigating methane utilization networks. Here we present a comprehensive metabolic framework of methane and methanol utilization in M. alcaliphilum 20Z R . A set of novel metabolic reactions governing carbon distribution across central pathways in methanotrophic bacteria was predicted by in-silico simulations and confirmed by global non-targeted metabolomics and enzymatic evidences. Our data highlight the importance of substitution of ATP-linked steps with PPi-dependent reactions and support the presence of a carbon shunt from acetyl-CoA to the pentose-phosphate pathway and highly branched TCA cycle. The diverged TCA reactions promote balance between anabolic reactions and redox demands. The computational framework of C 1 -metabolism in methanotrophic bacteria can represent an efficient tool for metabolic engineering or ecosystem modeling.

Nonequilibrium thermodynamics and a fluctuation theorem for individual reaction steps in a chemical reaction network

NASA Astrophysics Data System (ADS)

Pal, Krishnendu; Das, Biswajit; Banerjee, Kinshuk; Gangopadhyay, Gautam

2015-09-01

We have introduced an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the propensities of the individual elementary reactions and the corresponding reverse reactions. The method is a microscopic formulation of the dissipation function in terms of the relative entropy or Kullback-Leibler distance which is based on the analogy of phase space trajectory with the path of elementary reactions in a network of chemical process. We have introduced here a fluctuation theorem valid for each opposite pair of elementary reactions which is useful in determining the contribution of each sub-reaction on the nonequilibrium thermodynamics of overall reaction. The methodology is applied to an oligomeric enzyme kinetics at a chemiostatic condition that leads the reaction to a nonequilibrium steady state for which we have estimated how each step of the reaction is energy driven or entropy driven to contribute to the overall reaction.

Analysis of the enzyme network involved in cattle milk production using graph theory.

PubMed

Ghorbani, Sholeh; Tahmoorespur, Mojtaba; Masoudi Nejad, Ali; Nasiri, Mohammad; Asgari, Yazdan

2015-06-01

Understanding cattle metabolism and its relationship with milk products is important in bovine breeding. A systemic view could lead to consequences that will result in a better understanding of existing concepts. Topological indices and quantitative characterizations mostly result from the application of graph theory on biological data. In the present work, the enzyme network involved in cattle milk production was reconstructed and analyzed based on available bovine genome information using several public datasets (NCBI, Uniprot, KEGG, and Brenda). The reconstructed network consisted of 3605 reactions named by KEGG compound numbers and 646 enzymes that catalyzed the corresponding reactions. The characteristics of the directed and undirected network were analyzed using Graph Theory. The mean path length was calculated to be4.39 and 5.41 for directed and undirected networks, respectively. The top 11 hub enzymes whose abnormality could harm bovine health and reduce milk production were determined. Therefore, the aim of constructing the enzyme centric network was twofold; first to find out whether such network followed the same properties of other biological networks, and second, to find the key enzymes. The results of the present study can improve our understanding of milk production in cattle. Also, analysis of the enzyme network can help improve the modeling and simulation of biological systems and help design desired phenotypes to increase milk production quality or quantity.

Autocatalytic sets and chemical organizations: modeling self-sustaining reaction networks at the origin of life

NASA Astrophysics Data System (ADS)

Hordijk, Wim; Steel, Mike; Dittrich, Peter

2018-01-01

Two related but somewhat different approaches have been proposed to formalize the notion of a self-sustaining chemical reaction network. One is the notion of collectively autocatalytic sets, formalized as RAF theory, and the other is chemical organization theory. Both formalisms have been argued to be relevant to the origin of life. RAF sets and chemical organizations are defined differently, but previously some relationships between the two have been shown. Here, we refine and explore these connections in more detail. In particular, we show that so-called closed RAFs are chemical organizations, but that the converse is not necessarily true. We then introduce and apply a procedure to show how chemical organizations can be used to find all closed RAFs within any chemical reaction system. We end with a discussion of why and how closed RAFs could be important in the context of the origin and early evolution of life.

Gain Modulation by an Urgency Signal Controls the Speed–Accuracy Trade-Off in a Network Model of a Cortical Decision Circuit

PubMed Central

Standage, Dominic; You, Hongzhi; Wang, Da-Hui; Dorris, Michael C.

2011-01-01

The speed–accuracy trade-off (SAT) is ubiquitous in decision tasks. While the neural mechanisms underlying decisions are generally well characterized, the application of decision-theoretic methods to the SAT has been difficult to reconcile with experimental data suggesting that decision thresholds are inflexible. Using a network model of a cortical decision circuit, we demonstrate the SAT in a manner consistent with neural and behavioral data and with mathematical models that optimize speed and accuracy with respect to one another. In simulations of a reaction time task, we modulate the gain of the network with a signal encoding the urgency to respond. As the urgency signal builds up, the network progresses through a series of processing stages supporting noise filtering, integration of evidence, amplification of integrated evidence, and choice selection. Analysis of the network's dynamics formally characterizes this progression. Slower buildup of urgency increases accuracy by slowing down the progression. Faster buildup has the opposite effect. Because the network always progresses through the same stages, decision-selective firing rates are stereotyped at decision time. PMID:21415911

Gain modulation by an urgency signal controls the speed-accuracy trade-off in a network model of a cortical decision circuit.

PubMed

Standage, Dominic; You, Hongzhi; Wang, Da-Hui; Dorris, Michael C

2011-01-01

The speed-accuracy trade-off (SAT) is ubiquitous in decision tasks. While the neural mechanisms underlying decisions are generally well characterized, the application of decision-theoretic methods to the SAT has been difficult to reconcile with experimental data suggesting that decision thresholds are inflexible. Using a network model of a cortical decision circuit, we demonstrate the SAT in a manner consistent with neural and behavioral data and with mathematical models that optimize speed and accuracy with respect to one another. In simulations of a reaction time task, we modulate the gain of the network with a signal encoding the urgency to respond. As the urgency signal builds up, the network progresses through a series of processing stages supporting noise filtering, integration of evidence, amplification of integrated evidence, and choice selection. Analysis of the network's dynamics formally characterizes this progression. Slower buildup of urgency increases accuracy by slowing down the progression. Faster buildup has the opposite effect. Because the network always progresses through the same stages, decision-selective firing rates are stereotyped at decision time.

Likelihood-based gene annotations for gap filling and quality assessment in genome-scale metabolic models

DOE PAGES

Benedict, Matthew N.; Mundy, Michael B.; Henry, Christopher S.; ...

2014-10-16

Genome-scale metabolic models provide a powerful means to harness information from genomes to deepen biological insights. With exponentially increasing sequencing capacity, there is an enormous need for automated reconstruction techniques that can provide more accurate models in a short time frame. Current methods for automated metabolic network reconstruction rely on gene and reaction annotations to build draft metabolic networks and algorithms to fill gaps in these networks. However, automated reconstruction is hampered by database inconsistencies, incorrect annotations, and gap filling largely without considering genomic information. Here we develop an approach for applying genomic information to predict alternative functions for genesmore » and estimate their likelihoods from sequence homology. We show that computed likelihood values were significantly higher for annotations found in manually curated metabolic networks than those that were not. We then apply these alternative functional predictions to estimate reaction likelihoods, which are used in a new gap filling approach called likelihood-based gap filling to predict more genomically consistent solutions. To validate the likelihood-based gap filling approach, we applied it to models where essential pathways were removed, finding that likelihood-based gap filling identified more biologically relevant solutions than parsimony-based gap filling approaches. We also demonstrate that models gap filled using likelihood-based gap filling provide greater coverage and genomic consistency with metabolic gene functions compared to parsimony-based approaches. Interestingly, despite these findings, we found that likelihoods did not significantly affect consistency of gap filled models with Biolog and knockout lethality data. This indicates that the phenotype data alone cannot necessarily be used to discriminate between alternative solutions for gap filling and therefore, that the use of other information is necessary to obtain a more accurate network. All described workflows are implemented as part of the DOE Systems Biology Knowledgebase (KBase) and are publicly available via API or command-line web interface.« less

Likelihood-Based Gene Annotations for Gap Filling and Quality Assessment in Genome-Scale Metabolic Models

PubMed Central

Benedict, Matthew N.; Mundy, Michael B.; Henry, Christopher S.; Chia, Nicholas; Price, Nathan D.

2014-01-01

Genome-scale metabolic models provide a powerful means to harness information from genomes to deepen biological insights. With exponentially increasing sequencing capacity, there is an enormous need for automated reconstruction techniques that can provide more accurate models in a short time frame. Current methods for automated metabolic network reconstruction rely on gene and reaction annotations to build draft metabolic networks and algorithms to fill gaps in these networks. However, automated reconstruction is hampered by database inconsistencies, incorrect annotations, and gap filling largely without considering genomic information. Here we develop an approach for applying genomic information to predict alternative functions for genes and estimate their likelihoods from sequence homology. We show that computed likelihood values were significantly higher for annotations found in manually curated metabolic networks than those that were not. We then apply these alternative functional predictions to estimate reaction likelihoods, which are used in a new gap filling approach called likelihood-based gap filling to predict more genomically consistent solutions. To validate the likelihood-based gap filling approach, we applied it to models where essential pathways were removed, finding that likelihood-based gap filling identified more biologically relevant solutions than parsimony-based gap filling approaches. We also demonstrate that models gap filled using likelihood-based gap filling provide greater coverage and genomic consistency with metabolic gene functions compared to parsimony-based approaches. Interestingly, despite these findings, we found that likelihoods did not significantly affect consistency of gap filled models with Biolog and knockout lethality data. This indicates that the phenotype data alone cannot necessarily be used to discriminate between alternative solutions for gap filling and therefore, that the use of other information is necessary to obtain a more accurate network. All described workflows are implemented as part of the DOE Systems Biology Knowledgebase (KBase) and are publicly available via API or command-line web interface. PMID:25329157

Rule-based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems

PubMed Central

Chylek, Lily A.; Harris, Leonard A.; Tung, Chang-Shung; Faeder, James R.; Lopez, Carlos F.

2013-01-01

Rule-based modeling was developed to address the limitations of traditional approaches for modeling chemical kinetics in cell signaling systems. These systems consist of multiple interacting biomolecules (e.g., proteins), which themselves consist of multiple parts (e.g., domains, linear motifs, and sites of phosphorylation). Consequently, biomolecules that mediate information processing generally have the potential to interact in multiple ways, with the number of possible complexes and post-translational modification states tending to grow exponentially with the number of binary interactions considered. As a result, only large reaction networks capture all possible consequences of the molecular interactions that occur in a cell signaling system, which is problematic because traditional modeling approaches for chemical kinetics (e.g., ordinary differential equations) require explicit network specification. This problem is circumvented through representation of interactions in terms of local rules. With this approach, network specification is implicit and model specification is concise. Concise representation results in a coarse graining of chemical kinetics, which is introduced because all reactions implied by a rule inherit the rate law associated with that rule. Coarse graining can be appropriate if interactions are modular, and the coarseness of a model can be adjusted as needed. Rules can be specified using specialized model-specification languages, and recently developed tools designed for specification of rule-based models allow one to leverage powerful software engineering capabilities. A rule-based model comprises a set of rules, which can be processed by general-purpose simulation and analysis tools to achieve different objectives (e.g., to perform either a deterministic or stochastic simulation). PMID:24123887

Computing smallest intervention strategies for multiple metabolic networks in a boolean model.

PubMed

Lu, Wei; Tamura, Takeyuki; Song, Jiangning; Akutsu, Tatsuya

2015-02-01

This article considers the problem whereby, given two metabolic networks N1 and N2, a set of source compounds, and a set of target compounds, we must find the minimum set of reactions whose removal (knockout) ensures that the target compounds are not producible in N1 but are producible in N2. Similar studies exist for the problem of finding the minimum knockout with the smallest side effect for a single network. However, if technologies of external perturbations are advanced in the near future, it may be important to develop methods of computing the minimum knockout for multiple networks (MKMN). Flux balance analysis (FBA) is efficient if a well-polished model is available. However, that is not always the case. Therefore, in this article, we study MKMN in Boolean models and an elementary mode (EM)-based model. Integer linear programming (ILP)-based methods are developed for these models, since MKMN is NP-complete for both the Boolean model and the EM-based model. Computer experiments are conducted with metabolic networks of clostridium perfringens SM101 and bifidobacterium longum DJO10A, respectively known as bad bacteria and good bacteria for the human intestine. The results show that larger networks are more likely to have MKMN solutions. However, solving for these larger networks takes a very long time, and often the computation cannot be completed. This is reasonable, because small networks do not have many alternative pathways, making it difficult to satisfy the MKMN condition, whereas in large networks the number of candidate solutions explodes. Our developed software minFvskO is available online.

The Use of Artificial Neural Network for Prediction of Dissolution Kinetics

PubMed Central

Elçiçek, H.; Akdoğan, E.; Karagöz, S.

2014-01-01

Colemanite is a preferred boron mineral in industry, such as boric acid production, fabrication of heat resistant glass, and cleaning agents. Dissolution of the mineral is one of the most important processes for these industries. In this study, dissolution of colemanite was examined in water saturated with carbon dioxide solutions. Also, prediction of dissolution rate was determined using artificial neural networks (ANNs) which are based on the multilayered perceptron. Reaction temperature, total pressure, stirring speed, solid/liquid ratio, particle size, and reaction time were selected as input parameters to predict the dissolution rate. Experimental dataset was used to train multilayer perceptron (MLP) networks to allow for prediction of dissolution kinetics. Developing ANNs has provided highly accurate predictions in comparison with an obtained mathematical model used through regression method. We conclude that ANNs may be a preferred alternative approach instead of conventional statistical methods for prediction of boron minerals. PMID:25028674

Network Analysis of Postharvest Senescence Process in Citrus Fruits Revealed by Transcriptomic and Metabolomic Profiling1[OPEN

PubMed Central

Ding, Yuduan; Chang, Jiwei; Ma, Qiaoli; Chen, Lingling; Liu, Shuzhen; Jin, Shuai; Han, Jingwen; Xu, Rangwei; Zhu, Andan; Guo, Jing; Luo, Yi; Xu, Juan; Xu, Qiang; Zeng, YunLiu; Deng, Xiuxin

2015-01-01

Citrus (Citrus spp.), a nonclimacteric fruit, is one of the most important fruit crops in global fruit industry. However, the biological behavior of citrus fruit ripening and postharvest senescence remains unclear. To better understand the senescence process of citrus fruit, we analyzed data sets from commercial microarrays, gas chromatography-mass spectrometry, and liquid chromatography-mass spectrometry and validated physiological quality detection of four main varieties in the genus Citrus. Network-based approaches of data mining and modeling were used to investigate complex molecular processes in citrus. The Citrus Metabolic Pathway Network and correlation networks were constructed to explore the modules and relationships of the functional genes/metabolites. We found that the different flesh-rind transport of nutrients and water due to the anatomic structural differences among citrus varieties might be an important factor that influences fruit senescence behavior. We then modeled and verified the citrus senescence process. As fruit rind is exposed directly to the environment, which results in energy expenditure in response to biotic and abiotic stresses, nutrients are exported from flesh to rind to maintain the activity of the whole fruit. The depletion of internal substances causes abiotic stresses, which further induces phytohormone reactions, transcription factor regulation, and a series of physiological and biochemical reactions. PMID:25802366

Gaussian graphical modeling reconstructs pathway reactions from high-throughput metabolomics data

PubMed Central

2011-01-01

Background With the advent of high-throughput targeted metabolic profiling techniques, the question of how to interpret and analyze the resulting vast amount of data becomes more and more important. In this work we address the reconstruction of metabolic reactions from cross-sectional metabolomics data, that is without the requirement for time-resolved measurements or specific system perturbations. Previous studies in this area mainly focused on Pearson correlation coefficients, which however are generally incapable of distinguishing between direct and indirect metabolic interactions. Results In our new approach we propose the application of a Gaussian graphical model (GGM), an undirected probabilistic graphical model estimating the conditional dependence between variables. GGMs are based on partial correlation coefficients, that is pairwise Pearson correlation coefficients conditioned against the correlation with all other metabolites. We first demonstrate the general validity of the method and its advantages over regular correlation networks with computer-simulated reaction systems. Then we estimate a GGM on data from a large human population cohort, covering 1020 fasting blood serum samples with 151 quantified metabolites. The GGM is much sparser than the correlation network, shows a modular structure with respect to metabolite classes, and is stable to the choice of samples in the data set. On the example of human fatty acid metabolism, we demonstrate for the first time that high partial correlation coefficients generally correspond to known metabolic reactions. This feature is evaluated both manually by investigating specific pairs of high-scoring metabolites, and then systematically on a literature-curated model of fatty acid synthesis and degradation. Our method detects many known reactions along with possibly novel pathway interactions, representing candidates for further experimental examination. Conclusions In summary, we demonstrate strong signatures of intracellular pathways in blood serum data, and provide a valuable tool for the unbiased reconstruction of metabolic reactions from large-scale metabolomics data sets. PMID:21281499

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks

PubMed Central

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-01-01

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org. PMID:26063822

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks.

PubMed

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-07-06

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org.

Mechanisms of stochastic focusing and defocusing in biological reaction networks: insight from accurate chemical master equation (ACME) solutions.

PubMed

Gursoy, Gamze; Terebus, Anna; Youfang Cao; Jie Liang

2016-08-01

Stochasticity plays important roles in regulation of biochemical reaction networks when the copy numbers of molecular species are small. Studies based on Stochastic Simulation Algorithm (SSA) has shown that a basic reaction system can display stochastic focusing (SF) by increasing the sensitivity of the network as a result of the signal noise. Although SSA has been widely used to study stochastic networks, it is ineffective in examining rare events and this becomes a significant issue when the tails of probability distributions are relevant as is the case of SF. Here we use the ACME method to solve the exact solution of the discrete Chemical Master Equations and to study a network where SF was reported. We showed that the level of SF depends on the degree of the fluctuations of signal molecule. We discovered that signaling noise under certain conditions in the same reaction network can lead to a decrease in the system sensitivities, thus the network can experience stochastic defocusing. These results highlight the fundamental role of stochasticity in biological reaction networks and the need for exact computation of probability landscape of the molecules in the system.

The Genealogical Tree of Ethanol: Gas-phase Formation of Glycolaldehyde, Acetic Acid, and Formic Acid

NASA Astrophysics Data System (ADS)

Skouteris, Dimitrios; Balucani, Nadia; Ceccarelli, Cecilia; Vazart, Fanny; Puzzarini, Cristina; Barone, Vincenzo; Codella, Claudio; Lefloch, Bertrand

2018-02-01

Despite the harsh conditions of the interstellar medium, chemistry thrives in it, especially in star-forming regions where several interstellar complex organic molecules (iCOMs) have been detected. Yet, how these species are synthesized is a mystery. The majority of current models claim that this happens on interstellar grain surfaces. Nevertheless, evidence is mounting that neutral gas-phase chemistry plays an important role. In this paper, we propose a new scheme for the gas-phase synthesis of glycolaldehyde, a species with a prebiotic potential and for which no gas-phase formation route was previously known. In the proposed scheme, the ancestor is ethanol and the glycolaldehyde sister species are acetic acid (another iCOM with unknown gas-phase formation routes) and formic acid. For the reactions of the new scheme with no available data, we have performed electronic structure and kinetics calculations deriving rate coefficients and branching ratios. Furthermore, after a careful review of the chemistry literature, we revised the available chemical networks, adding and correcting several reactions related to glycolaldehyde, acetic acid, and formic acid. The new chemical network has been used in an astrochemical model to predict the abundance of glycolaldehyde, acetic acid, and formic acid. The predicted abundance of glycolaldehyde depends on the ethanol abundance in the gas phase and is in excellent agreement with the measured one in hot corinos and shock sites. Our new model overpredicts the abundance of acetic acid and formic acid by about a factor of 10, which might imply a yet incomplete reaction network.

Calculating degree-based topological indices of dominating David derived networks

NASA Astrophysics Data System (ADS)

Ahmad, Muhammad Saeed; Nazeer, Waqas; Kang, Shin Min; Imran, Muhammad; Gao, Wei

2017-12-01

An important area of applied mathematics is the Chemical reaction network theory. The behavior of real world problems can be modeled by using this theory. Due to applications in theoretical chemistry and biochemistry, it has attracted researchers since its foundation. It also attracts pure mathematicians because it involves interesting mathematical structures. In this report, we compute newly defined topological indices, namely, Arithmetic-Geometric index (AG1 index), SK index, SK1 index, and SK2 index of the dominating David derived networks [1, 2, 3, 4, 5].

Reply to 'Comment on kinetic modeling of microbially-driven redox chemistry of subsurface environments: coupling transport, microbial metabolism and geochemistry' by J. Griffioen

NASA Astrophysics Data System (ADS)

Hunter, K. S.; Van Cappellen, P.

2000-01-01

Our paper, 'Kinetic modeling of microbially-driven redox chemistry of subsurface environments: coupling transport, microbial metabolism and geochemistry' (Hunter et al., 1998), presents a theoretical exploration of biogeochemical reaction networks and their importance to the biogeochemistry of groundwater systems. As with any other model, the kinetic reaction-transport model developed in our paper includes only a subset of all physically, biologically and chemically relevant processes in subsurface environments. It considers aquifer systems where the primary energy source driving microbial activity is the degradation of organic matter. In addition to the primary biodegradation pathways of organic matter (i.e. respiration and fermentation), the redox chemistry of groundwaters is also affected by reactions not directly involving organic matter oxidation. We refer to the latter as secondary reactions. By including secondary redox reactions which consume reduced reaction products (e.g., Mn2+, FeS, H2S), and in the process compete with microbial heterotrophic populations for available oxidants (i.e. O2, NO3-, Mn(IV), Fe(III), SO42-), we predict spatio-temporal distributions of microbial activity which differ significantly from those of models which consider only the biodegradation reactions. That is, the secondary reactions have a significant impact on the distributions of the rates of heterotrophic and chemolithotrophic metabolic pathways. We further show that secondary redox reactions, as well as non-redox reactions, significantly influence the acid-base chemistry of groundwaters. The distributions of dissolved inorganic redox species along flowpaths, however, are similar in simulations with and without secondary reactions (see Figs. 3(b) and 7(b) in Hunter et al., 1998), indicating that very different biogeochemical reaction dynamics may lead to essentially the same chemical redox zonation of a groundwater system.

Revising the Representation of Fatty Acid, Glycerolipid, and Glycerophospholipid Metabolism in the Consensus Model of Yeast Metabolism

PubMed Central

Aung, Hnin W.; Henry, Susan A.

2013-01-01

Abstract Genome-scale metabolic models are built using information from an organism's annotated genome and, correspondingly, information on reactions catalyzed by the set of metabolic enzymes encoded by the genome. These models have been successfully applied to guide metabolic engineering to increase production of metabolites of industrial interest. Congruity between simulated and experimental metabolic behavior is influenced by the accuracy of the representation of the metabolic network in the model. In the interest of applying the consensus model of Saccharomyces cerevisiae metabolism for increased productivity of triglycerides, we manually evaluated the representation of fatty acid, glycerophospholipid, and glycerolipid metabolism in the consensus model (Yeast v6.0). These areas of metabolism were chosen due to their tightly interconnected nature to triglyceride synthesis. Manual curation was facilitated by custom MATLAB functions that return information contained in the model for reactions associated with genes and metabolites within the stated areas of metabolism. Through manual curation, we have identified inconsistencies between information contained in the model and literature knowledge. These inconsistencies include incorrect gene-reaction associations, improper definition of substrates/products in reactions, inappropriate assignments of reaction directionality, nonfunctional β-oxidation pathways, and missing reactions relevant to the synthesis and degradation of triglycerides. Suggestions to amend these inconsistencies in the Yeast v6.0 model can be implemented through a MATLAB script provided in the Supplementary Materials, Supplementary Data S1 (Supplementary Data are available online at www.liebertpub.com/ind). PMID:24678285

Simulated maximum likelihood method for estimating kinetic rates in gene expression.

PubMed

Tian, Tianhai; Xu, Songlin; Gao, Junbin; Burrage, Kevin

2007-01-01

Kinetic rate in gene expression is a key measurement of the stability of gene products and gives important information for the reconstruction of genetic regulatory networks. Recent developments in experimental technologies have made it possible to measure the numbers of transcripts and protein molecules in single cells. Although estimation methods based on deterministic models have been proposed aimed at evaluating kinetic rates from experimental observations, these methods cannot tackle noise in gene expression that may arise from discrete processes of gene expression, small numbers of mRNA transcript, fluctuations in the activity of transcriptional factors and variability in the experimental environment. In this paper, we develop effective methods for estimating kinetic rates in genetic regulatory networks. The simulated maximum likelihood method is used to evaluate parameters in stochastic models described by either stochastic differential equations or discrete biochemical reactions. Different types of non-parametric density functions are used to measure the transitional probability of experimental observations. For stochastic models described by biochemical reactions, we propose to use the simulated frequency distribution to evaluate the transitional density based on the discrete nature of stochastic simulations. The genetic optimization algorithm is used as an efficient tool to search for optimal reaction rates. Numerical results indicate that the proposed methods can give robust estimations of kinetic rates with good accuracy.

Cellular metabolic network analysis: discovering important reactions in Treponema pallidum.

PubMed

Chen, Xueying; Zhao, Min; Qu, Hong

2015-01-01

T. pallidum, the syphilis-causing pathogen, performs very differently in metabolism compared with other bacterial pathogens. The desire for safe and effective vaccine of syphilis requests identification of important steps in T. pallidum's metabolism. Here, we apply Flux Balance Analysis to represent the reactions quantitatively. Thus, it is possible to cluster all reactions in T. pallidum. By calculating minimal cut sets and analyzing topological structure for the metabolic network of T. pallidum, critical reactions are identified. As a comparison, we also apply the analytical approaches to the metabolic network of H. pylori to find coregulated drug targets and unique drug targets for different microorganisms. Based on the clustering results, all reactions are further classified into various roles. Therefore, the general picture of their metabolic network is obtained and two types of reactions, both of which are involved in nucleic acid metabolism, are found to be essential for T. pallidum. It is also discovered that both hubs of reactions and the isolated reactions in purine and pyrimidine metabolisms play important roles in T. pallidum. These reactions could be potential drug targets for treating syphilis.

Environmental versatility promotes modularity in genome-scale metabolic networks.

PubMed

Samal, Areejit; Wagner, Andreas; Martin, Olivier C

2011-08-24

The ubiquity of modules in biological networks may result from an evolutionary benefit of a modular organization. For instance, modularity may increase the rate of adaptive evolution, because modules can be easily combined into new arrangements that may benefit their carrier. Conversely, modularity may emerge as a by-product of some trait. We here ask whether this last scenario may play a role in genome-scale metabolic networks that need to sustain life in one or more chemical environments. For such networks, we define a network module as a maximal set of reactions that are fully coupled, i.e., whose fluxes can only vary in fixed proportions. This definition overcomes limitations of purely graph based analyses of metabolism by exploiting the functional links between reactions. We call a metabolic network viable in a given chemical environment if it can synthesize all of an organism's biomass compounds from nutrients in this environment. An organism's metabolism is highly versatile if it can sustain life in many different chemical environments. We here ask whether versatility affects the modularity of metabolic networks. Using recently developed techniques to randomly sample large numbers of viable metabolic networks from a vast space of metabolic networks, we use flux balance analysis to study in silico metabolic networks that differ in their versatility. We find that highly versatile networks are also highly modular. They contain more modules and more reactions that are organized into modules. Most or all reactions in a module are associated with the same biochemical pathways. Modules that arise in highly versatile networks generally involve reactions that process nutrients or closely related chemicals. We also observe that the metabolism of E. coli is significantly more modular than even our most versatile networks. Our work shows that modularity in metabolic networks can be a by-product of functional constraints, e.g., the need to sustain life in multiple environments. This organizational principle is insensitive to the environments we consider and to the number of reactions in a metabolic network. Because we observe this principle not just in one or few biological networks, but in large random samples of networks, we propose that it may be a generic principle of metabolic network organization.

Dynamical System Approach for Edge Detection Using Coupled FitzHugh-Nagumo Neurons.

PubMed

Li, Shaobai; Dasmahapatra, Srinandan; Maharatna, Koushik

2015-12-01

The prospect of emulating the impressive computational capabilities of biological systems has led to considerable interest in the design of analog circuits that are potentially implementable in very large scale integration CMOS technology and are guided by biologically motivated models. For example, simple image processing tasks, such as the detection of edges in binary and grayscale images, have been performed by networks of FitzHugh-Nagumo-type neurons using the reaction-diffusion models. However, in these studies, the one-to-one mapping of image pixels to component neurons makes the size of the network a critical factor in any such implementation. In this paper, we develop a simplified version of the employed reaction-diffusion model in three steps. In the first step, we perform a detailed study to locate this threshold using continuous Lyapunov exponents from dynamical system theory. Furthermore, we render the diffusion in the system to be anisotropic, with the degree of anisotropy being set by the gradients of grayscale values in each image. The final step involves a simplification of the model that is achieved by eliminating the terms that couple the membrane potentials of adjacent neurons. We apply our technique to detect edges in data sets of artificially generated and real images, and we demonstrate that the performance is as good if not better than that of the previous methods without increasing the size of the network.

Using chemical organization theory for model checking

PubMed Central

Kaleta, Christoph; Richter, Stephan; Dittrich, Peter

2009-01-01

Motivation: The increasing number and complexity of biomodels makes automatic procedures for checking the models' properties and quality necessary. Approaches like elementary mode analysis, flux balance analysis, deficiency analysis and chemical organization theory (OT) require only the stoichiometric structure of the reaction network for derivation of valuable information. In formalisms like Systems Biology Markup Language (SBML), however, information about the stoichiometric coefficients required for an analysis of chemical organizations can be hidden in kinetic laws. Results: First, we introduce an algorithm that uncovers stoichiometric information that might be hidden in the kinetic laws of a reaction network. This allows us to apply OT to SBML models using modifiers. Second, using the new algorithm, we performed a large-scale analysis of the 185 models contained in the manually curated BioModels Database. We found that for 41 models (22%) the set of organizations changes when modifiers are considered correctly. We discuss one of these models in detail (BIOMD149, a combined model of the ERK- and Wnt-signaling pathways), whose set of organizations drastically changes when modifiers are considered. Third, we found inconsistencies in 5 models (3%) and identified their characteristics. Compared with flux-based methods, OT is able to identify those species and reactions more accurately [in 26 cases (14%)] that can be present in a long-term simulation of the model. We conclude that our approach is a valuable tool that helps to improve the consistency of biomodels and their repositories. Availability: All data and a JAVA applet to check SBML-models is available from http://www.minet.uni-jena.de/csb/prj/ot/tools Contact: dittrich@minet.uni-jena.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:19468053

Synchronization of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions and Infinite Delays.

PubMed

Sheng, Yin; Zhang, Hao; Zeng, Zhigang

2017-10-01

This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.

Learning Universal Computations with Spikes

PubMed Central

Thalmeier, Dominik; Uhlmann, Marvin; Kappen, Hilbert J.; Memmesheimer, Raoul-Martin

2016-01-01

Providing the neurobiological basis of information processing in higher animals, spiking neural networks must be able to learn a variety of complicated computations, including the generation of appropriate, possibly delayed reactions to inputs and the self-sustained generation of complex activity patterns, e.g. for locomotion. Many such computations require previous building of intrinsic world models. Here we show how spiking neural networks may solve these different tasks. Firstly, we derive constraints under which classes of spiking neural networks lend themselves to substrates of powerful general purpose computing. The networks contain dendritic or synaptic nonlinearities and have a constrained connectivity. We then combine such networks with learning rules for outputs or recurrent connections. We show that this allows to learn even difficult benchmark tasks such as the self-sustained generation of desired low-dimensional chaotic dynamics or memory-dependent computations. Furthermore, we show how spiking networks can build models of external world systems and use the acquired knowledge to control them. PMID:27309381

Environmental and Molecular Science Laboratory Arrow

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

2016-06-24

Arrows is a software package that combines NWChem, SQL and NOSQL databases, email, and social networks (e.g. Twitter, Tumblr) that simplifies molecular and materials modeling and makes these modeling capabilities accessible to all scientists and engineers. EMSL Arrows is very simple to use. The user just emails chemical reactions to arrows@emsl.pnnl.gov and then an email is sent back with thermodynamic, reaction pathway (kinetic), spectroscopy, and other results. EMSL Arrows parses the email and then searches the database for the compounds in the reactions. If a compound isn't there, an NWChem calculation is setup and submitted to calculate it. Once themore » calculation is finished the results are entered into the database and then results are emailed back.« less

Prediction of enzyme activity with neural network models based on electronic and geometrical features of substrates.

PubMed

Szaleniec, Maciej

2012-01-01

Artificial Neural Networks (ANNs) are introduced as robust and versatile tools in quantitative structure-activity relationship (QSAR) modeling. Their application to the modeling of enzyme reactivity is discussed, along with methodological issues. Methods of input variable selection, optimization of network internal structure, data set division and model validation are discussed. The application of ANNs in the modeling of enzyme activity over the last 20 years is briefly recounted. The discussed methodology is exemplified by the case of ethylbenzene dehydrogenase (EBDH). Intelligent Problem Solver and genetic algorithms are applied for input vector selection, whereas k-means clustering is used to partition the data into training and test cases. The obtained models exhibit high correlation between the predicted and experimental values (R(2) > 0.9). Sensitivity analyses and study of the response curves are used as tools for the physicochemical interpretation of the models in terms of the EBDH reaction mechanism. Neural networks are shown to be a versatile tool for the construction of robust QSAR models that can be applied to a range of aspects important in drug design and the prediction of biological activity.

A metabolite-centric view on flux distributions in genome-scale metabolic models

PubMed Central

2013-01-01

Background Genome-scale metabolic models are important tools in systems biology. They permit the in-silico prediction of cellular phenotypes via mathematical optimisation procedures, most importantly flux balance analysis. Current studies on metabolic models mostly consider reaction fluxes in isolation. Based on a recently proposed metabolite-centric approach, we here describe a set of methods that enable the analysis and interpretation of flux distributions in an integrated metabolite-centric view. We demonstrate how this framework can be used for the refinement of genome-scale metabolic models. Results We applied the metabolite-centric view developed here to the most recent metabolic reconstruction of Escherichia coli. By compiling the balance sheets of a small number of currency metabolites, we were able to fully characterise the energy metabolism as predicted by the model and to identify a possibility for model refinement in NADPH metabolism. Selected branch points were examined in detail in order to demonstrate how a metabolite-centric view allows identifying functional roles of metabolites. Fructose 6-phosphate aldolase and the sedoheptulose bisphosphate bypass were identified as enzymatic reactions that can carry high fluxes in the model but are unlikely to exhibit significant activity in vivo. Performing a metabolite essentiality analysis, unconstrained import and export of iron ions could be identified as potentially problematic for the quality of model predictions. Conclusions The system-wide analysis of split ratios and branch points allows a much deeper insight into the metabolic network than reaction-centric analyses. Extending an earlier metabolite-centric approach, the methods introduced here establish an integrated metabolite-centric framework for the interpretation of flux distributions in genome-scale metabolic networks that can complement the classical reaction-centric framework. Analysing fluxes and their metabolic context simultaneously opens the door to systems biological interpretations that are not apparent from isolated reaction fluxes. Particularly powerful demonstrations of this are the analyses of the complete metabolic contexts of energy metabolism and the folate-dependent one-carbon pool presented in this work. Finally, a metabolite-centric view on flux distributions can guide the refinement of metabolic reconstructions for specific growth scenarios. PMID:23587327

A study on ?-dissipative synchronisation of coupled reaction-diffusion neural networks with time-varying delays

NASA Astrophysics Data System (ADS)

Ali, M. Syed; Zhu, Quanxin; Pavithra, S.; Gunasekaran, N.

2018-03-01

This study examines the problem of dissipative synchronisation of coupled reaction-diffusion neural networks with time-varying delays. This paper proposes a complex dynamical network consisting of N linearly and diffusively coupled identical reaction-diffusion neural networks. By constructing a suitable Lyapunov-Krasovskii functional (LKF), utilisation of Jensen's inequality and reciprocally convex combination (RCC) approach, strictly ?-dissipative conditions of the addressed systems are derived. Finally, a numerical example is given to show the effectiveness of the theoretical results.

Neural Networks for Rapid Design and Analysis

NASA Technical Reports Server (NTRS)

Sparks, Dean W., Jr.; Maghami, Peiman G.

1998-01-01

Artificial neural networks have been employed for rapid and efficient dynamics and control analysis of flexible systems. Specifically, feedforward neural networks are designed to approximate nonlinear dynamic components over prescribed input ranges, and are used in simulations as a means to speed up the overall time response analysis process. To capture the recursive nature of dynamic components with artificial neural networks, recurrent networks, which use state feedback with the appropriate number of time delays, as inputs to the networks, are employed. Once properly trained, neural networks can give very good approximations to nonlinear dynamic components, and by their judicious use in simulations, allow the analyst the potential to speed up the analysis process considerably. To illustrate this potential speed up, an existing simulation model of a spacecraft reaction wheel system is executed, first conventionally, and then with an artificial neural network in place.

Multilayer Network Analysis of Nuclear Reactions

NASA Astrophysics Data System (ADS)

Zhu, Liang; Ma, Yu-Gang; Chen, Qu; Han, Ding-Ding

2016-08-01

The nuclear reaction network is usually studied via precise calculation of differential equation sets, and much research interest has been focused on the characteristics of nuclides, such as half-life and size limit. In this paper, however, we adopt the methods from both multilayer and reaction networks, and obtain a distinctive view by mapping all the nuclear reactions in JINA REACLIB database into a directed network with 4 layers: neutron, proton, 4He and the remainder. The layer names correspond to reaction types decided by the currency particles consumed. This combined approach reveals that, in the remainder layer, the β-stability has high correlation with node degree difference and overlapping coefficient. Moreover, when reaction rates are considered as node strength, we find that, at lower temperatures, nuclide half-life scales reciprocally with its out-strength. The connection between physical properties and topological characteristics may help to explore the boundary of the nuclide chart.

In Silico Knockout Screening of Plasmodium falciparum Reactions and Prediction of Novel Essential Reactions by Analysing the Metabolic Network

PubMed Central

Isewon, Itunuoluwa; Aromolaran, Olufemi; Oladipupo, Olufunke

2018-01-01

Malaria is an infectious disease that affects close to half a million individuals every year and Plasmodium falciparum is a major cause of malaria. The treatment of this disease could be done effectively if the essential enzymes of this parasite are specifically targeted. Nevertheless, the development of the parasite in resisting existing drugs now makes discovering new drugs a core responsibility. In this study, a novel computational model that makes the prediction of new and validated antimalarial drug target cheaper, easier, and faster has been developed. We have identified new essential reactions as potential targets for drugs in the metabolic network of the parasite. Among the top seven (7) predicted essential reactions, four (4) have been previously identified in earlier studies with biological evidence and one (1) has been with computational evidence. The results from our study were compared with an extensive list of seventy-seven (77) essential reactions with biological evidence from a previous study. We present a list of thirty-one (31) potential candidates for drug targets in Plasmodium falciparum which includes twenty-four (24) new potential candidates for drug targets. PMID:29789805

Simulating Metabolism with Statistical Thermodynamics

PubMed Central

Cannon, William R.

2014-01-01

New methods are needed for large scale modeling of metabolism that predict metabolite levels and characterize the thermodynamics of individual reactions and pathways. Current approaches use either kinetic simulations, which are difficult to extend to large networks of reactions because of the need for rate constants, or flux-based methods, which have a large number of feasible solutions because they are unconstrained by the law of mass action. This report presents an alternative modeling approach based on statistical thermodynamics. The principles of this approach are demonstrated using a simple set of coupled reactions, and then the system is characterized with respect to the changes in energy, entropy, free energy, and entropy production. Finally, the physical and biochemical insights that this approach can provide for metabolism are demonstrated by application to the tricarboxylic acid (TCA) cycle of Escherichia coli. The reaction and pathway thermodynamics are evaluated and predictions are made regarding changes in concentration of TCA cycle intermediates due to 10- and 100-fold changes in the ratio of NAD+:NADH concentrations. Finally, the assumptions and caveats regarding the use of statistical thermodynamics to model non-equilibrium reactions are discussed. PMID:25089525

Simulating metabolism with statistical thermodynamics.

PubMed

Cannon, William R

2014-01-01

New methods are needed for large scale modeling of metabolism that predict metabolite levels and characterize the thermodynamics of individual reactions and pathways. Current approaches use either kinetic simulations, which are difficult to extend to large networks of reactions because of the need for rate constants, or flux-based methods, which have a large number of feasible solutions because they are unconstrained by the law of mass action. This report presents an alternative modeling approach based on statistical thermodynamics. The principles of this approach are demonstrated using a simple set of coupled reactions, and then the system is characterized with respect to the changes in energy, entropy, free energy, and entropy production. Finally, the physical and biochemical insights that this approach can provide for metabolism are demonstrated by application to the tricarboxylic acid (TCA) cycle of Escherichia coli. The reaction and pathway thermodynamics are evaluated and predictions are made regarding changes in concentration of TCA cycle intermediates due to 10- and 100-fold changes in the ratio of NAD+:NADH concentrations. Finally, the assumptions and caveats regarding the use of statistical thermodynamics to model non-equilibrium reactions are discussed.

Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning.

PubMed

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

2017-12-21

The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian dynamics or Green's function reaction dynamics, the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution. This renders mesoscopic simulation inefficient for systems with multiscale properties. Mesoscopic-microscopic hybrid methods address this problem by resolving the most challenging reactions with a microscale, off-lattice simulation. However, all methods to date require manual partitioning of a system, effectively limiting their usefulness as "black-box" simulation codes. In this paper, we propose a hybrid simulation algorithm with automatic system partitioning based on indirect a priori error estimates. We demonstrate the accuracy and efficiency of the method on models of diffusion-controlled networks in 3D.

Concordant Chemical Reaction Networks and the Species-Reaction Graph

PubMed Central

Shinar, Guy; Feinberg, Martin

2015-01-01

In a recent paper it was shown that, for chemical reaction networks possessing a subtle structural property called concordance, dynamical behavior of a very circumscribed (and largely stable) kind is enforced, so long as the kinetics lies within the very broad and natural weakly monotonic class. In particular, multiple equilibria are precluded, as are degenerate positive equilibria. Moreover, under certain circumstances, also related to concordance, all real eigenvalues associated with a positive equilibrium are negative. Although concordance of a reaction network can be decided by readily available computational means, we show here that, when a nondegenerate network’s Species-Reaction Graph satisfies certain mild conditions, concordance and its dynamical consequences are ensured. These conditions are weaker than earlier ones invoked to establish kinetic system injectivity, which, in turn, is just one ramification of network concordance. Because the Species-Reaction Graph resembles pathway depictions often drawn by biochemists, results here expand the possibility of inferring significant dynamical information directly from standard biochemical reaction diagrams. PMID:22940368

Framework for network modularization and Bayesian network analysis to investigate the perturbed metabolic network

PubMed Central

2011-01-01

Background Genome-scale metabolic network models have contributed to elucidating biological phenomena, and predicting gene targets to engineer for biotechnological applications. With their increasing importance, their precise network characterization has also been crucial for better understanding of the cellular physiology. Results We herein introduce a framework for network modularization and Bayesian network analysis (FMB) to investigate organism’s metabolism under perturbation. FMB reveals direction of influences among metabolic modules, in which reactions with similar or positively correlated flux variation patterns are clustered, in response to specific perturbation using metabolic flux data. With metabolic flux data calculated by constraints-based flux analysis under both control and perturbation conditions, FMB, in essence, reveals the effects of specific perturbations on the biological system through network modularization and Bayesian network analysis at metabolic modular level. As a demonstration, this framework was applied to the genetically perturbed Escherichia coli metabolism, which is a lpdA gene knockout mutant, using its genome-scale metabolic network model. Conclusions After all, it provides alternative scenarios of metabolic flux distributions in response to the perturbation, which are complementary to the data obtained from conventionally available genome-wide high-throughput techniques or metabolic flux analysis. PMID:22784571

Framework for network modularization and Bayesian network analysis to investigate the perturbed metabolic network.

PubMed

Kim, Hyun Uk; Kim, Tae Yong; Lee, Sang Yup

2011-01-01

Genome-scale metabolic network models have contributed to elucidating biological phenomena, and predicting gene targets to engineer for biotechnological applications. With their increasing importance, their precise network characterization has also been crucial for better understanding of the cellular physiology. We herein introduce a framework for network modularization and Bayesian network analysis (FMB) to investigate organism's metabolism under perturbation. FMB reveals direction of influences among metabolic modules, in which reactions with similar or positively correlated flux variation patterns are clustered, in response to specific perturbation using metabolic flux data. With metabolic flux data calculated by constraints-based flux analysis under both control and perturbation conditions, FMB, in essence, reveals the effects of specific perturbations on the biological system through network modularization and Bayesian network analysis at metabolic modular level. As a demonstration, this framework was applied to the genetically perturbed Escherichia coli metabolism, which is a lpdA gene knockout mutant, using its genome-scale metabolic network model. After all, it provides alternative scenarios of metabolic flux distributions in response to the perturbation, which are complementary to the data obtained from conventionally available genome-wide high-throughput techniques or metabolic flux analysis.

DMPy: a Python package for automated mathematical model construction of large-scale metabolic systems.

PubMed

Smith, Robert W; van Rosmalen, Rik P; Martins Dos Santos, Vitor A P; Fleck, Christian

2018-06-19

Models of metabolism are often used in biotechnology and pharmaceutical research to identify drug targets or increase the direct production of valuable compounds. Due to the complexity of large metabolic systems, a number of conclusions have been drawn using mathematical methods with simplifying assumptions. For example, constraint-based models describe changes of internal concentrations that occur much quicker than alterations in cell physiology. Thus, metabolite concentrations and reaction fluxes are fixed to constant values. This greatly reduces the mathematical complexity, while providing a reasonably good description of the system in steady state. However, without a large number of constraints, many different flux sets can describe the optimal model and we obtain no information on how metabolite levels dynamically change. Thus, to accurately determine what is taking place within the cell, finer quality data and more detailed models need to be constructed. In this paper we present a computational framework, DMPy, that uses a network scheme as input to automatically search for kinetic rates and produce a mathematical model that describes temporal changes of metabolite fluxes. The parameter search utilises several online databases to find measured reaction parameters. From this, we take advantage of previous modelling efforts, such as Parameter Balancing, to produce an initial mathematical model of a metabolic pathway. We analyse the effect of parameter uncertainty on model dynamics and test how recent flux-based model reduction techniques alter system properties. To our knowledge this is the first time such analysis has been performed on large models of metabolism. Our results highlight that good estimates of at least 80% of the reaction rates are required to accurately model metabolic systems. Furthermore, reducing the size of the model by grouping reactions together based on fluxes alters the resulting system dynamics. The presented pipeline automates the modelling process for large metabolic networks. From this, users can simulate their pathway of interest and obtain a better understanding of how altering conditions influences cellular dynamics. By testing the effects of different parameterisations we are also able to provide suggestions to help construct more accurate models of complete metabolic systems in the future.

Multi-equilibrium property of metabolic networks: SSI module.

PubMed

Lei, Hong-Bo; Zhang, Ji-Feng; Chen, Luonan

2011-06-20

Revealing the multi-equilibrium property of a metabolic network is a fundamental and important topic in systems biology. Due to the complexity of the metabolic network, it is generally a difficult task to study the problem as a whole from both analytical and numerical viewpoint. On the other hand, the structure-oriented modularization idea is a good choice to overcome such a difficulty, i.e. decomposing the network into several basic building blocks and then studying the whole network through investigating the dynamical characteristics of the basic building blocks and their interactions. Single substrate and single product with inhibition (SSI) metabolic module is one type of the basic building blocks of metabolic networks, and its multi-equilibrium property has important influence on that of the whole metabolic networks. In this paper, we describe what the SSI metabolic module is, characterize the rates of the metabolic reactions by Hill kinetics and give a unified model for SSI modules by using a set of nonlinear ordinary differential equations with multi-variables. Specifically, a sufficient and necessary condition is first given to describe the injectivity of a class of nonlinear systems, and then, the sufficient condition is used to study the multi-equilibrium property of SSI modules. As a main theoretical result, for the SSI modules in which each reaction has no more than one inhibitor, a sufficient condition is derived to rule out multiple equilibria, i.e. the Jacobian matrix of its rate function is nonsingular everywhere. In summary, we describe SSI modules and give a general modeling framework based on Hill kinetics, and provide a sufficient condition for ruling out multiple equilibria of a key type of SSI module.

Multi-equilibrium property of metabolic networks: SSI module

PubMed Central

2011-01-01

Background Revealing the multi-equilibrium property of a metabolic network is a fundamental and important topic in systems biology. Due to the complexity of the metabolic network, it is generally a difficult task to study the problem as a whole from both analytical and numerical viewpoint. On the other hand, the structure-oriented modularization idea is a good choice to overcome such a difficulty, i.e. decomposing the network into several basic building blocks and then studying the whole network through investigating the dynamical characteristics of the basic building blocks and their interactions. Single substrate and single product with inhibition (SSI) metabolic module is one type of the basic building blocks of metabolic networks, and its multi-equilibrium property has important influence on that of the whole metabolic networks. Results In this paper, we describe what the SSI metabolic module is, characterize the rates of the metabolic reactions by Hill kinetics and give a unified model for SSI modules by using a set of nonlinear ordinary differential equations with multi-variables. Specifically, a sufficient and necessary condition is first given to describe the injectivity of a class of nonlinear systems, and then, the sufficient condition is used to study the multi-equilibrium property of SSI modules. As a main theoretical result, for the SSI modules in which each reaction has no more than one inhibitor, a sufficient condition is derived to rule out multiple equilibria, i.e. the Jacobian matrix of its rate function is nonsingular everywhere. Conclusions In summary, we describe SSI modules and give a general modeling framework based on Hill kinetics, and provide a sufficient condition for ruling out multiple equilibria of a key type of SSI module. PMID:21689474

A Compartmentalized Out-of-Equilibrium Enzymatic Reaction Network for Sustained Autonomous Movement

PubMed Central

2016-01-01

Every living cell is a compartmentalized out-of-equilibrium system exquisitely able to convert chemical energy into function. In order to maintain homeostasis, the flux of metabolites is tightly controlled by regulatory enzymatic networks. A crucial prerequisite for the development of lifelike materials is the construction of synthetic systems with compartmentalized reaction networks that maintain out-of-equilibrium function. Here, we aim for autonomous movement as an example of the conversion of feedstock molecules into function. The flux of the conversion is regulated by a rationally designed enzymatic reaction network with multiple feedforward loops. By compartmentalizing the network into bowl-shaped nanocapsules the output of the network is harvested as kinetic energy. The entire system shows sustained and tunable microscopic motion resulting from the conversion of multiple external substrates. The successful compartmentalization of an out-of-equilibrium reaction network is a major first step in harnessing the design principles of life for construction of adaptive and internally regulated lifelike systems. PMID:27924313

Rule-based simulation models

NASA Technical Reports Server (NTRS)

Nieten, Joseph L.; Seraphine, Kathleen M.

1991-01-01

Procedural modeling systems, rule based modeling systems, and a method for converting a procedural model to a rule based model are described. Simulation models are used to represent real time engineering systems. A real time system can be represented by a set of equations or functions connected so that they perform in the same manner as the actual system. Most modeling system languages are based on FORTRAN or some other procedural language. Therefore, they must be enhanced with a reaction capability. Rule based systems are reactive by definition. Once the engineering system has been decomposed into a set of calculations using only basic algebraic unary operations, a knowledge network of calculations and functions can be constructed. The knowledge network required by a rule based system can be generated by a knowledge acquisition tool or a source level compiler. The compiler would take an existing model source file, a syntax template, and a symbol table and generate the knowledge network. Thus, existing procedural models can be translated and executed by a rule based system. Neural models can be provide the high capacity data manipulation required by the most complex real time models.

Modular rate laws for enzymatic reactions: thermodynamics, elasticities and implementation.

PubMed

Liebermeister, Wolfram; Uhlendorf, Jannis; Klipp, Edda

2010-06-15

Standard rate laws are a key requisite for systematically turning metabolic networks into kinetic models. They should provide simple, general and biochemically plausible formulae for reaction velocities and reaction elasticities. At the same time, they need to respect thermodynamic relations between the kinetic constants and the metabolic fluxes and concentrations. We present a family of reversible rate laws for reactions with arbitrary stoichiometries and various types of regulation, including mass-action, Michaelis-Menten and uni-uni reversible Hill kinetics as special cases. With a thermodynamically safe parameterization of these rate laws, parameter sets obtained by model fitting, sampling or optimization are guaranteed to lead to consistent chemical equilibrium states. A reformulation using saturation values yields simple formulae for rates and elasticities, which can be easily adjusted to the given stationary flux distributions. Furthermore, this formulation highlights the role of chemical potential differences as thermodynamic driving forces. We compare the modular rate laws to the thermodynamic-kinetic modelling formalism and discuss a simplified rate law in which the reaction rate directly depends on the reaction affinity. For automatic handling of modular rate laws, we propose a standard syntax and semantic annotations for the Systems Biology Markup Language. An online tool for inserting the rate laws into SBML models is freely available at www.semanticsbml.org. Supplementary data are available at Bioinformatics online.

On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

NASA Astrophysics Data System (ADS)

Plante, Ianik; Devroye, Luc

2015-09-01

Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well.

Constraint based modeling of metabolism allows finding metabolic cancer hallmarks and identifying personalized therapeutic windows.

PubMed

Bordel, Sergio

2018-04-13

In order to choose optimal personalized anticancer treatments, transcriptomic data should be analyzed within the frame of biological networks. The best known human biological network (in terms of the interactions between its different components) is metabolism. Cancer cells have been known to have specific metabolic features for a long time and currently there is a growing interest in characterizing new cancer specific metabolic hallmarks. In this article it is presented a method to find personalized therapeutic windows using RNA-seq data and Genome Scale Metabolic Models. This method is implemented in the python library, pyTARG. Our predictions showed that the most anticancer selective (affecting 27 out of 34 considered cancer cell lines and only 1 out of 6 healthy mesenchymal stem cell lines) single metabolic reactions are those involved in cholesterol biosynthesis. Excluding cholesterol biosynthesis, all the considered cell lines can be selectively affected by targeting different combinations (from 1 to 5 reactions) of only 18 metabolic reactions, which suggests that a small subset of drugs or siRNAs combined in patient specific manners could be at the core of metabolism based personalized treatments.

Model-based design of RNA hybridization networks implemented in living cells

PubMed Central

Rodrigo, Guillermo; Prakash, Satya; Shen, Shensi; Majer, Eszter

2017-01-01

Abstract Synthetic gene circuits allow the behavior of living cells to be reprogrammed, and non-coding small RNAs (sRNAs) are increasingly being used as programmable regulators of gene expression. However, sRNAs (natural or synthetic) are generally used to regulate single target genes, while complex dynamic behaviors would require networks of sRNAs regulating each other. Here, we report a strategy for implementing such networks that exploits hybridization reactions carried out exclusively by multifaceted sRNAs that are both targets of and triggers for other sRNAs. These networks are ultimately coupled to the control of gene expression. We relied on a thermodynamic model of the different stable conformational states underlying this system at the nucleotide level. To test our model, we designed five different RNA hybridization networks with a linear architecture, and we implemented them in Escherichia coli. We validated the network architecture at the molecular level by native polyacrylamide gel electrophoresis, as well as the network function at the bacterial population and single-cell levels with a fluorescent reporter. Our results suggest that it is possible to engineer complex cellular programs based on RNA from first principles. Because these networks are mainly based on physical interactions, our designs could be expanded to other organisms as portable regulatory resources or to implement biological computations. PMID:28934501

Network Reconstruction Using Nonparametric Additive ODE Models

PubMed Central

Henderson, James; Michailidis, George

2014-01-01

Network representations of biological systems are widespread and reconstructing unknown networks from data is a focal problem for computational biologists. For example, the series of biochemical reactions in a metabolic pathway can be represented as a network, with nodes corresponding to metabolites and edges linking reactants to products. In a different context, regulatory relationships among genes are commonly represented as directed networks with edges pointing from influential genes to their targets. Reconstructing such networks from data is a challenging problem receiving much attention in the literature. There is a particular need for approaches tailored to time-series data and not reliant on direct intervention experiments, as the former are often more readily available. In this paper, we introduce an approach to reconstructing directed networks based on dynamic systems models. Our approach generalizes commonly used ODE models based on linear or nonlinear dynamics by extending the functional class for the functions involved from parametric to nonparametric models. Concomitantly we limit the complexity by imposing an additive structure on the estimated slope functions. Thus the submodel associated with each node is a sum of univariate functions. These univariate component functions form the basis for a novel coupling metric that we define in order to quantify the strength of proposed relationships and hence rank potential edges. We show the utility of the method by reconstructing networks using simulated data from computational models for the glycolytic pathway of Lactocaccus Lactis and a gene network regulating the pluripotency of mouse embryonic stem cells. For purposes of comparison, we also assess reconstruction performance using gene networks from the DREAM challenges. We compare our method to those that similarly rely on dynamic systems models and use the results to attempt to disentangle the distinct roles of linearity, sparsity, and derivative estimation. PMID:24732037

Computing Smallest Intervention Strategies for Multiple Metabolic Networks in a Boolean Model

PubMed Central

Lu, Wei; Song, Jiangning; Akutsu, Tatsuya

2015-01-01

Abstract This article considers the problem whereby, given two metabolic networks N1 and N2, a set of source compounds, and a set of target compounds, we must find the minimum set of reactions whose removal (knockout) ensures that the target compounds are not producible in N1 but are producible in N2. Similar studies exist for the problem of finding the minimum knockout with the smallest side effect for a single network. However, if technologies of external perturbations are advanced in the near future, it may be important to develop methods of computing the minimum knockout for multiple networks (MKMN). Flux balance analysis (FBA) is efficient if a well-polished model is available. However, that is not always the case. Therefore, in this article, we study MKMN in Boolean models and an elementary mode (EM)-based model. Integer linear programming (ILP)-based methods are developed for these models, since MKMN is NP-complete for both the Boolean model and the EM-based model. Computer experiments are conducted with metabolic networks of clostridium perfringens SM101 and bifidobacterium longum DJO10A, respectively known as bad bacteria and good bacteria for the human intestine. The results show that larger networks are more likely to have MKMN solutions. However, solving for these larger networks takes a very long time, and often the computation cannot be completed. This is reasonable, because small networks do not have many alternative pathways, making it difficult to satisfy the MKMN condition, whereas in large networks the number of candidate solutions explodes. Our developed software minFvskO is available online. PMID:25684199

Lattice based Kinetic Monte Carlo Simulations of a complex chemical reaction network

NASA Astrophysics Data System (ADS)

Danielson, Thomas; Savara, Aditya; Hin, Celine

Lattice Kinetic Monte Carlo (KMC) simulations offer a powerful alternative to using ordinary differential equations for the simulation of complex chemical reaction networks. Lattice KMC provides the ability to account for local spatial configurations of species in the reaction network, resulting in a more detailed description of the reaction pathway. In KMC simulations with a large number of reactions, the range of transition probabilities can span many orders of magnitude, creating subsets of processes that occur more frequently or more rarely. Consequently, processes that have a high probability of occurring may be selected repeatedly without actually progressing the system (i.e. the forward and reverse process for the same reaction). In order to avoid the repeated occurrence of fast frivolous processes, it is necessary to throttle the transition probabilities in such a way that avoids altering the overall selectivity. Likewise, as the reaction progresses, new frequently occurring species and reactions may be introduced, making a dynamic throttling algorithm a necessity. We present a dynamic steady-state detection scheme with the goal of accurately throttling rate constants in order to optimize the KMC run time without compromising the selectivity of the reaction network. The algorithm has been applied to a large catalytic chemical reaction network, specifically that of methanol oxidative dehydrogenation, as well as additional pathways on CeO2(111) resulting in formaldehyde, CO, methanol, CO2, H2 and H2O as gas products.

Zea mays iRS1563: A Comprehensive Genome-Scale Metabolic Reconstruction of Maize Metabolism

PubMed Central

Saha, Rajib; Suthers, Patrick F.; Maranas, Costas D.

2011-01-01

The scope and breadth of genome-scale metabolic reconstructions have continued to expand over the last decade. Herein, we introduce a genome-scale model for a plant with direct applications to food and bioenergy production (i.e., maize). Maize annotation is still underway, which introduces significant challenges in the association of metabolic functions to genes. The developed model is designed to meet rigorous standards on gene-protein-reaction (GPR) associations, elementally and charged balanced reactions and a biomass reaction abstracting the relative contribution of all biomass constituents. The metabolic network contains 1,563 genes and 1,825 metabolites involved in 1,985 reactions from primary and secondary maize metabolism. For approximately 42% of the reactions direct literature evidence for the participation of the reaction in maize was found. As many as 445 reactions and 369 metabolites are unique to the maize model compared to the AraGEM model for A. thaliana. 674 metabolites and 893 reactions are present in Zea mays iRS1563 that are not accounted for in maize C4GEM. All reactions are elementally and charged balanced and localized into six different compartments (i.e., cytoplasm, mitochondrion, plastid, peroxisome, vacuole and extracellular). GPR associations are also established based on the functional annotation information and homology prediction accounting for monofunctional, multifunctional and multimeric proteins, isozymes and protein complexes. We describe results from performing flux balance analysis under different physiological conditions, (i.e., photosynthesis, photorespiration and respiration) of a C4 plant and also explore model predictions against experimental observations for two naturally occurring mutants (i.e., bm1 and bm3). The developed model corresponds to the largest and more complete to-date effort at cataloguing metabolism for a plant species. PMID:21755001

SUPECA kinetics for scaling redox reactions in networks of mixed substrates and consumers and an example application to aerobic soil respiration

DOE PAGES

Tang, Jin-Yun; Riley, William J.

2017-09-05

Several land biogeochemical models used for studying carbon–climate feedbacks have begun explicitly representing microbial dynamics. However, to our knowledge, there has been no theoretical work on how to achieve a consistent scaling of the complex biogeochemical reactions from microbial individuals to populations, communities, and interactions with plants and mineral soils. We focus here on developing a mathematical formulation of the substrate–consumer relationships for consumer-mediated redox reactions of the form A +  B E→  products, where products could be, e.g., microbial biomass or bioproducts. Under the quasi-steady-state approximation, these substrate–consumer relationships can be formulated as the computationally difficult full equilibrium chemistrymore » problem or approximated analytically with the dual Monod (DM) or synthesizing unit (SU) kinetics. We find that DM kinetics is scaling inconsistently for reaction networks because (1) substrate limitations are not considered, (2) contradictory assumptions are made regarding the substrate processing rate when transitioning from single- to multi-substrate redox reactions, and (3) the product generation rate cannot be scaled from one to multiple substrates. In contrast, SU kinetics consistently scales the product generation rate from one to multiple substrates but predicts unrealistic results as consumer abundances reach large values with respect to their substrates. We attribute this deficit to SU's failure to incorporate substrate limitation in its derivation. To address these issues, we propose SUPECA (SU plus the equilibrium chemistry approximation – ECA) kinetics, which consistently imposes substrate and consumer mass balance constraints. We show that SUPECA kinetics satisfies the partition principle, i.e., scaling invariance across a network of an arbitrary number of reactions (e.g., as in Newton's law of motion and Dalton's law of partial pressures). We tested SUPECA kinetics with the equilibrium chemistry solution for some simple problems and found SUPECA outperformed SU kinetics. As an example application, we show that a steady-state SUPECA-based approach predicted an aerobic soil respiration moisture response function that agreed well with laboratory observations. We conclude that, as an extension to SU and ECA kinetics, SUPECA provides a robust mathematical representation of complex soil substrate–consumer interactions and can be applied to improve Earth system model (ESM) land models.« less

SUPECA kinetics for scaling redox reactions in networks of mixed substrates and consumers and an example application to aerobic soil respiration

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

Tang, Jin-Yun; Riley, William J.

Several land biogeochemical models used for studying carbon–climate feedbacks have begun explicitly representing microbial dynamics. However, to our knowledge, there has been no theoretical work on how to achieve a consistent scaling of the complex biogeochemical reactions from microbial individuals to populations, communities, and interactions with plants and mineral soils. We focus here on developing a mathematical formulation of the substrate–consumer relationships for consumer-mediated redox reactions of the form A +  B E→  products, where products could be, e.g., microbial biomass or bioproducts. Under the quasi-steady-state approximation, these substrate–consumer relationships can be formulated as the computationally difficult full equilibrium chemistrymore » problem or approximated analytically with the dual Monod (DM) or synthesizing unit (SU) kinetics. We find that DM kinetics is scaling inconsistently for reaction networks because (1) substrate limitations are not considered, (2) contradictory assumptions are made regarding the substrate processing rate when transitioning from single- to multi-substrate redox reactions, and (3) the product generation rate cannot be scaled from one to multiple substrates. In contrast, SU kinetics consistently scales the product generation rate from one to multiple substrates but predicts unrealistic results as consumer abundances reach large values with respect to their substrates. We attribute this deficit to SU's failure to incorporate substrate limitation in its derivation. To address these issues, we propose SUPECA (SU plus the equilibrium chemistry approximation – ECA) kinetics, which consistently imposes substrate and consumer mass balance constraints. We show that SUPECA kinetics satisfies the partition principle, i.e., scaling invariance across a network of an arbitrary number of reactions (e.g., as in Newton's law of motion and Dalton's law of partial pressures). We tested SUPECA kinetics with the equilibrium chemistry solution for some simple problems and found SUPECA outperformed SU kinetics. As an example application, we show that a steady-state SUPECA-based approach predicted an aerobic soil respiration moisture response function that agreed well with laboratory observations. We conclude that, as an extension to SU and ECA kinetics, SUPECA provides a robust mathematical representation of complex soil substrate–consumer interactions and can be applied to improve Earth system model (ESM) land models.« less

SUPECA kinetics for scaling redox reactions in networks of mixed substrates and consumers and an example application to aerobic soil respiration

NASA Astrophysics Data System (ADS)

Tang, Jin-Yun; Riley, William J.

2017-09-01

Several land biogeochemical models used for studying carbon-climate feedbacks have begun explicitly representing microbial dynamics. However, to our knowledge, there has been no theoretical work on how to achieve a consistent scaling of the complex biogeochemical reactions from microbial individuals to populations, communities, and interactions with plants and mineral soils. We focus here on developing a mathematical formulation of the substrate-consumer relationships for consumer-mediated redox reactions of the form A + BE→ products, where products could be, e.g., microbial biomass or bioproducts. Under the quasi-steady-state approximation, these substrate-consumer relationships can be formulated as the computationally difficult full equilibrium chemistry problem or approximated analytically with the dual Monod (DM) or synthesizing unit (SU) kinetics. We find that DM kinetics is scaling inconsistently for reaction networks because (1) substrate limitations are not considered, (2) contradictory assumptions are made regarding the substrate processing rate when transitioning from single- to multi-substrate redox reactions, and (3) the product generation rate cannot be scaled from one to multiple substrates. In contrast, SU kinetics consistently scales the product generation rate from one to multiple substrates but predicts unrealistic results as consumer abundances reach large values with respect to their substrates. We attribute this deficit to SU's failure to incorporate substrate limitation in its derivation. To address these issues, we propose SUPECA (SU plus the equilibrium chemistry approximation - ECA) kinetics, which consistently imposes substrate and consumer mass balance constraints. We show that SUPECA kinetics satisfies the partition principle, i.e., scaling invariance across a network of an arbitrary number of reactions (e.g., as in Newton's law of motion and Dalton's law of partial pressures). We tested SUPECA kinetics with the equilibrium chemistry solution for some simple problems and found SUPECA outperformed SU kinetics. As an example application, we show that a steady-state SUPECA-based approach predicted an aerobic soil respiration moisture response function that agreed well with laboratory observations. We conclude that, as an extension to SU and ECA kinetics, SUPECA provides a robust mathematical representation of complex soil substrate-consumer interactions and can be applied to improve Earth system model (ESM) land models.