Graph Theory for Rule-Based Modeling of Biochemical Networks

bnglViz: online visualization of rule-based models

MOTIVATION

Rule-based modeling is a powerful method to describe and simulate interactions among multi-site molecules and multi-molecular species, accounting for the internal connectivity of molecules in chemical species. This modeling technique is implemented in BioNetGen software that is used by various tools and software frameworks, such as BioNetGen stand-alone software, NFSim simulation engine, Virtual Cell simulation and modeling framework, SmolDyn and PySB software tools. These tools exchange models using BioNetGen scripting language (BNGL). Until now, there was no online visualization of such rule-based models. Modelers and researchers reading the manuscripts describing rule-based models had to learn BNGL scripting or master one of these tools to understand the models.

RESULTS

Here, we introduce bnglViz, an online platform for visualizing BNGL files as graphical cartoons, empowering researchers to grasp the nuances of rule-based models swiftly and efficiently, and making the exploration of complex biological systems more accessible than ever before. The produced visualizations can be used as supplemental figures in publications or as a way to annotate BNGL models on web repositories.

AVAILABILITY AND IMPLEMENTATION

Available at https://bnglviz.github.io/.

Negative feedback systems for modelling NF-κB transcription factor oscillatory activity

Low-dimensional negative feedback systems (NFSs) were developed within a signal flow model to describe the oscillatory activities of NF-κB caused by interactions with its inhibitor IκBα. The NFSs were established as 3rd- and 4th-order linear systems containing unperturbed and perturbed negative feedback (NF) loops with constant or time-varying NF strengths and a feed-forward loop. NF-related analytical solutions to the NFSs representing the time courses of NF-κB and IκBα were determined and their exact mathematical relationship was found. The NFS's parameters were determined to fit the experimental time courses of NF-κB in TNF-α-stimulated embryonic fibroblasts, rela-/- embryonic fibroblasts reconstituted with RelA, C9L cells, GFP-p65 knock-in embryonic fibroblasts and embryogenic fibroblasts lacking Iκβ and IκBε, LPS-stimulated IC-21 macrophages treated or not with DCPA, and anti-IgM-stimulated DT40 B-lymphocytes. The unperturbed and perturbed NFSs describing the above biosystems generated isochronous and non-isochronous solutions, depending on a constant or time-varying NF strength, respectively. The oscillation period of the NF-coupled solutions, the phase difference between them and the time delays in the appearance of cytoplasmic IκBα after stimulation of NF-κB were determined. A significant divergence between the IκBα solutions to the NFSs and the IκBα experimental courses led to a rejection of the NF coupling between NF-κB and IκBα in the above biosystems. It was shown that neither the linearity nor the low dimensionality of the NFSs altered the NF relationship and the divergence between the IκBα solutions to the NFS and IκBα experimental time courses. Although the NF relationship between IκBα and NF-κB was not confirmed in all the experimental data analyzed, delayed negative feedback was found in some cases.

A multiscale model of the regulation of aquaporin 2 recycling

The response of cells to their environment is driven by a variety of proteins and messenger molecules. In eukaryotes, their distribution and location in the cell are regulated by the vesicular transport system. The transport of aquaporin 2 between membrane and storage region is a crucial part of the water reabsorption in renal principal cells, and its malfunction can lead to Diabetes insipidus. To understand the regulation of this system, we aggregated pathways and mechanisms from literature and derived three models in a hypothesis-driven approach. Furthermore, we combined the models to a single system to gain insight into key regulatory mechanisms of Aquaporin 2 recycling. To achieve this, we developed a multiscale computational framework for the modeling and simulation of cellular systems. The analysis of the system rationalizes that the compartmentalization of cAMP in renal principal cells is a result of the protein kinase A signalosome and can only occur if specific cellular components are observed in conjunction. Endocytotic and exocytotic processes are inherently connected and can be regulated by the same protein kinase A signal.

A Step-by-Step Guide to Using BioNetFit

BioNetFit is a software tool designed for solving parameter identification problems that arise in the development of rule-based models. It solves these problems through curve fitting (i.e., nonlinear regression). BioNetFit is compatible with deterministic and stochastic simulators that accept BioNetGen language (BNGL)-formatted files as inputs, such as those available within the BioNetGen framework. BioNetFit can be used on a laptop or stand-alone multicore workstation as well as on many Linux clusters, such as those that use the Slurm Workload Manager to schedule jobs. BioNetFit implements a metaheuristic population-based global optimization procedure, an evolutionary algorithm (EA), to minimize a user-defined objective function, such as a residual sum of squares (RSS) function. BioNetFit also implements a bootstrapping procedure for determining confidence intervals for parameter estimates. Here, we provide step-by-step instructions for using BioNetFit to estimate the values of parameters of a BNGL-encoded model and to define bootstrap confidence intervals. The process entails the use of several plain-text files, which are processed by BioNetFit and BioNetGen. In general, these files include (1) one or more EXP files, which each contains (experimental) data to be used in parameter identification/bootstrapping; (2) a BNGL file containing a model section, which defines a (rule-based) model, and an actions section, which defines simulation protocols that generate GDAT and/or SCAN files with model predictions corresponding to the data in the EXP file(s); and (3) a CONF file that configures the fitting/bootstrapping job and that defines algorithmic parameter settings.

Automated visualization of rule-based models

Frameworks such as BioNetGen, Kappa and Simmune use "reaction rules" to specify biochemical interactions compactly, where each rule specifies a mechanism such as binding or phosphorylation and its structural requirements. Current rule-based models of signaling pathways have tens to hundreds of rules, and these numbers are expected to increase as more molecule types and pathways are added. Visual representations are critical for conveying rule-based models, but current approaches to show rules and interactions between rules scale poorly with model size. Also, inferring design motifs that emerge from biochemical interactions is an open problem, so current approaches to visualize model architecture rely on manual interpretation of the model. Here, we present three new visualization tools that constitute an automated visualization framework for rule-based models: (i) a compact rule visualization that efficiently displays each rule, (ii) the atom-rule graph that conveys regulatory interactions in the model as a bipartite network, and (iii) a tunable compression pipeline that incorporates expert knowledge and produces compact diagrams of model architecture when applied to the atom-rule graph. The compressed graphs convey network motifs and architectural features useful for understanding both small and large rule-based models, as we show by application to specific examples. Our tools also produce more readable diagrams than current approaches, as we show by comparing visualizations of 27 published models using standard graph metrics. We provide an implementation in the open source and freely available BioNetGen framework, but the underlying methods are general and can be applied to rule-based models from the Kappa and Simmune frameworks also. We expect that these tools will promote communication and analysis of rule-based models and their eventual integration into comprehensive whole-cell models.

Modeling for (physical) biologists: an introduction to the rule-based approach

Models that capture the chemical kinetics of cellular regulatory networks can be specified in terms of rules for biomolecular interactions. A rule defines a generalized reaction, meaning a reaction that permits multiple reactants, each capable of participating in a characteristic transformation and each possessing certain, specified properties, which may be local, such as the state of a particular site or domain of a protein. In other words, a rule defines a transformation and the properties that reactants must possess to participate in the transformation. A rule also provides a rate law. A rule-based approach to modeling enables consideration of mechanistic details at the level of functional sites of biomolecules and provides a facile and visual means for constructing computational models, which can be analyzed to study how system-level behaviors emerge from component interactions.

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

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.

Rule-based modeling is a modeling paradigm that addresses the problem of combinatorial complexity in biochemical systems. The key idea is to specify only those components of a biological macromolecule that are directly involved in a biochemical transformation. Until recently, this “pattern-based” approach greatly simplified the process of model building but did nothing to improve the performance of model simulation. This changed with the introduction of “network-free” simulation methods, which operate directly on the compressed rule set of a rule-based model rather than on a fully-enumerated set of reactions and species. However, these methods represent every molecule in a system as a particle, limiting their use to systems containing less than a few million molecules. Here, we describe an extension to the network-free approach that treats rare, complex species as particles and plentiful, simple species as population variables, while retaining the exact dynamics of the model system. By making more efficient use of computational resources for species that do not require the level of detail of a particle representation, this hybrid particle/population approach can simulate systems much larger than is possible using network-free methods and is an important step towards realizing the practical simulation of detailed, mechanistic models of whole cells.

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

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 posttranslational 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).

Leveraging modeling approaches: reaction networks and rules

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.

Combinatorial complexity and compositional drift in protein interaction networks

The assembly of molecular machines and transient signaling complexes does not typically occur under circumstances in which the appropriate proteins are isolated from all others present in the cell. Rather, assembly must proceed in the context of large-scale protein-protein interaction (PPI) networks that are characterized both by conflict and combinatorial complexity. Conflict refers to the fact that protein interfaces can often bind many different partners in a mutually exclusive way, while combinatorial complexity refers to the explosion in the number of distinct complexes that can be formed by a network of binding possibilities. Using computational models, we explore the consequences of these characteristics for the global dynamics of a PPI network based on highly curated yeast two-hybrid data. The limited molecular context represented in this data-type translates formally into an assumption of independent binding sites for each protein. The challenge of avoiding the explicit enumeration of the astronomically many possibilities for complex formation is met by a rule-based approach to kinetic modeling. Despite imposing global biophysical constraints, we find that initially identical simulations rapidly diverge in the space of molecular possibilities, eventually sampling disjoint sets of large complexes. We refer to this phenomenon as "compositional drift". Since interaction data in PPI networks lack detailed information about geometric and biological constraints, our study does not represent a quantitative description of cellular dynamics. Rather, our work brings to light a fundamental problem (the control of compositional drift) that must be solved by mechanisms of assembly in the context of large networks. In cases where drift is not (or cannot be) completely controlled by the cell, this phenomenon could constitute a novel source of phenotypic heterogeneity in cell populations.

Guidelines for visualizing and annotating rule-based models

Rule-based modeling provides a means to represent cell signaling systems in a way that captures site-specific details of molecular interactions. For rule-based models to be more widely understood and (re)used, conventions for model visualization and annotation are needed. We have developed the concepts of an extended contact map and a model guide for illustrating and annotating rule-based models. An extended contact map represents the scope of a model by providing an illustration of each molecule, molecular component, direct physical interaction, post-translational modification, and enzyme-substrate relationship considered in a model. A map can also illustrate allosteric effects, structural relationships among molecular components, and compartmental locations of molecules. A model guide associates elements of a contact map with annotation and elements of an underlying model, which may be fully or partially specified. A guide can also serve to document the biological knowledge upon which a model is based. We provide examples of a map and guide for a published rule-based model that characterizes early events in IgE receptor (FcεRI) signaling. We also provide examples of how to visualize a variety of processes that are common in cell signaling systems but not considered in the example model, such as ubiquitination. An extended contact map and an associated guide can document knowledge of a cell signaling system in a form that is visual as well as executable. As a tool for model annotation, a map and guide can communicate the content of a model clearly and with precision, even for large models.

Hierarchical graphs for rule-based modeling of biochemical systems

Background

In rule-based modeling, graphs are used to represent molecules: a colored vertex represents a component of a molecule, a vertex attribute represents the internal state of a component, and an edge represents a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions. A rule that specifies addition (removal) of an edge represents a class of association (dissociation) reactions, and a rule that specifies a change of a vertex attribute represents a class of reactions that affect the internal state of a molecular component. A set of rules comprises an executable model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system.

Results

For purposes of model annotation, we propose the use of hierarchical graphs to represent structural relationships among components and subcomponents of molecules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR) complex. We also show that computational methods developed for regular graphs can be applied to hierarchical graphs. In particular, we describe a generalization of Nauty, a graph isomorphism and canonical labeling algorithm. The generalized version of the Nauty procedure, which we call HNauty, can be used to assign canonical labels to hierarchical graphs or more generally to graphs with multiple edge types. The difference between the Nauty and HNauty procedures is minor, but for completeness, we provide an explanation of the entire HNauty algorithm.

Conclusions

Hierarchical graphs provide more intuitive formal representations of proteins and other structured molecules with multiple functional components than do the regular graphs of current languages for specifying rule-based models, such as the BioNetGen language (BNGL). Thus, the proposed use of hierarchical graphs should promote clarity and better understanding of rule-based models.

Intrinsic information carriers in combinatorial dynamical systems

Many proteins are composed of structural and chemical features--"sites" for short--characterized by definite interaction capabilities, such as noncovalent binding or covalent modification of other proteins. This modularity allows for varying degrees of independence, as the behavior of a site might be controlled by the state of some but not all sites of the ambient protein. Independence quickly generates a startling combinatorial complexity that shapes most biological networks, such as mammalian signaling systems, and effectively prevents their study in terms of kinetic equations-unless the complexity is radically trimmed. Yet, if combinatorial complexity is key to the system's behavior, eliminating it will prevent, not facilitate, understanding. A more adequate representation of a combinatorial system is provided by a graph-based framework of rewrite rules where each rule specifies only the information that an interaction mechanism depends on. Unlike reactions, which deal with molecular species, rules deal with patterns, i.e., multisets of molecular species. Although the stochastic dynamics induced by a collection of rules on a mixture of molecules can be simulated, it appears useful to capture the system's average or deterministic behavior by means of differential equations. However, expansion of the rules into kinetic equations at the level of molecular species is not only impractical, but conceptually indefensible. If rules describe bona fide patterns of interaction, molecular species are unlikely to constitute appropriate units of dynamics. Rather, we must seek aggregate variables reflective of the causal structure laid down by the rules. We call these variables "fragments" and the process of identifying them "fragmentation." Ideally, fragments are aspects of the system's microscopic population that the set of rules can actually distinguish on average; in practice, it may only be feasible to identify an approximation to this. Most importantly, fragments are self-consistent descriptors of system dynamics in that their time-evolution is governed by a closed system of kinetic equations. Taken together, fragments are endogenous distinctions that matter for the dynamics of a system, which warrants viewing them as the carriers of information. Although fragments can be thought of as multisets of molecular species (an extensional view), their self-consistency suggests treating them as autonomous aspects cut off from their microscopic realization (an intensional view). Fragmentation is a seeded process that depends on the choice of observables whose dynamics one insists to describe. Different observables can cause distinct fragmentations, in effect altering the set of information carriers that govern the behavior of a system, even though nothing has changed in its microscopic constitution. In this contribution, we present a mathematical specification of fragments, but not an algorithmic implementation. We have described the latter elsewhere in rather technical terms that, although effective, were lacking an embedding into a more general conceptual framework, which we here provide.

RuleMonkey: software for stochastic simulation of rule-based models

Background

The system-level dynamics of many molecular interactions, particularly protein-protein interactions, can be conveniently represented using reaction rules, which can be specified using model-specification languages, such as the BioNetGen language (BNGL). A set of rules implicitly defines a (bio)chemical reaction network. The reaction network implied by a set of rules is often very large, and as a result, generation of the network implied by rules tends to be computationally expensive. Moreover, the cost of many commonly used methods for simulating network dynamics is a function of network size. Together these factors have limited application of the rule-based modeling approach. Recently, several methods for simulating rule-based models have been developed that avoid the expensive step of network generation. The cost of these "network-free" simulation methods is independent of the number of reactions implied by rules. Software implementing such methods is now needed for the simulation and analysis of rule-based models of biochemical systems.

Results

Here, we present a software tool called RuleMonkey, which implements a network-free method for simulation of rule-based models that is similar to Gillespie's method. The method is suitable for rule-based models that can be encoded in BNGL, including models with rules that have global application conditions, such as rules for intramolecular association reactions. In addition, the method is rejection free, unlike other network-free methods that introduce null events, i.e., steps in the simulation procedure that do not change the state of the reaction system being simulated. We verify that RuleMonkey produces correct simulation results, and we compare its performance against DYNSTOC, another BNGL-compliant tool for network-free simulation of rule-based models. We also compare RuleMonkey against problem-specific codes implementing network-free simulation methods.

Conclusions

RuleMonkey enables the simulation of rule-based models for which the underlying reaction networks are large. It is typically faster than DYNSTOC for benchmark problems that we have examined. RuleMonkey is freely available as a stand-alone application http://public.tgen.org/rulemonkey. It is also available as a simulation engine within GetBonNie, a web-based environment for building, analyzing and sharing rule-based models.

Rule-based spatial modeling with diffusing, geometrically constrained molecules

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.

Simulation of large-scale rule-based models

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/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Rule-based modeling of biochemical systems with BioNetGen

Rule-based modeling involves the representation of molecules as structured objects and molecular interactions as rules for transforming the attributes of these objects. The approach is notable in that it allows one to systematically incorporate site-specific details about protein-protein interactions into a model for the dynamics of a signal-transduction system, but the method has other applications as well, such as following the fates of individual carbon atoms in metabolic reactions. The consequences of protein-protein interactions are difficult to specify and track with a conventional modeling approach because of the large number of protein phosphoforms and protein complexes that these interactions potentially generate. Here, we focus on how a rule-based model is specified in the BioNetGen language (BNGL) and how a model specification is analyzed using the BioNetGen software tool. We also discuss new developments in rule-based modeling that should enable the construction and analyses of comprehensive models for signal transduction pathways and similarly large-scale models for other biochemical systems.

ALC: automated reduction of rule-based models

Background

Combinatorial complexity is a challenging problem for the modeling of cellular signal transduction since the association of a few proteins can give rise to an enormous amount of feasible protein complexes. The layer-based approach is an approximative, but accurate method for the mathematical modeling of signaling systems with inherent combinatorial complexity. The number of variables in the simulation equations is highly reduced and the resulting dynamic models show a pronounced modularity. Layer-based modeling allows for the modeling of systems not accessible previously.

Results

ALC (Automated Layer Construction) is a computer program that highly simplifies the building of reduced modular models, according to the layer-based approach. The model is defined using a simple but powerful rule-based syntax that supports the concepts of modularity and macrostates. ALC performs consistency checks on the model definition and provides the model output in different formats (C MEX, MATLAB, Mathematica and SBML) as ready-to-run simulation files. ALC also provides additional documentation files that simplify the publication or presentation of the models. The tool can be used offline or via a form on the ALC website.

Conclusion

ALC allows for a simple rule-based generation of layer-based reduced models. The model files are given in different formats as ready-to-run simulation files.

Kinetic Monte Carlo method for rule-based modeling of biochemical networks

We present a kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes. A rule identifies the molecular components involved in a transformation, how these components change, conditions that affect whether a transformation occurs, and a rate law. The computational cost of the method, unlike conventional simulation approaches, is independent of the number of possible reactions, which need not be specified in advance or explicitly generated in a simulation. To demonstrate the method, we apply it to study the kinetics of multivalent ligand-receptor interactions. We expect the method will be useful for studying cellular signaling systems and other physical systems involving aggregation phenomena.

Exact model reduction of combinatorial reaction networks

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.

Stochastic effects and bistability in T cell receptor signaling

The stochastic dynamics of T cell receptor (TCR) signaling are studied using a mathematical model intended to capture kinetic proofreading (sensitivity to ligand-receptor binding kinetics) and negative and positive feedback regulation mediated, respectively, by the phosphatase SHP1 and the MAP kinase ERK. The model incorporates protein-protein interactions involved in initiating TCR-mediated cellular responses and reproduces several experimental observations about the behavior of TCR signaling, including robust responses to as few as a handful of ligands (agonist peptide-MHC complexes on an antigen-presenting cell), distinct responses to ligands that bind TCR with different lifetimes, and antagonism. Analysis of the model indicates that TCR signaling dynamics are marked by significant stochastic fluctuations and bistability, which is caused by the competition between the positive and negative feedbacks. Stochastic fluctuations are such that single-cell trajectories differ qualitatively from the trajectory predicted in the deterministic approximation of the dynamics. Because of bistability, the average of single-cell trajectories differs markedly from the deterministic trajectory. Bistability combined with stochastic fluctuations allows for switch-like responses to signals, which may aid T cells in making committed cell-fate decisions.

Carbon-fate maps for metabolic reactions

MOTIVATION

Stable isotope labeling of small-molecule metabolites (e.g. (13)C-labeling of glucose) is a powerful tool for characterizing pathways and reaction fluxes in a metabolic network. Analysis of isotope labeling patterns requires knowledge of the fates of individual atoms and moieties in reactions, which can be difficult to collect in a useful form when considering a large number of enzymatic reactions.

RESULTS

We report carbon-fate maps for 4605 enzyme-catalyzed reactions documented in the KEGG database. Every fate map has been manually checked for consistency with known reaction mechanisms. A map includes a standardized structure-based identifier for each reactant (namely, an InChI string); indices for carbon atoms that are uniquely derived from the metabolite identifiers; structural data, including an identification of homotopic and prochiral carbon atoms; and a bijective map relating the corresponding carbon atoms in substrates and products. Fate maps are defined using the BioNetGen language (BNGL), a formal model-specification language, which allows a set of maps to be automatically translated into isotopomer mass-balance equations.

AVAILABILITY

The carbon-fate maps and software for visualizing the maps are freely available (http://cellsignaling.lanl.gov/FateMaps/).