Specification, annotation, visualization and simulation of a large rule-based model for ERBB receptor signaling

BACKGROUND

Mathematical/computational models are needed to understand cell signaling networks, which are complex. Signaling proteins contain multiple functional components and multiple sites of post-translational modification. The multiplicity of components and sites of modification ensures that interactions among signaling proteins have the potential to generate myriad protein complexes and post-translational modification states. As a result, the number of chemical species that can be populated in a cell signaling network, and hence the number of equations in an ordinary differential equation model required to capture the dynamics of these species, is prohibitively large. To overcome this problem, the rule-based modeling approach has been developed for representing interactions within signaling networks efficiently and compactly through coarse-graining of the chemical kinetics of molecular interactions.

RESULTS

Here, we provide a demonstration that the rule-based modeling approach can be used to specify and simulate a large model for ERBB receptor signaling that accounts for site-specific details of protein-protein interactions. The model is considered large because it corresponds to a reaction network containing more reactions than can be practically enumerated. The model encompasses activation of ERK and Akt, and it can be simulated using a network-free simulator, such as NFsim, to generate time courses of phosphorylation for 55 individual serine, threonine, and tyrosine residues. The model is annotated and visualized in the form of an extended contact map.

CONCLUSIONS

With the development of software that implements novel computational methods for calculating the dynamics of large-scale rule-based representations of cellular signaling networks, it is now possible to build and analyze models that include a significant fraction of the protein interactions that comprise a signaling network, with incorporation of the site-specific details of the interactions. Modeling at this level of detail is important for understanding cellular signaling.

A computational model for early events in B cell antigen receptor signaling: analysis of the roles of Lyn and Fyn

BCR signaling regulates the activities and fates of B cells. BCR signaling encompasses two feedback loops emanating from Lyn and Fyn, which are Src family protein tyrosine kinases (SFKs). Positive feedback arises from SFK-mediated trans phosphorylation of BCR and receptor-bound Lyn and Fyn, which increases the kinase activities of Lyn and Fyn. Negative feedback arises from SFK-mediated cis phosphorylation of the transmembrane adapter protein PAG1, which recruits the cytosolic protein tyrosine kinase Csk to the plasma membrane, where it acts to decrease the kinase activities of Lyn and Fyn. To study the effects of the positive and negative feedback loops on the dynamical stability of BCR signaling and the relative contributions of Lyn and Fyn to BCR signaling, we consider in this study a rule-based model for early events in BCR signaling that encompasses membrane-proximal interactions of six proteins, as follows: BCR, Lyn, Fyn, Csk, PAG1, and Syk, a cytosolic protein tyrosine kinase that is activated as a result of SFK-mediated phosphorylation of BCR. The model is consistent with known effects of Lyn and Fyn deletions. We find that BCR signaling can generate a single pulse or oscillations of Syk activation depending on the strength of Ag signal and the relative levels of Lyn and Fyn. We also show that bistability can arise in Lyn- or Csk-deficient cells.

The Brucella TIR-like protein TcpB interacts with the death domain of MyD88

The pathogen Brucella melitensis secretes a Toll/interleukin-1 receptor (TIR) domain containing protein that abrogates host innate immune responses. In this study, we have characterized the biochemical interactions of Brucella TIR-like protein TcpB with host innate immune adaptor proteins. Using protein-fragment complementation assays based on Gaussia luciferase and green fluorescent protein, we find that TcpB interacts directly with MyD88 and that this interaction is significantly stronger than the interaction of TcpB with TIRAP, the only other adaptor protein that detectably interacts with TcpB. Surprisingly, the TcpB-MyD88 interaction depends on the death domain (DD) of MyD88, and TcpB does not interact with the isolated TIR domain of MyD88. TcpB disrupts MyD88(DD)-MyD88(DD), MyD88(DD)-MyD88(TIR) and MyD88(DD)-MyD88 interactions but not MyD88-MyD88 or MyD88(TIR)-MyD88(TIR) interactions. Structural models consistent with these results suggest how TcpB might inhibit TLR signaling by targeting MyD88 via a DD-TIR domain interface.

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.

Selected papers from the Fourth Annual q-bio Conference on Cellular Information Processing

This special issue consists of 11 original papers that elaborate on work presented at the Fourth Annual q-bio Conference on Cellular Information Processing, which was held on the campus of St John's College in Santa Fe, New Mexico, USA, 11-14 August 2010. Now in its fourth year, the q-bio conference has changed considerably over time. It is now well established and a major event in systems biology. The 2010 conference saw attendees from all continents (except Antarctica!) sharing novel results and participating in lively discussions at both the oral and poster sessions. The conference was oversubscribed and grew to 27 contributed talks, 16 poster spotlights and 137 contributed posters. We deliberately decreased the number of invited speakers to 21 to leave more space for contributed presentations, and the attendee feedback confirmed that the choice was a success. Although the q-bio conference has grown and matured, it has remained true to the original goal of being an intimate and dynamic event that brings together modeling, theory and quantitative experimentation for the study of cell regulation and information processing. Funded in part by a grant from NIGMS and by DOE funds through the Los Alamos National Laboratory Directed Research and Development program, the conference has continued to exhibit youth and vigor by attracting (and partially supporting) over 100 undergraduate, graduate and postdoctoral researchers. The associated q-bio summer school, which precedes the conference each year, further emphasizes the development of junior scientists and makes q-bio a singular event in its impact on the future of quantitative biology. In addition to an increased international presence, the conference has notably diversified its demographic representation within the USA, including increased participation from the southeastern corner of the country. One big change in the conference this year is our new publication partner, Physical Biology. Although we are very grateful to our previous partner, IET Systems Biology, for their help over the years in publicizing the work presented at the conference, we felt that the changing needs of our participants required that we find a new partner. We are thrilled that Physical Biology is publishing the q-bio proceedings this year. It has been a great collaboration, as evidenced by the high quality of this special issue. What's next for q-bio? We are happy to report that NIGMS has recently extended the q-bio conference grant for the next three years, ensuring strong support for junior researchers who need financial assistance to participate in the event. The conference will retain its emphasis on cellular information processing, but will also build connections to other areas of modern biology and biotechnology, focusing specifically on ecology and evolutionary biology next year. Indeed, to fully understand biological information processing systems, they must be studied in their ecological contexts. We will continue to honor distinguished contributors to the field in our opening banquets; the tradition started with Howard Berg, Bruce Alberts and Michael Savageau in previous years, and continues with Dennis Bray at the upcoming 2011 event. Starting in 2011, the conference will also venture into exploration of the social aspects of science. The future is bright for q-bio! We will see you at the Fifth Annual q-bio Conference on 10-13 August 2011, in Santa Fe, New Mexico, USA and at the Sixth Annual q-bio Conference in early August 2012.

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

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.

Prediction of metabolic reactions based on atomic and molecular properties of small-molecule compounds

MOTIVATION

Our knowledge of the metabolites in cells and their reactions is far from complete as revealed by metabolomic measurements that detect many more small molecules than are documented in metabolic databases. Here, we develop an approach for predicting the reactivity of small-molecule metabolites in enzyme-catalyzed reactions that combines expert knowledge, computational chemistry and machine learning.

RESULTS

We classified 4843 reactions documented in the KEGG database, from all six Enzyme Commission classes (EC 1-6), into 80 reaction classes, each of which is marked by a characteristic functional group transformation. Reaction centers and surrounding local structures in substrates and products of these reactions were represented using SMARTS. We found that each of the SMARTS-defined chemical substructures is widely distributed among metabolites, but only a fraction of the functional groups in these substructures are reactive. Using atomic properties of atoms in a putative reaction center and molecular properties as features, we trained support vector machine (SVM) classifiers to discriminate between functional groups that are reactive and non-reactive. Classifier accuracy was assessed by cross-validation analysis. A typical sensitivity [TP/(TP+FN)] or specificity [TN/(TN+FP)] is ≈0.8. Our results suggest that metabolic reactivity of small-molecule compounds can be predicted with reasonable accuracy based on the presence of a potentially reactive functional group and the chemical features of its local environment.

AVAILABILITY

The classifiers presented here can be used to predict reactions via a web site (http://cellsignaling.lanl.gov/Reactivity/). The web site is freely available.

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.

Rule-based modelling and simulation of biochemical systems with molecular finite automata

The authors propose a theoretical formalism, molecular finite automata (MFA), to describe individual proteins as rule-based computing machines. The MFA formalism provides a framework for modelling individual protein behaviours and systems-level dynamics via construction of programmable and executable machines. Models specified within this formalism explicitly represent the context-sensitive dynamics of individual proteins driven by external inputs and represent protein-protein interactions as synchronised machine reconfigurations. Both deterministic and stochastic simulations can be applied to quantitatively compute the dynamics of MFA models. They apply the MFA formalism to model and simulate a simple example of a signal-transduction system that involves an MAP kinase cascade and a scaffold protein.

Using sequence-specific chemical and structural properties of DNA to predict transcription factor binding sites

An important step in understanding gene regulation is to identify the DNA binding sites recognized by each transcription factor (TF). Conventional approaches to prediction of TF binding sites involve the definition of consensus sequences or position-specific weight matrices and rely on statistical analysis of DNA sequences of known binding sites. Here, we present a method called SiteSleuth in which DNA structure prediction, computational chemistry, and machine learning are applied to develop models for TF binding sites. In this approach, binary classifiers are trained to discriminate between true and false binding sites based on the sequence-specific chemical and structural features of DNA. These features are determined via molecular dynamics calculations in which we consider each base in different local neighborhoods. For each of 54 TFs in Escherichia coli, for which at least five DNA binding sites are documented in RegulonDB, the TF binding sites and portions of the non-coding genome sequence are mapped to feature vectors and used in training. According to cross-validation analysis and a comparison of computational predictions against ChIP-chip data available for the TF Fis, SiteSleuth outperforms three conventional approaches: Match, MATRIX SEARCH, and the method of Berg and von Hippel. SiteSleuth also outperforms QPMEME, a method similar to SiteSleuth in that it involves a learning algorithm. The main advantage of SiteSleuth is a lower false positive rate.

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.

Modeling multivalent ligand-receptor interactions with steric constraints on configurations of cell-surface receptor aggregates

We use flow cytometry to characterize equilibrium binding of a fluorophore-labeled trivalent model antigen to bivalent IgE-FcepsilonRI complexes on RBL cells. We find that flow cytometric measurements are consistent with an equilibrium model for ligand-receptor binding in which binding sites are assumed to be equivalent and ligand-induced receptor aggregates are assumed to be acyclic. However, this model predicts extensive receptor aggregation at antigen concentrations that yield strong cellular secretory responses, which is inconsistent with the expectation that large receptor aggregates should inhibit such responses. To investigate possible explanations for this discrepancy, we evaluate four rule-based models for interaction of a trivalent ligand with a bivalent cell-surface receptor that relax simplifying assumptions of the equilibrium model. These models are simulated using a rule-based kinetic Monte Carlo approach to investigate the kinetics of ligand-induced receptor aggregation and to study how the kinetics and equilibria of ligand-receptor interaction are affected by steric constraints on receptor aggregate configurations and by the formation of cyclic receptor aggregates. The results suggest that formation of linear chains of cyclic receptor dimers may be important for generating secretory signals. Steric effects that limit receptor aggregation and transient formation of small receptor aggregates may also be important.

The complexity of cell signaling and the need for a new mechanics

Cell signaling systems respond to multiple inputs, such as ligands of cell-surface receptors; and produce multiple outputs, such as changes in gene expression and cellular activities, including motility, proliferation, and death. This "macroscopic" input-output behavior is generated by a web of molecular interactions that can be viewed as taking place at a lower, "microscopic" level. These interactions prominently involve posttranslational modification of proteins and the nucleation of protein complexes. Behaviors at both the micro- and macroscopic levels are complex and must be probed systematically and characterized quantitatively as a prelude to the development of a predictive understanding of a cell signaling system. We must also have a theoretical framework or a mechanics within which we can determine how macroscopic behaviors emerge from known microscopic behaviors or change with manipulations of microscopic behaviors. To connect behaviors at both levels, we suggest that a new mechanics is now required. Newly available data support the idea that this mechanics should enable one to track the site-specific details of molecular interactions in a model, such as the phosphorylation status of individual amino acid residues within a protein.

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.

GetBonNie for building, analyzing and sharing rule-based models

SUMMARY

GetBonNie is a web-based application for building, analyzing and sharing rule-based models encoded in the BioNetGen language (BNGL). Tools accessible within the GetBonNie environment include (i) an applet for drawing graphs that correspond to BNGL code; (ii) a network-generation engine for translating a set of rules into a chemical reaction network; (iii) simulation engines that implement generate-first, on-the-fly and network-free methods for simulating rule-based models; and (iv) a database for sharing models, parameter values, annotations, simulation tasks and results.

AVAILABILITY

GetBonNie is free at (http://getbonnie.org).

Determinants of bistability in induction of the Escherichia coli lac operon

The authors have developed a mathematical model of regulation of expression of the Escherichia coli lac operon, and have investigated bistability in its steady-state induction behaviour in the absence of external glucose. Numerical analysis of equations describing regulation by artificial inducers revealed two natural bistability parameters that can be used to control the range of inducer concentrations over which the model exhibits bistability. By tuning these bistability parameters, the authors found a family of biophysically reasonable systems that are consistent with an experimentally determined bistable region for induction by thio-methylgalactoside (TMG) (in Ozbudak et al. Nature, 2004, 427; p. 737). To model regulation by lactose, the authors developed similar equations in which allolactose, a metabolic intermediate in lactose metabolism and a natural inducer of lac, is the inducer. For biophysically reasonable parameter values, these equations yield no bistability in response to induction by lactose - only systems with an unphysically small permease-dependent export effect can exhibit small amounts of bistability for limited ranges of parameter values. These results cast doubt on the relevance of bistability in the lac operon within the natural context of E. coli, and help shed light on the controversy among existing theoretical studies that address this issue. The results also motivate a deeper experimental characterisation of permease-independent transport of lac inducers, and suggest an experimental approach to address the relevance of bistability in the lac operon within the natural context of E. coli. The sensitivity of lac bistability to the type of inducer emphasises the importance of metabolism in determining the functions of genetic regulatory networks.

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.

Kinetic proofreading model

Kinetic proofreading is an intrinsic property of the cell signaling process. It arises as a consequence of the multiple interactions that occur after a ligand triggers a receptor to initiate a ignaling cascade and it ensures that false signals do not propagate to completion. In order for an active signaling complex to form after a ligand binds to a cell surface receptor, a sequence of binding and phosphorylation events must occur that are rapidly reversed if the ligand dissociates from the receptor. This gives rise to a mechanism by which cells can discriminate among ligands that bind to the same receptor but form ligand-receptor complexes with different lifetimes. We review experiments designed to test for kinetic proofreading and models that exhibit kinetic proofreading.

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.

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/).

Dynamics of the nucleated polymerization model of prion replication

The disease process for transmissible spongiform encephalopathies (TSEs), in one way or another, involves the conversion of a predominantly alpha-helical normal host-coded prion protein (PrP(C)) to an abnormally folded (predominantly beta sheet) protease resistant isoform (PrP(Sc)). Several alternative mechanisms have been proposed for this auto-catalytic process. Here the dynamical behavior of one of these models, the nucleated polymerization model, is studied by Monte Carlo discrete-event simulation of the explicit conversion reactions. These simulations demonstrate the characteristic dynamical behavior of this model for prion replication. Using estimates for the reaction rates and concentrations, time courses are estimated for concentration of PrP(Sc), PrP(Sc) aggregates, and PrP(C) as well as size distributions for the aggregates. The implications of these dynamics on protein misfolding cyclic amplification (PMCA) is discussed.