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.

[1]  B. George Barisas,et al.  Aggregation and gelation of divalent cell surface receptors by rigid polyvalent ligands: examination by theoretical, kinetic and thermodynamic techniques☆ , 2003 .

[2]  Vincent Danos,et al.  Internal coarse-graining of molecular systems , 2009, Proceedings of the National Academy of Sciences.

[3]  T. Pawson,et al.  Assembly of Cell Regulatory Systems Through Protein Interaction Domains , 2003, Science.

[4]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[5]  James R Faeder,et al.  Aggregation of membrane proteins by cytosolic cross-linkers: theory and simulation of the LAT-Grb2-SOS1 system. , 2009, Biophysical journal.

[6]  J C Hewson,et al.  Stochastic simulation of transport and chemical kinetics in turbulent CO/H2/N2 flames , 2001 .

[7]  Ivo F Sbalzarini,et al.  A new class of highly efficient exact stochastic simulation algorithms for chemical reaction networks. , 2009, The Journal of chemical physics.

[8]  Bruce E. Shapiro,et al.  Cellerator: extending a computer algebra system to include biochemical arrows for signal transduction simulations , 2003, Bioinform..

[9]  James R Faeder,et al.  Efficient modeling, simulation and coarse-graining of biological complexity with NFsim , 2011, Nature Methods.

[10]  James R Faeder,et al.  The complexity of complexes in signal transduction , 2003, Biotechnology and bioengineering.

[11]  Richard G Posner,et al.  Trivalent antigens for degranulation of mast cells. , 2007, Organic letters.

[12]  Jeremy Gunawardena,et al.  Programming with models: modularity and abstraction provide powerful capabilities for systems biology , 2009, Journal of The Royal Society Interface.

[13]  A S Perelson,et al.  Equilibrium theory for the clustering of bivalent cell surface receptors by trivalent ligands. Application to histamine release from basophils. , 1984, Biophysical journal.

[14]  L. Kiessling,et al.  Synthetic multivalent ligands in the exploration of cell-surface interactions. , 2000, Current opinion in chemical biology.

[15]  A. B. Bortz,et al.  A new algorithm for Monte Carlo simulation of Ising spin systems , 1975 .

[16]  William S. Hlavacek,et al.  Simulation of large-scale rule-based models , 2009, Bioinform..

[17]  James R Faeder,et al.  Kinetic Monte Carlo method for rule-based modeling of biochemical networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Roger Brent,et al.  Automatic generation of cellular reaction networks with Moleculizer 1.0 , 2005, Nature Biotechnology.

[19]  Alan S. Perelson,et al.  Some mathematical models of receptor clustering by multivalent ligands , 1984 .

[20]  Leslie M Loew,et al.  Molecular machines or pleiomorphic ensembles: signaling complexes revisited , 2009, Journal of biology.

[21]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[22]  H. Metzger,et al.  Transmembrane signaling: the joy of aggregation. , 1992, Journal of immunology.

[23]  Vincent Danos,et al.  Rule-Based Modelling of Cellular Signalling , 2007, CONCUR.

[24]  George M Whitesides,et al.  Polyvalent Interactions in Biological Systems: Implications for Design and Use of Multivalent Ligands and Inhibitors. , 1998, Angewandte Chemie.

[25]  M. Dembo,et al.  Theory of equilibrium binding of symmetric bivalent haptens to cell surface antibody: application to histamine release from basophils. , 1978, Journal of immunology.

[26]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[27]  F. Einar Kruis,et al.  Direct simulation Monte Carlo method for particle coagulation and aggregation , 2000 .

[28]  T. Hunter,et al.  Signaling—2000 and Beyond , 2000, Cell.

[29]  Qiang Chang,et al.  Monte Carlo algorithm for simulating reversible aggregation of multisite particles. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Arthur F. Voter,et al.  Introduction to the Kinetic Monte Carlo Method , 2007 .

[31]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[32]  William S. Hlavacek,et al.  BioNetGen: software for rule-based modeling of signal transduction based on the interactions of molecular domains , 2004, Bioinform..

[33]  H. Levine,et al.  A thermodynamic model for receptor clustering. , 1999, Biophysical journal.

[34]  William S. Hlavacek,et al.  RuleMonkey: software for stochastic simulation of rule-based models , 2010, BMC Bioinformatics.

[35]  D. Lauffenburger,et al.  Receptors: Models for Binding, Trafficking, and Signaling , 1993 .

[36]  Béla Bollobás,et al.  Modern Graph Theory , 2002, Graduate Texts in Mathematics.

[37]  W. S. Hlavacek,et al.  Mathematical and computational models of immune-receptor signalling , 2004, Nature Reviews Immunology.

[38]  A. Perelson.  Receptor clustering on a cell surface. I. theory of receptor cross-linking by ligands bearing two chemically identical functional groups , 1980 .

[39]  W. S. Hlavacek,et al.  Modeling multivalent ligand-receptor interactions with steric constraints on configurations of cell-surface receptor aggregates. , 2010, Biophysical journal.

[40]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[41]  Michael Hucka,et al.  A Correction to the Review Titled "Rules for Modeling Signal-Transduction Systems" by W. S. Hlavacek et al. , 2006, Science's STKE.

[42]  B. Goldstein,et al.  The kinetics of bivalent ligand-bivalent receptor aggregation: ring formation and the breakdown of the equivalent site approximation. , 1995, Mathematical biosciences.

[43]  Vincent Danos,et al.  Scalable Simulation of Cellular Signaling Networks , 2007, APLAS.

[44]  James R Faeder,et al.  Rule-based modeling of biochemical systems with BioNetGen. , 2009, Methods in molecular biology.