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). WIREs Syst Biol Med 2014, 6:13–36. doi: 10.1002/wsbm.1245

[1]  D. Lauffenburger,et al.  Input–output behavior of ErbB signaling pathways as revealed by a mass action model trained against dynamic data , 2009, Molecular systems biology.

[2]  Hugh D. Spence,et al.  Minimum information requested in the annotation of biochemical models (MIRIAM) , 2005, Nature Biotechnology.

[3]  Vincent Danos,et al.  Combinatorial Complexity and Compositional Drift in Protein Interaction Networks , 2012, PloS one.

[4]  Jayajit Das,et al.  Monovalent and Multivalent Ligation of the B Cell Receptor Exhibit Differential Dependence upon Syk and Src Family Kinases , 2013, Science Signaling.

[5]  Boris N. Kholodenko,et al.  Ligand-Specific c-Fos Expression Emerges from the Spatiotemporal Control of ErbB Network Dynamics , 2010, Cell.

[6]  Leslie M. Loew,et al.  Computational Analysis of Rho GTPase Cycling , 2013, PLoS Comput. Biol..

[7]  D. Bray Protein molecules as computational elements in living cells , 1995, Nature.

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

[9]  M. Meyerson,et al.  The T790M mutation in EGFR kinase causes drug resistance by increasing the affinity for ATP , 2008, Proceedings of the National Academy of Sciences.

[10]  Chi V Dang,et al.  MYC on the Path to Cancer , 2012, Cell.

[11]  Holger Conzelmann,et al.  Dynamic pathway modeling of signal transduction networks: a domain-oriented approach. , 2008, Methods in molecular biology.

[12]  Jianpeng Ma,et al.  CHARMM: The biomolecular simulation program , 2009, J. Comput. Chem..

[13]  L M Loew,et al.  CaMKII activation and dynamics are independent of the holoenzyme structure: an infinite subunit holoenzyme approximation , 2012, Physical biology.

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

[15]  Gerhard Hummer,et al.  Interface-Resolved Network of Protein-Protein Interactions , 2013, PLoS Comput. Biol..

[16]  Andrea Asztalos,et al.  A coarse-grained model for synergistic action of multiple enzymes on cellulose , 2012, Biotechnology for Biofuels.

[17]  Scott B. Baden,et al.  Fast Monte Carlo Simulation Methods for Biological Reaction-Diffusion Systems in Solution and on Surfaces , 2008, SIAM J. Sci. Comput..

[18]  Aviv Regev,et al.  Representation and Simulation of Biochemical Processes Using the pi-Calculus Process Algebra , 2000, Pacific Symposium on Biocomputing.

[19]  F. Klauschen,et al.  Computational Modeling of Cellular Signaling Processes Embedded into Dynamic Spatial Contexts , 2012, Nature Methods.

[20]  Michael Hucka,et al.  LibSBML: an API Library for SBML , 2008, Bioinform..

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

[22]  Augustus George Vernon Harcourt,et al.  III. On the laws of connexion between the conditions of a chemical change and its amount , 2022, Proceedings of the Royal Society of London.

[23]  T Pawson,et al.  Formation of Shc-Grb2 complexes is necessary to induce neoplastic transformation by overexpression of Shc proteins. , 1994, Oncogene.

[24]  Hod Lipson,et al.  The evolutionary origins of modularity , 2012, Proceedings of the Royal Society B: Biological Sciences.

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

[26]  J Yang,et al.  Rule-based modelling and simulation of biochemical systems with molecular finite automata. , 2010, IET systems biology.

[27]  Melanie I. Stefan,et al.  BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models , 2010, BMC Systems Biology.

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

[29]  Jason A. Papin,et al.  The JAK-STAT signaling network in the human B-cell: an extreme signaling pathway analysis. , 2004, Biophysical journal.

[30]  Hiroaki Kitano,et al.  A framework for mapping, visualisation and automatic model creation of signal-transduction networks , 2012, Molecular systems biology.

[31]  G. M. Walton,et al.  Analysis of deletions of the carboxyl terminus of the epidermal growth factor receptor reveals self-phosphorylation at tyrosine 992 and enhanced in vivo tyrosine phosphorylation of cell substrates. , 1990, The Journal of biological chemistry.

[32]  W. S. Hlavacek,et al.  Two Challenges of Systems Biology , 2011 .

[33]  Nirmalya Chowdhury,et al.  Applied Computing , 2004, Lecture Notes in Computer Science.

[34]  M. Hayman,et al.  Molecular Mechanism for a Role of SHP2 in Epidermal Growth Factor Receptor Signaling , 2003, Molecular and Cellular Biology.

[35]  Bastian Robert Angermann,et al.  The Simmune Modeler visual interface for creating signaling networks based on bi-molecular interactions , 2013, Bioinform..

[36]  Omer Dushek,et al.  Systems Model of T Cell Receptor Proximal Signaling Reveals Emergent Ultrasensitivity , 2013, PLoS Comput. Biol..

[37]  M. Mann,et al.  Global, In Vivo, and Site-Specific Phosphorylation Dynamics in Signaling Networks , 2006, Cell.

[38]  Daniel T Gillespie,et al.  Stochastic simulation of chemical kinetics. , 2007, Annual review of physical chemistry.

[39]  J. Downward,et al.  Autophosphorylation sites on the epidermal growth factor receptor , 1984, Nature.

[40]  Sven Sahle,et al.  Computational modeling of biochemical networks using COPASI. , 2009, Methods in molecular biology.

[41]  Vincent Danos,et al.  Equilibrium and termination II: the case of Petri nets , 2013, Mathematical Structures in Computer Science.

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

[43]  William S. Hlavacek,et al.  Rule-based modeling of biochemical networks , 2005, Complex..

[44]  E. Shapiro,et al.  Cellular abstractions: Cells as computation , 2002, Nature.

[45]  Gary D Bader,et al.  NetPath: a public resource of curated signal transduction pathways , 2010, Genome Biology.

[46]  Tobias Heindel,et al.  Pattern Graphs and Rule-Based Models: The Semantics of Kappa , 2013, FoSSaCS.

[47]  Fangping Mu,et al.  Carbon-fate maps for metabolic reactions , 2007, Bioinform..

[48]  T. Pawson,et al.  Cell Signaling in Space and Time: Where Proteins Come Together and When They’re Apart , 2009, Science.

[49]  M Beato,et al.  On Imposing Detailed Balance in Complex Reaction Mechanisms , 2006 .

[50]  Mudita Singhal,et al.  COPASI - a COmplex PAthway SImulator , 2006, Bioinform..

[51]  Omer Dushek,et al.  Ultrasensitivity in multisite phosphorylation of membrane-anchored proteins. , 2011, Biophysical journal.

[52]  Peter Dittrich,et al.  Rule-based modeling and simulations of the inner kinetochore structure. , 2013, Progress in biophysics and molecular biology.

[53]  Stacey D. Finley,et al.  Timescale analysis of rule‐based biochemical reaction networks , 2012, Biotechnology progress.

[54]  Keith Devlin,et al.  Logic and information , 1991 .

[55]  J. Schlessinger,et al.  Hierarchy of binding sites for Grb2 and Shc on the epidermal growth factor receptor , 1994, Molecular and cellular biology.

[56]  Christiane Garbay,et al.  p120-Ras GTPase activating protein (RasGAP): a multi-interacting protein in downstream signaling. , 2009, Biochimie.

[57]  Angelo D. Favia,et al.  Protein promiscuity and its implications for biotechnology , 2009, Nature Biotechnology.

[58]  John J Tyson,et al.  Functional motifs in biochemical reaction networks. , 2010, Annual review of physical chemistry.

[59]  Michelle L. Wynn,et al.  Logic-based models in systems biology: a predictive and parameter-free network analysis method. , 2012, Integrative biology : quantitative biosciences from nano to macro.

[60]  Daniel A Beard,et al.  Specification, construction, and exact reduction of state transition system models of biochemical processes. , 2012, The Journal of chemical physics.

[61]  D. Shaw,et al.  Conformational Coupling across the Plasma Membrane in Activation of the EGF Receptor , 2013, Cell.

[62]  C. J.,et al.  Predicting Temporal Fluctuations in an Intracellular Signalling Pathway , 1998 .

[63]  H. Kitano Systems Biology: A Brief Overview , 2002, Science.

[64]  Holger Conzelmann,et al.  Rapid phospho-turnover by receptor tyrosine kinases impacts downstream signaling and drug binding. , 2011, Molecular cell.

[65]  F. J. Poelwijk,et al.  The spatial architecture of protein function and adaptation , 2012, Nature.

[66]  Lei Deng,et al.  PrePPI: a structure-informed database of protein–protein interactions , 2012, Nucleic Acids Res..

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

[68]  Y. Kido,et al.  Grb2/Ash binds directly to tyrosines 1068 and 1086 and indirectly to tyrosine 1148 of activated human epidermal growth factor receptors in intact cells. , 1994, The Journal of biological chemistry.

[69]  M. Mann,et al.  Quantitative, high-resolution proteomics for data-driven systems biology. , 2011, Annual review of biochemistry.

[70]  Xingming Zhao,et al.  Computational Systems Biology , 2013, TheScientificWorldJournal.

[71]  Dietmar Wendt,et al.  The Markoff Automaton: A New Algorithm For Simulating The Time-Evolution Of Large Stochastic Dynamic Systems , 1995 .

[72]  Jacky L. Snoep,et al.  BioModels Database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems , 2005, Nucleic Acids Res..

[73]  Jin Yang,et al.  Graph Theory for Rule-Based Modeling of Biochemical Networks , 2006, Trans. Comp. Sys. Biology.

[74]  John Kuriyan,et al.  Regulation of the catalytic activity of the EGF receptor. , 2011, Current opinion in structural biology.

[75]  S. Mangan,et al.  Structure and function of the feed-forward loop network motif , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[76]  Dipak Barua,et al.  Single-Cell Measurements of IgE-Mediated FcεRI Signaling Using an Integrated Microfluidic Platform , 2013, PloS one.

[77]  D. Lauffenburger,et al.  Systems Analysis of EGF Receptor Signaling Dynamics with Micro-Western Arrays , 2010, Nature Methods.

[78]  Matthew S. Creamer,et al.  Specification, annotation, visualization and simulation of a large rule-based model for ERBB receptor signaling , 2012, BMC Systems Biology.

[79]  Ernst Dieter Gilles,et al.  Exact model reduction of combinatorial reaction networks , 2008, BMC Systems Biology.

[80]  Erich Bornberg-Bauer,et al.  Dynamics and adaptive benefits of modular protein evolution. , 2013, Current opinion in structural biology.

[81]  R. Bernards,et al.  Unresponsiveness of colon cancer to BRAF(V600E) inhibition through feedback activation of EGFR , 2012, Nature.

[82]  Nicolas Le Novère,et al.  Supporting SBML as a model exchange format in software applications. , 2013, Methods in molecular biology.

[83]  Roger Brent,et al.  Detailed Simulations of Cell Biology with Smoldyn 2.1 , 2010, PLoS Comput. Biol..

[84]  Shigeyuki Yokoyama,et al.  Structural Evidence for Loose Linkage between Ligand Binding and Kinase Activation in the Epidermal Growth Factor Receptor , 2010, Molecular and Cellular Biology.

[85]  Corrado Priami,et al.  Application of a stochastic name-passing calculus to representation and simulation of molecular processes , 2001, Inf. Process. Lett..

[86]  U. Bhalla,et al.  Complexity in biological signaling systems. , 1999, Science.

[87]  K. Lidke,et al.  supplementary figures , 2018 .

[88]  Alan S. Perelson,et al.  Modeling and Simulation of Aggregation of Membrane Protein LAT with Molecular Variability in the Number of Binding Sites for Cytosolic Grb2-SOS1-Grb2 , 2012, PloS one.

[89]  Andre Hoelz,et al.  Structural Evidence for Feedback Activation by Ras·GTP of the Ras-Specific Nucleotide Exchange Factor SOS , 2003, Cell.

[90]  Tony Pawson,et al.  Phosphotyrosine Signaling: Evolving a New Cellular Communication System , 2010, Cell.

[91]  Peter K. Sorger,et al.  Measuring and Modeling Apoptosis in Single Cells , 2011, Cell.

[92]  K. Sachs,et al.  Causal Protein-Signaling Networks Derived from Multiparameter Single-Cell Data , 2005, Science.

[93]  Lily A. Chylek Decoding the Language of Phosphorylation Site Dynamics , 2013, Science Signaling.

[94]  Lily A Chylek,et al.  Modeling biomolecular site dynamics in immunoreceptor signaling systems. , 2014, Advances in experimental medicine and biology.

[95]  A. Ullrich,et al.  All autophosphorylation sites of epidermal growth factor (EGF) receptor and HER2/neu are located in their carboxyl-terminal tails. Identification of a novel site in EGF receptor. , 1989, The Journal of biological chemistry.

[96]  Nicolas Le Novère,et al.  BioModels Database: a repository of mathematical models of biological processes. , 2013, Methods in molecular biology.

[97]  Antony W Burgess,et al.  Epidermal growth factor receptor: mechanisms of activation and signalling. , 2003, Experimental cell research.

[98]  U. Bhalla,et al.  Emergent properties of networks of biological signaling pathways. , 1999, Science.

[99]  M. Sliwkowski,et al.  An open-and-shut case? Recent insights into the activation of EGF/ErbB receptors. , 2003, Molecular cell.

[100]  Timothy C Elston,et al.  A predictive mathematical model of the DNA damage G2 checkpoint. , 2013, Journal of theoretical biology.

[101]  Y. Kido,et al.  Shc phosphotyrosine-binding domain dominantly interacts with epidermal growth factor receptors and mediates Ras activation in intact cells. , 1998, Molecular endocrinology.

[102]  T. Henzinger,et al.  Executable cell biology , 2007, Nature Biotechnology.

[103]  Luca Cardelli,et al.  Artificial Biochemistry , 2009, Algorithmic Bioprocesses.

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

[105]  Yan Liu,et al.  The gift of Gab , 2002, FEBS letters.

[106]  Michael L. Blinov,et al.  A Detailed Mathematical Model Predicts That Serial Engagement of IgE–FcεRI Complexes Can Enhance Syk Activation in Mast Cells , 2010, The Journal of Immunology.

[107]  J. Faeder,et al.  The interplay of double phosphorylation and scaffolding in MAPK pathways. , 2012, Journal of theoretical biology.

[108]  Hiroaki Kitano,et al.  The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models , 2003, Bioinform..

[109]  O. Keskin,et al.  Transient protein-protein interactions. , 2011, Protein engineering, design & selection : PEDS.

[110]  Bin Hu,et al.  Hierarchical graphs for rule-based modeling of biochemical systems , 2011, BMC Bioinformatics.

[111]  Marco Scotti,et al.  Modeling cellular compartmentation in one‐carbon metabolism , 2013, Wiley interdisciplinary reviews. Systems biology and medicine.

[112]  B. Goldstein,et al.  A Mechanistic Model of Early FcεRI Signaling: Lipid Rafts and the Question of Protection from Dephosphorylation , 2012, PloS one.

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

[114]  Boris N. Kholodenko,et al.  Signalling ballet in space and time , 2010, Nature Reviews Molecular Cell Biology.

[115]  Eric Mjolsness,et al.  Time-ordered product expansions for computational stochastic system biology , 2012, Physical biology.

[116]  B. Kholodenko,et al.  Computational Approaches for Analyzing Information Flow in Biological Networks , 2012, Science Signaling.

[117]  Ronald J. Hause,et al.  Comprehensive Binary Interaction Mapping of SH2 Domains via Fluorescence Polarization Reveals Novel Functional Diversification of ErbB Receptors , 2012, PloS one.

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

[119]  Dipak Barua,et al.  A Computational Model for Early Events in B Cell Antigen Receptor Signaling: Analysis of the Roles of Lyn and Fyn , 2012, The Journal of Immunology.

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

[121]  Tian Jin,et al.  Key Role of Local Regulation in Chemosensing Revealed by a New Molecular Interaction-Based Modeling Method , 2006, PLoS Comput. Biol..

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

[123]  P. Bork,et al.  Systematic Discovery of In Vivo Phosphorylation Networks , 2007, Cell.

[124]  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.

[125]  G. Elisabeta Marai,et al.  RuleBender: a visual interface for rule-based modeling , 2011, Bioinform..

[126]  Drew Endy,et al.  Scaffold number in yeast signaling system sets tradeoff between system output and dynamic range , 2011, Proceedings of the National Academy of Sciences.

[127]  Hanno Steen,et al.  Post‐translational modification: nature's escape from genetic imprisonment and the basis for dynamic information encoding , 2012, Wiley interdisciplinary reviews. Systems biology and medicine.

[128]  E. Gilles,et al.  Thermodynamically feasible kinetic models of reaction networks. , 2007, Biophysical journal.

[129]  Leonor Saiz,et al.  Reliable prediction of complex phenotypes from a modular design in free energy space: an extensive exploration of the lac operon. , 2013, ACS synthetic biology.

[130]  Wendell A. Lim,et al.  Rapid Diversification of Cell Signaling Phenotypes by Modular Domain Recombination , 2010, Science.

[131]  A. I. Torres,et al.  Engineering Biomass Conversion Processes: A Systems Perspective , 2013 .

[132]  E. Gilles,et al.  Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors , 2002, Nature Biotechnology.

[133]  U. Alon Network motifs: theory and experimental approaches , 2007, Nature Reviews Genetics.

[134]  James R Faeder,et al.  Rule-based modeling of signal transduction: a primer. , 2012, Methods in molecular biology.

[135]  Lukas Endler,et al.  Using chemical kinetics to model biochemical pathways. , 2013, Methods in molecular biology.

[136]  Laxmikant V. Kalé,et al.  Scalable molecular dynamics with NAMD , 2005, J. Comput. Chem..

[137]  Eric J. Deeds,et al.  Crosstalk and competition in signaling networks. , 2012, Biophysical journal.

[138]  Russell Schwartz,et al.  Queue-based method for efficient simulation of biological self-assembly systems , 2005 .

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

[140]  Andrea Califano,et al.  Reverse‐engineering human regulatory networks , 2012, Wiley interdisciplinary reviews. Systems biology and medicine.

[141]  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.

[142]  G. Lahav,et al.  Encoding and Decoding Cellular Information through Signaling Dynamics , 2013, Cell.

[143]  James R Faeder,et al.  Toward a comprehensive language for biological systems , 2011, BMC Biology.

[144]  James R Faeder,et al.  Shaping the response: the role of FcεRI and Syk expression levels in mast cell signaling. , 2010, IET systems biology.

[145]  Tony Pawson,et al.  Modular evolution of phosphorylation-based signalling systems , 2012, Philosophical Transactions of the Royal Society B: Biological Sciences.

[146]  Conrad C. Huang,et al.  UCSF Chimera—A visualization system for exploratory research and analysis , 2004, J. Comput. Chem..

[147]  Markus J. Herrgård,et al.  Integrating high-throughput and computational data elucidates bacterial networks , 2004, Nature.

[148]  Jonathan G. Lees,et al.  Transient protein-protein interactions: structural, functional, and network properties. , 2010, Structure.

[149]  Michael B. Yaffe,et al.  Data-driven modelling of signal-transduction networks , 2006, Nature Reviews Molecular Cell Biology.

[150]  E. Stites The Response of Cancers to BRAF Inhibition Underscores the Importance of Cancer Systems Biology , 2012, Science Signaling.

[151]  Bin Hu,et al.  Guidelines for visualizing and annotating rule-based models. , 2011, Molecular bioSystems.

[152]  Dipak Barua,et al.  Modeling the Effect of APC Truncation on Destruction Complex Function in Colorectal Cancer Cells , 2013, PLoS Comput. Biol..

[153]  W. S. Hlavacek,et al.  A network model of early events in epidermal growth factor receptor signaling that accounts for combinatorial complexity. , 2006, Bio Systems.

[154]  Carlos F. Lopez,et al.  Programming biological models in Python using PySB , 2013, Molecular systems biology.

[155]  D. Lauffenburger,et al.  Multiple reaction monitoring for robust quantitative proteomic analysis of cellular signaling networks , 2007, Proceedings of the National Academy of Sciences.

[156]  Eric Bonabeau,et al.  Agent-based modeling: Methods and techniques for simulating human systems , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[157]  M. Mann,et al.  Phosphotyrosine interactome of the ErbB-receptor kinase family , 2005, Molecular systems biology.

[158]  Glynn Winskel,et al.  Constraining rule-based dynamics with types , 2013, Math. Struct. Comput. Sci..

[159]  Carol S. Woodward,et al.  Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers , 2020, ACM Trans. Math. Softw..

[160]  B. Kholodenko,et al.  Ligand-dependent responses of the ErbB signaling network: experimental and modeling analyses , 2007, Molecular systems biology.

[161]  I. Nemenman,et al.  Information Transduction Capacity of Noisy Biochemical Signaling Networks , 2011, Science.

[162]  P. Shannon,et al.  Cytoscape: a software environment for integrated models of biomolecular interaction networks. , 2003, Genome research.

[163]  Desmond J. Higham,et al.  Multilevel Monte Carlo for Continuous Time Markov Chains, with Applications in Biochemical Kinetics , 2011, Multiscale Model. Simul..

[164]  Jin Yang,et al.  The efficiency of reactant site sampling in network-free simulation of rule-based models for biochemical systems , 2011, Physical biology.

[165]  Gregory A Voth,et al.  Coarse-graining of multiprotein assemblies. , 2012, Current opinion in structural biology.

[166]  Jie Wu,et al.  Phosphotyrosines 627 and 659 of Gab1 Constitute a Bisphosphoryl Tyrosine-based Activation Motif (BTAM) Conferring Binding and Activation of SHP2* , 2001, The Journal of Biological Chemistry.

[167]  Amjad Farooq,et al.  Multivalent binding and facilitated diffusion account for the formation of the Grb2-Sos1 signaling complex in a cooperative manner. , 2012, Biochemistry.

[168]  B. Kholodenko,et al.  Domain-oriented reduction of rule-based network models. , 2008, IET systems biology.

[169]  Jonathan R. Karr,et al.  A Whole-Cell Computational Model Predicts Phenotype from Genotype , 2012, Cell.

[170]  Jayajit Das,et al.  Digital Signaling and Hysteresis Characterize Ras Activation in Lymphoid Cells , 2009, Cell.

[171]  Holger Sondermann,et al.  Regulation of Ras Signaling Dynamics by Sos-Mediated Positive Feedback , 2006, Current Biology.

[172]  Alfred Wittinghofer,et al.  GEFs and GAPs: Critical Elements in the Control of Small G Proteins , 2007, Cell.

[173]  Vincent Danos,et al.  Intrinsic information carriers in combinatorial dynamical systems. , 2010, Chaos.

[174]  Michael Löwe,et al.  Algebraic Approach to Single-Pushout Graph Transformation , 1993, Theor. Comput. Sci..

[175]  Russell Schwartz,et al.  Implementation of a discrete event simulator for biological self-assembly systems , 2005, Proceedings of the Winter Simulation Conference, 2005..

[176]  Andreas Hellander,et al.  Perspective: Stochastic algorithms for chemical kinetics. , 2013, The Journal of chemical physics.

[177]  Michael L Klein,et al.  Understanding nature's design for a nanosyringe. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[178]  D. Lauffenburger,et al.  Computational modeling of the EGF-receptor system: a paradigm for systems biology. , 2003, Trends in cell biology.

[179]  Ronan M. T. Fleming,et al.  A community-driven global reconstruction of human metabolism , 2013, Nature Biotechnology.

[180]  James R. Faeder,et al.  Exact Hybrid Particle/Population Simulation of Rule-Based Models of Biochemical Systems , 2013, PLoS Comput. Biol..

[181]  Vincent Danos,et al.  Rule-Based Modelling and Model Perturbation , 2009, Trans. Comp. Sys. Biology.

[182]  Anurag Sethi,et al.  Quantifying Intramolecular Binding in Multivalent Interactions: A Structure-Based Synergistic Study on Grb2-Sos1 Complex , 2011, PLoS Comput. Biol..

[183]  Thomas Hinze,et al.  Rule-based spatial modeling with diffusing, geometrically constrained molecules , 2010, BMC Bioinformatics.

[184]  Paul Nurse,et al.  Life, logic and information , 2008, Nature.

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

[186]  M. Mann,et al.  Kinase-selective enrichment enables quantitative phosphoproteomics of the kinome across the cell cycle. , 2008, Molecular cell.

[187]  Ehud Shapiro,et al.  Cells as Computation , 2003, CMSB.

[188]  Martin Meier-Schellersheim,et al.  Computational modeling of signaling networks for eukaryotic chemosensing. , 2009, Methods in molecular biology.

[189]  Srinivas Devadas,et al.  CD4 and CD8 binding to MHC molecules primarily acts to enhance Lck delivery , 2010, Proceedings of the National Academy of Sciences.

[190]  Edmund M. Clarke,et al.  Analysis and verification of the HMGB1 signaling pathway , 2010, BMC Bioinformatics.

[191]  Cosimo Laneve,et al.  Formal molecular biology , 2004, Theor. Comput. Sci..

[192]  Linda R. Petzold,et al.  Accelerated maximum likelihood parameter estimation for stochastic biochemical systems , 2012, BMC Bioinformatics.

[193]  Gavin MacBeath,et al.  Phosphotyrosine Signaling Proteins that Drive Oncogenesis Tend to be Highly Interconnected* , 2013, Molecular & Cellular Proteomics.

[194]  J. Schlessinger Cell Signaling by Receptor Tyrosine Kinases , 2000, Cell.

[195]  J. Brüning,et al.  Identification of tyrosine phosphorylation sites in human Gab-1 protein by EGF receptor kinase in vitro. , 1999, Biochemistry.

[196]  W. S. Hlavacek,et al.  How to deal with large models? , 2009, Molecular systems biology.

[197]  J. Goutsias,et al.  Markovian dynamics on complex reaction networks , 2012, 1205.5524.

[198]  Oleg A. Igoshin,et al.  Adaptable Functionality of Transcriptional Feedback in Bacterial Two-Component Systems , 2010, PLoS Comput. Biol..

[199]  Sarala M. Wimalaratne,et al.  The Systems Biology Graphical Notation , 2009, Nature Biotechnology.

[200]  J C Schaff,et al.  Virtual Cell modelling and simulation software environment. , 2008, IET systems biology.

[201]  William S. Hlavacek,et al.  Innovations of the Rule-Based Modeling Approach , 2013 .

[202]  Amjad Farooq,et al.  Assembly of the Sos1-Grb2-Gab1 ternary signaling complex is under allosteric control. , 2010, Archives of biochemistry and biophysics.

[203]  Jörg Stelling,et al.  Modular, rule-based modeling for the design of eukaryotic synthetic gene circuits , 2013, BMC Systems Biology.

[204]  Yao Sun,et al.  RuleBender: integrated modeling, simulation and visualization for rule-based intracellular biochemistry , 2012, BMC Bioinformatics.

[205]  Dagmar Iber,et al.  A Computational Analysis of the Dynamic Roles of Talin, Dok1, and PIPKI for Integrin Activation , 2011, PloS one.

[206]  Boris N Kholodenko,et al.  Scaffolding Protein Grb2-associated Binder 1 Sustains Epidermal Growth Factor-induced Mitogenic and Survival Signaling by Multiple Positive Feedback Loops* , 2006, Journal of Biological Chemistry.

[207]  Steven S Andrews,et al.  Spatial and stochastic cellular modeling with the Smoldyn simulator. , 2012, Methods in molecular biology.

[208]  V. Kiselyov,et al.  Harmonic oscillator model of the insulin and IGF1 receptors' allosteric binding and activation , 2009, Molecular systems biology.

[209]  William S. Hlavacek,et al.  Graphical rule-based representation of signal-transduction networks , 2005, SAC '05.

[210]  B. Kholodenko,et al.  Quantification of Short Term Signaling by the Epidermal Growth Factor Receptor* , 1999, The Journal of Biological Chemistry.

[211]  Zhihui Wang,et al.  Accelerating cancer systems biology research through Semantic Web technology , 2013, Wiley interdisciplinary reviews. Systems biology and medicine.

[212]  Julio Saez-Rodriguez,et al.  Creating and analyzing pathway and protein interaction compendia for modelling signal transduction networks , 2012, BMC Systems Biology.

[213]  Srinivas Devadas,et al.  Efficient stochastic simulation of reaction–diffusion processes via direct compilation , 2009, Bioinform..

[214]  D. Lauffenburger,et al.  Measurement and modeling of signaling at the single-cell level. , 2012, Biochemistry.

[215]  Xiang-Jiao Yang,et al.  Multisite protein modification and intramolecular signaling , 2005, Oncogene.

[216]  B. Honig,et al.  Structure-based prediction of protein-protein interactions on a genome-wide scale , 2012, Nature.

[217]  W. S. Hlavacek,et al.  Exploring higher-order EGFR oligomerisation and phosphorylation--a combined experimental and theoretical approach. , 2013, Molecular bioSystems.

[218]  Ozlem Keskin,et al.  Constructing structural networks of signaling pathways on the proteome scale. , 2012, Current opinion in structural biology.

[219]  Paulette Clancy,et al.  A "partitioned leaping" approach for multiscale modeling of chemical reaction dynamics. , 2006, The Journal of chemical physics.