Scalable Rule-Based Modelling of Allosteric Proteins and Biochemical Networks

Much of the complexity of biochemical networks comes from the information-processing abilities of allosteric proteins, be they receptors, ion-channels, signalling molecules or transcription factors. An allosteric protein can be uniquely regulated by each combination of input molecules that it binds. This “regulatory complexity” causes a combinatorial increase in the number of parameters required to fit experimental data as the number of protein interactions increases. It therefore challenges the creation, updating, and re-use of biochemical models. Here, we propose a rule-based modelling framework that exploits the intrinsic modularity of protein structure to address regulatory complexity. Rather than treating proteins as “black boxes”, we model their hierarchical structure and, as conformational changes, internal dynamics. By modelling the regulation of allosteric proteins through these conformational changes, we often decrease the number of parameters required to fit data, and so reduce over-fitting and improve the predictive power of a model. Our method is thermodynamically grounded, imposes detailed balance, and also includes molecular cross-talk and the background activity of enzymes. We use our Allosteric Network Compiler to examine how allostery can facilitate macromolecular assembly and how competitive ligands can change the observed cooperativity of an allosteric protein. We also develop a parsimonious model of G protein-coupled receptors that explains functional selectivity and can predict the rank order of potency of agonists acting through a receptor. Our methodology should provide a basis for scalable, modular and executable modelling of biochemical networks in systems and synthetic biology.

[1]  T. Kenakin,et al.  Agonist-receptor efficacy. II. Agonist trafficking of receptor signals. , 1995, Trends in pharmacological sciences.

[2]  J. Changeux,et al.  ON THE NATURE OF ALLOSTERIC TRANSITIONS: A PLAUSIBLE MODEL. , 1965, Journal of molecular biology.

[3]  J E Leffler,et al.  Parameters for the Description of Transition States. , 1953, Science.

[4]  J. W. Wells,et al.  Recovery of oligomers and cooperativity when monomers of the M2 muscarinic cholinergic receptor are reconstituted into phospholipid vesicles. , 2007, Biochemistry.

[5]  D. Koshland,et al.  Comparison of experimental binding data and theoretical models in proteins containing subunits. , 1966, Biochemistry.

[6]  T. Kenakin,et al.  G Protein-Coupled Receptor Allosterism and Complexing , 2002, Pharmacological Reviews.

[7]  J. Hopfield,et al.  From molecular to modular cell biology , 1999, Nature.

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

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

[10]  N. M. Senozan,et al.  Hemoglobin-oxygen-carbon monoxide equilibria with the MWC model. , 1998, Biophysical Chemistry.

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

[12]  N. Lavine,et al.  G Protein-coupled Receptors Form Stable Complexes with Inwardly Rectifying Potassium Channels and Adenylyl Cyclase* , 2002, The Journal of Biological Chemistry.

[13]  Peter Klein,et al.  On the nature of low- and high-affinity EGF receptors on living cells. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Graeme Milligan,et al.  G Protein-Coupled Receptor Dimerization: Function and Ligand Pharmacology , 2004, Molecular Pharmacology.

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

[16]  Ming Zhou,et al.  Mapping the conformational wave of acetylcholine receptor channel gating , 2000, Nature.

[17]  Krzysztof Palczewski,et al.  Oligomerization of G protein-coupled receptors: past, present, and future. , 2004, Biochemistry.

[18]  T. Durroux Principles: a model for the allosteric interactions between ligand binding sites within a dimeric GPCR. , 2005, Trends in pharmacological sciences.

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

[20]  Lila M. Gierasch,et al.  Sending Signals Dynamically , 2009, Science.

[21]  Peter S Swain,et al.  Efficient attenuation of stochasticity in gene expression through post-transcriptional control. , 2004, Journal of molecular biology.

[22]  L. Devi,et al.  Heterodimerization of G-protein-coupled receptors: pharmacology, signaling and trafficking. , 2001, Trends in pharmacological sciences.

[23]  Leonor Saiz,et al.  Stochastic dynamics of macromolecular-assembly networks , 2006, Molecular systems biology.

[24]  Julien F. Ollivier,et al.  Colored extrinsic fluctuations and stochastic gene expression , 2008, Molecular systems biology.

[25]  Terry Kenakin,et al.  Ligand-selective receptor conformations revisited: the promise and the problem. , 2003, Trends in pharmacological sciences.

[26]  J. Tuszynski,et al.  Molecular and Cellular Biophysics , 2005 .

[27]  M. Robitaille,et al.  Seven Transmembrane Receptor Core Signaling Complexes Are Assembled Prior to Plasma Membrane Trafficking* , 2006, Journal of Biological Chemistry.

[28]  Katherine C. Chen,et al.  Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. , 2003, Current opinion in cell biology.

[29]  C. Shayo,et al.  Tiotidine, a histamine H2 receptor inverse agonist that binds with high affinity to an inactive G-protein-coupled form of the receptor. Experimental support for the cubic ternary complex model. , 2003, Molecular pharmacology.

[30]  G. Wahl,et al.  Regulating the p53 pathway: in vitro hypotheses, in vivo veritas , 2006, Nature Reviews Cancer.

[31]  E. Henry,et al.  Application of linear free energy relations to protein conformational changes: the quaternary structural change of hemoglobin. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[32]  T. Kenakin,et al.  The cubic ternary complex receptor-occupancy model. III. resurrecting efficacy. , 1996, Journal of theoretical biology.

[33]  D E Wemmer,et al.  Two-state allosteric behavior in a single-domain signaling protein. , 2001, Science.

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

[35]  Melanie I. Stefan,et al.  An allosteric model of calmodulin explains differential activation of PP2B and CaMKII , 2008, Proceedings of the National Academy of Sciences.

[36]  J. Kukkonen,et al.  Modelling of promiscuous receptor-Gi/Gs-protein coupling and effector response. , 2001, Trends in pharmacological sciences.

[37]  M. Greenwood,et al.  Physiological relevance of GPCR oligomerization and its impact on drug discovery. , 2008, Drug discovery today.

[38]  Wendell A Lim,et al.  Rewiring cell signaling: the logic and plasticity of eukaryotic protein circuitry. , 2004, Current opinion in structural biology.

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

[40]  Edgar Jacoby,et al.  The 7 TM G‐Protein‐Coupled Receptor Target Family , 2006, ChemMedChem.

[41]  M. Beato,et al.  How to impose microscopic reversibility in complex reaction mechanisms. , 2004, Biophysical journal.

[42]  S. Asakura,et al.  Two-state model for bacterial chemoreceptor proteins. The role of multiple methylation. , 1984, Journal of molecular biology.

[43]  T. Kenakin Principles: receptor theory in pharmacology. , 2004, Trends in pharmacological sciences.

[44]  Stuart J. Edelstein,et al.  A kinetic mechanism for nicotinic acetylcholine receptors based on multiple allosteric transitions , 1996, Biological Cybernetics.

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

[46]  H. Stanley,et al.  A general approach to co-operativity and its application to the oxygen equilibrium of hemoglobin and its effectors. , 1974, Journal of molecular biology.

[47]  E. Henry,et al.  A tertiary two-state allosteric model for hemoglobin. , 2002, Biophysical chemistry.

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

[49]  T. Kenakin,et al.  The use of stimulus-biased assay systems to detect agonist-specific receptor active states: implications for the trafficking of receptor stimulus by agonists. , 2000, Molecular pharmacology.

[50]  Ernst Dieter Gilles,et al.  Thermodynamic Constraints in Kinetic Modeling: Thermodynamic‐Kinetic Modeling in Comparison to Other Approaches , 2008 .

[51]  T. Gudermann,et al.  Diversity and selectivity of receptor-G protein interaction. , 1996, Annual review of pharmacology and toxicology.

[52]  T Pawson,et al.  SH2 domains, interaction modules and cellular wiring. , 2001, Trends in cell biology.

[53]  T. Kortemme,et al.  Complex topology rather than complex membership is a determinant of protein dosage sensitivity , 2009, Molecular Systems Biology.

[54]  D. Bray,et al.  Computer-based analysis of the binding steps in protein complex formation. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[55]  Susan R. George,et al.  G-Protein-coupled receptor oligomerization and its potential for drug discovery , 2002, Nature Reviews Drug Discovery.

[56]  R. Brent,et al.  Modelling cellular behaviour , 2001, Nature.

[57]  Wendell A Lim,et al.  The modular logic of signaling proteins: building allosteric switches from simple binding domains. , 2002, Current opinion in structural biology.

[58]  A. Levitzki,et al.  Ligand competition curves as a diagnostic tool for delineating the nature of site-site interactions: theory. , 1979, European journal of biochemistry.

[59]  Julio Saez-Rodriguez,et al.  A domain-oriented approach to the reduction of combinatorial complexity in signal transduction networks , 2006, BMC Bioinformatics.

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

[61]  Tony Pawson,et al.  Protein modules and signalling networks , 1995, Nature.

[62]  D. Hall,et al.  Modeling the functional effects of allosteric modulators at pharmacological receptors: an extension of the two-state model of receptor activation. , 2000, Molecular pharmacology.

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

[64]  G. K. Ackers,et al.  Quantitative model for gene regulation by lambda phage repressor. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[65]  Nicolas Le Novère,et al.  STOCHSIM: modelling of stochastic biomolecular processes , 2001, Bioinform..

[66]  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.

[67]  Peter S. Swain,et al.  Facile: a command-line network compiler for systems biology , 2007, BMC Systems Biology.

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

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

[70]  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.