Statistical mechanics of Monod-Wyman-Changeux (MWC) models.

The 50th anniversary of the classic Monod-Wyman-Changeux (MWC) model provides an opportunity to survey the broader conceptual and quantitative implications of this quintessential biophysical model. With the use of statistical mechanics, the mathematical implementation of the MWC concept links problems that seem otherwise to have no ostensible biological connection including ligand-receptor binding, ligand-gated ion channels, chemotaxis, chromatin structure and gene regulation. Hence, a thorough mathematical analysis of the MWC model can illuminate the performance limits of a number of unrelated biological systems in one stroke. The goal of our review is twofold. First, we describe in detail the general physical principles that are used to derive the activity of MWC molecules as a function of their regulatory ligands. Second, we illustrate the power of ideas from information theory and dynamical systems for quantifying how well the output of MWC molecules tracks their sensory input, giving a sense of the "design" constraints faced by these receptors.

[1]  D. A. Dougherty,et al.  From ab initio quantum mechanics to molecular neurobiology: a cation-pi binding site in the nicotinic receptor. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Ned S. Wingreen,et al.  Self-Organization of the Escherichia coli Chemotaxis Network Imaged with Super-Resolution Light Microscopy , 2009, PLoS biology.

[3]  H. Schiessel,et al.  Nucleosome stability and accessibility of its DNA to proteins. , 2010, Biochimie.

[4]  Robert G. Endres,et al.  Chemotactic Response and Adaptation Dynamics in Escherichia coli , 2010, PLoS Comput. Biol..

[5]  J. Changeux,et al.  Nicotinic receptors at the amino acid level. , 2000, Annual review of pharmacology and toxicology.

[6]  W. Bialek,et al.  Optimizing information flow in small genetic networks. II. Feed-forward interactions. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Monica L. Skoge,et al.  Chemosensing in Escherichia coli: two regimes of two-state receptors. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Christoph Adami,et al.  Information theory in molecular biology , 2004, q-bio/0405004.

[9]  S. Laughlin,et al.  An Energy Budget for Signaling in the Grey Matter of the Brain , 2001, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[10]  Jose C. Martínez,et al.  Kinetic analysis and modelling of the allosteric behaviour of liver and muscle glycogen phosphorylases , 2006, Journal of molecular recognition : JMR.

[11]  L. Shapiro,et al.  Polar location of the chemoreceptor complex in the Escherichia coli cell. , 1993, Science.

[12]  James O. Wrabl,et al.  Structural and energetic basis of allostery. , 2012, Annual review of biophysics.

[13]  M. Alexander,et al.  Principles of Neural Science , 1981 .

[14]  H. Judson.  The Eighth Day of Creation: Makers of the Revolution in Biology , 2013 .

[15]  W. Austin Elam,et al.  Physical Biology of the Cell , 2014, The Yale Journal of Biology and Medicine.

[16]  H. Berg,et al.  Binding of the Escherichia coli response regulator CheY to its target measured in vivo by fluorescence resonance energy transfer , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Aleksandra M Walczak,et al.  Information transmission in genetic regulatory networks: a review , 2011, Journal of physics. Condensed matter : an Institute of Physics journal.

[18]  A. Oudenaarden,et al.  Nature, Nurture, or Chance: Stochastic Gene Expression and Its Consequences , 2008, Cell.

[19]  William Bialek,et al.  Spikes: Exploring the Neural Code , 1996 .

[20]  C. M. Jones,et al.  Can a two-state MWC allosteric model explain hemoglobin kinetics? , 1997, Biochemistry.

[21]  J. Gerhart,et al.  The enzymology of control by feedback inhibition. , 1962, The Journal of biological chemistry.

[22]  Ellen S. Vitetta,et al.  An allosteric model for heterogeneous receptor complexes : Understanding bacterial chemotaxis responses to multiple stimuli , 2006 .

[23]  M. Wulff,et al.  Unveiling the timescale of the R-T transition in human hemoglobin. , 2010, Journal of molecular biology.

[24]  J. Changeux.  Allostery and the Monod-Wyman-Changeux model after 50 years. , 2012, Annual review of biophysics.

[25]  Thomas Duke,et al.  The logical repertoire of ligand-binding proteins , 2005, Physical biology.

[26]  Michael L. Hines,et al.  NeuroML: A Language for Describing Data Driven Models of Neurons and Networks with a High Degree of Biological Detail , 2010, PLoS Comput. Biol..

[27]  M. Kreitman,et al.  Functional Evolution of a cis-Regulatory Module , 2005, PLoS biology.

[28]  John Reinitz,et al.  A database for management of gene expression data in situ , 2004, Bioinform..

[29]  J. Widom,et al.  Mechanism of protein access to specific DNA sequences in chromatin: a dynamic equilibrium model for gene regulation. , 1995, Journal of molecular biology.

[30]  Yuhong Yang,et al.  Information Theory, Inference, and Learning Algorithms , 2005 .

[31]  Y. Tu,et al.  Quantitative modeling of sensitivity in bacterial chemotaxis: The role of coupling among different chemoreceptor species , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[32]  R. Shulman.  Spectroscopic Contributions to the Understanding of Hemoglobin Function: Implications for Structural Biology , 2001, IUBMB life.

[33]  E. Klipp,et al.  Information theory based approaches to cellular signaling. , 2011, Biochimica et biophysica acta.

[34]  H. Berg.  Random Walks in Biology , 2018 .

[35]  G. Kellett,et al.  Kinetics of the cooperative binding of glucose to dimeric yeast hexokinase P-I. , 1995, The Biochemical journal.

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

[37]  N. Patel,et al.  Evidence for stabilizing selection in a eukaryotic enhancer element , 2000, Nature.

[38]  M. Eigen.  New looks and outlooks on physical enzymology , 1968, Quarterly Reviews of Biophysics.

[39]  H. Berg,et al.  Receptor sensitivity in bacterial chemotaxis , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[40]  H. Berg.  Motile Behavior of Bacteria , 2000 .

[41]  Andre Levchenko,et al.  The application of information theory to biochemical signaling systems , 2012, Physical biology.

[42]  D. Fisher.  The Eighth Day of Creation: Makers of the Revolution in Biology , 1979 .

[43]  K. Laidler,et al.  Development of transition-state theory , 1983 .

[44]  Jorge Goncalves,et al.  Control theory and systems biology , 2009 .

[45]  Ned S. Wingreen,et al.  Self-Organization of the Escherichia Coli Chemotaxis Network Imaged with Super-Resolution Light Microscopy , 2010 .

[46]  L. Mirny,et al.  Nucleosome-mediated cooperativity between transcription factors , 2009, Proceedings of the National Academy of Sciences.

[47]  W. Bialek,et al.  Optimizing information flow in small genetic networks. III. A self-interacting gene. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  S. Sine,et al.  Acetylcholine and Epibatidine Binding to Muscle Acetylcholine Receptors Distinguish between Concerted and Uncoupled Models* , 1999, The Journal of Biological Chemistry.

[49]  N. Sakamoto.  A transfer-function representation for regulatory responses of a controlled metabolic pathway. , 1987, Bio Systems.

[50]  Ken A. Dill,et al.  Molecular driving forces : statistical thermodynamics in biology, chemistry, physics, and nanoscience , 2012 .

[51]  W. Bialek.  Biophysics: Searching for Principles , 2012 .

[52]  E. Davidson.  The Regulatory Genome: Gene Regulatory Networks In Development And Evolution , 2006 .

[53]  W. Bialek,et al.  Information flow and optimization in transcriptional regulation , 2007, Proceedings of the National Academy of Sciences.

[54]  S. Siegelbaum,et al.  Molecular mechanism of cyclic-nucleotide-gated channel activation , 1994, Nature.

[55]  Davi R. Ortega,et al.  Universal architecture of bacterial chemoreceptor arrays , 2009, Proceedings of the National Academy of Sciences.

[56]  Ned S. Wingreen,et al.  Precise adaptation in bacterial chemotaxis through “assistance neighborhoods” , 2006, Proceedings of the National Academy of Sciences.

[57]  A. P. Davenport,et al.  Nicotinic Acetylcholine receptors: from molecular biology to cognition , 2006 .

[58]  J. Widom,et al.  Collaborative Competition Mechanism for Gene Activation In Vivo , 2003, Molecular and Cellular Biology.

[59]  Gasper Tkacik,et al.  Information capacity of genetic regulatory elements. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[61]  F. Leroy,et al.  Molecular Driving Forces. Statistical Thermodynamics in Biology, Chemistry, Physics, and Nanoscience , 2013 .

[62]  T. L. Hill.  Cooperativity Theory in Biochemistry: Steady-State and Equilibrium Systems , 2011 .

[63]  E. Henry,et al.  Evolution of allosteric models for hemoglobin , 2007, IUBMB life.

[64]  R. W. Rodieck.  The First Steps in Seeing , 1998 .

[65]  T. Naka,et al.  Validity of transfer-function representation of input-output relation in allosteric models. , 1986, Bio Systems.

[66]  Lani F. Wu,et al.  Genome-Scale Identification of Nucleosome Positions in S. cerevisiae , 2005, Science.

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

[68]  John McCarthy,et al.  Mathematical Theory of Computation , 1991 .

[69]  Farren J. Isaacs,et al.  Phenotypic consequences of promoter-mediated transcriptional noise. , 2006, Molecular cell.

[70]  A. Karlin.  Ion channel structure: Emerging structure of the Nicotinic Acetylcholine receptors , 2002, Nature Reviews Neuroscience.

[71]  J. Ruppersberg.  Ion Channels in Excitable Membranes , 1996 .

[72]  R. Jiao,et al.  Efficient and specific modifications of the Drosophila genome by means of an easy TALEN strategy. , 2012, Journal of genetics and genomics = Yi chuan xue bao.

[73]  Alessandro Spilotros,et al.  The Monod-Wyman-Changeux allosteric model accounts for the quaternary transition dynamics in wild type and a recombinant mutant human hemoglobin , 2012, Proceedings of the National Academy of Sciences.

[74]  M. Levine,et al.  Regulation of even‐skipped stripe 2 in the Drosophila embryo. , 1992, The EMBO journal.

[75]  I. Módy,et al.  Resolving the Fast Kinetics of Cooperative Binding: Ca2+ Buffering by Calretinin , 2007, PLoS biology.

[76]  Peter S. Swain,et al.  Trade-Offs and Constraints in Allosteric Sensing , 2011, PLoS Comput. Biol..

[77]  Irene K. Moore,et al.  The DNA-encoded nucleosome organization of a eukaryotic genome , 2009, Nature.

[78]  K. Kuwajima,et al.  The allosteric transition of GroEL induced by metal fluoride-ADP complexes. , 2003, Journal of molecular biology.

[79]  J. Changeux,et al.  Allosteric proteins and cellular control systems. , 1963, Journal of molecular biology.

[80]  Alexander Borst,et al.  Information theory and neural coding , 1999, Nature Neuroscience.

[81]  J. Davies,et al.  Molecular Biology of the Cell , 1983, Bristol Medico-Chirurgical Journal.

[82]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[83]  J. Boyle.  Molecular biology of the cell, 5th edition by B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter , 2008 .

[84]  N. Patel,et al.  Functional analysis of eve stripe 2 enhancer evolution in Drosophila: rules governing conservation and change. , 1998, Development.

[85]  Pablo A. Iglesias,et al.  An Information-Theoretic Characterization of the Optimal Gradient Sensing Response of Cells , 2007, PLoS Comput. Biol..

[86]  Nicolas E. Buchler,et al.  On schemes of combinatorial transcription logic , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[87]  F. Schotte,et al.  Tracking the structural dynamics of proteins in solution using time-resolved wide-angle X-ray scattering , 2008, Nature Methods.

[88]  M. Elowitz,et al.  Functional roles for noise in genetic circuits , 2010, Nature.

[89]  Equilibrium and kinetics of the allosteric transition of GroEL studied by solution X-ray scattering and fluorescence spectroscopy. , 2003, Journal of molecular biology.

[90]  N. Goldenfeld.  Lectures On Phase Transitions And The Renormalization Group , 1972 .

[91]  L. V. Belousov,et al.  Scott F. Gilbert—Developmental Biology, 2010, Sinauer Associates, Inc., Sunderland, MA Ninth Edition , 2011, Russian Journal of Developmental Biology.

[92]  M. Hoagland,et al.  Feedback Systems An Introduction for Scientists and Engineers SECOND EDITION , 2015 .

[93]  Gasper Tkacik,et al.  Optimizing information flow in small genetic networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[94]  B. C. Garrett,et al.  Current status of transition-state theory , 1983 .

[95]  M. Aminoff.  Principles of Neural Science. 4th edition , 2001 .

[96]  B. Franklin Pugh,et al.  High-Resolution Genome-wide Mapping of the Primary Structure of Chromatin , 2011, Cell.

[97]  Pablo A. Iglesias,et al.  Optimal Noise Filtering in the Chemotactic Response of Escherichia coli , 2006, PLoS Comput. Biol..

[98]  J. Changeux,et al.  Functional architecture of the nicotinic acetylcholine receptor: from electric organ to brain. , 1991, Annual review of pharmacology and toxicology.

[99]  O. Igoshin,et al.  Thermodynamic models of combinatorial gene regulation by distant enhancers. , 2010, IET systems biology.