Analyse qualitative de la dynamique de réseaux de régulation génique par des modèles linéaires par morceaux

In this review we discuss a method for the qualitative modeling and simulation of genetic regulatory networks which is well-adapted to the current lack of precise and quantitative biological data. The method is based on a class of piecewise-linear (PL) differential equation models with favorable mathematical properties. We review some basic results concerning the dynamics of PL systems, describe a discrete abstraction underlying the qualitative simulation method, and illustrate our approach by means of an application in the context of the nutritional stress response in the bacterium Escherichia coli.

[1]  Bruce H. Krogh,et al.  Verification of infinite-state dynamic systems using approximate quotient transition systems , 2001, IEEE Trans. Autom. Control..

[2]  Monika Heiner,et al.  Application of Petri net theory for modelling and validation of the sucrose breakdown pathway in the potato tuber , 2005, Bioinform..

[3]  Vincent Danos,et al.  Modeling and querying biomolecular interaction networks , 2004, Theor. Comput. Sci..

[4]  George J. Pappas,et al.  Discrete abstractions of hybrid systems , 2000, Proceedings of the IEEE.

[5]  U. Sauer.  High-throughput phenomics: experimental methods for mapping fluxomes. , 2004, Current opinion in biotechnology.

[6]  Hidde de Jong,et al.  Genetic Network Analyzer: qualitative simulation of genetic regulatory networks , 2003, Bioinform..

[7]  Kathy Chen,et al.  Network dynamics and cell physiology , 2001, Nature Reviews Molecular Cell Biology.

[8]  Denis Thieffry,et al.  Genetic control of flower morphogenesis in Arabidopsis thaliana: a logical analysis , 1999, Bioinform..

[9]  G. Casari,et al.  From molecular networks to qualitative cell behavior , 2005, FEBS letters.

[10]  Hidde de Jong,et al.  Qualitative simulation and related approaches for the analysis of dynamic systems , 2004, The Knowledge Engineering Review.

[11]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[12]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[13]  A. Barabasi,et al.  Network biology: understanding the cell's functional organization , 2004, Nature Reviews Genetics.

[14]  Andrew W. Murray,et al.  The Ups and Downs of Modeling the Cell Cycle , 2004, Current Biology.

[15]  C. Tomlin,et al.  Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta-Notch protein signalling. , 2004, Systems biology.

[16]  S. Kauffman.  Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[17]  Benjamin Kuipers,et al.  Proving Properties of Continuous Systems: Qualitative Simulation and Temporal Logic , 1997, Artif. Intell..

[18]  K. Kohn.  Molecular interaction maps as information organizers and simulation guides. , 2001, Chaos.

[19]  H. D. Jong,et al.  Piecewise-linear Models of Genetic Regulatory Networks: Equilibria and their Stability , 2006, Journal of mathematical biology.

[20]  Adam P Arkin,et al.  Design and Diversity in Bacterial Chemotaxis: A Comparative Study in Escherichia coli and Bacillus subtilis , 2004, PLoS biology.

[21]  M. Egerstedt,et al.  On the regularization of Zeno hybrid automata , 1999 .

[22]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

[23]  N. Barkai,et al.  Robustness of the BMP morphogen gradient in Drosophila embryonic patterning , 2022 .

[24]  Thomas Mestl,et al.  Global analysis of steady points for systems of differential equations with sigmoid interactions , 1994 .

[25]  Dan ie l T. Gil lespie.  A rigorous derivation of the chemical master equation , 1992 .

[26]  D. Chatterji,et al.  Revisiting the stringent response, ppGpp and starvation signaling. , 2001, Current opinion in microbiology.

[27]  A. Zeng,et al.  An extended transcriptional regulatory network of Escherichia coli and analysis of its hierarchical structure and network motifs. , 2004, Nucleic acids research.

[28]  S. Leibler,et al.  Robustness in simple biochemical networks , 1997, Nature.

[29]  Vipul Periwal,et al.  System Modeling in Cellular Biology: From Concepts to Nuts and Bolts , 2006 .

[30]  J. Gralla,et al.  Changes in the linking number of supercoiled DNA accompany growth transitions in Escherichia coli , 1987, Journal of bacteriology.

[31]  Orna Kupferman,et al.  Modular Model Checking , 1997, COMPOS.

[32]  Denis Thieffry,et al.  Segmenting the fly embryo: a logical analysis of the pair-rule cross-regulatory module. , 2003, Journal of theoretical biology.

[33]  R. C. Johnson,et al.  Control of transcription by nucleoid proteins. , 2001, Current opinion in microbiology.

[34]  Erik Plahte,et al.  Analysis and generic properties of gene regulatory networks with graded response functions , 2005 .

[35]  El Houssine Snoussi.  Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach , 1989 .

[36]  F. Rechenmann.  1- Le vivant en equations , 2005 .

[37]  D. Kell,et al.  Metabolomics by numbers: acquiring and understanding global metabolite data. , 2004, Trends in biotechnology.

[38]  J. Gouzé,et al.  A class of piecewise linear differential equations arising in biological models , 2002 .

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

[40]  J. Collado-Vides,et al.  Identifying global regulators in transcriptional regulatory networks in bacteria. , 2003, Current opinion in microbiology.

[41]  H. D. Jong,et al.  Qualitative simulation of the initiation of sporulation in Bacillus subtilis , 2004, Bulletin of mathematical biology.

[42]  A. Goldbeter,et al.  Toward a detailed computational model for the mammalian circadian clock , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[43]  M. Levin,et al.  Fluorescence correlation spectroscopy and quantitative cell biology. , 2004, Differentiation; research in biological diversity.

[44]  H. McAdams,et al.  Circuit simulation of genetic networks. , 1995, Science.

[45]  J. Stelling,et al.  Robustness of Cellular Functions , 2004, Cell.

[46]  H. D. Jong,et al.  Qualitative simulation of genetic regulatory networks using piecewise-linear models , 2004, Bulletin of mathematical biology.

[47]  J. Lygeros,et al.  AN INTRODUCTION TO HYBRID SYSTEM MODELING ANALYSIS AND CONTROL JOHN LYGEROS GEORGE PAPPAS AND SHANKAR SASTRY , 1999 .

[48]  D. A. Baxter,et al.  Modeling transcriptional control in gene networks—methods, recent results, and future directions , 2000, Bulletin of mathematical biology.

[49]  R. Edwards.  Analysis of continuous-time switching networks , 2000 .

[50]  G. Yagil,et al.  On the relation between effector concentration and the rate of induced enzyme synthesis. , 1971, Biophysical journal.

[51]  Eduardo Sontag,et al.  Untangling the wires: A strategy to trace functional interactions in signaling and gene networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[52]  M Sugita,et al.  Functional analysis of chemical systems in vivo using a logical circuit equivalent. II. The idea of a molecular automation. , 1963, Journal of theoretical biology.

[53]  J. Ecker,et al.  Applications of DNA tiling arrays for whole-genome analysis. , 2005, Genomics.

[54]  Thomas Egli,et al.  Molecular components of physiological stress responses in Escherichia coli. , 2004, Advances in biochemical engineering/biotechnology.

[55]  Araceli M. Huerta,et al.  From specific gene regulation to genomic networks: a global analysis of transcriptional regulation in Escherichia coli. , 1998, BioEssays : news and reviews in molecular, cellular and developmental biology.

[56]  Benjamin Kuipers,et al.  Qualitative reasoning: Modeling and simulation with incomplete knowledge , 1994, Autom..

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

[58]  Martin Fussenegger,et al.  Modeling the Quorum Sensing Regulatory Network of Human‐Pathogenic Pseudomonas aeruginosa , 2004, Biotechnology progress.

[59]  K. Drlica,et al.  Bacterial topoisomerases and the control of DNA supercoiling. , 1990, Trends in genetics : TIG.

[60]  S. Teichmann,et al.  Evolution of transcription factors and the gene regulatory network in Escherichia coli. , 2003, Nucleic acids research.

[61]  A. Arkin,et al.  Simulation of prokaryotic genetic circuits. , 1998, Annual review of biophysics and biomolecular structure.

[62]  Stanislas Leibler,et al.  Resilient circadian oscillator revealed in individual cyanobacteria , 2004, Nature.

[63]  Hiroaki Kitano,et al.  Foundations of systems biology , 2001 .

[64]  D. Schneider,et al.  Qualitative simulation of the carbon starvation response in Escherichia coli. , 2006, Bio Systems.

[65]  Denis Thieffry,et al.  Qualitative modelling of regulated metabolic pathways: application to the tryptophan biosynthesis in E.Coli , 2005, ECCB/JBI.

[66]  Tom Misteli,et al.  Kinetic modelling approaches to in vivo imaging , 2001, Nature Reviews Molecular Cell Biology.

[67]  T. Mestl,et al.  A mathematical framework for describing and analysing gene regulatory networks. , 1995, Journal of theoretical biology.

[68]  R. Thomas,et al.  Boolean formalization of genetic control circuits. , 1973, Journal of theoretical biology.

[69]  L. Glass,et al.  STEADY STATES, LIMIT CYCLES, AND CHAOS IN MODELS OF COMPLEX BIOLOGICAL NETWORKS , 1991 .

[70]  Roland Somogyi,et al.  Modeling the complexity of genetic networks: Understanding multigenic and pleiotropic regulation , 1996, Complex..

[71]  E. Winzeler,et al.  Genomics, gene expression and DNA arrays , 2000, Nature.

[72]  J. Collado-Vides.  Integrative Approaches to Molecular Biology , 1996 .

[73]  Andreas Kremling,et al.  A Quantitative Approach to Catabolite Repression in Escherichia coli* , 2006, Journal of Biological Chemistry.

[74]  J L Botsford,et al.  Cyclic AMP in prokaryotes , 1992, Microbiological reviews.

[75]  James M. Bower,et al.  Computational modeling of genetic and biochemical networks , 2001 .

[76]  Radu Mateescu,et al.  Validation of qualitative models of genetic regulatory networks by model checking: analysis of the nutritional stress response in Escherichia coli , 2005, ISMB.

[77]  L. Glass,et al.  Symbolic dynamics and computation in model gene networks. , 2001, Chaos.

[78]  Hidde de Jong,et al.  Modeling and Simulation of Genetic Regulatory Systems: A Literature Review , 2002, J. Comput. Biol..

[79]  R. Coutinho,et al.  Discrete time piecewise affine models of genetic regulatory networks , 2005, Journal of mathematical biology.

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

[81]  E D Gilles,et al.  Modeling of inducer exclusion and catabolite repression based on a PTS-dependent sucrose and non-PTS-dependent glycerol transport systems in Escherichia coli K-12 and its experimental verification. , 2001, Journal of biotechnology.

[82]  Calin Belta,et al.  Hybrid Modeling and Simulation of Biomolecular Networks , 2001, HSCC.

[83]  Marco Pistore,et al.  NuSMV 2: An OpenSource Tool for Symbolic Model Checking , 2002, CAV.

[84]  E. F. ARMSTRONG,et al.  Annual Review of Biochemistry , 1944, Nature.

[85]  Steffen Schulze-Kremer,et al.  Design and implementation of a qualitative simulation model of lambda phage infection , 1998, Bioinform..

[86]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

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

[88]  S. Shen-Orr,et al.  Network motifs in the transcriptional regulation network of Escherichia coli , 2002, Nature Genetics.

[89]  L. Glass,et al.  Stable oscillations in mathematical models of biological control systems , 1978 .

[90]  Adrien Richard,et al.  Application of formal methods to biological regulatory networks: extending Thomas' asynchronous logical approach with temporal logic. , 2004, Journal of theoretical biology.

[91]  L. Glass,et al.  Common Chaos in Arbitrarily Complex Feedback Networks , 1997 .

[92]  Mihaela Sighireanu,et al.  Efficient on-the-fly model-checking for regular alternation-free mu-calculus , 2003, Sci. Comput. Program..

[93]  L. Glass,et al.  The logical analysis of continuous, non-linear biochemical control networks. , 1973, Journal of theoretical biology.

[94]  Stephan Merz,et al.  Model Checking , 2000 .

[95]  Marcelle Kaufman,et al.  Modélisation et simulation pour la post-génomique , 2007 .

[96]  Denyse Baillargeon,et al.  Bibliographie , 1929 .

[97]  M. Mann,et al.  Proteomics to study genes and genomes , 2000, Nature.

[98]  E. Davidson,et al.  Genomic cis-regulatory logic: experimental and computational analysis of a sea urchin gene. , 1998, Science.

[99]  R. Heinrich,et al.  The Regulation of Cellular Systems , 1996, Springer US.

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

[101]  A. Arkin,et al.  Motifs, modules and games in bacteria. , 2003, Current opinion in microbiology.

[102]  A. Arkin,et al.  Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. , 1998, Genetics.

[103]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[104]  Farren J. Isaacs,et al.  Computational studies of gene regulatory networks: in numero molecular biology , 2001, Nature Reviews Genetics.

[105]  Karsten R. Heidtke,et al.  Design and implementation of a qualitative simulation model of λ phage infection , 1997 .

[106]  Hidde de Jong,et al.  6 – Qualitative modelling and simulation of developmental regulatory networks , 2003 .

[107]  Xavier Darzacq,et al.  Imaging gene expression in single living cells , 2004, Nature Reviews Molecular Cell Biology.

[108]  J G Harman,et al.  Allosteric regulation of the cAMP receptor protein. , 2001, Biochimica et biophysica acta.

[109]  Etienne Farcot,et al.  Geometric properties of a class of piecewise affine biological network models , 2006, Journal of mathematical biology.