Course 10Modeling, analysis, and simulation of genetic regulatory networks: From differential equations to logical models

Publisher Summary This chapter discusses genetic regulatory networks, which mainly concern interactions between proteins and nucleic acids, controlling the transcription and translation of genes. Genetic regulatory networks play an important role in the functioning and differentiation of cells. A large part of the experimental data available notably transcriptome data, concern these networks. Notwithstanding their importance, one should bear in mind that genetic regulatory networks are integrated in the cell with other types of networks, sometimes to the point that they become difficult to separate. In addition to high-throughput experimental methods, mathematical, and computational approaches are indispensable for the analysis of genetic regulatory networks. Given the large number of components of most networks of biological interest often connected by positive and negative feedback loops, an intuitive comprehension of the dynamics of the system is difficult, if not impossible to obtain. Mathematical modeling supported by computer tools can contribute to the analysis of a regulatory network by allowing the biologist to focus on a restricted number of plausible hypotheses.

[1]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

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

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

[4]  R Thomas,et al.  Dynamical behaviour of biological regulatory networks--I. Biological role of feedback loops and practical use of the concept of the loop-characteristic state. , 1995, Bulletin of mathematical biology.

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

[6]  David H. Sharp,et al.  Dynamical Analysis of Regulatory Interactions in the Gap Gene System of Drosophila melanogaster , 2004, Genetics.

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

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

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

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

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

[12]  A. Grossman,et al.  Regulation of the Initiation of Endospore Formation in Bacillus subtilis , 2000 .

[13]  J. Helden,et al.  Establishement of the dorso-ventral pattern during embryonic development of drosophila melanogasater: a logical analysis , 1997, Journal of theoretical biology.

[14]  L. Glass,et al.  Understanding Nonlinear Dynamics , 1995 .

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

[16]  Denis Thieffry,et al.  Qualitative Analysis of Regulatory Graphs: A Computational Tool Based on a Discrete Formal Framework , 2003, POSTA.

[17]  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.

[18]  A. Arkin,et al.  Genetic "code": representations and dynamical models of genetic components and networks. , 2002, Annual review of genomics and human genetics.

[19]  F. Cross,et al.  Testing a mathematical model of the yeast cell cycle. , 2002, Molecular biology of the cell.

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

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

[22]  D. Thieffry,et al.  A logical analysis of the Drosophila gap-gene system. , 2001, Journal of theoretical biology.

[23]  R. Losick,et al.  The transcriptional profile of early to middle sporulation in Bacillus subtilis. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[24]  John J Tyson,et al.  A model for restriction point control of the mammalian cell cycle. , 2004, Journal of theoretical biology.

[25]  T. Ideker,et al.  A new approach to decoding life: systems biology. , 2001, Annual review of genomics and human genetics.

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

[27]  Dominique Schneider,et al.  Qualitative Simulation of the Nutritional Stress Response in Escherichia coli , 2003 .

[28]  Pedro Mendes,et al.  GEPASI: a software package for modelling the dynamics, steady states and control of biochemical and other systems , 1993, Comput. Appl. Biosci..

[29]  M. Ptashne.  A genetic switch : phage λ and higher organisms , 1992 .

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

[31]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering , 1994 .

[32]  J. Collins,et al.  Construction of a genetic toggle switch in Escherichia coli , 2000, Nature.

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

[34]  J. Monod,et al.  General Conclusions: Teleonomic Mechanisms in Cellular Metabolism, Growth, and Differentiation , 1978 .

[35]  D. Sharp,et al.  Stripe forming architecture of the gap gene system. , 1998, Developmental genetics.

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

[37]  David H. Sharp,et al.  Dynamic control of positional information in the early Drosophila embryo , 2004, Nature.

[38]  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.

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

[40]  A. Goldbeter.  Computational approaches to cellular rhythms , 2002, Nature.

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

[42]  S. Strogatz.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

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

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

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

[46]  Igor Goryanin,et al.  Mathematical simulation and analysis of cellular metabolism and regulation , 1999, Bioinform..

[47]  René Thomas.  Regulatory networks seen as asynchronous automata: A logical description , 1991 .

[48]  Bard Ermentrout,et al.  Simulating, analyzing, and animating dynamical systems - a guide to XPPAUT for researchers and students , 2002, Software, environments, tools.

[49]  R. Thomas,et al.  Dynamical behaviour of biological regulatory networks--II. Immunity control in bacteriophage lambda. , 1995, Bulletin of mathematical biology.

[50]  Katherine C. Chen,et al.  Integrative analysis of cell cycle control in budding yeast. , 2004, Molecular biology of the cell.

[51]  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.

[52]  J. Butcher.  Numerical methods for ordinary differential equations , 2003 .

[53]  J Reinitz,et al.  Theoretical and experimental analysis of the phage lambda genetic switch implies missing levels of co-operativity. , 1990, Journal of theoretical biology.

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

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

[56]  Martine Labbé,et al.  Identification of all steady states in large networks by logical analysis , 2003, Bulletin of mathematical biology.

[57]  G. Odell,et al.  Ingeneue: a versatile tool for reconstituting genetic networks, with examples from the segment polarity network. , 2002, The Journal of experimental zoology.

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

[59]  G. Odell,et al.  The segment polarity network is a robust developmental module , 2000, Nature.

[60]  R. Losick,et al.  Molecular genetics of sporulation in Bacillus subtilis. , 1996, Annual review of genetics.

[61]  A. Grossman,et al.  Cell cycle and sporulation in Bacillus subtilis. , 1998, Current opinion in microbiology.

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

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