Abstract

In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rule-based formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems. Key words: genetic regulatory networks, mathematical modeling, simulation, computational biology.

Citations

5666	Probabilistic reasoning in intelligent systems - Pearl - 1988
1176	Cluster analysis and display of genome-wide expression patterns - Eisen, Spellman, et al. - 1998
753	The origins of order: Self-organization and selection in evolution - Kauffman - 1993
710	A tutorial on learning with Bayesian networks - Heckerman - 1995
590	Qualitative Process Theory - Forbus - 1984
526	D: Using Bayesian networks to analyze expression data - Friedman, Linial, et al.
521	Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc Natl Acad Sci USA 96: 6745–6750 Balbin M and Lopez-Otin C - Alon, Barkai, et al. - 1999
503	Exact stochastic simulation of coupled chemical reactions - Gillespie - 1977
450	The Chemical Basis of Morphogenesis - Turing - 1952
441	S: KEGG: Kyoto Encyclopedia of Genes and Genomes - Kanehisa, Goto
384	Qualitative simulation - Kuipers - 1986
374	T: Interpreting patterns of gene expression with selforganizing maps: Methods and applications tohematopoietic differention - Tamayo, Slonim, et al. - 1999
355	Systematic determination of genetic network architecture - Tavazoie, Hughes, et al. - 1999
273	Yakhini Z: Clustering Gene Expression Patterns - Ben-Dor, Shamir - 1999
268	Knowledge-based analysis of microarray gene expression data by using support vector machines - Brown, Grundy, et al. - 2000
240	A genome-wide transcriptional analysis of the mitotic cell cycle - Cho, Campbell, et al. - 1998
237	Qualitative Reasoning ⎯ Modeling and Simulation with Incomplete Knowledge - Kuipers - 1994
231	Metabolic stability and epigenesis in randomly constructed genetic nets - Kauffman - 1969
224	Functional discovery via a compendium of expression profiles - Hughes, Marton, et al. - 2000
217	A theory of biological pattern formation - Meinhardt, A, et al. - 1972
203	From molecular to modular cell biology - Hartwell, Hopfield, et al. - 1999
198	HH: Stochastic kinetic analysis of developmental pathway bifurcation in phage lambdainfected Escherichia coli cells. Genetics - Arkin, Ross, et al. - 1998
168	R: REVEAL, a general reverse engineering algorithm for inference of genetic network architectures. Pac Symp Biocomput - Liang, Fuhrman, et al. - 1998
163	A synthetic oscillatory network of transcriptional regulators - Elowitz, Leibler - 2000
162	Representation and simulation of biochemical processes using the pi-calculus process algebra - Regev, Silverman, et al. - 2001
157	The Regulation of Cellular Systems - Heinrich, Schuster - 1996
156	R: Genetic network inference: from co-expression clustering to reverse engineering. Bioinformatics 2000, 16(8):707-26. Page 14 of 15 (page number not for citation purposes) Bioinformatics 2007, 8(Suppl 5):S2 - D'haeseleer, Liang, et al.
156	Genomewide location and function of DNA binding proteins - Ren, Robert, et al. - 2000
154	Arkin A: Stochastic mechanisms in gene expression - McAdams - 1997
150	Exploring the new world of the genome with DNA microarrays - Brown, Botstein - 1999
146	Building Expert Systems - Hayes-Roth, Waterman, et al. - 1983
132	The logical analysis of continuous, non-linear biochemical control networks - Glass, SA - 1973
127	Construction of a genetic toggle switch in Escherichia coli - Gardner, Cantor, et al. - 2000
126	Inferring subnetworks from perturbed expression profiles. Bioinformatics 17(suppl 1):S215–S224 - Pe’er, Regev, et al. - 2001
121	Modeling gene expression with differential equations. Pac Symp Biocomput 4:29–40 - Chen, He, et al. - 1999
119	Mian S: Modelling gene expression data using dynamic Bayesian networks - Murphy - 1999
114	High density synthetic oligonucleotide arrays - Lipshutz, Fodor, et al. - 1999
112	GM: The segment polarity network is a robust developmental module - Dassow, Meir, et al.
108	R: Large-scale temporal gene expression mapping of central nervous system development - Wen, Fuhrman, et al. - 1998
107	Modelling regulatory networks with weight matrices. Pac Symp Biocomput 4 - Weaver, Workman, et al. - 1999
105	Qualitative simulation of genetic regulatory networks using piecewise-linear models - Jong, Gouzé, et al. - 2004
95	Prigogine I: Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order through Fluctuations - Nicolis - 1977
94	Circuit simulation of genetic networks - McAdams, Shapiro - 1995
92	Hybrid Petri net representation of gene regulatory network - Matsuno, Doi, et al. - 2000
90	L (2000) Engineering stability in gene networks by autoregulation. Nature 405: 590–593 - Becskei, Serrano
86	Genomic cis-regulatory logic: Experimental and computational analysis of a sea urchin gene - CH, Bolouri, et al. - 1998
85	Molecular interaction map of the mammalian cell cycle control and DNA repair systems - Kohn - 1999
81	A connectionist model of development - Mjolsness, DH, et al. - 1991
81	Dynamical behaviour of biological regulatory networks-i. biological role of feedback loops and practical use of the concept of the loop-characteristic state - Thomas, Thieffry, et al. - 1995
80	Genomic binding sites of the yeast cell-cycle transcription factors SBF and MBF - Iyer, Horak, et al. - 2001