Open Regulatory Networks and Modularity

We study the dynamical properties of small regulatory networks treated as non autonomous dynamical systems called modules when working inside larger networks or, equivalently when subject to external signal inputs. Particular emphasis is put on the interplay between the internal properties of the open systems and the different possible inputs on them to deduce new functionalities of the modules. We use discrete-time, piecewise-affine and piecewise-contracting models with interactions of a regulatory nature to perform our study.

[1]  A. Isidori.  Nonlinear Control Systems: An Introduction , 1986 .

[2]  H. D. Jong,et al.  Modeling the Dynamics of Genetic Regulatory Networks: Continuous and Discrete Approaches , 2005 .

[3]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

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

[5]  Mats G. Nordahl,et al.  Universal Computation in Simple One-Dimensional Cellular Automata , 1990, Complex Syst..

[6]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[7]  R. Lima,et al.  Random Shuffling of Switching Parameters in a Model of Gene Expression Regulatory Network , 2005 .

[8]  Carlos Aguirre,et al.  Dynamics and Coding of a Biologically-Motivated Network , 2004, Int. J. Bifurc. Chaos.

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

[10]  S. Mangan,et al.  Structure and function of the feed-forward loop network motif , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[11]  M A Savageau,et al.  Design of molecular control mechanisms and the demand for gene expression. , 1977, Proceedings of the National Academy of Sciences of the United States of America.

[12]  D. Thieffry,et al.  Modularity in development and evolution. , 2000, BioEssays : news and reviews in molecular, cellular and developmental biology.

[13]  R. Thomas,et al.  Logical analysis of systems comprising feedback loops. , 1978, Journal of theoretical biology.

[14]  L. Arnold.  Random Dynamical Systems , 2003 .

[15]  J. Stark,et al.  Network motifs: structure does not determine function , 2006, BMC Genomics.

[16]  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.

[17]  R. Lima,et al.  Dynamical complexity of discrete-time regulatory networks , 2005, math/0509141.

[18]  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.

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

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

[22]  Dan Gordon,et al.  On the computational power of totalistic cellular automata , 1987, Mathematical systems theory.

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

[24]  M. Elowitz,et al.  A synthetic oscillatory network of transcriptional regulators , 2000, Nature.