Genetic networks with SUM regulatory functions: Characterizing the equilibrium points

Genetic networks with SUM regulatory functions are a fundamental class of models studied in systems biology. A primary issue for these models consists of establishing the number of the equilibrium points and their location. Unfortunately, this is a difficult problem, indeed existing methods very often do not allow one to solve it. This paper proposes a study of this problem, and describes an approach that exploits the properties of SUM regulatory functions in order to correctly characterize these points of interest. This is verified by some numerical examples, which illustrate the proposed solution and show the advantages with respect to existing methods.

[1]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[2]  Kazuyuki Aihara,et al.  Stability of Genetic Networks With SUM Regulatory Logic: Lur'e System and LMI Approach , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[4]  Graziano Chesi,et al.  Characterizing the solution set of polynomial systems in terms of homogeneous forms: an LMI approach , 2003 .

[5]  Kazuyuki Aihara,et al.  Stochastic Stability of Genetic Networks With Disturbance Attenuation , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[6]  Patrik D'haeseleer,et al.  Genetic network inference: from co-expression clustering to reverse engineering , 2000, Bioinform..

[7]  Jacques Demongeot,et al.  Mathematical modeling in genetic networks: relationships between the genetic expression and both chromosomic breakage and positive circuits , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[8]  James M. Bower,et al.  Computational Modeling of Genetic and Biochemical Networks (Computational Molecular Biology) , 2004 .

[9]  Yeung Sam Hung,et al.  Stability analysis of uncertain genetic sum regulatory networks , 2008, Autom..

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

[11]  R. Somogyi,et al.  Gene Expression Data Analysis and Modeling , 1999 .

[12]  W. T. Tutte,et al.  Encyclopedia of Mathematics and its Applications , 2001 .

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

[14]  A. Bezerianos,et al.  Gene networks reconstruction and time-series prediction from microarray data using recurrent neural fuzzy networks. , 2007, IET systems biology.

[15]  D. A. Baxter,et al.  Mathematical Modeling of Gene Networks , 2000, Neuron.

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

[17]  Graziano Chesi.  OPTIMAL REPRESENTATION MATRICES FOR SOLVING POLYNOMIAL SYSTEMS VIA LMI , 2008 .

[18]  P. D’haeseleer,et al.  Mining the gene expression matrix: inferring gene relationships from large scale gene expression data , 1998 .

[19]  K. Aihara,et al.  A Systems Biology Perspective on Signal Processing in Genetic Network Motifs [Life Sciences] , 2007, IEEE Signal Processing Magazine.