Switch Detection in Genetic Regulatory Networks

This paper considers piecewise affine models of genetic regulatory networks and focuses on the problem of detecting switches among different modes of operation in gene expression data. This task constitutes the first step of a procedure for the complete identification of the network. We propose two methods and illustrate the application to the reconstruction of switching times in data produced by a piecewise affine model of the network regulating the carbon starvation response in Escherichia coli.

[1]  Giancarlo Ferrari-Trecate,et al.  Reconstruction of Switching Thresholds in Piecewise-Affine Models of Genetic Regulatory Networks , 2006, HSCC.

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

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

[4]  E. C. Fieller THE DISTRIBUTION OF THE INDEX IN A NORMAL BIVARIATE POPULATION , 1932 .

[5]  René Vidal,et al.  Identification of Deterministic Switched ARX Systems via Identification of Algebraic Varieties , 2005, HSCC.

[6]  William Mendenhall,et al.  Introduction to Probability and Statistics , 1961, The Mathematical Gazette.

[7]  G. Marsaglia Ratios of Normal Variables and Ratios of Sums of Uniform Variables , 1965 .

[8]  Thomas A. Henzinger,et al.  Hybrid Systems: Computation and Control , 1998, Lecture Notes in Computer Science.

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

[10]  D. Hinkley On the ratio of two correlated normal random variables , 1969 .

[11]  W. P. M. H. Heemels,et al.  Comparison of Four Procedures for the Identification of Hybrid Systems , 2005, HSCC.

[12]  T. Pham-Gia,et al.  Density of the Ratio of Two Normal Random Variables and Applications , 2006 .

[13]  Alberto Bemporad,et al.  A bounded-error approach to piecewise affine system identification , 2005, IEEE Transactions on Automatic Control.

[14]  V. Rohatgi,et al.  An introduction to probability and statistics , 1968 .

[15]  F. Rosenqvist,et al.  Realisation and estimation of piecewise-linear output-error models , 2005, Autom..

[16]  A. Juloski,et al.  A Bayesian approach to identification of hybrid systems , 2004, CDC.

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

[18]  U. Alon,et al.  Assigning numbers to the arrows: Parameterizing a gene regulation network by using accurate expression kinetics , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Dominique Schneider,et al.  Qualitative Analysis and Verification of Hybrid Models of Genetic Regulatory Networks: Nutritional Stress Response in , 2005, HSCC.

[20]  A. Juloski,et al.  A BAYESIAN APPROACH TO THE IDENTIFICATION OF PIECEWISE LINEAR OUTPUT ERROR MODELS , 2006 .

[21]  Fredrik Gustafsson,et al.  Adaptive filtering and change detection , 2000 .

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

[23]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[24]  Manfred Morari,et al.  A clustering technique for the identification of piecewise affine systems , 2001, Autom..