Structural Identification of Piecewise-Linear Models of Genetic Regulatory Networks

We present a method for the structural identification of genetic regulatory networks (GRNs), based on the use of a class of Piecewise-Linear (PL) models. These models consist of a set of decoupled linear models describing the different modes of operation of the GRN and discrete switches between the modes accounting for the nonlinear character of gene regulation. They thus form a compromise between the mathematical simplicity of linear models and the biological expressiveness of nonlinear models. The input of the PL identification method consists of time-series measurements of concentrations of gene products. As output it produces estimates of the modes of operation of the GRN, as well as all possible minimal combinations of threshold concentrations of the gene products accounting for switches between the modes of operation. The applicability of the PL identification method has been evaluated using simulated data obtained from a model of the carbon starvation response in the bacterium Escherichia coli. This has allowed us to systematically test the performance of the method under different data characteristics, notably variations in the noise level and the sampling density.

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

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

[3]  Maria Rodriguez-Fernandez,et al.  A hybrid approach for efficient and robust parameter estimation in biochemical pathways. , 2006, Bio Systems.

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

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

[6]  Jonas S. Almeida,et al.  Parameter optimization in S-system models , 2008, BMC Systems Biology.

[7]  J. Stelling,et al.  Ensemble modeling for analysis of cell signaling dynamics , 2007, Nature Biotechnology.

[8]  Reinhard Guthke,et al.  Dynamic network reconstruction from gene expression data applied to immune response during bacterial infection , 2005, Bioinform..

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

[10]  Eduardo Sontag,et al.  Parameter estimation in models combining signal transduction and metabolic pathways: the dependent input approach. , 2006, Systems biology.

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

[12]  Natal A. W. van Riel,et al.  Dynamic modelling and analysis of biochemical networks: mechanism-based models and model-based experiments , 2006, Briefings Bioinform..

[13]  Olivier Bernard,et al.  Switch Detection in Genetic Regulatory Networks , 2007, HSCC.

[14]  C. Tomlin,et al.  Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta-Notch protein signalling. , 2004, Systems biology.

[15]  Rainer Spang,et al.  Inferring cellular networks – a review , 2007, BMC Bioinformatics.

[16]  U. Alon,et al.  A comprehensive library of fluorescent transcriptional reporters for Escherichia coli , 2006, Nature Methods.

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

[18]  Ádám M. Halász,et al.  Understanding the Bacterial Stringent Response Using Reachability Analysis of Hybrid Systems , 2004, HSCC.

[19]  Timothy S Gardner,et al.  Reverse-engineering transcription control networks. , 2005, Physics of life reviews.

[20]  L. Glass,et al.  Inferring models of gene expression dynamics. , 2004, Journal of theoretical biology.

[21]  Hidde de Jong,et al.  Symbolic reachability analysis of genetic regulatory networks using discrete abstractions , 2008, Autom..

[22]  Johannes Geiselmann,et al.  Inferring the connectivity of a regulatory network from mRNA quantification in Synechocystis PCC6803 , 2005, Nucleic acids research.

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

[24]  René Vidal,et al.  Identification of Hybrid Systems: A Tutorial , 2007, Eur. J. Control.

[25]  Marc Gyssens,et al.  The Identification of Dynamic Gene-Protein Networks , 2006, KDECB.

[26]  J. Collins,et al.  Inferring Genetic Networks and Identifying Compound Mode of Action via Expression Profiling , 2003, Science.

[27]  Nicolas Brunel,et al.  Estimating parameters and hidden variables in non-linear state-space models based on ODEs for biological networks inference , 2007, Bioinform..

[28]  D. di Bernardo,et al.  How to infer gene networks from expression profiles , 2007, Molecular systems biology.

[29]  Ting Chen,et al.  Modeling Gene Expression with Differential Equations , 1998, Pacific Symposium on Biocomputing.

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

[31]  Nir Friedman,et al.  Inferring subnetworks from perturbed expression profiles , 2001, ISMB.

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

[33]  Giancarlo Ferrari-Trecate,et al.  Identification of PieceWise Affine Models of Genetic Regulatory Networks: the Data Classification Problem , 2008 .

[34]  H. Mori,et al.  Construction of Escherichia coli K-12 in-frame, single-gene knockout mutants: the Keio collection , 2006, Molecular systems biology.

[35]  L. Finch.  A hybrid approach , 1998 .

[36]  John J. Tyson,et al.  Parameter Estimation for a Mathematical Model of the Cell Cycle in Frog Eggs , 2005, J. Comput. Biol..

[37]  Masaru Tomita,et al.  Dynamic modeling of genetic networks using genetic algorithm and S-system , 2003, Bioinform..

[38]  Giancarlo Ferrari-Trecate,et al.  Partitioning datasets based on equalities among parameters , 2010, Autom..

[39]  H. Mori,et al.  Complete set of ORF clones of Escherichia coli ASKA library (a complete set of E. coli K-12 ORF archive): unique resources for biological research. , 2006, DNA research : an international journal for rapid publication of reports on genes and genomes.

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

[41]  A. Gallant,et al.  Nonlinear Statistical Models , 1988 .

[42]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[43]  Giancarlo Ferrari-Trecate,et al.  The Switching Threshold Reconstruction Problem for Piecewise-Affine Models of Genetic Regulatory Networks , 2008, IEEE Transactions on Automatic Control.

[44]  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.

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

[46]  Hyung-Seok Choi,et al.  Reverse engineering of gene regulatory networks. , 2007, IET systems biology.

[47]  Marcel J. T. Reinders,et al.  Linear Modeling of Genetic Networks from Experimental Data , 2000, ISMB.

[48]  Jesper Tegnér,et al.  Reverse engineering gene networks using singular value decomposition and robust regression , 2002, Proceedings of the National Academy of Sciences of the United States of America.

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