Inferring Gene Regulatory Networks from Time-Ordered Gene Expression Data of Bacillus Subtilis Using Differential Equations

We describe a new method to infer a gene regulatory network, in terms of a linear system of differential equations, from time course gene expression data. As biologically the gene regulatory network is known to be sparse, we expect most coefficients in such a linear system of differential equations to be zero. In previously proposed methods, the number of nonzero coefficients in the system was limited based on ad hoc assumptions. Instead, we propose to infer the degree of sparseness of the gene regulatory network from the data, where we use Akaike's Information Criterion to determine which coefficients are nonzero. We apply our method to MMGE time course data of Bacillus subtilis.

[1]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[2]  H. Akaike.  A new look at the statistical model identification , 1974 .

[3]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[4]  I. Moszer.  The complete genome of Bacillus subtilis: from sequence annotation to data management and analysis , 1998, FEBS letters.

[5]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[6]  Michael Ruogu Zhang,et al.  Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. , 1998, Molecular biology of the cell.

[7]  S Fuhrman,et al.  Reveal, a general reverse engineering algorithm for inference of genetic network architectures. , 1998, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[8]  Michal Linial,et al.  Using Bayesian Networks to Analyze Expression Data , 2000, J. Comput. Biol..

[9]  Y. Hihara,et al.  DNA Microarray Analysis of Cyanobacterial Gene Expression during Acclimation to High Light , 2001, Plant Cell.

[10]  Satoru Miyano,et al.  Bayesian Network and Nonparametric Heteroscedastic Regression for Nonlinear Modeling of Genetic Network , 2003, J. Bioinform. Comput. Biol..

[11]  Hitoshi Iba,et al.  Evolutionary Inference of a Biological Network as Differential Equations by Genetic Programming , 2001 .

[12]  H Matsuno,et al.  XML documentation of biopathways and their simulations in Genomic Object Net. , 2001, Genome informatics. International Conference on Genome Informatics.

[13]  Mark Carpenter,et al.  The New Statistical Analysis of Data , 2000, Technometrics.

[14]  P. Brown,et al.  Exploring the metabolic and genetic control of gene expression on a genomic scale. , 1997, Science.

[15]  J. Mesirov,et al.  Interpreting patterns of gene expression with self-organizing maps: methods and application to hematopoietic differentiation. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[16]  A Danchin,et al.  SubtiList: a relational database for the Bacillus subtilis genome. , 1995, Microbiology.

[17]  Satoru Miyano,et al.  Estimation of Genetic Networks and Functional Structures Between Genes by Using Bayesian Networks and Nonparametric Regression , 2001, Pacific Symposium on Biocomputing.

[18]  D. Botstein,et al.  Cluster analysis and display of genome-wide expression patterns. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

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

[20]  Satoru Miyano,et al.  Inferring qualitative relations in genetic networks and metabolic pathways , 2000, Bioinform..

[21]  Satoru Miyano,et al.  Statistical analysis of a small set of time-ordered gene expression data using linear splines , 2002, Bioinform..