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

Spurred by advances in cDNA microarray technology, gene expression data are increasingly becoming available. In time-ordered data, the expression levels are measured at several points in time following some experimental manipulation. A gene regulatory network can be inferred by fitting a linear system of differential equations to the 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 to infer such a linear system, ad hoc assumptions were made to limit the number of nonzero coefficients in the system. Instead, we propose to infer the degree of sparseness of the gene regulatory network from the data, where we determine which coefficients are nonzero by using Akaike's Information Criterion.

[1]  V. Anne Smith,et al.  Evaluating functional network inference using simulations of complex biological systems , 2002, ISMB.

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

[3]  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.

[4]  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.

[5]  Satoru Miyano,et al.  Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network , 2003, Proceedings. IEEE Computer Society Bioinformatics Conference.

[6]  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.

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

[8]  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.

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

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

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

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

[13]  David Page,et al.  Modelling regulatory pathways in E. coli from time series expression profiles , 2002, ISMB.

[14]  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.

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

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

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

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

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

[20]  E. P. van Someren.  Searching for Limited Connectivity in Genetic Network Models , 2004 .

[21]  Wentian Li,et al.  How Many Genes are Needed for a Discriminant Microarray Data Analysis , 2001, physics/0104029.

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