Temporal Boolean Network Models of Genetic Networks and their Inference from Gene Expression Time Series

Identification of genetic regulatory networks and genetic signal transduction pathways from gene expression data is one of the key problems in computational molecular biology. Boolean networks offer a discrete time Boolean model of gene expression. In this model, each gene can be in one of two states (on or off) at any given time, and the expression of a given gene at time t " 1 can be modeled by a Boolean function of the expression of at most k genes at time t. Typically k # n, where n is the total number of genes under consideration. This paper motivates and introduces a generalization of the Boolean network model to address dependencies among activity of genes that span for more than one unit of time. The resulting model, called the temporal Boolean network or the TBN(n, k, T) model, allows the expression of each gene to be controlled by a Boolean function of the expression levels of at most k genes at times in $t . . . t % (T % 1)&. We apply an adaptation of a popular machine learning algorithm for decision tree induction for inference of a TBN(n, k, T) network from artificially generated gene expression data. Preliminary experiments with synthetic gene expression data generated from known TBN(n, k, T) networks demonstrate the feasibility of this approach. We conclude with a discussion of some of the limitations of the proposed approach and some directions for further research.

[1]  Stormo Identification of coordinated gene expression and regulatory sequences , 2000, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[2]  G S Michaels,et al.  Cluster analysis and data visualization of large-scale gene expression data. , 1998, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[3]  Hillol Kargupta,et al.  A Striking Property of Genetic Code-like Transformations , 2001, Complex Syst..

[4]  P J Goss,et al.  Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

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

[6]  Mike Mannion,et al.  Complex systems , 1997, Proceedings International Conference and Workshop on Engineering of Computer-Based Systems.

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

[8]  V. Thorsson,et al.  Discovery of regulatory interactions through perturbation: inference and experimental design. , 1999, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[9]  H. McAdams,et al.  Circuit simulation of genetic networks. , 1995, Science.

[10]  Satoru Miyano,et al.  Identification of Genetic Networks from a Small Number of Gene Expression Patterns Under the Boolean Network Model , 1998, Pacific Symposium on Biocomputing.

[11]  Gary D. Stormo,et al.  Modeling Regulatory Networks with Weight Matrices , 1998, Pacific Symposium on Biocomputing.

[12]  M A Savageau Rules for the evolution of gene circuitry. , 1998, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[13]  Arantxa Etxeverria The Origins of Order , 1993 .

[14]  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.

[15]  S Miyano,et al.  Algorithms for inferring qualitative models of biological networks. , 2000, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[16]  Ron Shamir,et al.  Clustering Gene Expression Patterns , 1999, J. Comput. Biol..

[17]  D Thieffry,et al.  Qualitative analysis of gene networks. , 1998, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[18]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[19]  S. Gygi,et al.  Correlation between Protein and mRNA Abundance in Yeast , 1999, Molecular and Cellular Biology.

[20]  Savageau Ma Rules for the evolution of gene circuitry. , 1998 .

[21]  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.

[22]  Roland Somogyi,et al.  Modeling the complexity of genetic networks: Understanding multigenic and pleiotropic regulation , 1996, Complex..

[23]  John Mingers,et al.  Rule Induction with Statistical Data—A Comparison with Multiple Regression , 1987 .

[24]  Somogyi,et al.  Molecular network modeling and data analysis , 2000, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[25]  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.

[26]  H Matsuno,et al.  Hybrid Petri net representation of gene regulatory network. , 1999, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[27]  J. Barker,et al.  Large-scale temporal gene expression mapping of central nervous system development. , 1998, Proceedings of the National Academy of Sciences of the United States of America.