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.