Bayesian Models and Gibbs Sampling Strategies for Local Graph Alignment and Motif Identification in Stochastic Biological Networks∗

With increasing amounts of interaction data collected by high-throughput techniques, understanding the structure and dynamics of biological networks becomes one of the central tasks in post-genomic molecular biology. Recent studies have shown that many biological networks contain a small set of “network motifs,” which are suggested to be the basic cellular information-processing units in these networks. Nevertheless, most biological networks have stochastic nature, due to the intrinsic uncertainties of biological interactions and/or experimental noises accompanying the highthroughput data. The building blocks in these networks thus also have stochastic properties. In this paper, we study the problem of identifying stochastic network motifs that are derived from families of mutually similar but not necessarily identical patterns of interactions. Motivated by existing methods for detecting sequence motifs in biopolymer sequences, we establish Bayesian models for stochastic biological networks and develop a group of Gibbs sampling strategies for finding stochastic network motifs. The methods are applied to several available transcriptional regulatory networks and protein-protein interaction networks, and several stochastic network motifs are successfully identified.