Comparative analysis of molecular interaction data provides
understanding of functional modularity in the cell by integrating
cellular organization, functional hierarchy, and evolutionary
conservation. In this talk, we address a number of algorithmic issues associated with comparative analysis of interaction networks. We first discuss the problem of identifying common sub-networks in a collection of networks belonging to diverse species. The main algorithmic challenges stem from the exponential worst-case complexity of the underlying mining problem involving large patterns, as well as the NP-hardness of the subgraph isomorphism problem. Using a biologically motivated ortholog-contraction technique for relating proteins across species, we render this problem tractable. We experimentally show that the proposed method can be used as a pruning heuristic that accelerates existing techniques significantly, as well as a stand-alone tool that conveys significant biological insights at near-interactive rates.
With a view to understanding the conservation and divergence of functional modules, we have developed a network alignment algorithm, which is grounded in theoretical models of network evolution. Through graph-theoretic modeling of evolutionary events in terms of matches, mismatches, and duplications, we reduce the alignment problem into a graph optimization problem, and develop effective heuristics to solve this problem efficiently. We probabilistically analyze the existence of highly connected and conserved subgraphs in random graphs, in order to assess the statistical significance of identified patterns. Our methods and algorithms are implemented on various
platforms and tested extensively on a comprehensive collection of molecular interaction data, illustrating the effectiveness of the algorithms in terms of providing novel biological insights as well as computational efficiency.