Probabilistic Biological Network Alignment

Interactions between molecules are probabilistic events. An interaction may or may not happen with some probability, depending on a variety of factors such as the size, abundance, or proximity of the interacting molecules. In this paper, we consider the problem of aligning two biological networks. Unlike existing methods, we allow one of the two networks to contain probabilistic interactions. Allowing interaction probabilities makes the alignment more biologically relevant at the expense of explosive growth in the number of alternative topologies that may arise from different subsets of interactions that take place. We develop a novel method that efficiently and precisely characterizes this massive search space. We represent the topological similarity between pairs of aligned molecules (i.e., proteins) with the help of random variables and compute their expected values. We validate our method showing that, without sacrificing the running time performance, it can produce novel alignments. Our results also demonstrate that our method identifies biologically meaningful mappings under a comprehensive set of criteria used in the literature as well as the statistical coherence measure that we developed to analyze the statistical significance of the similarity of the functions of the aligned protein pairs.