Fast Approximate IsoRank for Scalable Global Alignment of Biological Networks

A well-studied approximate version of the graph matching problem is directly relevant for the study of protein-protein interaction networks. Called by the computational biology community Global Network Alignment, the two networks to be matched are derived from the protein-protein interaction (PPI) networks from organisms of two different species. If these two species evolved recently from a common ancestor, we can view the two PPI networks as a single network that evolved over time. It is the two versions of this network that we want to align using approximate graph matching. The first spectral method for the PPI global alignment problem proposed by the biological community was the IsoRank method of Singh et al. This method for global biological network alignment is still used today. However, with the advent of many more experiments, the size of the networks available to match has grown considerably, making running IsoRank unfeasible on these networks without access to state of the art computational resources. In this paper, we develop a new IsoRank approximation, which exploits the mathematical properties of IsoRanks linear system to solve the problem in quadratic time with respect to the maximum size of the two PPI networks. We further propose a computationally cheaper refinement to this initial approximation so that the updated result is even closer to the original IsoRank formulation. In experiments on synthetic and real PPI networks, we find that the results of our approximate IsoRank are not only nearly as accurate as the original IsoRank results but are also much faster, which makes the global alignment of large-scale biological networks feasible and scalable.