Protein Mover’s Distance: A Geometric Framework for Solving Global Alignment of PPI Networks

Abstract

A protein-protein interaction (PPI) network is an unweighted and undirected graph representing the interactions among proteins, where each node denotes a protein and each edge connecting two nodes indicates their interaction. Given two PPI networks, finding their alignment is a fundamental problem and has many important applications in bioinformatics. However, it often needs to solve some generalized version of subgraph isomorphism problem which is challenging and NP-hard. Following our previous geometric approach [21], we propose a unified algorithmic framework for PPI networks alignment. We first define a general concept called “Protein Mover’s Distance (PMD)” to evaluate the alignment of two PPI networks. PMD is similar to the well known “Earth Mover’s Distance”; however, we also incorporate some other information, e.g., the functional annotation of proteins. Our algorithmic framework consists of two steps, Embedding and Matching. For the embedding step, we apply three different graph embedding techniques to preserve the topological structures of the original PPI networks. For the matching step, we compute a rigid transformation for one of the embedded PPI networks so as to minimize its PMD to the other PPI network; by using the flow values of the resulting PMD as the matching scores, we are able to obtain the desired alignment. Also, our framework can be easily extended to joint alignment of multiple PPI networks. The experimental results on two popular benchmark datasets suggest that our method outperforms existing approaches in terms of the quality of alignment.