Novel geometric approach for global alignment of PPI networks

In this paper we present a novel geometric method for the problem of global pairwise alignment of protein-protein interaction (PPI) networks. A PPI network can be viewed as a node-edge graph and its alignment often needs to solve some generalized version of the subgraph isomorphism problem which is notoriously challenging and NP-hard. All existing research has focused on designing algorithms with good practical performance. In this paper we propose a two-step algorithm for the global pairwise PPI network alignment which consists of a Geometric Step and an MCMF Step. Our algorithm first applies a graph embedding technique that preserves the topological structure of the original PPI networks and maps the problem from graph domain to geometric domain, and computes a rigid transformation for one of the embedded PPI networks so as to minimize its Earth Mover's Distance (EMD) to the other PPI network. It then solves a Min-Cost Max-Flow problem using the (scaled) inverse of sequence similarity scores as edge weight. By using the flow values from the two steps (i.e., EMD and Min-Cost Max-Flow) as the matching scores, we are able to combine the two matching results to obtain the desired alignment. Unlike other popular alignment algorithms which are either greedy or incremental, our algorithm globally optimizes the problem to yield an alignment with better quality.