Functional module identification in protein interaction networks by interaction patterns

Motivation: Identifying functional modules in protein-protein interaction (PPI) networks may shed light on cellular functional organization and thereafter underlying cellular mechanisms. Many existing module identification algorithms aim to detect densely connected groups of proteins as potential modules. However, based on this simple topological criterion of 'higher than expected connectivity', those algorithms may miss biologically meaningful modules of functional significance, in which proteins have similar interaction patterns to other proteins in networks but may not be densely connected to each other. A few blockmodel module identification algorithms have been proposed to address the problem but the lack of global optimum guarantee and the prohibitive computational complexity have been the bottleneck of their applications in real-world large-scale PPI networks. Results: In this article, we propose a novel optimization formulation LCP2 (low two-hop conductance sets) using the concept of Markov random walk on graphs, which enables simultaneous identification of both dense and sparse modules based on protein interaction patterns in given networks through searching for LCP2 by random walk. A spectral approximate algorithm SLCP2 is derived to identify non-overlapping functional modules. Based on a bottom-up greedy strategy, we further extend LCP2 to a new algorithm (greedy algorithm for LCP2) GLCP(2) to identify overlapping functional modules. We compare SLCP2 and GLCP(2) with a range of state-of-the-art algorithms on synthetic networks and real-world PPI networks. The performance evaluation based on several criteria with respect to protein complex prediction, high level Gene Ontology term prediction and especially sparse module detection, has demonstrated that our algorithms based on searching for LCP2 outperform all other compared algorithms.