Finding low-conductance sets with dense interactions (FLCD) for better protein complex prediction

Intuitively, proteins in the same protein complexes should highly interact with each other but rarely interact with the other proteins in protein-protein interaction (PPI) networks. Surprisingly, many existing computational algorithms do not directly detect protein complexes based on both of these topological properties. Most of them, depending on mathematical definitions of either "modularity" or "conductance", have their own limitations: Modularity has the inherent resolution problem ignoring small protein complexes; and conductance characterizes the separability of complexes but fails to capture the interaction density within complexes.

In this paper, we propose a two-step algorithm FLCD (Finding Low-Conductance sets with Dense interactions) to predict overlapping protein complexes with the desired topological structure, which is densely connected inside and well separated from the rest of the networks. First, FLCD detects well-separated subnetworks based on approximating a potential low-conductance set through a personalized PageRank vector from a protein and then solving a mixed integer programming (MIP) problem to find the minimum-conductance set within the identified low-conductance set. At the second step, the densely connected parts in those subnetworks are discovered as the protein complexes by solving another MIP problem that aims to find the dense subnetwork in the minimum-conductance set.

Experiments on four large-scale yeast PPI networks from different public databases demonstrate that the complexes predicted by FLCD have better correspondence with the yeast protein complex gold standards than other three state-of-the-art algorithms (ClusterONE, LinkComm, and SR-MCL). Additionally, results of FLCD show higher biological relevance with respect to Gene Ontology (GO) terms by GO enrichment analysis.