Detection of complexes in biological networks through diversified dense subgraph mining

Protein-protein interaction (PPI) networks, providing a comprehensive landscape of protein interaction patterns, enable us to explore biological processes and cellular components at multiple resolutions. For a biological process, a number of proteins need to work together to perform a job. Proteins densely interact with each other, forming large molecular machines or cellular building blocks. Identification of such densely interconnected clusters or protein complexes from PPI networks enables us to obtain a better understanding of the hierarchy and organization of biological processes and cellular components. However, most existing graph clustering algorithms on PPI networks often cannot effectively detect densely connected subgraphs and overlapped subgraphs. In this article, we formulate the problem of complex detection as diversified dense subgraph mining and introduce a novel approximation algorithm to efficiently enumerate putative protein complexes from biological networks. The key insight of our algorithm is that instead of enumerating all dense subgraphs, we only need to find a small diverse subset of subgraphs that cover as many proteins as possible. The problem is modeled as finding a diverse set of maximal dense subgraphs where we develop highly effective pruning techniques to guarantee efficiency. To scale up to large networks, we devise a divide-and-conquer approach to speed up the algorithm in a distributed manner. By comparing with existing clustering and dense subgraph-based algorithms on several yeast and human PPI networks, we demonstrate that our method can detect more putative protein complexes and achieves better prediction accuracy.∗