Modeling Protein Interacting Groups by Quasi-Bicliques: Complexity, Algorithm, and Application

Protein-protein interactions (PPIs) are one of the most important mechanisms in cellular processes. To model protein interaction sites, recent studies have suggested to find interacting protein group pairs from large PPI networks at the first step and then to search conserved motifs within the protein groups to form interacting motif pairs. To consider the noise effect and the incompleteness of biological data, we propose to use quasi-bicliquesior finding interacting protein group pairs. We investigate two new problems that arise from finding interacting protein group pairs: the maximum vertex quasi-biclique problem and the maximum balanced quasi-biclique problem. We prove that both problems are NP-hard. This is a surprising result as the widely known maximum vertex biclique problem is polynomial time solvable [1]. We then propose a heuristic algorithm that uses the greedy method to find the quasi-bicliques from PPI networks. Our experiment results on real data show that this algorithm has a better performance than a benchmark algorithm for identifying highly matched BLOCKS and PRINTS motifs. We also report results of two case studies on interacting motif pairs that map well with two interacting domain pairs in iPfam. Availability: The software and supplementary information are available at http://www.cs.cityu.edu.hk/~lwang/software/ppi/index.html.

1 Introduction

Proteins with interactions carry out most biological functions within living cells such as gene expression, enzymatic reactions, signal transduction, intercellular communications, and immunoreactions. As the interactions are mediated by a short sequence of residues among the long stretches of interacting sequences, these interacting residues or so-called interaction (binding) sites are at the central spot of proteome research. Although many imaging wet-laboratory techniques like X-ray crystallography, nuclear magnetic resonance spectroscopy, electron microscopy, and mass spectrometry have been developed to determine protein interaction sites, the solved amount of protein interaction sites constitute only a tiny proportion among the whole population due to high cost and low throughput. Computational methods are still considered as the major approaches for the deep understanding of protein binding sites, especially for their subtle 3D structure properties that are not accessible by experimental methods.