Solving Maximum Clique Problem for Protein Structure Similarity

TL;DR

This paper introduces a new integer programming model and a specialized branch and bound algorithm to efficiently solve the maximum clique problem in protein structure similarity, significantly outperforming existing methods.

Contribution

It presents a novel integer programming formulation and a dedicated branch and bound algorithm for protein structure alignment, integrated into the VAST tool.

Findings

Branch and bound algorithm is up to 116 times faster than BK

New model improves efficiency of protein structure similarity computation

Enhanced VAST tool for protein alignment

Abstract

A basic assumption of molecular biology is that proteins sharing close three-dimensional (3D) structures are likely to share a common function and in most cases derive from a same ancestor. Computing the similarity between two protein structures is therefore a crucial task and has been extensively investigated. Evaluating the similarity of two proteins can be done by finding an optimal one-to-one matching between their components, which is equivalent to identifying a maximum weighted clique in a specific "alignment graph". In this paper we present a new integer programming formulation for solving such clique problems. The model has been implemented using the ILOG CPLEX Callable Library. In addition, we designed a dedicated branch and bound algorithm for solving the maximum cardinality clique problem. Both approaches have been integrated in VAST (Vector Alignment Search Tool) - a software for aligning protein 3D structures largely used in NCBI (National Center for Biotechnology Information). The original VAST clique solver uses the well known Bron and Kerbosh algorithm (BK). Our computational results on real life protein alignment instances show that our branch and bound algorithm is up to 116 times faster than BK for the largest proteins.