Optimization of Side Chain Conformations via Beta-complex

Abstract

A molecular structure determines a molecular function(s) and a correct understanding of molecular structure is important for biotechnology. The computational prediction of molecular structure is a frequent requirement for important biomolecular applications such as a homology modeling, a docking simulation, a protein design, etc. where the optimization of molecular structure is fundamental. One of the core problems in the optimization of protein structure is the optimization of side-chains called the side-chain positioning problem. The side-chain positioning problem, assuming the rigidity of backbone and a rotamer library, attempts to optimally assign a rotamer to each residue so that the potential energy of protein is minimized in its entirety. The optimal solution approach using (mixed) integer linear programming, with the dead-end elimination technique, suffers even for moderate-sized proteins because the side-chain positioning problem is NP-hard. On the other hand, popular heuristic approaches focusing on speed produce solutions of low quality. This paper presents an efficient algorithm, called the BetaSCP, for the side-chain positioning problem based on the beta-complex which is a derivative geometric construct of the Voronoi diagram. Placing a higher priority on solution quality, the BetaSCP algorithm produces a solution very close to the optima within a reasonable computation time. The effectiveness and efficiency of the BetaSCP are experimentally shown via a benchmark test against well-known algorithms using twenty test models selected from Protein Data Bank.