An Exact Algorithm for Side-Chain Placement in Protein Design

Computational protein design aims at constructing novel or improved func-tions on the structure of a given protein backbone and has important applica-tions in the pharmaceutical and biotechnical industry. The underlying combi-natorial side-chain placement problem consists of choosing a side-chain place-ment for each residue position such that the resulting overall energy is mini-mum. The choice of the side-chain then also determines the amino acid for this position. Many algorithms for thisN P-hard problem have been proposed in the context of homology modeling, which, however, reach their limits when faced with large protein design instances. In this paper, we propose a new exact method for the side-chain placement problem that works well even for large instance sizes as they appear in pro-tein design. Our main contribution is a dedicated branch-and-bound algorithm that combines tight upper and lower bounds resulting from a novel Lagrangian relaxation approach for side-chain placement. Our experimental results show that our method outperforms alternative state-of-the-art exact approaches and makes it possible to optimally solve large protein design instances routinely.