An exact algorithm for side-chain placement in protein design

Computational protein design aims at constructing novel or improved functions on the structure of a given protein backbone and has important applications in the pharmaceutical and biotechnical industry. The underlying combinatorial side-chain placement (SCP) problem consists of choosing a SCP for each residue position such that the resulting overall energy is minimum. The choice of the side-chain then also determines the amino acid for this position. Many algorithms for this $${\mathcal{NP}}$$-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 SCP problem that works well even for large instance sizes as they appear in protein 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 SCP. 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.