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 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.