  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 problem consists of choosing a side-chain placement 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 side-chain placement
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 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.
