An Exact Algorithm for Side-Chain Placement in Protein Design

TL;DR

This paper introduces a new exact branch-and-bound algorithm with Lagrangian relaxation for the NP-hard side-chain placement problem in protein design, enabling optimal solutions for large instances.

Contribution

A novel branch-and-bound method with tight bounds from Lagrangian relaxation, improving the solvability of large protein design problems.

Findings

Outperforms existing exact methods on large instances.

Enables routine optimal solutions for large protein design problems.

Efficiently handles the combinatorial complexity of side-chain placement.

Abstract

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.