BWM∗: A novel, provable, ensemble-based dynamic programming algorithm for sparse approximations of computational protein design

Abstract

Current dynamic programming protein design algorithms that exploit the optimal substructure induced by sparse energy functions compute only the Global Minimum Energy Conformation (GMEC). This disproportionately favors the sequence of a single, static conformation and overlooks better sequences with multiple low-energy conformations. We propose a novel, provable, dynamic programming algorithm called Branch-Width Minimization∗ (BWM∗) to enumerate a gap-free ensemble of conformations in order of increasing energy. Given a branchdecomposition of branch-width w for an n-residue protein design with at most q discrete side-chain conformations per residue, BWM∗ returns the sparse GMEC in O(nw2q3/2w) time, and enumerates each additional conformation in O(n log q) time. BWM∗ outperforms the classical search algorithm A∗ in 49 of 67 protein design problems, computing the full ensemble or a close approximation up to two orders of magnitude faster. Performance of BWM∗ can be predicted cheaply beforehand, allowing selection of the most efficient algorithm for each design problem.