Trading accuracy for speed: A quantitative comparison of search algorithms in protein sequence design

Finding the minimum energy amino acid side-chain conformation is a fundamental problem in both homology modeling and protein design. To address this issue, numerous computational algorithms have been proposed. However, there have been few quantitative comparisons between methods and there is very little general understanding of the types of problems that are appropriate for each algorithm. Here, we study four common search techniques: Monte Carlo (MC) and Monte Carlo plus quench (MCQ); genetic algorithms (GA); self-consistent mean field (SCMF); and dead-end elimination (DEE). Both SCMF and DEE are deterministic, and if DEE converges, it is guaranteed that its solution is the global minimum energy conformation (GMEC). This provides a means to compare the accuracy of SCMF and the stochastic methods. For the side-chain placement calculations, we find that DEE rapidly converges to the GMEC in all the test cases. The other algorithms converge on significantly incorrect solutions; the average fraction of incorrect rotamers for SCMF is 0.12, GA 0.09, and MCQ 0.05. For the protein design calculations, design positions are progressively added to the side-chain placement calculation until the time required for DEE diverges sharply. As the complexity of the problem increases, the accuracy of each method is determined so that the results can be extrapolated into the region where DEE is no longer tractable. We find that both SCMF and MCQ perform reasonably well on core calculations (fraction amino acids incorrect is SCMF 0.07, MCQ 0.04), but fail considerably on the boundary (SCMF 0.28, MCQ 0.32) and surface calculations (SCMF 0.37, MCQ 0.44).