Comparing three stochastic search algorithms for computational protein design: Monte Carlo, replica exchange Monte Carlo, and a multistart, steepest‐descent heuristic

Abstract

Computational protein design depends on an energy function and an algorithm to search the sequence/conformation space. We compare three stochastic search algorithms: a heuristic, Monte Carlo (MC), and a Replica Exchange Monte Carlo method (REMC). The heuristic performs a steepest-descent minimization starting from thousands of random starting points. The methods are applied to nine test proteins from three structural families, with a fixed backbone structure, a molecular mechanics energy function, and with 1, 5, 10, 20, 30, or all amino acids allowed to mutate. Results are compared to an exact, "Cost Function Network" method that identifies the global minimum energy conformation (GMEC) in favorable cases. The designed sequences accurately reproduce experimental sequences in the hydrophobic core. The heuristic and REMC agree closely and reproduce the GMEC when it is known, with a few exceptions. Plain MC performs well for most cases, occasionally departing from the GMEC by 3-4 kcal/mol. With REMC, the diversity of the sequences sampled agrees with exact enumeration where the latter is possible: up to 2 kcal/mol above the GMEC. Beyond, room temperature replicas sample sequences up to 10 kcal/mol above the GMEC, providing thermal averages and a solution to the inverse protein folding problem. © 2016 Wiley Periodicals, Inc.

Comparing pairwise‐additive and many‐body generalized Born models for acid/base calculations and protein design

“…This framework uses a precalculated energy matrix to allow very efficient Monte Carlo simulations of proteins, where rotamers, protonation states, and side chain types can all vary. [45,94] The present implementation is about four times as costly as the NEA method; its cost is reduced by half compared to an earlier FDB implementation. [37] The present implementation is also much friendlier and more flexible than the earlier one.…”

“…Our first goal was to implement the more rigorous GB method within the Proteus software and model framework. This framework uses a precalculated energy matrix to allow very efficient Monte Carlo simulations of proteins, where rotamers, protonation states, and side chain types can all vary . The present implementation is about four times as costly as the NEA method; its cost is reduced by half compared to an earlier FDB implementation .…”

“…The simulations used a replica exchange MC procedure, where eight simulations were run in parallel at different temperatures, and the instantaneous conformations were exchanged randomly according to a Metropolis criterion . Temperatures ranged from 0.125 to 2 kT units.…”

“…The simulations used a replica exchange MC procedure, where eight simulations were run in parallel at different temperatures, and the instantaneous conformations were exchanged randomly according to a Metropolis criterion. [94] Temperatures ranged from 0.125 to 2 kT units. Gly and Pro residues present in the wildtype protein were not allowed to mutate, and positions that did mutate could not change into Gly or Pro.…”

Recent advances in automated protein design and its future challenges

“…With the latter, several trajectories, each runs at a different T value, are generated so that the simulation trajectory can jump to adjacent trajectory with a higher/lower T according to Boltzman’s probability, thus allowing it to explore the global energy scoring surface in a more efficient way. Besides the memory and CPU advantages compared to deterministic techniques, replica exchange and Monte Carlo techniques have the advantage of providing Boltzmann like sampling of the conformation/sequence space near the GMEC [184]. Boltzmann sampling of rotamers for a given sequence may provide a measure of the conformational entropy of a design, a factor which has largely been neglected in energy functions to this date.…”