Robust and efficient configurational molecular sampling via Langevin Dynamics

TL;DR

This paper evaluates and compares numerical methods for stochastic differential equations in molecular dynamics, introducing an optimal scheme that improves sampling accuracy and efficiency, especially for biomolecular simulations.

Contribution

The authors identify and validate an optimal Langevin dynamics scheme that reduces bias and enhances efficiency in molecular sampling, outperforming existing methods.

Findings

Higher accuracy in alanine dipeptide simulations.

Efficiency improvements of 25% or more in practical timestep size.

Reductions in configurational average errors by a factor of ten or more.

Abstract

A wide variety of numerical methods are evaluated and compared for solving the stochastic differential equations encountered in molecular dynamics. The methods are based on the application of deterministic impulses, drifts, and Brownian motions in some combination. The Baker-Campbell-Hausdorff expansion is used to study sampling accuracy following recent work by the authors, which allows determination of the stepsize-dependent bias in configurational averaging. For harmonic oscillators, configurational averaging is exact for certain schemes, which may result in improved performance in the modelling of biomolecules where bond stretches play a prominent role. For general systems, an optimal method can be identified that has very low bias compared to alternatives. In simulations of the alanine dipeptide reported here (both solvated and unsolvated), higher accuracy is obtained without loss of computational efficiency, while allowing large timestep, and with no impairment of the conformational exploration rate (the effective diffusion rate observed in simulation). The optimal scheme is a uniformly better performing algorithm for molecular sampling, with overall efficiency improvements of 25% or more in practical timestep size achievable in vacuum, and with reductions in the error of configurational averages of a factor of ten or more attainable in solvated simulations at large timestep.