Molecular dynamics based enhanced sampling of collective variables with very large time steps

Abstract

Enhanced sampling techniques that target a set of collective variables and that use molecular dynamics as the driving engine have seen widespread application in the computational molecular sciences as a means to explore the free-energy landscapes of complex systems. The use of molecular dynamics as the fundamental driver of the sampling requires the introduction of a time step whose magnitude is limited by the fastest motions in a system. While standard multiple time-stepping methods allow larger time steps to be employed for the slower and computationally more expensive forces, the maximum achievable increase in time step is limited by resonance phenomena, which inextricably couple fast and slow motions. Recently, we introduced deterministic and stochastic resonance-free multiple time step algorithms for molecular dynamics that solve this resonance problem and allow ten- to twenty-fold gains in the large time step compared to standard multiple time step algorithms [P. Minary et al., Phys. Rev. Lett. 93, 150201 (2004); B. Leimkuhler et al., Mol. Phys. 111, 3579-3594 (2013)]. These methods are based on the imposition of isokinetic constraints that couple the physical system to Nosé-Hoover chains or Nosé-Hoover Langevin schemes. In this paper, we show how to adapt these methods for collective variable-based enhanced sampling techniques, specifically adiabatic free-energy dynamics/temperature-accelerated molecular dynamics, unified free-energy dynamics, and by extension, metadynamics, thus allowing simulations employing these methods to employ similarly very large time steps. The combination of resonance-free multiple time step integrators with free-energy-based enhanced sampling significantly improves the efficiency of conformational exploration.

Biomolecular modeling thrives in the age of technology

“…MD algorithms such as multiple timestep approaches, in contrast, have achieved far less impact than hardware innovations, due to a relatively small net computational gain. However, their framework may be useful in combination with other improvements such as enhanced sampling algorithms 77 or optimized particle-mesh Ewald algorithms 78 . The complexity and size of the biological systems of interest increases every year and thus continued algorithm development is crucial to obtain reliable methods that balance accuracy and performance.…”

Advances in enhanced sampling molecular dynamics simulations for biomolecules

“…However, the intrinsic nature of conventional enhanced sampling methods such as the demand for multiple replicas in REMD further increases MD's computational expense. As a consequence, standard enhanced sampling methods should be coupled with other advanced techniques such as multiple time-stepping methods [152] and coarse-grained models [153−155] to further improve their sampling efficiency for extremely large-scale biomolecular systems. On the other hand, the precision of force fields is another critical factor that affects DOI:10.1063/1674-0068/cjcp1905091 c ⃝2019 Chinese Physical Society the accuracy of MD simulations.…”

Collective Variables for the Simulation of Crystallization of Organic Compounds: Some Case Studies

“…The prerequisite for the formation of a prenucleating micelle is that the solutes should concentrate by reducing the distance between their centres of mass. Calling D(i,j) the distance between the centres of molecules i and j in the solute cluster, a simple collective variable can be set up as their average: A S ¼ 1=ðN ði,j Þ S i,j Dði,jÞ (4) where N (i,j) is the total number of pairs. The decrease in A S , eq.…”

“…[1] The subject has been amply debated and reviewed. [2][3][4][5][6] To clarify at least in part what is the situation, consider a set of N molecules placed in close contact in space (the "computational box"). Each atom in each molecule is described by three Cartesian coordinates plus a type designator that indicates on what kind of potential energy function the atom or the molecule will ride.…”