Molecular Dynamics at Low Time Resolution

TL;DR

This paper introduces an analytical method to integrate out fast molecular dynamics in over-damped Langevin systems, enabling larger time steps in simulations while accurately capturing long-time behavior.

Contribution

It provides a rigorous way to account for fast dynamics effects in Langevin equations, allowing for more efficient simulations with larger time steps.

Findings

Validated on a one-dimensional diffusion model

Applied to protein denaturation simulation

Demonstrated computational efficiency improvements

Abstract

The internal dynamics of macro-molecular systems is characterized by widely separated time scales, ranging from fraction of ps to ns. In ordinary molecular dynamics simulations, the elementary time step dt used to integrate the equation of motion needs to be chosen much smaller of the shortest time scale, in order not to cut-off important physical effects. We show that, in systems obeying the over-damped Langevin Eq., the fast molecular dynamics which occurs at time scales smaller than dt can be analytically integrated out and gives raise to a time-dependent correction to the diffusion coefficient, which we rigorously compute. The resulting effective Langevin equation describes by construction the same long-time dynamics, but has a lower time resolution power, hence it can be integrated using larger time steps dt. We illustrate and validate this method by studying the diffusion of a point-particle in a one-dimensional toy-model and the denaturation of a protein.