Transition rates, survival probabilities, and quality of bias from time-dependent biased simulations

TL;DR

This paper introduces a Kramers' theory-based method to accurately estimate transition rates in time-dependent biased simulations, overcoming limitations of existing approaches especially for complex molecular systems.

Contribution

It develops an analytical framework to extract unbiased transition rates from biased simulations with adaptive time-dependent biases, improving accuracy in complex scenarios.

Findings

Analytical expressions accurately reproduce barrier-crossing time statistics.

Method effectively estimates unbiased transition rates in complex molecular simulations.

Assesses bias quality by comparing acceleration efficiency.

Abstract

Simulations with an adaptive time-dependent bias, such as metadynamics, enable an efficient exploration of the conformational space of a system. However, the dynamic information of the system is altered by the bias. With infrequent metadynamics it is possible to recover the transition rate of crossing a barrier, if the collective variables are ideal and there is no bias deposition near the transition state. Unfortunately, for simulations of complex molecules, these conditions are not always fulfilled. To overcome these limitations, and inspired by single-molecule force spectroscopy, we developed a method based on Kramers' theory for calculating the barrier-crossing rate when a time-dependent bias is added to the system. We assess the quality of the bias parameter by measuring how efficiently the bias accelerates the transitions compared to ideal behavior. We present approximate analytical expressions of the survival probability that accurately reproduce the barrier-crossing time statistics, and enable the extraction of the unbiased transition rate even for challenging cases, where previous methods fail.