Statistically Unbiased Free Energy Estimates from Biased Simulations

TL;DR

This paper presents a new method for unbiased free energy estimation from biased molecular simulations, improving accuracy and stability by removing external bias effects using a recently developed estimator.

Contribution

It introduces a novel approach that leverages a recently proposed free energy estimator to achieve statistically unbiased estimates from biased simulation data.

Findings

The method provides unbiased free energy estimates on model systems.

It accurately estimates free energy for a small peptide in unbiased simulations.

The error magnitude of estimates is reliably predicted by the model.

Abstract

Estimating the free energy in molecular simulation requires, implicitly or explicitly, counting how many times the system is observed in a finite region. If the simulation is biased by an external potential, the weight of the configurations within the region can vary significantly, and this can make the estimate numerically unstable. We introduce an approach to estimate the free energy as a simultaneous function of several collective variables starting from data generated in a statically-biased simulation. The approach exploits the property of a free energy estimator recently introduced by us which provides by construction the estimate in a region of infinitely small size. We show that this property allows removing the effect of the external bias in a simple and rigorous manner. The approach is validated on model systems for which the free energy is known analytically and on a small peptide for which the ground truth free energy is estimated in an independent unbiased run. In both cases the free energy obtained with our approach is an unbiased estimator of the ground-truth free energy, with an error whose magnitude is also predicted by the model.