Variationally derived intermediates for correlated free-energy estimates between intermediate states.

Martin Reinhardt,Helmut Grubmüller

doi:10.1103/physreve.102.043312

Martin Reinhardt, Helmut Grubmüller

Open Access

https://doi.org/10.1103/physreve.102.043312

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Abstract

Free-energy difference calculations based on atomistic simulations generally improve in accuracy when sampling from a sequence of intermediate equilibrium thermodynamic states that bridge the configuration space between two states of interest. For reasons of efficiency, usually the same samples are used to calculate the stepwise difference of such an intermediate to both adjacent intermediates. However, this procedure violates the assumption of uncorrelated estimates that is necessary to derive both the optimal sequence of intermediate states and the widely used Bennett acceptance ratio estimator. In this work, via a variational approach, we derive the sequence of intermediate states and the corresponding estimator with minimal mean-squared error that account for these correlations and assess its accuracy.

Highlights

Free-energy calculations are widely used to investigate physical and chemical processes [1,2,3,4,5,6,7]
Different estimators that determine the free-energy differences between these intermediates and the end states have been developed, most prominently the Zwanzig formula [16] for free-energy perturbation (FEP), the Bennett acceptance ratio method (BAR) [23], and multistate BAR (MBAR) [24]
The corresponding configuration space densities of variationally derived intermediates (VI) and correlated variational intermediates (cVI) are shown in the upper row of Fig. 2(a)

Summary

Introduction

Free-energy calculations are widely used to investigate physical and chemical processes [1,2,3,4,5,6,7]. Among the most widely used methods based on simulations with atomistic Hamiltonians are alchemical equilibrium techniques, including the free-energy perturbation (FEP) [16] and thermodynamic integration (TI) [17] methods. These techniques determine the free-energy difference between two states, representing, for example, two different ligands bound to a target, by sampling from intermediate states whose Hamiltonians are constructed from those of the end states. Different estimators that determine the free-energy differences between these intermediates and the end states have been developed, most prominently the Zwanzig formula [16] for FEP, the Bennett acceptance ratio method (BAR) [23], and multistate BAR (MBAR) [24]

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Results

Conclusion