A Monte Carlo Resampling Approach for the Calculation of Hybrid Classical and Quantum Free Energies.

Christopher Cave-Ayland,Jonathan W Essex,Chris-Kriton Skylaris

doi:10.1021/acs.jctc.6b00506

Christopher Cave-Ayland, Jonathan W Essex + Show 1 more

Open Access

https://doi.org/10.1021/acs.jctc.6b00506

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Abstract

Hybrid free energy methods allow estimation of free energy differences at the quantum mechanics (QM) level with high efficiency by performing sampling at the classical mechanics (MM) level. Various approaches to allow the calculation of QM corrections to classical free energies have been proposed. The single step free energy perturbation approach starts with a classically generated ensemble, a subset of structures of which are postprocessed to obtain QM energies for use with the Zwanzig equation. This gives an estimate of the free energy difference associated with the change from an MM to a QM Hamiltonian. Owing to the poor numerical properties of the Zwanzig equation, however, recent developments have produced alternative methods which aim to provide access to the properties of the true QM ensemble. Here we propose an approach based on the resampling of MM structural ensembles and application of a Monte Carlo acceptance test which in principle, can generate the exact QM ensemble or intermediate ensembles between the MM and QM states. We carry out a detailed comparison against the Zwanzig equation and recently proposed non-Boltzmann methods. As a test system we use a set of small molecule hydration free energies for which hybrid free energy calculations are performed at the semiempirical Density Functional Tight Binding level. Equivalent ensembles at this level of theory have also been generated allowing the reverse QM to MM perturbations to be performed along with a detailed analysis of the results. Additionally, a previously published nucleotide base pair data set simulated at the QM level using ab initio molecular dynamics is also considered. We provide a strong rationale for the use of the Monte Carlo Resampling and non-Boltzmann approaches by showing that configuration space overlaps can be estimated which provide useful diagnostic information regarding the accuracy of these hybrid approaches.

Highlights

The prediction of protein−ligand binding affinities and free energies of hydration remains a grand challenge of computational chemistry
Each of these methods requires only an MM ensemble to be explicitly generated, but RSM and Non-Boltzmann Reweighting (NBR) use this ensemble to build a quantum mechanics (QM) ensemble which is subsequently used in the free energy calculation
We have sought diagnostics which can be used to indicate under what circumstances Single-Step Free Energy Perturbation (SSFEP), NBR, and RSM become unreliable

Summary

Introduction

The prediction of protein−ligand binding affinities and free energies of hydration remains a grand challenge of computational chemistry. A notable drawback of free energy perturbation is the requirement for extensive sampling of relevant thermodynamic states with Monte Carlo (MC) or molecular dynamics (MD). This places a practical limitation on the accuracy of the energy models that can be used to describe the states of interest. While in many cases the MM level of theory can be surprisingly accurate ( when exploiting cancellation of errors within relative free energies) there are numerous examples in the literature highlighting its insufficiency in binding affinity predictions.[1−5]

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