Estimating Atomic Contributions to Hydration and Binding Using Free Energy Perturbation.

Benedict W J Irwin,David J Huggins

doi:10.1021/acs.jctc.8b00027

Abstract

We present a general method called atom-wise free energy perturbation (AFEP), which extends a conventional molecular dynamics free energy perturbation (FEP) simulation to give the contribution to a free energy change from each atom. AFEP is derived from an expansion of the Zwanzig equation used in the exponential averaging method by defining that the system total energy can be partitioned into contributions from each atom. A partitioning method is assumed and used to group terms in the expansion to correspond to individual atoms. AFEP is applied to six example free energy changes to demonstrate the method. Firstly, the hydration free energies of methane, methanol, methylamine, methanethiol, and caffeine in water. AFEP highlights the atoms in the molecules that interact favorably or unfavorably with water. Finally AFEP is applied to the binding free energy of human immunodeficiency virus type 1 protease to lopinavir, and AFEP reveals the contribution of each atom to the binding free energy, indicating candidate areas of the molecule to improve to produce a more strongly binding inhibitor. FEP gives a single value for the free energy change and is already a very useful method. AFEP gives a free energy change for each "part" of the system being simulated, where part can mean individual atoms, chemical groups, amino acids, or larger partitions depending on what the user is trying to measure. This method should have various applications in molecular dynamics studies of physical, chemical, or biochemical phenomena, specifically in the field of computational drug discovery.

Highlights

Free energy methods refer to an existing set of methods for estimating free energy differences, for example traditional Free Energy Perturbation (FEP) summed using either exponential averaging (EXP) or the Bennett Acceptance Ratio (BAR) and thermodynamic integration (TI)
A free energy calculation was performed for caffeine solvated in water; atom-wise free energy perturbation (AFEP) was applied to the trajectory information to produce an atom-wise breakdown of the hydration free energy
The Atom-wise Free Energy Perturbation (AFEP) method described in this article provides a detailed breakdown of a free energy change across partitions of atoms in a molecular dynamics simulation

Summary

Introduction

Free energy methods refer to an existing set of methods for estimating free energy differences, for example traditional Free Energy Perturbation (FEP) summed using either exponential averaging (EXP) or the Bennett Acceptance Ratio (BAR) and thermodynamic integration (TI) These methods have become a cornerstone of accurate binding free energy calculations,[1,2] and many reviews have scrutinized the details of such methods, concluding that they are a promising addition to the set of tools used in the drug discovery industry.[3−8] Free energy methods are implemented in many commonly used biological simulation packages, for example NAMD,[9−11] Desmond,[12] GROMACS,[13] BOSS,[14] AMBER,[15] and others. FEP can be used to extract hydration free energies,[16−18] free energies associated with mutating one molecule into another or one protein into another,[19] and in the context of drug discovery, binding free energies of inhibitors to proteins[12,20,21]

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