Alchemical transformations for concerted hydration free energy estimation with explicit solvation

Abstract

We present a family of alchemical perturbation potentials that enable the calculation of hydration free energies of small- to medium-sized molecules in a single concerted alchemical coupling step instead of the commonly used sequence of two distinct coupling steps for Lennard-Jones and electrostatic interactions. The perturbation potentials we employ are non-linear functions of the solute–solvent interaction energy designed to focus sampling near entropic bottlenecks along the alchemical pathway. We present a general framework to optimize the parameters of alchemical perturbation potentials of this kind. The optimization procedure is based on the λ-function formalism and the maximum-likelihood parameter estimation procedure we developed earlier to avoid the occurrence of multi-modal distributions of the coupling energy along the alchemical path. A novel soft-core function applied to the overall solute–solvent interaction energy rather than individual interatomic pair potentials critical for this result is also presented. Because it does not require modifications of core force and energy routines, the soft-core formulation can be easily deployed in molecular dynamics simulation codes. We illustrate the method by applying it to the estimation of the hydration free energy in water droplets of compounds of varying size and complexity. In each case, we show that convergence of the hydration free energy is achieved rapidly. This work paves the way for the ongoing development of more streamlined algorithms to estimate free energies of molecular binding with explicit solvation.

Relative Binding Free Energy Calculations for Ligands with Diverse Scaffolds with the Alchemical Transfer Method

“…42 The method has its roots in the development of a statistical mechanics formulation of alchemical binding 56 and the discovery of coordinate-based free energy perturbation schemes and novel alchemical potential functions capable of removing sampling bottlenecks along the alchemical thermodynamic path. 48 The resulting ATM method has been recently extended to the modeling of hydration 49 and molecular binding 27,50 with explicit solvation. In the present work, we combine ATM with a ligand alignment restraints protocol to model relative binding free energies.…”

“…40,41 The specific alchemical protocol we employ is described in detail in previous publications. 27,48,49 Briefly, in this work we employ a linear λ-dependent alchemical potential energy function of the form…”

“…The parameters λ 2 , λ 1 , α, u 0 , and w 0 are functions of λ which are adjusted to enhance convergence, 49 and…”

Alchemical Transfer Approach to Absolute Binding Free Energy Estimation

“…( 3) with 24 λ-states and the parameters listed in Tables 1 and 2 for each leg. The parameters of the softplus perturbation potential were optimized using the scheme described previously 23,25 which involved running trial calculations with the linear potential, fitting the analytical model of binding 28 to each transformation, and adjusting the parameters of the softplus potential to the resulting λ-function 23 to obtain a smooth alchemical transition.…”

“…23 We have recently shown that the same approach is applicable to the estimation of the concerted hydration free energies of drug-sized solutes in water droplets with explicit solvation. 25 In this work, we extend this concerted alchemical scheme to the calculations of absolute binding free energies with explicit solvation. In the resulting alchemical scheme, called the Alchemical Transfer Method (ATM) (Figure 1B), the unbound and bound states of the molecular complex are related by a translation vector that brings the ligand from the solvent bulk to the receptor binding site in a single solvent box.…”