The Variationally Derived Intermediates Method to Calculate Free Energy Differences

Abstract

Accurate and fast free energy calculations, based on atomistic simulations, are key to a first principles understanding of many-particle systems in biophysics, and enable quantitative descriptions of molecular recognition processes, drug binding, transmembrane transport, or functional conformational motions of proteins or complexes. To this aim, alchemical methods, such as the Free Energy Perturbation or the Bennett Acceptance Ratio method, require ‘morphing’ between the Hamiltonians of the involved molecular end states, typically in terms of a linear interpolation. However, linear transformations and soft-core variants thereof are still a very special case amongst all possible transformations. Here, we present the Variationally Derived Intermediates (VI) method that generalizes this approach and yields, under the assumption of uncorrelated sampling points, the intermediates with optimal sampling accuracy, which differ markedly from the established ones. We present applications to the challenging case of solvation free energies, yielding improved accuracies for decoupling electrostatic interactions, and similar ones for Lennard-Jones interactions, compared to state of the art soft-core transformations.