Linear-Scaling Soft Core Scheme for Alchemical Free Energy Calculations

Abstract

Alchemical free energy calculations hold the promise of unrivalled quantitative accuracy in the computational study of molecular recognition and related biochemical processes. Although noteworthy successes have been reported, there remains significant room for improvement in algorithm design and sampling methods. We here present an alternative formulation of a soft-core nonbonded potential, designed to be suitable for linear mixing of potential functions. The use of soft-core potentials is essential when considering thermodynamic cycles involving the insertion / removal of atoms from the surroundings. Existing formulations resolve the numerical instabilities that normally accompany linear mixing, but render the mixing of potential functions a non-linear function of the coupling parameter (lambda). Our formulation permits linear mixing while avoiding the numerical instability normally associated with simple scaling of the Lennard-Jones and Coulomb potentials. We demonstrate the advantages of linear mixing with reference to optimisation of free energy estimation, and of protocol design from the perspective of phase space overlap. We assess the performance of protocols based on the linear scaling soft-core potential as applied to the calculation of relative binding free energies for a complex biomolecular system, consisting of a zinc finger protein and a series of bound DNA oligonucleotides.