Modeling solvation contributions to conformational free energy changes of biomolecules using a potential of mean force expansion

Abstract

The standard free energy perturbation (FEP) techniques for the calculation of conformational free energy changes of a solvated biomolecule involve long molecular dynamics (MD) simulations. We have developed a method for performing the same calculations many orders of magnitude faster. We model the average solvent density around a solute as the product of the relevant solute–solvent correlation functions (CF), following the work of García, Hummer, and Soumpasis. We calculate the CF’s by running Monte Carlo simulations of a single solute atom in a box of explicit water molecules and also angular dependent CF’s for selected pairs of solute atoms. We then build the water shell around a larger solute (e.g., alanine dipeptide) by taking the product of the appropriate CF’s. Using FEP techniques we are able to calculate free energy changes as we rotate the dihedral angles of the alanine dipeptide and we find they are in close agreement with the MD results. We also compute the potential of mean force as a function of distance between two solvated methanes and calculate the contribution of the solvent to the free energy change that results from rotating n-butane about its dihedral angle.