Alternative approaches to potential of mean force calculations: Free energy perturbation versus thermodynamic integration. The case study of hydrophobic interactions

Abstract

We have investigated the convergence behavior of potential of mean force (PMF) calculations, using free energy perturbation (FEP) and thermodynamic integration (TI) techniques. The critical comparison of these alternative approaches is illustrated by the study of a system consisting of two methane molecules embedded in a periodic box of water. Complete PMF simulations were carried out over one nanosecond of Molecular Dynamics each, using different methods and sampling protocols. We find that (i) the TI/PMF protocol is considerably more efficient than the FEP/PMF method, and, (ii) in the case of TI simulations, it is preferable to employ a limited number of λ points of the integrand involving extensive sampling, rather than numerous points with less sampling. On account of the deleterious effects of the FEP approach on PMF computations, we have applied the TI protocol to determine the PMF of two toluene molecules in an aqueous solution. The curves corresponding to both the T‐shaped and the stacked configurations have been derived and compared to the FEP results obtained by Per Linse on the hydrated benzene dimer.