Adaptive Biasing Combined with Hamiltonian Replica Exchange to Improve Umbrella Sampling Free Energy Simulations

Abstract

The calculation of binding free energies using potential of mean force based techniques is an important application of molecular simulations. Typically, a potential of mean force (PMF) along the separation distance between two binding molecules is calculated using umbrella sampling (US). Convergence can be improved by introducing restraints on the relative position and orientation of the molecules as well as on their configurational freedom. Application of such umbrella sampling protocol on DNA in complex with the minor-groove binding ligand furamidine failed to yield converged results within reasonable simulation time. Significant energy barriers and tightly bound water molecules in the DNA minor groove that only occasionally exchanged with the bulk appeared to be a major reason for insufficient convergence. However, convergence could be greatly improved by a combination of standard phase space reduction techniques with flattening of the free energy landscape and configurational exchanges using the Hamiltonian replica exchange method. The approach uses an iteratively adapting biasing potential that corresponds to a previously calculated PMF and smoothens the free energy surface in combination with replica exchanges along the reaction coordinate. In contrast to standard US, the combined method resulted in rapid convergence of calculated free energy changes along the separation distance coordinate and excellent agreement of dissociation and association calculations with experimental results.