A targeted reweighting method for accelerating the exploration of high-dimensional configuration space

Abstract

Time scales available to biomolecular simulations are limited by barriers among states in a high-dimensional configuration space. If equilibrium averages are to be computed, methods that accelerate barrier passage can be carried out by non-Boltzmann sampling. Barriers can be reduced by modifying the potential-energy function and running dynamics on the modified surface. The Boltzmann average can be restored by reweighting each point along the trajectory. We introduce a targeted reweighting scheme where some barriers are reduced, while others are not modified. If only equilibrium properties are desired, trajectories in configuration space can be generated by Langevin dynamics. Once past a transient time, these trajectories guarantee equilibrium sampling when reweighted. A relatively high-order stochastic integration method can be used to generate trajectories. The targeted reweighting scheme is illustrated by a series of double-well models with varying degrees of freedom and shown to be a very efficient method to provide the correct equilibrium distributions, in comparison with analytic results. The scheme is applied to a protein model consisting of a chain of connected beads characterized by dihedral angles and the van der Waals interactions among the beads. We investigate the sampling of configuration space for a model of a helix-turn-helix motif. The targeted reweighting is found to be essential to permit the original all-helical conformation to bend and generate turn structures while still maintaining the alpha-helical segments.