A theoretical framework for random acceleration molecular dynamics simulations

The dissociation of a ligand bound to a receptor is a rare events occurring on a timescale that is far longer than can be afforded by standard simulation methodologies. A number of specialized approaches have been designed to overcome this challenge. One of these, Random Acceleration Molecular Dynamics (RAMD), is a biased simulation method that is particularly effective at accelerating the dissociation of ligands bound to protein receptors. However, no theoretical framework is currently available to extract unbiased estimates from the RAMD simulation results. In this work, we develop a simple theory for its interpretation based on the assumption that the RAMD simulations can be approximated by an overdamped Langevin dynamics with an additional force of fixed magnitude changing direction randomly at exponentially distributed times. We shown that the dynamics of the model is consistent with a Smoluchowski equation with an effective temperature and diffusion coefficient that depend quadratically on the magnitude of the random force. These observations explain why the RAMD simulations yields accelerated dynamics. Importantly, we derive an analytical expression for the unbiased escape time of a particle over a free-energy barrier based on the modified Smoluchowski equation. The theoretical framework was used to analyse RAMD simulations monitoring the dissociation of the Trypsin-Benzamidine protein-ligand complex. The results indicate that the theoretical framework is sound and could potentially be used to unbias the results from RAMD simulations.