Capacities and the Free Passage of Entropic Barriers
Abstract
We propose an approach for estimating the probability that a given small target, among many, will be the first to be reached in a molecular dynamics simulation. Reaching small targets out of a vast number of possible configurations constitutes an entropic barrier. Experimental evidence suggests that entropic barriers are ubiquitous in biomolecular systems, and often characterize the ratelimiting step of biomolecular processes. Presumably for the same reasons, they often characterize the ratelimiting step in simulations. To the extent that firstpassage probabilities can be computed without requiring direct simulation, the process of traversing entropic barriers can replaced by a single choice from the computed ("firstpassage") distribution. We will show that in the presence of certain entropic barriers, firstpassage probabilities are approximately invariant to the initial configuration, provided that it is modestly far away from each of the targets. We will further show that as a consequence of this invariance, the firstpassage distribution can be wellapproximated in terms of "capacities" of local sets around the targets. Using these theoretical results and a Monte Carlo mechanism for approximating capacities, we provide a method for estimating the hitting probabilities of small targets in the presence of entropic barriers. In numerical experiments with an idealized ("golfcourse") potential, the estimates are as accurate as the results of direct simulations, but far faster to compute.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 arXiv:
 arXiv:1811.00205
 Bibcode:
 2018arXiv181100205L
 Keywords:

 Physics  Computational Physics
 EPrint:
 Phys. Rev. E 102, 023304 (2020)