  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 rate-limiting step of biomolecular processes. Presumably for
the same reasons, they often characterize the rate-limiting step in
simulations. To the extent that first-passage probabilities can be computed
without requiring direct simulation, the process of traversing entropic
barriers can replaced by a single choice from the computed ("first-passage")
distribution. We will show that in the presence of certain entropic barriers,
first-passage 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
first-passage distribution can be well-approximated 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 ("golf-course")
potential, the estimates are as accurate as the results of direct simulations,
but far faster to compute.
