Quantitative Assessment of Molecular Dynamics Sampling for Flexible Systems

Molecular
dynamics (MD) simulation is a natural method for the
study of flexible molecules but at the same time is limited by the
large size of the conformational space of these molecules. We ask
by how much the MD sampling quality for flexible molecules can be
improved by two means: the use of diverse sets of trajectories starting
from different initial conformations to detect deviations between
samples and sampling with enhanced methods such as accelerated MD
(aMD) or scaled MD (sMD) that distort the energy landscape in controlled
ways. To this end, we test the effects of these approaches on MD simulations
of two flexible biomolecules in aqueous solution, Met-Enkephalin (5
amino acids) and HIV-1 gp120 V3 (a cycle of 35 amino acids). We assess
the convergence of the sampling quantitatively with known, extensive
measures of cluster number Nc and cluster
distribution entropy Sc and with two new
quantities, conformational overlap Oconf and density overlap Odens, both conveniently
ranging from 0 to 1. These new overlap measures quantify self-consistency
of sampling in multitrajectory MD experiments, a necessary condition
for converged sampling. A comprehensive assessment of sampling quality
of MD experiments identifies the combination of diverse trajectory
sets and aMD as the most efficient approach among those tested. However,
analysis of Odens between conventional
and aMD trajectories also reveals that we have not completely corrected
aMD sampling for the distorted energy landscape. Moreover, for V3,
the courses of Nc and Odens indicate that much higher resources than those generally
invested today will probably be needed to achieve convergence. The
comparative analysis also shows that conventional MD simulations with
insufficient sampling can be easily misinterpreted as being converged.