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 <i>N</i>_c and cluster distribution entropy <i>S</i>_c and with two new quantities, conformational overlap <i>O</i>_conf and density overlap <i>O</i>_dens, 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 <i>O</i>_dens 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 <i>N</i>_c and <i>O</i>_dens 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