Enhanced Conformational Sampling in Molecular Dynamics Simulations of Solvated Peptides: Fragment-Based Local Elevation Umbrella Sampling.

A new method, fragment-based local elevation umbrella sampling (FB-LEUS), is proposed to enhance the conformational sampling in explicit-solvent molecular dynamics (MD) simulations of solvated polymers. The method is derived from the local elevation umbrella sampling (LEUS) method [ Hansen and Hünenberger , J. Comput. Chem. 2010 , 31 , 1 - 23 ], which combines the local elevation (LE) conformational searching and the umbrella sampling (US) conformational sampling approaches into a single scheme. In LEUS, an initial (relatively short) LE build-up (searching) phase is used to construct an optimized (grid-based) biasing potential within a subspace of conformationally relevant degrees of freedom, which is then frozen and used in a (comparatively longer) US sampling phase. This combination dramatically enhances the sampling power of MD simulations but, due to computational and memory costs, is only applicable to relevant subspaces of low dimensionalities. As an attempt to expand the scope of the LEUS approach to solvated polymers with more than a few relevant degrees of freedom, the FB-LEUS scheme involves an US sampling phase that relies on a superposition of low-dimensionality biasing potentials optimized using LEUS at the fragment level. The feasibility of this approach is tested using polyalanine (poly-Ala) and polyvaline (poly-Val) oligopeptides. Two-dimensional biasing potentials are preoptimized at the monopeptide level, and subsequently applied to all dihedral-angle pairs within oligopeptides of 4,  6,  8, or 10 residues. Two types of fragment-based biasing potentials are distinguished: (i) the basin-filling (BF) potentials act so as to "fill" free-energy basins up to a prescribed free-energy level above the global minimum; (ii) the valley-digging (VD) potentials act so as to "dig" valleys between the (four) free-energy minima of the two-dimensional maps, preserving barriers (relative to linearly interpolated free-energy changes) of a prescribed magnitude. The application of these biasing potentials may lead to an impressive enhancement of the searching power (volume of conformational space visited in a given amount of simulation time). However, this increase is largely offset by a deterioration of the statistical efficiency (representativeness of the biased ensemble in terms of the conformational distribution appropriate for the physical ensemble). As a result, it appears difficult to engineer FB-LEUS schemes representing a significant improvement over plain MD, at least for the systems considered here.