Using the local elevation method to construct optimized umbrella sampling potentials: calculation of the relative free energies and interconversion barriers of glucopyranose ring conformers in water

Abstract

A method is proposed to combine the local elevation (LE) conformational searching and the umbrella sampling (US) conformational sampling approaches into a single local elevation umbrella sampling (LEUS) scheme for (explicit-solvent) molecular dynamics (MD) simulations. In this approach, an initial (relatively short) LE build-up (searching) phase is used to construct an optimized biasing potential within a subspace of conformationally relevant degrees of freedom, that is then used in a (comparatively longer) US sampling phase. This scheme dramatically enhances (in comparison with plain MD) the sampling power of MD simulations, taking advantage of the fact that the preoptimized biasing potential represents a reasonable approximation to the negative of the free energy surface in the considered conformational subspace. The method is applied to the calculation of the relative free energies of beta-D-glucopyranose ring conformers in water (within the GROMOS 45A4 force field). Different schemes to assign sampled conformational regions to distinct states are also compared. This approach, which bears some analogies with adaptive umbrella sampling and metadynamics (but within a very distinct implementation), is shown to be: (i) efficient (nearly all the computational effort is invested in the actual sampling phase rather than in searching and equilibration); (ii) robust (the method is only weakly sensitive to the details of the build-up protocol, even for relatively short build-up times); (iii) versatile (a LEUS biasing potential database could easily be preoptimized for small molecules and assembled on a fragment basis for larger ones).