Use of locally enhanced sampling in free energy calculations: Testing and application to the α → β anomerization of glucose

We present a new approach to calculating conformational equilibria in complex molecules, multiple-copy locally enhanced sampling (LES), and apply this approach to the well-known α → β anomeric equilibrium in glucose. Although a variant of this method has been previously applied to protein stability mutations, it is particularly suited to analyze conformational equilibria in molecules such as glucose, with its many OH groups. This methodology allows us to more rapidly calculate complex equilibria both in vacuo and in solution. We have employed a 'generic' force field using 1,1- dimethoxymethane and 1,1-dihydroxymethane as models to derive the torsional parameters associated with O-C-O-C and O-C-O-H fragments. Within this model, we can definitively establish the magnitude of intramolecular and solvation contributions to the α → β equilibrium. Specifically, we find that in vacuo glucose prefers to be in the α configuration by ~0.5-1.0 kcal/mol (predominantly because of the gauche tendency of the O-C-O-C linkage), and it is the solvation free energy which drives the equilibrium to the β form (ΔG in solution = -0.2 kcal/mol calculated, -0.3 kcal/mol experimental). Using the LES approach, which reduces barriers to conformational transitions, we obtain free energies converged (compared to longer calculations) within 0.2 kcal/mol in 200 ps, both in vacuo and in water. Convergence for the single- copy method is considerably slower; variations in the calculated free energy of over 1 kcal/mol in vacuo and 0.5 kcal/mol in water are still observed in simulations of several nanoseconds in length. Thus, it appears that LES can be at least an order of magnitude faster to converge than single-copy methods.