Conformational sampling of oligosaccharides using Hamiltonian replica exchange with two-dimensional dihedral biasing potentials and the weighted histogram analysis method (WHAM).

Abstract

Oligosaccharides and polysaccharides exert numerous functional roles in biology through their structural diversity and conformational properties. To investigate their conformational properties using computational methods, Hamiltonian replica exchange (H-REX) combined with two-dimensional grid-based correction maps as biasing potentials (bpCMAP) significantly improves the sampling efficiency about glycosidic linkages. In the current study, we extend the application of H-REX with bpCMAP to complex saccharides and establish systematic procedures for bpCMAP construction, determination of replica distribution, and data analysis. Our main findings are that (1) the bpCMAP for each type of glycosidic linkage can be constructed from the corresponding disaccharide using gas-phase umbrella sampling simulations, (2) the replica distribution can be conveniently determined following the exact definition of the average acceptance ratio based on the assigned distribution of biasing potentials, and (3) the extracted free energy surface (or potential of mean force (PMF)) can be improved using the weighted histogram analysis method (WHAM) allowing for the inclusion of data from the excited state replicas in the calculated probability distribution. The method is applied to a branched N-glycan found on the HIV gp120 protein, and a linear N-glycan. Considering the general importance of N-glycans and the wide appreciation of the sampling problem, the present method represents an efficient procedure for the conformational sampling of complex oligo- and polysaccharides under explicit solvent conditions. More generally, the use of WHAM is anticipated to be of general utility for the calculation of PMFs from H-REX simulations in a wide range of macromolecular systems.