Multiscale enhanced sampling of glucokinase: Regulation of the enzymatic reaction via a large scale domain motion.

Enhanced sampling yields a comprehensive structural ensemble or a free energy landscape, which is beyond the capability of a conventional molecular dynamics simulation. Our recently developed multiscale enhanced sampling (MSES) method employs a coarse-grained model coupled with the target physical system for the efficient acceleration of the dynamics. MSES has demonstrated applicability to large protein systems in solution, such as intrinsically disordered proteins and protein-protein and protein-ligand interactions. Here, we applied the MSES simulation to an important drug discovery target, glucokinase (GCK), to elucidate the structural basis of the positive cooperativity of the enzymatic reaction at an atomistic resolution. MSES enabled us to compare two sets of the free energy landscapes of GCK, for the glucose-bound and glucose-unbound forms, and thus demonstrated the drastic change of the free energy surface depending on the glucose concentration. In the glucose-bound form, we found two distinct basins separated by a high energy barrier originating from the domain motion and the folding/unfolding of the α13 helix. By contrast, in the glucose-unbound form, a single flat basin extended to the open and super-open states. These features illustrated the two distinct phases achieving the cooperativity, the fast reaction cycle staying in the closed state at a high glucose concentration and the slow cycle primarily in the open/super-open state at a low concentration. The weighted ensemble simulations revealed the kinetics of the structural changes in GCK with the synergetic use of the MSES results; the rate constant of the transition between the closed state and the open/super-open states, = 1.1 ms, is on the same order as the experimental catalytic rate, = 0.22 ms. Finally, we discuss the pharmacological activities of GCK activators (small molecular drugs modulating the GCK activity) in terms of the slight changes in the domain motion, depending on their chemical structures as regulators. The present study demonstrated the capability of the enhanced sampling and the associated kinetic calculations for understanding the atomistic structural dynamics of protein systems in physiological environments.