A milestoning study of the kinetics of an allosteric transition:: Atomically detailed simulations of deoxy Scapharca hemoglobin

Atomically detailed simulations are used to compute the kinetics of the R-to-T transition in deoxy Scapharca hemoglobin. A computational approach called milestoning is utilized that combines 1), an efficient reaction path algorithm; and 2), a "fragment and glue'' approach for classical trajectories. Milestoning computes the R-to-T transition kinetics on the microsecond timescale based on atomically detailed trajectories that rarely exceed a nanosecond. Eleven reference hyper-surfaces (milestones) are constructed along the reaction coordinate, which is computed with a global path optimization algorithm. Two-hundred classical trajectories are calculated for each of the milestones to collect local distributions of first passage times. These local distributions are used in a non-Markovian theory to compute the overall timescale. Exponential enrichment of reactive trajectories, an important component of the milestoning approach, makes these calculations possible. The overall timescale of the reaction is estimated as 10 +/- 9 mu s, in accord with available experimental data. The barrier is not sharp and is spread over four milestones. Even after the most significant structural changes are completed (phenylalanine F4 ring flips), highly collective and activated motions continue. The calculations suggest an additional late free energy barrier.