Full Kinetics of CO Entry, Internal Diffusion, and
Exit in Myoglobin from Transition-Path Theory Simulations
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Abstract
We use Markovian milestoning molecular
dynamics (MD) simulations
on a tessellation of the collective variable space for CO localization
in myoglobin to estimate the kinetics of entry, exit, and internal
site-hopping. The tessellation is determined by analysis of the free-energy
surface in that space using transition-path theory (TPT), which provides
criteria for defining optimal milestones, allowing short, independent,
cell-constrained MD simulations to provide properly weighted kinetic
data. We coarse grain the resulting kinetic model at two levels: first,
using crystallographically relevant internal cavities and their predicted
interconnections and solvent portals; and second, as a three-state
side-path scheme inspired by similar models developed from geminate
recombination experiments. We show semiquantitative agreement with
experiment on entry and exit rates and in the identification of the
so-called “histidine gate” at position 64 through which
≈90% of flux between solvent and the distal pocket passes.
We also show with six-dimensional calculations that the minimum free-energy
pathway of escape through the histidine gate is a “knock-on”
mechanism in which motion of the ligand and the gate are sequential
and interdependent. In total, these results suggest that such TPT
simulations are indeed a promising approach to overcome the practical
time-scale limitations of MD to allow reliable estimation of transition
mechanisms and rates among metastable states