  A Markov state model is a powerful tool that can be used to track the
evolution of populations of configurations in an atomistic representation of a
protein. For a coarse-grained linear chain model with discontinuous
interactions, the transition rates among states that appear in the Markov model
when the monomer dynamics is diffusive can be determined by computing the
relative entropy of states and their mean first passage times, quantities that
are unchanged by the specification of the energies of the relevant states. In
this paper, we verify the folding dynamics described by a diffusive linear
chain model of the crambin protein under three distinct solvent systems, each
differing in complexity: a hard-sphere solvent, a solvent undergoing
multi-particle collision dynamics, and an implicit solvent model. The predicted
transition rates among configurations agree quantitatively with those observed
in explicit molecular dynamics simulations for all three solvent models. These
results suggest that the local monomer-monomer interactions provide sufficient
friction for the monomer dynamics to be diffusive on timescales relevant to
changes in conformation. Factors such as structural ordering and dynamic
hydrodynamic effects appear to have minimal influence on transition rates
within the studied solvent densities.
