  Discrete-space kinetic models, i.e., Markov state models, have emerged as
powerful tools for reducing the complexity of trajectories generated from
molecular dynamics simulations. These models require configuration-space
representations that accurately characterize the relevant dynamics.
Well-established, low-dimensional order parameters for constructing this
representation have led to widespread application of Markov state models to
study conformational dynamics in biomolecular systems. On the contrary,
applications to characterize single-molecule diffusion processes have been
scarce and typically employ system-specific, higher-dimensional order
parameters to characterize the local solvation state of the molecule. In this
work, we propose an automated method for generating a coarse
configuration-space representation, using generic features of solvation
structure---the coordination numbers about each particle. To overcome the
inherent noisy behavior of these low-dimensional observables, we treat the
features as indicators of an underlying, latent Markov process. The resulting
hidden Markov models filter the trajectories of each feature into the most
likely latent solvation state at each time step. The filtered trajectories are
then used to construct a configuration-space discretization, which accurately
describes the diffusion kinetics. The method is validated on a standard model
for glassy liquids, where particle jumps between local cages determine the
diffusion properties of the system. Not only do the resulting models provide
quantitatively accurate characterizations of the diffusion constant, but they
also reveal a mechanistic description of diffusive jumps, quantifying the
heterogeneity of local diffusion.
