Surprisal
Metrics for Quantifying Perturbed Conformational
Dynamics in Markov State Models
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Abstract
Markov state models (MSMs), which
model conformational dynamics
as a network of transitions between metastable states, have been increasingly
used to model the thermodynamics and kinetics of biomolecules. In
considering perturbations to molecular dynamics induced by sequence
mutations, chemical modifications, or changes in external conditions,
it is important to assess how transition rates change, independent
of changes in metastable state definitions. Here, we present a surprisal
metric to quantify the difference in metastable state transitions
for two closely related MSMs, taking into account the statistical
uncertainty in observed transition counts. We show that the surprisal
is a relative entropy metric closely related to the Jensen–Shannon
divergence between two MSMs, which can be used to identify conformational
states most affected by perturbations. As examples, we apply the surprisal
metric to a two-dimensional lattice model of a protein hairpin with
mutations to hydrophobic residues, all-atom simulations of the Fs
peptide α-helix with a salt-bridge mutation, and a comparison
of protein G β-hairpin with its trpzip4 variant. Moreover, we
show that surprisal-based adaptive sampling is an efficient strategy
to reduce the statistical uncertainty in the Jensen–Shannon
divergence, which could be a useful strategy for molecular simulation-based <i>ab initio</i> design