Building multiscale Markov state models by systematic mapping of temporal communities

Biomolecules undergo dynamic transitions among metastable states to carry out their biological functions. Markov State Models (MSMs) effectively capture these metastable states and transitions at a defined temporal scale. However, biomolecular dynamics typically span multiple temporal scales, ranging from fast atomic vibrations to slower conformational changes and folding events.

We introduce multiscale Markov State Models (mMSMs), which capture biomolecular dynamics across multiple temporal resolutions simultaneously via a hierarchy of MSMs, and mMSM-explore, an unsupervised algorithm for generating mMSMs through multiscale adaptive sampling with on-the-fly identification of temporally metastable states. We benchmark our method on a toy system with nested energy minima; on alanine dipeptide, first with and then without assuming prior knowledge of its two reaction coordinates; and finally, on a fast-folding 35-residue miniprotein, where we map folding pathways across scales. We demonstrate efficient mapping of energy landscapes, correct representation of multiscale hierarchies and transition states, accurate inference of stationary probabilities and transition kinetics, as well as de novo identification of underlying slow, intermediate, and fast reaction coordinates. mMSMs reveal how dynamic processes at different scales contribute collectively to the functional mechanisms of biomolecular machines.

Python code and instructions are available at https://github.com/ravehlab/mMSM.