Projected and Hidden Markov Models for calculating kinetics and metastable states of complex molecules

TL;DR

This paper introduces Projected and Hidden Markov Models as a new framework to more accurately analyze complex molecular dynamics, overcoming limitations of traditional Markov State Models by not assuming Markovian behavior on discretized states.

Contribution

The paper develops a novel approach using Projected Markov Models and Hidden Markov Models to better estimate molecular kinetics without Markovian assumptions on discretized states.

Findings

Applicable to both simulation and experimental data

Successfully analyzed a 1 ms protein MD simulation

Demonstrated versatility with RNA hairpin data

Abstract

Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of molecular dynamics simulation data. However, MSMs approximate the true dynamics by assuming a Markov chain on a clusters discretization of the state space. This approximation is difficult to make for high-dimensional biomolecular systems, and the quality and reproducibility of MSMs has therefore been limited. Here, we discard the assumption that dynamics are Markovian on the discrete clusters. Instead, we only assume that the full phase- space molecular dynamics is Markovian, and a projection of this full dynamics is observed on the discrete states, leading to the concept of Projected Markov Models (PMMs). Robust estimation methods for PMMs are not yet available, but we derive a practically feasible approximation via Hidden Markov Models (HMMs). It is shown how various molecular observables of interest that are often computed from MSMs can be computed from HMMs / PMMs. The new framework is applicable to both, simulation and single-molecule experimental data. We demonstrate its versatility by applications to educative model systems, an 1 ms Anton MD simulation of the BPTI protein, and an optical tweezer force probe trajectory of an RNA hairpin.