Optimized Markov State Models for Metastable Systems

TL;DR

This paper introduces a new method for constructing Markov State Models that optimally identify metastable states, improving accuracy and interpretability in complex molecular systems without requiring Markovian dynamics on trial states.

Contribution

The method automatically optimizes metastability indices to identify target states, enhancing MSM accuracy and enabling state-space partitioning without prior metastable state knowledge.

Findings

Successfully identified metastable states in Gly-Ala-Gly peptide

Analyzed folding landscape of Beta3s mini-protein

Demonstrated improved MSM accuracy and interpretability

Abstract

A method is proposed to identify target states that optimize a metastability index amongst a set of trial states and use these target states as milestones (or core sets) to build Markov State Models (MSMs). If the optimized metastability index is small, this automatically guarantees the accuracy of the MSM, in the sense that the transitions between the target milestones is indeed approximately Markovian. The method is simple to implement and use, it does not require that the dynamics on the trial milestones be Markovian, and it also offers the possibility to partition the system's state-space by assigning every trial milestone to the target milestones it is most likely to visit next and to identify transition state regions. Here the method is tested on the Gly-Ala-Gly peptide, where it shown to correctly identify the expected metastable states in the dihedral angle space of the molecule without \textit{a~priori} information about these states. It is also applied to analyze the folding landscape of the Beta3s mini-protein, where it is shown to identify the folded basin as a connecting hub between an helix-rich region, which is entropically stabilized, and a beta-rich region, which is energetically stabilized and acts as a kinetic trap.