Mechanism Beyond Markov Models: History Information is Needed for Unbiased Pathway Reconstruction of Protein Folding

Abstract

Understanding the mechanisms (pathways through configuration space) of biomolecular processes such as protein folding is a major challenge for molecular dynamics (MD) simulations. Markov state models (MSMs), which discretize simulation data by projecting onto a relatively small number of states, have become increasingly popular compact representations of the overwhelming complexity of protein configuration space and the vast quantity of trajectory data. Building on previous work showing the potential for significant bias in MSM estimates of folding and unfolding rates [Suarez et al., JCTC 2016, 12 (8), 3473], here we study MSM descriptions of (un)folding mechanisms. By comparing to independent long-time MD simulations, as well as non-Markov (NM) analyses which include history information, we find that MSMs tend to infer overly broad distributions of more equally probable pathways. By contrast, NM analyses using MSM states agree well with the narrower distributions observed in the long-time MD data. The MSMs appear to be overly permissive because they exclude the history information accounting for previous discrete states occurring in trajectories, which is necessary for an unbiased mapping of the underlying dynamics in the full configuration space to the substantially reduced discrete state space.