Markov-Type State Models to Describe Non-Markovian Dynamics

When clustering molecular dynamics (MD) trajectories into a few metastable conformational states, the assumption of time scale separation between fast intrastate fluctuations and rarely occurring interstate transitions is often not valid. Hence, when we construct a Markov state model (MSM) from these states, the naive estimation of the macrostate transition matrix via simply counting transitions between the states may lead to significantly too-short implied time scales and thus to too-fast population decays. In this work, we discuss advanced approaches to estimate the transition matrix. Assuming that Markovianity is at least given at the microstate level, we consider the Laplace-transform-based method by Hummer and Szabo, as well as a direct microstate-to-macrostate projection, which by design yields correct macrostate population dynamics. Alternatively, we study the recently proposed quasi-MSM ansatz of Huang and co-workers to solve a generalized master equation, as well as a hybrid method that employs MD at short times and MSM at long times. Adopting a one-dimensional toy model and an all-atom folding trajectory of HP35, we discuss the virtues and shortcomings of the various approaches.