A Step-by-Step Guide on How to Construct Quasi-Markov State Models to Study Functional Conformational Changes of Biological Macromolecules

Conformational changes play an important role for many biomolecules to perform their functions. In recent years, Markov State Model (MSM) has become a powerful tool to investigate these functional conformational changes by predicting long timescale dynamics from many short molecular dynamics (MD) simulations. In MSM, dynamics are modelled by a first-order master equation, in which a biomolecule undergoes Markovian transitions among conformational states at discrete-time intervals, called lag time. The lag time has to be sufficiently long to build a Markovian model, but this parameter is often bound by the length of MD simulations available for estimating the frequency of interstate transitions. To address this challenge, we recently employed the generalized master equation (GME) formalism (e.g., the quasi-Markov State Model or qMSM) to encode non-Markovian dynamics in a time-dependent memory kernel. When applied to study protein dynamics, our qMSM can be built from MD simulations that are an order-of-magnitude shorter than MSM would have required. The construction of qMSM is more complicated than that of MSM, as time-dependent memory kernels need to be properly extracted from the MD simulation trajectories. In this chapter, we will present a step-by-step guide on how to build qMSM from MD simulation datasets, and the accompanying materials are publicly available on Github: https://github.com/ykhdrew/qMSM_tutorial. We hope this tutorial is useful for researchers who want to apply qMSM and study functional conformational changes in biomolecules.