From molecular energy landscapes to equilibrium dynamics via landscape analysis and markov state models.

Molecular dynamics (MD) simulation software allows probing the equilibrium structural dynamics of a molecule of interest, revealing how a molecule navigates its structure space one structure at a time. To obtain a broader view of dynamics, typically one needs to launch many such simulations, obtaining many trajectories. A summarization of the equilibrium dynamics requires integrating the information in the various trajectories, and Markov State Models (MSM) are increasingly being used for this task. At its core, the task involves organizing the structures accessed in simulation into structural states, and then constructing a transition probability matrix revealing the transitions between states. While now considered a mature technology and widely used to summarize equilibrium dynamics, the underlying computational process in the construction of an MSM ignores energetics even though the transition of a molecule between two nearby structures in an MD trajectory is governed by the corresponding energies. In this paper, we connect theory with simulation and analysis of equilibrium dynamics. A molecule navigates the energy landscape underlying the structure space. The structural states that are identified via off-the-shelf clustering algorithms need to be connected to thermodynamically-stable and semi-stable (macro)states among which transitions can then be quantified. Leveraging recent developments in the analysis of energy landscapes that identify basins in the landscape, we evaluate the hypothesis that basins, directly tied to stable and semi-stable states, lead to better models of dynamics. Our analysis indicates that basins lead to MSMs of better quality and thus can be useful to further advance this widely-used technology for summarization of molecular equilibrium dynamics.