Seminar #9 - Thermodynamics - Markov State Model

2024 Winter Molecular Simulation Seminar
Room 302, the 2nd experimental building at POSTECH
Presenter: Junho Lim

Many experimental and theoretical models have been proposed to understand the thermodynamic and dynamical properties of molecular systems, among which atomistic molecular dynamics simulation has been used as a powerful tool to reflect the atomic motions of the system. However, the timescale of atomistic MD simulation is not suitable to characterize molecular processes which involve long timescale dynamics (e.g. biological processes) and sometimes results in poor statistical results. Many methods have been developed to address the timescale issue, and they can be broadly divided into 2 groups: enhanced sampling techniques and mathematical models. In this talk, I will introduce the Markov State Model (MSM) as a representative example of mathematical models. MSM is a kinetic network model that describes the dynamics of a system using a coarse-grained model in space and time, starting from the assumption that we can define a transition matrix and express the dynamics of the system as a single master equation. Once a suitable transition matrix is defined, the thermodynamic and kinetic properties of the system can be investigated.

In this talk, I will first discuss the theoretical backgrounds of MSM. [1-2] The knowledge of statistics and stochastic processes in the undergraduate level will be reviewed. Second, I will describe the building process of MSMs. [1,3] It includes the clustering methods and implied timescale plot, used for correct coarse graining in space and time. Finally, we will review some research examples using MSMs and figure out what thermodynamic and kinetic properties were calculated. [4,5] And If I have some time left, I will give a brief introduction to the concept of Transition Path Theory(TPT), which is further developed theory in MSM. [1]

Reference

[1] Bowman, G. R., Pande, V. S., Noé, F. An introduction to Markov state models and their application to long timescale molecular simulation. Springer Science & Business Media, 2013, Vol. 797.
[2] Prinz, J. H., Wu, H., Sarich, M., Keller, B., Senne, M., Held, M., Chodera, J. D., Schütte, C., & Noé, F. Markov models of molecular kinetics: generation and validation.J. Chem. Phys., 2011, 134, 174105.
[3] Husic, B. E., & Pande, V. S. Markov State Models: From an Art to a Science. J. Am. Chem. Soc., 2018, 140(7), 2386–2396.
[4] Da, L. T., Wang, D., & Huang, X. Dynamics of pyrophosphate ion release and its coupled trigger loop motion from closed to open state in RNA polymerase II. J. Am. Chem. Soc., 2012, 134(4), 2399-2406
[5] Gao, K., & Zhao, Y. A Network of Conformational Transitions in the Apo Form of NDM-1 Enzyme Revealed by MD Simulation and a Markov State Model. J. Phys. Chem. B., 2017, 121(14), 2952–2960.