Markov state modeling and dynamical coarse-graining via discrete relaxation path sampling

Area of Science:

• Computational physics
• Statistical mechanics
• Molecular dynamics

Background:

• Complex molecular systems require simplified models for efficient analysis.
• Coarse-graining aims to reduce the dimensionality of molecular dynamics.
• Markov jump processes (MJPs) offer a framework for describing transitions between system states.

Purpose of the Study:

• To develop a robust method for coarse-graining molecular dynamics to a Markov jump process.
• To establish a computationally efficient approach for estimating the MJP rate matrix.
• To demonstrate the applicability of the method to diverse complex systems.

Main Methods:

• Derivation of a coarse-graining method mapping molecular dynamics to an MJP.
• Calculation of cell-pair relaxation times using molecular dynamics simulations within individual cells.
• Development of an efficient estimator for the MJP rate matrix utilizing relaxation times.
• Robustness analysis of relaxation times with respect to cell boundary placement.

Main Results:

• A novel method successfully coarse-grains complex molecular dynamics to an MJP.
• Relaxation times are demonstrated to be robust against variations in cell boundary definitions.
• The method provides an efficient means to estimate the rate matrix of the MJP.
• Successful application of the method to Sinai billiards and Lennard-Jones disc clusters.

Conclusions:

• The developed method offers an efficient and robust approach for coarse-graining molecular dynamics to MJPs.
• This technique facilitates the study of complex molecular systems by simplifying their dynamics.
• The findings have broad implications for computational modeling in physics and chemistry.