Markov models of molecular kinetics: generation and validation

Area of Science:

• Computational Chemistry
• Molecular Dynamics
• Statistical Mechanics

Background:

• Markov state models (MSMs) are widely used to approximate long-time molecular dynamics.
• MSMs offer advantages over direct simulation, including sampling efficiency and uncertainty quantification.

Purpose of the Study:

• To summarize the state-of-the-art in MSM generation and validation.
• To present new results on MSM approximation error and optimization.

Main Methods:

• Analysis of approximation error bounds for MSMs.
• Development of strategies for optimal state space discretization.
• Introduction of efficient estimators for reversible transition matrices.
• Presentation of a robust validation test for MSM kinetics.

Main Results:

• An upper bound for MSM approximation error was derived and shown to be reducible.
• Introducing non-metastable states near transition states improves MSM accuracy.
• Individual kinetic processes can be resolved without partitioning all slow dynamics.
• An efficient estimator for reversible transition matrices and a validation test were developed.

Conclusions:

• MSM accuracy can be significantly improved with optimized discretization strategies.
• The developed methods provide robust tools for generating and validating accurate MSMs.
• These advancements enhance the utility of MSMs for analyzing molecular kinetics.