Mean first passage times in variational coarse graining using Markov state models.

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Biophysics

Background:

• Markov state models (MSMs) are essential for describing complex system dynamics and thermodynamics.
• High dimensionality in biological systems often necessitates coarse-graining for computational feasibility.
• Existing coarse-graining methods include local equilibrium and Hummer-Szabo approaches.

Purpose of the Study:

• To introduce and evaluate novel Markovian coarse-graining options for complex systems.
• To demonstrate that coarse-grained MSMs satisfy a variational principle for optimal slowest relaxation timescales.
• To provide a physical interpretation of optimal coarse-graining in terms of mean first passage times and fluxes.

Main Methods:

• Development of Markovian coarse-graining strategies.
• Mathematical proof of a variational principle for coarse-grained MSMs.
• Numerical verification using analytic potentials and molecular dynamics simulations (pentalanine).

Main Results:

• The proposed coarse-graining methods satisfy a variational principle related to the slowest timescale.
• Optimal coarse-graining to two or three states exhibits clear physical interpretations.
• The approach was validated with both theoretical models and experimental simulation data.

Conclusions:

• Optimal coarse-graining provides a robust framework for analyzing complex system dynamics.
• The physical interpretation of coarse-grained states enhances understanding of system behavior.
• This methodology is broadly applicable to time series analysis and large datasets in various scientific fields.