Generalized Markov modeling of nonreversible molecular kinetics

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Molecular Dynamics

Background:

• Markov state models (MSMs) are standard for analyzing molecular kinetics in equilibrium systems.
• Current MSMs struggle with nonreversible or nonequilibrium processes.
• Metastable states and kinetics are key to understanding molecular behavior.

Purpose of the Study:

• To generalize Markov state modeling for nonequilibrium systems.
• To develop a method capable of analyzing nonreversible and cyclic molecular processes.
• To extend the Robust Perron Cluster Cluster Analysis (PCCA+) method.

Main Methods:

• Generalized the Robust Perron Cluster Cluster Analysis (PCCA+) method to create Generalized PCCA (G-PCCA).
• Utilized real Schur vectors instead of eigenvectors to handle diverse data.
• Implemented the G-PCCA algorithm for semiautomatic coarse-graining of molecular kinetics.

Main Results:

• The G-PCCA method successfully models both equilibrium and nonequilibrium data.
• G-PCCA identifies and models cyclic processes, not just metastable states.
• Demonstrated efficacy through three examples of nonreversible systems.

Conclusions:

• G-PCCA provides a robust framework for analyzing complex molecular kinetics beyond equilibrium.
• This generalization expands the applicability of Markov state modeling to broader chemical and physical systems.
• The method facilitates the study of non-equilibrium dynamics and cyclic behaviors in molecules.