What Markov State Models Can and Cannot Do: Correlation versus Path-Based Observables in Protein-Folding Models

Area of Science:

• Computational Biophysics
• Protein Dynamics
• Statistical Mechanics

Background:

• Markov state models (MSMs) are widely used to analyze molecular dynamics (MD) simulations of protein conformational changes.
• MSMs simplify complex systems by coarse-graining space and time, which can limit the accuracy of certain dynamic properties.
• Understanding the limitations of MSMs for various biophysical observables is crucial for reliable interpretation of simulation data.

Purpose of the Study:

• To assess the accuracy of standard MSMs and history-augmented MSMs (haMSMs) in reproducing path-based observables.
• To compare MSM-derived path observables against direct trajectory analysis for protein folding dynamics.
• To provide guidance on the appropriate use of MSMs for studying biomolecular conformational dynamics.

Main Methods:

• Analysis of well-validated protein folding MSMs derived from molecular dynamics simulations.
• Comparison of mean first-passage times (MFPTs) and transition path mechanisms computed from MSMs versus direct trajectory analysis.
• Evaluation of history-augmented MSMs (haMSMs) that incorporate additional temporal information.

Main Results:

• Standard MSMs can accurately reproduce time-correlation functions slower than the chosen lag time.
• Reliable reproduction of path-based observables requires state lifetimes to significantly exceed the lag time, a stricter condition.
• haMSMs demonstrate improved accuracy in reproducing path-based observables, particularly when dealing with short-lived states.

Conclusions:

• The accuracy of MSMs is dependent on the timescale of the observable relative to the model's lag time.
• Path-based observables are more sensitive to the coarse-graining limitations of standard MSMs than equilibrium kinetics.
• haMSMs offer a more robust approach for studying detailed conformational pathways and kinetics in biomolecules.