Caliber Corrected Markov Modeling (C₂M₂): Correcting Equilibrium Markov Models.

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Biophysics

Background:

• Markov State Models (MSMs) are widely used for modeling rate processes.
• Existing MSMs may produce inaccurate predictions for observable rates, such as protein folding rates from molecular dynamics simulations.
• Correcting these inaccuracies in the entire MSM is a significant challenge.

Purpose of the Study:

• To develop a principled method for updating existing Markov State Models.
• To address discrepancies between predicted and experimentally observed rates.
• To provide a framework for enhancing the accuracy of dynamic process modeling.

Main Methods:

• Introduced Caliber Corrected Markov Modeling (C2M2), a novel approach based on the principle of maximum entropy.
• Applied state- and trajectory-based constraints to update the Markov model.
• Demonstrated the equivalence of C2M2 corrections to position-dependent diffusion coefficients in continuous-space Markov processes.

Main Results:

• Derived the explicit functional form of the position-dependent diffusion coefficient using trajectory-based constraints.
• Showcased the application of C2M2 in correcting MSMs for 2D particle diffusion.
• Validated the method with an example of an overdamped harmonic oscillator.

Conclusions:

• C2M2 offers a robust method for refining Markov State Models when predictions deviate from experimental data.
• The approach provides a clear link between model corrections and physical parameters like diffusion coefficients.
• This work advances the accuracy and reliability of MSMs in simulating complex dynamic systems.