Free energies from dynamic weighted histogram analysis using unbiased Markov state model

Area of Science:

• Computational Chemistry
• Biophysics
• Molecular Dynamics

Background:

• Weighted Histogram Analysis Method (WHAM) is standard for free energy calculations in biased molecular simulations.
• WHAM accuracy diminishes with incomplete equilibration across simulation windows.
• Errors in WHAM can arise from non-equilibrated biasing windows.

Purpose of the Study:

• To develop a novel method, Dynamic Histogram Analysis Method (DHAM), to address limitations in WHAM.
• To improve the accuracy of free energy calculations from biased molecular simulations.
• To provide kinetic information and assess simulation convergence.

Main Methods:

• DHAM utilizes a global Markov state model to determine free energy along a reaction coordinate.
• Constructs a maximum likelihood estimate of the Markov transition matrix by jointly unbiasing transition counts.
• Employs an explicit approximation for the Markov matrix, avoiding iterative WHAM solutions.
• Applies DHAM to model systems, QM/MM simulations of a chemical reaction, and ion channel simulations (GLIC).

Main Results:

• DHAM yields accurate free energies, even in scenarios where WHAM fails.
• The method successfully calculates free energy profiles as the stationary distribution of the Markov matrix.
• DHAM provides valuable kinetic information for assessing simulation window convergence.
• Demonstrates applicability across diverse systems, including QM/MM and ion channel simulations.

Conclusions:

• DHAM offers a robust alternative to WHAM for free energy calculations, particularly with non-equilibrated data.
• The method enhances the reliability of molecular simulation free energy results.
• DHAM's kinetic insights aid in evaluating simulation quality and convergence.
• Potential utility in constructing Markov state models from biased simulations in sparsely populated regions.