A variational method for efficient estimation of diffusion and free-energy profiles along collective variables

Area of Science:

• Computational chemistry and biophysics.
• Statistical mechanics and molecular modeling.

Background:

• Estimating diffusion coefficients and free-energy landscapes is crucial for understanding molecular dynamics.
• Existing methods often struggle with accuracy or efficiency, especially for complex systems or non-equilibrium conditions.

Purpose of the Study:

• To develop an efficient variational method for calculating diffusion coefficients and free-energy profiles.
• To enable accurate analysis of projected molecular dynamics trajectories under both equilibrium and non-equilibrium conditions.

Main Methods:

• A variational method based on approximating short-time transition probability densities with a Gaussian form.
• Utilizing Kullback-Leibler divergences to maximize agreement between an overdamped Langevin model and projected trajectories.
• Employing an adaptive Monte Carlo scheme for efficient loss function minimization.

Main Results:

• The method accurately estimates diffusion coefficients and free-energy profiles.
• Demonstrated robustness and accuracy on model systems with diffusive dynamics.
• Successfully applied to analyze water diffusion at a biomolecular condensate interface.

Conclusions:

• The presented variational method offers an efficient and accurate approach for analyzing molecular dynamics data.
• It provides valuable insights into diffusion and thermodynamics in complex systems.
• The method is applicable to a range of systems, including biological interfaces.