Position-Dependent Diffusion from Biased Simulations and Markov State Model Analysis

Area of Science:

• Computational chemistry and physics
• Statistical mechanics
• Biophysics

Background:

• Molecular simulations generate large, complex datasets for thermodynamic and kinetic analysis.
• Markov state models (MSMs) are widely used for kinetic properties but struggle with high energy barriers and rare events.
• Calculating diffusion coefficients from biased simulations remains a significant challenge.

Purpose of the Study:

• To develop a novel method for calculating multidimensional, position-dependent diffusion coefficients.
• To enable accurate diffusion coefficient calculations from both biased and unbiased molecular simulation data.
• To improve the analysis of rare event dynamics, such as solute transport through complex media.

Main Methods:

• Building upon Markov state model analysis and the Kramers-Moyal expansion.
• Applying the formalism to one- and two-dimensional analytic potentials.
• Validating the method with explicit solvent molecular dynamics simulations (alanine dipeptide) and umbrella sampling (drug transport across lipid bilayers).

Main Results:

• The proposed method successfully calculates multidimensional position-dependent diffusion coefficients.
• Demonstrated validity across analytic potentials and complex molecular dynamics simulation data.
• Significant improvements observed in predicting solute transport across 3D heterogeneous porous media, including drug permeation.

Conclusions:

• The novel formalism provides a unified approach to calculating diffusion coefficients from biased or unbiased simulation data.
• This method overcomes limitations of existing techniques for systems with high energy barriers.
• Offers enhanced accuracy for predicting molecular transport phenomena, crucial for drug development and materials science.