Brownian simulations and unidirectional flux in diffusion.

Area of Science:

• Computational molecular biophysics
• Biophysics
• Physical chemistry

Background:

• Predicting ionic currents in biological membranes is crucial for understanding cellular processes.
• Continuum models fail to capture complex ionic permeation, necessitating particle simulations.
• Brownian dynamics (BD) simulations require accurate modeling of particle exchange with boundary baths.

Purpose of the Study:

• To develop a more physically accurate method for maintaining boundary concentrations in BD simulations.
• To address the artifact of infinite unidirectional fluxes in classical diffusion approximations.
• To ensure BD simulations correctly represent the physics of particle interfaces.

Main Methods:

• Utilized stochastic formulation of diffusion and Wiener path integrals.
• Analyzed the relationship between Langevin dynamics and its Smoluchowski approximation.
• Derived conditions for accurate representation of Brownian trajectories at interfaces.

Main Results:

• Identified infinite unidirectional flux as an artifact of the Smoluchowski approximation.
• Established that the Smoluchowski approximation fails at short time scales.
• Determined the correct unidirectional flux proportional to concentration and inversely proportional to sqrt[time step].

Conclusions:

• The developed BD simulation method accurately maintains boundary concentrations.
• This approach resolves spurious boundary layers and aligns with Brownian particle physics.
• Enables more reliable computational biophysics studies of ion channel function.