An Unstructured Mesh Reaction-Drift-Diffusion Master Equation with Reversible Reactions.

Area of Science:

• Computational chemistry
• Biophysics
• Mathematical modeling

Background:

• Simulating particle transport with drift and diffusion in complex geometries is challenging.
• Existing models may not accurately capture equilibrium dynamics or detailed balance in reaction-diffusion processes.

Purpose of the Study:

• To develop a novel computational method for studying reaction processes influenced by drift-diffusion.
• To enable accurate simulations of systems with one-body potential fields in general domains.

Main Methods:

• Developed a convergent reaction-drift-diffusion master equation (CRDDME) using an unstructured grid jump process approximation.
• Leveraged the Edge-Averaged Finite Element method to preserve detailed balance and Gibbs-Boltzmann distribution.
• Formulated a particle-based reaction-drift-diffusion model with finite volume discretization for reaction terms.

Main Results:

• The CRDDME accurately simulates drift-diffusion processes biased by conservative fields.
• The method preserves detailed balance for both drift-diffusion and reaction fluxes at equilibrium.
• Demonstrated convergence and accuracy through numerical examples and an application to T cell signaling.

Conclusions:

• The CRDDME provides a robust framework for simulating complex reaction-drift-diffusion phenomena.
• This method enhances the study of biological processes like membrane protein receptor dynamics.
• The CRDDME offers a powerful tool for computational biophysics and chemistry.