Reaction rates for reaction-diffusion kinetics on unstructured meshes.

Area of Science:

• Computational biology
• Biophysical modeling
• Stochastic processes

Background:

• The reaction-diffusion master equation (RDME) models biochemical reactions in cells, crucial when molecular spatial distribution impacts system dynamics.
• Accurate cell geometry representation requires discretizing space using unstructured meshes.
• Current methods struggle to compute accurate reaction rates within refined mesh voxels.

Purpose of the Study:

• To develop a method for computing accurate reaction rates between molecules within the same voxel of an unstructured mesh.
• To improve the fidelity of the reaction-diffusion master equation (RDME) for cellular simulations.

Main Methods:

• Discretization of space using unstructured meshes for cellular geometry.
• Modeling diffusion as discrete molecular jumps between mesh nodes.
• Developing an efficient numerical scheme to estimate reaction rates in small voxels as a preprocessing step.

Main Results:

• A novel method for computing accurate reaction rates in unstructured meshes was developed.
• The proposed method reduces reaction rate computation to a mesh-dependent preprocessing step.
• Numerical examples demonstrate that refined meshes yield RDME results approaching a Smoluchowski particle-tracking model.

Conclusions:

• The developed method enhances the accuracy of the reaction-diffusion master equation (RDME) in spatially complex cellular environments.
• This approach provides a robust way to estimate reaction rates, improving the predictive power of stochastic cellular simulations.
• The findings bridge the gap between simplified reaction-diffusion models and more detailed particle-based simulations.