Simulation of stochastic diffusion via first exit times.

Area of Science:

• Molecular Biology
• Computational Biology
• Biophysics

Background:

• Stochastic simulation of molecular diffusion is crucial in molecular biology.
• Mesoscopic models partition cells into subvolumes for simulating molecular movement.
• Poor mesh quality in complex geometries can lead to non-physical negative jump rates.

Purpose of the Study:

• To develop a robust method for calculating positive jump coefficients in mesoscopic diffusion simulations.
• To ensure accurate probabilistic interpretation of molecular movement in biologically relevant geometries.
• To address limitations of standard discretization methods in poor-quality meshes.

Main Methods:

• Proposing a novel method based on the mean first exit time of molecules from subvolumes.
• Implementing global and local approaches to calculate these exit times.
• Testing the method on meshes of varying quality in 2D and 3D simulations.

Main Results:

• The proposed mean first exit time method guarantees positive jump coefficients.
• The method ensures physically meaningful probabilities for molecular diffusion.
• Simulations demonstrated the effectiveness of the approach across different mesh qualities and dimensions.

Conclusions:

• The mean first exit time method provides a reliable way to simulate stochastic diffusion in complex cellular environments.
• This approach overcomes the issue of negative jump coefficients encountered with standard discretization.
• The findings enhance the accuracy and applicability of mesoscopic models in computational biology.