Diffusion on a Curved Surface Coupled to Diffusion in the Volume: Application to Cell Biology

Area of Science:

• Computational Biology
• Mathematical Modeling
• Cell Biology

Background:

• Modeling diffusion on complex cellular geometries is essential for understanding biological processes.
• Existing methods may be computationally expensive or lack accuracy for curved surfaces.

Purpose of the Study:

• To develop an efficient and accurate algorithm for solving diffusion equations on curved surfaces coupled with volume diffusion.
• To apply this algorithm to a cell biology problem involving signaling molecule transport.
• To validate a simplified quantitative analysis of fluorescence loss in photobleaching.

Main Methods:

• Approximation of the Laplace-Beltrami operator using the tangential plane Laplacian.
• Finite volume discretization with Voronoi decomposition for pixilated surfaces.
• Implementation within the Virtual Cell computational framework.

Main Results:

• The algorithm achieves spatial convergence with an order between 1 and 2, ensured by mass conservation and sampling error cancellation.
• Simulations on realistic cell geometries successfully validated a simplified quantitative analysis of fluorescence loss in photobleaching.
• The method demonstrates low computational cost and applicability to experimental image data.

Conclusions:

• The developed algorithm provides an efficient and accurate solution for diffusion problems on curved biological surfaces.
• This method enhances the quantitative analysis of dynamic cellular processes, such as signaling molecule transport.
• The freely accessible implementation facilitates further research in computational cell biology.