RESUMO
An algorithm is presented for solving a diffusion equation on a curved surface coupled to diffusion in the volume, a problem often arising in cell biology. It applies to pixilated surfaces obtained from experimental images and performs at low computational cost. In the method, the Laplace-Beltrami operator is approximated locally by the Laplacian on the tangential plane and then a finite volume discretization scheme based on a Voronoi decomposition is applied. Convergence studies show that mass conservation built in the discretization scheme and cancellation of sampling error ensure convergence of the solution in space with an order between 1 and 2. The method is applied to a cell-biological problem where a signaling molecule, G-protein Rac, cycles between the cytoplasm and cell membrane thus coupling its diffusion in the membrane to that in the cell interior. Simulations on realistic cell geometry are performed to validate, and determine the accuracy of, a recently proposed simplified quantitative analysis of fluorescence loss in photobleaching. The method is implemented within the Virtual Cell computational framework freely accessible at www.vcell.org.
RESUMO
The Virtual Cell is a modeling tool that allows biologists and theorists alike to specify and simulate cell-biophysical models on arbitrarily complex geometries. The framework combines an intuitive, front-end graphical user interface that runs in a web browser, sophisticated server-side numerical algorithms, a database for storage of models and simulation results, and flexible visualization capabilities. In this paper, we present an overview of the capabilities of the Virtual Cell, and, for the first time, the detailed mathematical formulation used as the basis for spatial computations. We also present summaries of two rather typical modeling projects, in order to illustrate the principal capabilities of the Virtual Cell. (c) 2001 American Institute of Physics.
