Diffusion in inhomogeneous media: Theory and simulations applied to whole cell photobleach recovery

A continuum description for diffusion in a simple model for an inhomogeneous but isotropic media is derived and implemented numerically. The locally averaged density of diffusible marker is input from experiment to define the sample. Then a single additional parameter, the effective diffusion constant, permits the quantitative simulation of diffusive relaxation from any initial condition. Using this simulation, it is possible to model the recovery of a fluorescently tagged protein in the endoplasmic reticulum (ER) after photobleaching a substantial region of a live cell, and fit an effective diffusion constant which is a property both of the geometry of the ER and the marker. Such quantitative measurements permit inferences about the topology and internal organization of this organelle.