A Nonfitting Method Using a Spatial Sine Window Transform for Inhomogeneous Effective-Diffusion Measurements by FRAP

Determining averaged effective diffusion constants from experimental measurements of fluorescent proteins in an inhomogeneous medium in the presence of ligand-receptor interactions poses problems of analytical tractability. Here, we introduced a nonfitting method to evaluate the averaged effective diffusion coefficient of a region of interest (which may include a whole nucleus) by mathematical processing of the entire cellular two-dimensional spatial pattern of recovered fluorescence. Spatially and temporally resolved measurements of protein transport inside cells were obtained using the fluorescence recovery after photobleaching technique. Two-dimensional images of fluorescence patterns were collected by laser-scanning confocal microscopy. The method was demonstrated by applying it to an estimation of the mobility of green fluorescent protein-tagged heterochromatin protein 1 in the nuclei of living mouse embryonic fibroblasts. This approach does not require the mathematical solution of a corresponding system of diffusion-reaction equations that is typical of conventional fluorescence recovery after photobleaching data processing, and is most useful for investigating highly inhomogeneous areas, such as cell nuclei, which contain many protein foci and chromatin domains.