Fluorescence recovery after photobleaching (FRAP) experiments under conditions of uniform disk illumination. Critical comparison of analytical solutions, and a new mathematical method for calculation of diffusion coefficient D

A simple fluorescence recovery after photobleaching (FRAP) apparatus using a fluorescence microscope with a conventional mercury arc lamp, working under conditions of "uniform disk illumination" is described. This set-up was designed essentially for the use of anthracene as fluorescent probe, which is bleached (photodimerization reaction) by illumination in the near ultraviolet range (360 nm). It is shown that the lateral diffusion coefficients D can be readily calculated from fluorescence recovery curves using a finite differentiate method in combination with statistical analysis of the data. In contrast to the analytical solutions so far described, this numerical approach is particularly versatile. With a minimization algorithm, D and the probe mobile fraction can be readily calculated for any recovery time under various experimental conditions. These include different probe concentration profiles in the illuminated area after the bleaching step, and situations of infinite or noninfinite reservoir in the diffusion area outside the illuminated area