Anomalous Diffusion and Angle-Dependency in the Theory of Fluorescence Recovery after Photobleaching

Fluorescence recovery after photobleaching (FRAP) is an experimental method for the investigation of transport processes of fluorescent molecules. Under total reflection conditions a selective measurement of processes in thin surface layers is achieved. We present theoretical calculations demonstrating the influence of the angle under which the detection beam is directed to the probe on the fluorescence signal. Apart from the angle dependency, we consider anomalous diffusion processes with the mean square displacement ∝ t α . Modeling the process by a fractional order diffusion equation, we find that the relaxation of the fluorescence to the equilibrium value is asymptotically ∝ t −α for large t.