A new FRAP/FRAPa method for three-dimensional diffusion measurements based on multiphoton excitation microscopy

We present a new convenient method for quantitative three-dimensionally resolved diffusion measurements based on the photobleaching (FRAP) or photoactivation (FRAPa) of a disk-shaped area by the scanning laser beam of a multiphoton microscope. Contrary to previously reported spot-photobleaching protocols, this method has the advantage of full scalability of the size of the photobleached area and thus the range of diffusion coefficients, which can be measured conveniently. The method is compatible with low as well as high numerical aperture objective lenses, allowing us to perform quantitative diffusion measurements in three-dimensional extended samples as well as in very small volumes, such as cell nuclei. Furthermore, by photobleaching/ photoactivating a large area, diffusion along the optical axis can be measured separately, which is convenient when studying anisotropic diffusion. First, we show the rigorous mathematical derivation of the model, leading to a closed-form formula describing the fluorescence recovery/redistribution phase. Next, the ability of the multiphoton FRAP method to correctly measure absolute diffusion coefficients is tested thoroughly on many test solutions of FITC-dextrans covering a wide range of diffusion coefficients. The same is done for the FRAPa method on a series of photoactivatable green fluorescent protein solutions with different viscosities. Finally, we apply the method to photoactivatable green fluorescent protein diffusing freely in the nucleus of living NIH-3T3 mouse embryo fibroblasts.