Fluorescence recovery after photobleaching: the case of anomalous diffusion

The method of FRAP (fluorescence recovery after photobleaching), which has been broadly used to measure lateral mobility of fluorescent-labeled molecules in cell membranes, is formulated here in terms of continuous time random walks (CTRWs), which offer both analytical expressions and a scheme for numerical simulations. We propose an approach based on the CTRW and the corresponding fractional diffusion equation (FDE) to analyze FRAP results in the presence of anomalous subdiffusion. The FDE generalizes the simple diffusive picture, which has been applied to FRAP when assuming regular diffusion, to account for subdiffusion. We use a subordination relationship between the solutions of the fractional and normal diffusion equations to fit FRAP recovery curves obtained from CTRW simulations, and compare the fits to the commonly used approach based on the simple diffusion equation with a time dependent diffusion coefficient (TDDC). The CTRW and TDDC describe two different dynamical schemes, and although the CTRW formalism appears to be more complicated, it provides a physical description that underlies anomalous lateral diffusion.