Universal Approach to FRAP Analysis of Arbitrary Bleaching Patterns

Fluorescence recovery after photobleaching (FRAP) is a classical biophysical method, that has been used extensively in the study of numerous systems, particularly cell membranes. It consists of irreversibly photobleaching a fluorescently labeled diffusing species, and then following the fluorescence recovery over time. By analyzing the fluorescence recovery dynamics it is possible to extract the diffusion coefficient of the fluorescent species. While the experimental setup is relatively simple, the interpretation of the results is complex, severely limiting the quantitative use of the technique.With the introduction of digital imaging and the Laser Scanning Confocal Microscope (LSCM), a multitude of variations of the technique became possible. While these modern options offer high flexibility and extend the availability of the method, the initial and boundary conditions are too complex to allow a precise closed, analytical solution of the diffusion problem, and thus quantitative extraction of the diffusion coefficient.We have developed a fast algorithm that allows the extraction of diffusion coefficients given a stack of images representing a FRAP experiment, and acquired with any method, for a completely arbitrary geometry of the initially bleached area. The algorithm treats the first post-bleach frame as the initial and boundary conditions, and simulates the diffusion of the fluorescent molecules. The lack of closed analytical solutions for complex geometries is not a limiting factor, since the diffusion equation is effectively solved numerically by iterative simulation.We validated our approach using a well characterized diffusing molecule (DiIC18) and against the well-established analytical procedures for Gaussian (Axelrod, Koppel et al. 1976) and box bleaching geometries (Ellenberg, Siggia et al. 1997). Furthermore, we show that the algorithm can deduce the diffusion coefficient for an arbitrary bleaching geometrys.The authors gratefully acknowledge a grant from the US-Israel Binational Science Foundation, #2009345.