A reaction-subdiffusion model of fluorescence recovery after photobleaching (FRAP)

Anomalous diffusion, in particular subdiffusion, is frequently invoked as a mechanism of motion in dense biological media, and may have a significant impact on the kinetics of binding/unbinding events at the cellular level. In this work we incorporate anomalous diffusion in a previously developed model for FRAP experiments. Our particular implementation of subdiffusive transport is based on a continuous time random walk (CTRW) description of the motion of fluorescent particles, as CTRWs lend themselves particularly well to the inclusion of binding/unbinding events. In order to model switching between bound and unbound states of fluorescent subdiffusive particles, we derive a fractional reaction-subdiffusion equation of rather general applicability. Using suitable initial and boundary conditions, this equation is then incorporated in the model describing two-dimensional kinetics of FRAP experiments. We find that this model can be used to obtain excellent fits to experimental data. Moreover, recovery curves corresponding to different radii of the circular bleach spot can be fitted by a single set of parameters. While not enough evidence has been collected to claim with certainty that CTRW is the underlying transport mechanism in FRAP experiments, the compatibility of our results with experimental data fuels the discussion as to whether normal diffusion or anomalous diffusion is the appropriate model, and as to whether anomalous diffusion effects are important to fully understand the outcomes of FRAP experiments. On a more technical side, we derive explicit analytic solutions of our model in certain limits.
Comment: 21 pages, 3 figures, submitted to "Journal of Statistical Mechanics: Theory and Experiment": Special Issue "Fractional Dynamics: Theory and Applications"