Inferring diffusion, reaction, and exchange parameters from imperfect FRAP

Fluorescence recovery after photobleaching (FRAP) is broadly used to investigate the dynamics of molecules in cells and tissues, notably to quantify diffusion coefficients. FRAP is based on the spatiotemporal imaging of fluorescent molecules after an initial bleaching of fluorescence in a region of the sample. Although a large number of methods have been developed to infer kinetic parameters from experiments, it is still a challenge to fully characterize molecular dynamics from noisy experiments in which diffusion is coupled to other molecular processes or in which the initial bleaching profile is not perfectly controlled. To address this challenge, we have developed HiFRAP to quantify the reaction- (or exchange-) diffusion kinetic parameters from FRAP under imperfect experimental conditions. HiFRAP is based on a low-rank approximation of a kernel related to the model Green's function and is implemented as an ImageJ/Python macro for (potentially curved) one-dimensional systems and for two-dimensional systems. To the best of our knowledge, HiFRAP offers features that have not been combined together: making no assumption on the initial bleaching profile, which does not need to be known; accounting for the limitation of the optical setup by diffraction; inferring several kinetic parameters from a single experiment; providing errors on parameter estimation; and testing model goodness. In the future, our approach could be applied to other dynamical processes described by linear partial differential equations, which could be useful beyond FRAP, in experiments where the concentration fields are monitored over space and time.