Estimation of diffusivity of phycobilisomes on thylakoid membrane based on spatio-temporal FRAP images

The determination of phycobilisome diffusivity (diffusion coefficient D) on thylakoid membrane from fluorescence recovery after photobleaching (FRAP) experiments is usually done by analytical models. However, analytical models need some unrealistic conditions to be supposed. This study describes the development of a method based on finite difference approximation of the process governed by the Fickian diffusion equation and on the minimization of an objective function representing the disparity between the experimental and simulated time-varying concentration profiles. Our method improves on other models by accounting for experimentally measured time-varying Dirichlet boundary conditions, and can include a reaction term as well. As a result we obtain both the overall (time averaged) diffusion coefficient D and the sequence of diffusivities Dj based on two successive fluorescence profiles in j-th time interval. Due to the noisy data, we cope with an inverse ill-posed problem and a regularization technique is mandatory.