Many of the processes related to morphogenesis depend critically on the maintenance of the spatial distribution of certain polarity proteins on the plasma membrane of the cell. Maintenance of this epithelial polarity depends on the localization and concentration of the polarity proteins. The transmembrane protein Crumbs (Crb) is vital for the dimensions and integrity of the apical membrane. However, there is a little knowledge on the molecular mechanism controlling Crumbs dynamics during morphogenesis. Fluorescence recovery after photobleaching (FRAP) is a live cell imaging technique allowing for the functional measurement of protein mobility in living cells. FRAP experiments we performed in different parts of the Drosophila melanogaster embryonic epithelium and in different developmental stages show significant differences in their characteristics. We analyze the relationship of the changes in the FRAP experiments with the different morphogenetic states of the embryo. To this end, we develop a reaction-diffusion spatiotemporal model involving processes in the membrane and in the cytosol. Moreover, we model the fluorescent tags of proteins and the bleaching process to get in silico FRAP experiments. These in silico FRAPs are then used together with the experimental data to perform parameter estimation based on a multi-objective optimization design procedure. The multi-objective optimization is suitable to understand how morphogenetic events result in different sets of model parameters. Our parameter identification can reveal the mechanisms involved in the regulation of the Crb protein in the different stages of embryonic development and how morphogenesis affects these mechanisms.