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This thesis presents the first use of the Partition of Unity Method in quantifying the spatio-temporal dynamics of a fluorescent protein targeted to the chloroplast twin-arginine translocation pathway. The fluorescence loss in photobleaching technique is applied in a modified fashion to the measurement of substrate mobilities in the chloroplast stroma. Our in vivo results address the two suggested protein targeting mechanisms of membrane-binding before lateral movement to the translocon and direct binding to the translocon. A high performance computing C/C++ implementation of the Partition of Unity Method is used to perform simulations of fluoresence loss in photobleaching and allow a compelling comparison to photobleaching data series. The implementation is both mesh-free and particle-less.