Studying Smad2 intranuclear diffusion dynamics by mathematical modelling of FRAP experiments

We combine Fluorescence Recovery After Photobleaching (FRAP) experiments with mathematical modelling to study the dynamics inside the nucleus of both the TGF-β-sensitive transcriptional regulator Smad2, and Green-Fluorescent Protein (GFP). We show how combining modelling with bleaching strips of different areas allows a rigorous test of whether or not a protein is moving via diffusion as a single species. As noted recently by others, it is important to consider diffusion during the bleaching process. Neglecting it can cause serious error. Also, it is possible to use the bleaching process itself to provide an extra consistency test to the models predicting the recovery. With our method we show that the dynamics of GFP are consistent with it diffusing as a single species in a uniform environment in which flow is negligible. In contrast, the dynamics of the intracellular signal transducer Smad2 are never consistent with it moving as a single species via simple diffusion in a homogeneous environment without flow. Adding TGF-β slows down the dynamics of Smad2 but even without TGF-β, the Smad2 dynamics are influenced by one or more of: association, flow, and inhomogeneity in space of the dynamics. We suggest that the dynamics inside cells of many proteins may be poorly described by simple diffusion of a single species, and that our methodology provides a general and powerful way to test this hypothesis.