Total Internal Reflection Fluorescence Microscopy (TIRFM) allows us to image fluorescent-tagged proteins near the plasma membrane of living cells with high spatial-temporal resolution. Using TIRFM imaging of GFP-tagged clathrin endocytic proteins, areas of fluorescence are observed as overlapping spots of different sizes and durations. Standard procedures to measure protein-protein colocalization of dual labeled samples threshold the original graylevel images to segment areas covered by different proteins. This binary logic is not appropriate as it leaves a free tuning parameter which can influence the conclusions. Moreover, these procedures rely on simple statistical analysis based on correlation coefficients or visual inspection. We propose a probabilistic model to examine spatial-temporal dependencies. Image sequences of two proteins are modeled as a realization of a bivariate fuzzy temporal random set. Spatial-temporal dependencies are described by means of the pair-correlation function and the K-function and are tested using a Monte Carlo test. Five simulated image sequences were used to validate the performance of the procedure. Spatial and spatial-temporal dependencies were generated using a linked pairs model and a Poisson cluster model for the germs. To demonstrate the applicability in addressing current biological questions, we applied the procedure to fluorescent-tagged proteins involved in endocytosis (Clathrin, Hip1R, Epsin, and Caveolin). Results show that this procedure allows biologists to automatically quantify dependencies between molecules in a more formal and robust way. Image sequences and a Matlab toolbox for simulation and testing are available at http://www.uv.es/tracs/.
