Analyzing protein-protein spatial-temporal dependencies from image sequences using fuzzy temporal random sets

Total Internal Reflection Fluorescence Microscopy (TIRFM) allows us to image fluorescenttagged 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/.