Testing independence between two random sets for the analysis of colocalization in bio-imaging

Colocalization aims at characterizing spatial associations between two fluorescently-tagged biomolecules by quantifying the co-occurrence and correlation between the two channels acquired in fluorescence microscopy. Colocalization is presented either as the degree of overlap between the two channels or the overlays of the red and green images, with areas of yellow indicating colocalization of the molecules. This problem remains an open issue in diffraction-limited microscopy and raises new challenges with the emergence of super-resolution imaging, a microscopic technique awarded by the 2014 Nobel prize in chemistry. We propose GcoPS, for Geo-coPositioning System, an original method that exploits the random sets structure of the tagged molecules to provide an explicit testing procedure. Our simulation study shows that GcoPS unequivocally outperforms the best competitive methods in adverse situations (noise, irregularly shaped fluorescent patterns, different optical resolutions). GcoPS is also much faster, a decisive advantage to face the huge amount of data in super-resolution imaging. We demonstrate the performances of GcoPS on two biological real datasets, obtained by conventional diffraction-limited microscopy technique and by super-resolution technique, respectively.