Testing independence between two random sets for the analysis of colocalization in bioimaging.

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 superresolution 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, and different optical resolutions). GcoPS is also much faster, a decisive advantage to face the huge amount of data in superresolution imaging. We demonstrate the performances of GcoPS on two biological real data sets, obtained by conventional diffraction-limited microscopy technique and by superresolution technique, respectively.

A quantitative approach for analyzing the spatio-temporal distribution of 3D intracellular events in fluorescence microscopy.

Analysis of the spatial distribution of endomembrane trafficking is fundamental to understand the mechanisms controlling cellular dynamics, cell homeostasy, and cell interaction with its external environment in normal and pathological situations. We present a semi-parametric framework to quantitatively analyze and visualize the spatio-temporal distribution of intracellular events from different conditions. From the spatial coordinates of intracellular features such as segmented subcellular structures or vesicle trajectories, QuantEv automatically estimates weighted densities that are easy to interpret and performs a comprehensive statistical analysis from distribution distances. We apply this approach to study the spatio-temporal distribution of moving Rab6 fluorescently labeled membranes with respect to their direction of movement in crossbow- and disk-shaped cells. We also investigate the position of the generating hub of Rab11-positive membranes and the effect of actin disruption on Rab11 trafficking in coordination with cell shape.