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

## TL;DR

This paper introduces GcoPS, a novel statistical method for testing independence between two sets of biomolecules in bio-imaging, effectively handling noise and irregular patterns, and suitable for large super-resolution datasets.

## Contribution

The paper presents GcoPS, a new explicit testing procedure leveraging the structure of random sets for colocalization analysis in microscopy, outperforming existing methods.

## Key findings

- GcoPS outperforms competitive methods in noisy and irregular conditions.
- GcoPS is significantly faster, suitable for large super-resolution datasets.
- Validated on real biological datasets from diffraction-limited and super-resolution microscopy.

## Abstract

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.