Efficient Cross-Correlation Filtering of One- and Two-Color Single Molecule Localization Microscopy Data

Single molecule localization microscopy has become a prominent technique to quantitatively study biological processes below the optical diffraction limit. By fitting the intensity profile of single sparsely activated fluorophores, which are often attached to a specific biomolecule within a cell, the locations of all imaged fluorophores are obtained with ∼20 nm resolution in the form of a coordinate table. While rendered super-resolution images reveal structural features of intracellular structures below the optical diffraction limit, the ability to further analyze the molecular coordinates presents opportunities to gain additional quantitative insights into the spatial distribution of a biomolecule of interest. For instance, pair-correlation or radial distribution functions are employed as a measure of clustering, and cross-correlation analysis reveals the colocalization of two biomolecules in two-color SMLM data. Here, we present an efficient filtering method for SMLM data sets based on pair- or cross-correlation to isolate localizations that are clustered or appear in proximity to a second set of localizations in two-color SMLM data. In this way, clustered or colocalized localizations can be separately rendered and analyzed to compare other molecular properties to the remaining localizations, such as their oligomeric state or mobility in live cell experiments. Current matrix-based cross-correlation analyses of large data sets quickly reach the limitations of computer memory due to the space complexity of constructing the distance matrices. Our approach leverages k-dimensional trees to efficiently perform range searches, which dramatically reduces memory needs and the time for the analysis. We demonstrate the versatile applications of this method with simulated data sets as well as examples of two-color SMLM data. The provided MATLAB code and its description can be integrated into existing localization analysis packages and provides a useful resource to analyze SMLM data with new detail.