Robust Nonparametric Descriptors for Clustering Quantification in Single-Molecule Localization Microscopy

Abstract

Single-molecule localization microscopy (SMLM) has been utilized broadly in imaging biological molecules in various biological systems, allowing quantitative analyses on the spatial organizations and patterns of these molecules. However, parameters are needed in many of the currently available methods or algorithms, likely introducing subjective bias in the analyses. Here, we report a robust nonparametric descriptor, J'(r) , for quantifying the spatial organization of molecules in single-molecule localization microscopy. J'(r) , based on nearest neighbor distribution functions, does not require any parameter as an input for analyzing point patterns. We show that it displays a valley shape in the presence of clusters of molecules, and the characteristics of the valley reliably report the clustering features in the data. More importantly, the position of the J'(r) valley (rJ'm) depends exclusively on the density of clustering molecules. Therefore, it is ideal for direct measurements of clustering density of molecules in single-molecule localization microscopy.