Accurate and precise measurement of cluster sizes in localisation microscopy images using the Rényi divergence

Abstract

Localisation microscopy is a super‐resolution imaging technique based on detecting randomly activated single molecules in a sequence of images. A super‐resolution image is then reconstructed as a collection of discrete points, using all of the localised single molecule positions. Clustering analysis of these points can provide quantitative information about sample structure, size of features and/or their number. The information obtained from clustering analysis allows characterisation of the functions or properties of biological systems, for example examining signalling pathways in T‐cells antigen receptors. However, quantitative analysis of clusters in localisation microscopy images is challenging because the clusters are usually small and surrounded by relatively high noise. The Rényi divergence quantifies differences between two distributions (in this case the observed data and a reference distribution). Its sensitivity to the degree to which one distribution differed from another can be tuned with a scaling parameter α, which allows us to adapt its robustness to noise. We approximated the data distribution by counting all points which were positioned closer to each other than a set threshold and the reference distribution as all the points concentrated in a single cluster. Ripley's K function, which is widely used for performing localisation microscopy analysis, is a special case of the Rényi divergence. Here we present a comparison of the accuracy and precision of cluster size measurement performed using the Rényi divergence and Ripley's K function. Initial tests involved establishing noise adaptability of the two analysis methods using simulated data sets with characteristics similar to experimental images (with increasing noise levels), and optimising the tunable parameter of the Rényi divergence. We find that the adaptability of the Renyi divergence method is a particular advantage when dealing with localisation microscopy data, in which characteristics can vary a great deal between datasets.