Correlation functions quantify super-resolution images and estimate apparent clustering due to over-counting

TL;DR

This paper introduces an analytical approach to quantify clustering in super-resolution images, accounting for over-counting effects, and applies it to determine the true distribution of IgE receptors on cell membranes.

Contribution

The paper develops a method to distinguish true clustering from over-counting artifacts in super-resolution images, enhancing the accuracy of membrane heterogeneity analysis.

Findings

Over-counting causes apparent clustering inversely related to surface density.

No co-clustering detected in double label experiments due to over-counting.

IgE receptors are randomly distributed on cell membranes within experimental resolution.

Abstract

We present an analytical method to quantify clustering in super-resolution localization images of static surfaces in two dimensions. The method also describes how over-counting of labeled molecules contributes to apparent self-clustering and how the effective lateral resolution of an image can be determined. This treatment applies to clustering of proteins and lipids in membranes, where there is significant interest in using super-resolution localization techniques to probe membrane heterogeneity. When images are quantified using pair correlation functions, the magnitude of apparent clustering due to over-counting will vary inversely with the surface density of labeled molecules and does not depend on the number of times an average molecule is counted. Over-counting does not yield apparent co-clustering in double label experiments when pair cross-correlation functions are measured. We apply our analytical method to quantify the distribution of the IgE receptor (Fc{\epsilon}RI) on the plasma membranes of chemically fixed RBL-2H3 mast cells from images acquired using stochastic optical reconstruction microscopy (STORM) and scanning electron microscopy (SEM). We find that apparent clustering of labeled IgE bound to Fc{\epsilon}RI detected with both methods arises from over-counting of individual complexes. Thus our results indicate that these receptors are randomly distributed within the resolution and sensitivity limits of these experiments.