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

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