Correlation Functions Quantify Super-Resolution Images and Estimate Apparent Clustering Due to Over-Counting
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We present an analytical method using correlation functions to quantify clustering in super-resolution fluorescence localization images and electron microscopy images of static surfaces in two dimensions. We use this method to quantify how over-counting of labeled molecules contributes to apparent self-clustering and to calculate the effective lateral resolution of an image. This treatment applies to distributions of proteins and lipids in cell membranes, where there is significant interest in using electron microscopy and super-resolution fluorescence localization techniques to probe membrane heterogeneity. When images are quantified using pair auto-correlation functions, the magnitude of apparent clustering arising from over-counting varies inversely with the surface density of labeled molecules and does not depend on the number of times an average molecule is counted. In contrast, we demonstrate that over-counting does not give rise to 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 (FcεRI) on the plasma membranes of chemically fixed RBL-2H3 mast cells from images acquired using stochastic optical reconstruction microscopy (STORM/dSTORM) and scanning electron microscopy (SEM). We find that apparent clustering of FcεRI-bound IgE is dominated by over-counting labels on individual complexes when IgE is directly conjugated to organic fluorophores. We verify this observation by measuring pair cross-correlation functions between two distinguishably labeled pools of IgE-FcεRI on the cell surface using both imaging methods. After correcting for over-counting, we observe weak but significant self-clustering of IgE-FcεRI in fluorescence localization measurements, and no residual self-clustering as detected with SEM. We also apply this method to quantify IgE-FcεRI redistribution after deliberate clustering by crosslinking with two distinct trivalent ligands of defined architectures, and we evaluate contributions from both over-counting of labels and redistribution of proteins.
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Overcounting has no effect on the PCF.
“Different from the ACF, overcounting has no effect on the PCF39.”
From A trans-synaptic nanocolumn aligns neurotransmitter release to receptors (2016) · cites this paper as [39]
In Materials and Methods (“Modifications for measured cross-correlation functions”; page unavailable), the paper says pair cross-correlation functions have no over-counting artifact, unlike pair auto-correlation functions. It limits this result to labeling schemes in which two distinguishable probes cannot label the same molecule; the unqualified claim omits that condition. (LLM, conf=0.82)
Experimental — accuracy not yet measuredThe extent of ga(r) over 1, r0 for ga(r0)=1, is related to the pattern size of the internal heterogeneity.
“The extent of ga(r) over 1, i.e. r0 for ga(r0) =1, is related to the pattern size of the internal heterogeneity (Extended Data Figure 2b–c)39.”
From A trans-synaptic nanocolumn aligns neurotransmitter release to receptors (2016) · cites this paper as [39]
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- Authors
- Veatch, S. L., Machta, B. B., Shelby, S. A., Chiang, E. N., Holowka, D. A., & Baird, B. A.
- Affiliations
- Cornell University (US)
- Corresponding author
- Veatch, Sarah L.
- Venue
- PLoS ONE
- Publisher
- Public Library of Science (PLoS)
- Published
- 2012-02-27
- Volume
- 7
- Issue
- 2
- Pages
- e31457
- ISSN
- 1932-6203 (ISSN-L)
- PMC
- PMC3288038
- OpenAlex
- W2073576660
- Cited by
- 290
- References
- 35
- Citations by year
- 2026: 6 · 2025: 11 · 2024: 12 · 2023: 13 · 2022: 19 · 2021: 22 · 2020: 16 · 2019: 24 · 2018: 24 · 2017: 23 · 2016: 33 · 2015: 21 · 2014: 36 · 2013: 23 · 2012: 7
- FWCI
- 12.73
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- PLoS ONE (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- National Institutes of Health
- National Institute of General Medical Sciences (R00GM087810)
- National Institute of Allergy and Infectious Diseases (R01-AI18306, R01AI018306)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Biophysics › Advanced Fluorescence Microscopy Techniques
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Biophysics › Cell Image Analysis Techniques
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Lipid Membrane Structure and Behavior
- Keywords
- super-resolution imaging, storms, scanning electron microscopy, FcεRI, IgE receptor, mast cells, membrane protein clustering, protein redistribution, crosslinking
- MeSH terms
- Animals, Cell Line, Cell Membrane, Fluorescent Dyes, Fourier Analysis, Immunoglobulin E, Image Processing, Computer-Assisted, Ligands, Microscopy, Electron, Microscopy, Electron, Scanning, Stochastic Processes, Models, Statistical, Cluster Analysis, Normal Distribution, Poisson Distribution, Receptors, IgE, Rats
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