Coordinate based co-localization

Co-localization is used to measure spatial overlap between two (or more) different fluorescent labels, each having a separate emission wavelength. Traditional co-localization analysis of conventional, dual-color fluorescence microscopy images suffers from a limited spatial resolution and chromatic errors [2]. Coordinate based co-localization (CBC) of dual-color super-resolution images provides much better approach as it allows to determine co-localization on a molecular level, it overcomes the dynamic range of a camera, and it is not sensitive to cross talks [1].

Calculation of the CBC value around a given molecule $A_{i}$ , according to [1], starts by determining two distributions of distances

	$\displaystyle D_{A_{i},A}\left(r\right)$	$\displaystyle=$	$\displaystyle\frac{N_{A_{i},A}\left(r\right)}{N_{A_{i},A}\left(R_{\mathrm{max}% }\right)}\frac{R_{\mathrm{max}}^{2}}{r^{2}}\,,$
	$\displaystyle D_{A_{i},B}\left(r\right)$	$\displaystyle=$	$\displaystyle\frac{N_{A_{i},B}\left(r\right)}{N_{A_{i},B}\left(R_{\mathrm{max}% }\right)}\frac{R_{\mathrm{max}}^{2}}{r^{2}}\,.$

Here $N_{A_{i},A}\left(r\right)$ , resp. $N_{A_{i},B}\left(r\right)$ , is the number of localized molecules in channel , resp. , within the distance $r=0,\ldots,R_{\mathrm{max}}$ around $A_{i}$ . These distributions are corrected for the area given by and normalized by the number of localizations within the largest observed distance $R_{\mathrm{max}}$ .

Having these two distributions of distances, Sperman’s rank correlation coefficient $S_{A_{i}}=\left\langle D_{A_{i},A}\,,\,D_{A_{i},B}\right\rangle$ is calculated. The co-localization value is determined for every single molecule according to

$C_{A_{i}}=S_{A_{i}}\exp\left(-\frac{E_{A_{i},B}}{R_{\mathrm{max}}}\right)\,,$

where $E_{A_{i},B}$ is a distance from localization $A_{i}$ to the nearest neighbor localization in channel .

In ThunderSTORM, the input data for channels and are provided as a table of results and a ground-truth table, respectively. Computed values with the co-localization coefficient $C_{A_{i}}$ , with the distance to the nearest neighbor $E_{A_{i},B}$ , and with the number of neighbors $N_{A_{i},B}\left(r\right)$ within the radius $r=0,\ldots,R_{\mathrm{max}}$ , are displayed in the table of results as new columns.

References

[1] S. Malkusch, U. Endesfelder, J. Mondry, M. Gelléri, P. Verveer and Heilemann(2012-01) Coordinate-based colocalization analysis of single-molecule localization microscopy data, Histochemistry and Cell Biology 137 (1), pp. 1–10. Note: Springer-Verlag External Links: Document. Cited by: Coordinate based co-localization, Coordinate based co-localization.
[2] O. Ronneberger, D. Baddeley, F. Scheipl, P.J. Verveer, H. Burkhardt, C. Cremer, L. Fahrmeir, T. Cremer and B. Joffe(2008-05) Spatial quantitative analysis of fluorescently labeled nuclear structures: problems, methods, pitfalls, Chromosome Research 16 (3), pp. 523–562. Note: Springer Netherlands External Links: Document. Cited by: Coordinate based co-localization.

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Coordinate based co-localization

See also

References