Colocalization Coefficient Calculator

Pearson's Correlation Coefficient (PCC) is calculated according to the following formula:

$\text{PCC}=\frac{\sum {}_i\left(C{1}_i-\stackrel{-}{C1}\right)\times \left(C{2}_i-\stackrel{-}{C2}\right)}{\sqrt{\sum {}_i{\left(C{1}_i-\stackrel{-}{C1}\right)}^2\times \sum {}_i{\left(C{2}_i-\stackrel{-}{C2}\right)}^2}}$

In the above formula for PCC, C1 and C2 are the signal intensity of pixels in the first and second channels, respectively, and C1 and C2 refer to the mean intensity of the first and second channels, respectively. PCC values range from -1 to 1, where 1 corresponds to images with complete correlation, -1 for images with complete inverse correlation, and 0 for no correlation.

Manders Overlap Coefficient (MOC) is calculated according to the following formula:

$MOC=\frac{{\sum }_i^{}\left(C{1}_i\times C{2}_i\right)}{\sqrt{{\sum }_i^{}C{1}_i^2\times {\sum }_i^{}C{2}_i^2}}$

In the above formula for MOC, C1 and C2 are the signal intensity of pixels in the first and second channels, respectively. MOC values range from 0 to 1.

Manders Colocalization Coefficients (MCC), M1 and M2, are calculated according to the following formulas:

$M_1=\frac{{\sum }_i^{}C{1}_{i,colocal}}{C{1}_i}$,   $M_2=\frac{{\sum }_i^{}C{2}_{i,colocal}}{C{2}_i}$

For the M1 formula, C1_i,colocal = C1_i if C2_i > 0 and C1_i,colocal = 0 if C2_i = 0,
and for M2 formula, C2_i,colocal = C2_i if C1_i > 0 and C2_i,colocal = 0 if C1_i = 0.

This calculator attemps to determine thresholds for both channels based on the Costes et al. approach. This approach aims to automatically determine threshold values by identifying the range of pixel values for which a positive PCC is obtained. PCC is first calculated for all pixels, and then repeated while progressively lowering the each channel's intensity values along a regression line. This continues until the PCC drops to or below zero, at which point each channel's intensity values are used as the channel's thresholds.
These threshold values can then be used for the same MCC cauculations above where, for example, C1_i,colocal = C1_i if C2_i is above it's threshold.

• Dunn, Kenneth W et al. A practical guide to evaluating colocalization in biological microscopy. American journal of physiology. Cell physiology vol. 300,4 (2011): C723-42. doi:10.1152/ajpcell.00462.2010
• Manders, Erik MM, F. J. Verbeek, and J. A. Aten. Measurement of co-localization of objects in dual-colour confocal images. Journal of microscopy 169.3 (1993): 375-382.
• Pearson, Karl. VII. Mathematical contributions to the theory of evolution.—III. Regression, heredity, and panmixia. Philosophical Transactions of the Royal Society of London. Series A, containing papers of a mathematical or physical character 187 (1896): 253-318.
• Costes, Sylvain V., et al. Automatic and Quantitative Measurement of Protein-Protein Colocalization in Live Cells. Biophysical journal 86.6 (2004): 3993-4003