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Licensed Unlicensed Requires Authentication Published by De Gruyter September 18, 2020

Co-localization analysis in fluorescence microscopy via maximum entropy copula

Zahra Amini Farsani and Volker J. Schmid


Co-localization analysis is a popular method for quantitative analysis in fluorescence microscopy imaging. The localization of marked proteins in the cell nucleus allows a deep insight into biological processes in the nucleus. Several metrics have been developed for measuring the co-localization of two markers, however, they depend on subjective thresholding of background and the assumption of linearity. We propose a robust method to estimate the bivariate distribution function of two color channels. From this, we can quantify their co- or anti-colocalization. The proposed method is a combination of the Maximum Entropy Method (MEM) and a Gaussian Copula, which we call the Maximum Entropy Copula (MEC). This new method can measure the spatial and nonlinear correlation of signals to determine the marker colocalization in fluorescence microscopy images. The proposed method is compared with MEM for bivariate probability distributions. The new colocalization metric is validated on simulated and real data. The results show that MEC can determine co- and anti-colocalization even in high background settings. MEC can, therefore, be used as a robust tool for colocalization analysis.

Corresponding author: Zahra Amini Farsani, Statistics Department, Faculty of Science, Lorestan University, 68151-44316 Khorramabad, Islamic Republic of Iran; and Bioimaging Group, Department of Statistics, Ludwig-Maximilians-Universität München, Ludwigstraße 33, 80539 Munich, Germany, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.


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Received: 2019-02-19
Accepted: 2020-08-08
Published Online: 2020-09-18

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