# Image analysis of fluorescent probe colocalization

## The problem

In cell biology research, we often use DNA that codes for a fluorescent probe to see whether a cell is a expressing a section of their genetic code. This ability lends itself to more complex questions: what fraction of cells are expressing sequence A and sequence B? only expressing sequence A? expressing A and C? etc. This is called probe colocalization and it is a valuable part of biological research.

I start with some images from a client that look something like this for each of the three probes we had in this sample. Here we were looking at differences between core and peritumoral tissues.

Next, produce scatter plots showing the correlations between different probes.

Colocalization of fluorescent probes is most accurately quantified by one variable as Pearson's coefficient but it is better to view as a scatter plot array. Let $$r_{xy}$$ be Pearson's coefficient, $$x$$ be the pixel intensities of image 1, and $$y$$ be the pixel intensities of image 2.

$$r_{xy} = \frac{\sum \left(x_i - \langle x\rangle\right)\left(y_i - \langle y\rangle\right) }{\left( \sum_i \left(x_i-\langle x\rangle\right)^2 \right)^{1/2} \left( \sum_i \left(y_i-\langle y\rangle\right)^2 \right)^{1/2}}$$

Finally, science is a visual art so to turn this into a publication requires some pretty images.