Square root scaling

This is a small note that I hope will appear on Google for future researchers.

There are various methods for imaging DNA or protein having been separated via gel electrophoresis. If, for example, you’re using radio-labelled DNA you may image the resulting gel on a phosphorimager. One brand is a “Typhoon”.

The resuting image may look something like this;

However, what you may not be aware of is this file format (.gel) has square root enconding. That is, if the phosphorimager measures an intenisty of 49 it will be stored as 7 and if it measures 100, it will be stored as 10. The reason for this is to increase the dynamic range it is possible to store in the image.

Apparently this is common knowledge. But, it’s not that common as I’ve seen 1000s of these gels presented in talks and it has never been mentioned.

If you linearize the gel data (https://imagej.nih.gov/ij/plugins/linearize-gel-data.html) and place it next to the square root scaled image then it looks like this;

Left) Square root scaled. Right) Linearized. Here the images have adjusted contrast using ImagjeJ ‘auto’ adjust setting.

Clearly the ratio of background to signal has changed but it’s difficult to discern exactly how from looking at the gel. Below I’ve crudely quantified the second lane.

The ratios od the peaks is significantly different when linearized.

Clearly linearizing the data cahnges the ratios of the bands in the lanes. This is expected as the pixel values are squared when linearizing.

So, be careful, if you’re quantifying gels make sure you know if it is square root scaled or not. It could severely effect your conclusions. To be honest I think the machines that make these images should have a big plaque with huge font saying “IMAGES ARE NOT LINEAR”. I don’t know of any other imaging devices that save with square root scaling.