A common method to study DNA in the laboratory is by agarose gel electrophoresis. A slab of agarose is placed in a buffer between two electrodes and an electrical field is applied (Fig 1). DNA will migrate through the agarose at a rate that depends on the size of the molecule, where shorter molecules migrate faster than longer ones.

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We can determine the length of a DNA fragment using agarose gel electrophoresis by comparison to a set of known molecular weight fragments run on the same gel. The set of known molecular weight fragments is often called a “DNA ladder” or a “Marker” (below).

The most accurate way to determine the molecular weight of an unknown DNA fragment is to construct a standard curve from the known fragments and use this to calculate the length.

Constructing a standard curve from a gel image starts with measuring all the distances between the well where the DNA was loaded (see “samples” above) and the gel bands of the standard (the “Marker” lane).

The migration rate depends on the size of the molecule and can be approximated by plotting the migration distance on the x-axis against the logarithm of the length of the DNA molecules on the y-axis below.

However, this is not a very good approximation. As can be seen in Fig 3, Some points are located on top of the straight line and some below and there are no points on the curve.

A better approximation can be done using a cubic spline approximation. This method is used in several publications such as Russell 1984, Gariepy 1986. The curve below shows the fit of migration distances and sizes for ten DNA fragments using a cubic spline.

The following section contain a step-by step instruction for constructing a calibration curve and calculating the molecular weight of a sample using the method outlined in the previous section.

We will use the Marker (left lane above) to calculate the length of the DNA fragment in the right lane in the figure. The fragment sizes are 500, 750, 1000, 1500, 2000, 3000, 4000, 5000, 7750 and 10000 bp as indicated.

Rotating the image 90 degrees is not strictly necessary, but makes the analysis easier. The PINETOOLS "rotate image" web tool (below) can be found here. Copy and paste the gel image into the tool. Then select rotate 90 degrees left and click "Rotate!".

Copy and paste the rotated image into opied and pasted into the pix spy tool (below) link.

Collect the pixel x-positions positions for all bands in the standard and for the well. You can zoom in to make this easier:

The image above shows an x-position of 674. The y-position is also shown, but not used in the analysis.

Note that this collection is done manually, for example in a spreadsheet:

Format a table with x-position in first column and basepairs in the second as in the image above. Copy the table and and paste into a Cubic spline interpolation tool available on-line here. Click the blue Interpolate button.

We had previously measured the distance for the unknown band in Fig 7 to be 673 pixels (see spreadsheet above). We enter this data and get a result of 1244.8 ≈ 1245 bp (see below). The expected size was 1250 bp which makes the error less that 1%.

Question 1:

The image above shows an agarose gel with two lanes. The right lane is a molecular weight standard containing bands of the following sizes: 10000, 8000, 6000, 5000, 4000, 3000, 2000, 1500, 1000 and 500 bp (base pairs). The left lane has three DNA bands of unknown size. Your task is to calculate the length (in** bp of each of the three unknown bands.

Question 2:

This is an individual question for each student. There is gel file for each student in the dropbox in a folder called "student_gels_EGB...". The files are named “student_name_number.png”. Calculate the length of the unknown sample in the right lane using the molecular weight standard in the right lane.

Go to the Google Spreadsheet for this exercise. You should find your name in the "Name" column. Please answer with the size of the fragment as indicated for the first example student "Max Maximus".

Cubic spline interpolation tool

There are several tools available online to perform cubic spline interpolation. One such tool is the cubic spline interpolation tool available here. See a list of alternative tools below. Alternative online cubic spline tools:

http://www.akiti.ca/CubicSpline.html

https://solvemymath.com/online_math_calculator/interpolation.php

There is a Google spreadsheet add-on that is called “Interpolation” here.

There could be a practical reason for performing the analysis locally on your computer instead of using an online tool. The cubic spline functionality can be added to Microsoft Excel by installing the SRS1 Cubic Spline for Excel tool. It can be downloaded for free here.

there is an informative video on YouTube about how to use the tool.

The cubic spline function is built in to the free spreadsheet software “Gnumeric”.

Gnumeric is not a native Windows app. If you have Windows Subsystem for Linux (WSL), you can first install for example Ubuntu on your WSL and then install Gnumeric using the command line. Here are some instructions.

Photoshop GIMP or other image software

The graphics programs Photoshop or the similar, but free GNU Image Manipulation Program (GIMP) can do this.

RapidTables On screen pixel ruler

Pixel ruler should work on any computer that has a web browser. This tool is very easy to use. Just copy and paste a gel image on the screen and you can start measuring. This tool allows you to form boxes (see blue arrow in Fig 16) and the size of the box in pixels is shown (see blue box in Fig 16). This tool is available here.

Fig 16: Online pixel ruler

Measure-it for Firefox

For Mozilla Firefox there is a tool for measuring distance in images called “Measure-it” (Fig 17). You can install it here.

Fig 17 Measure-it for Firefox

PixelZoomer for Chrome

For Google Chrome there is a tool for measuring distance in images called “PixelZoomer” (Fig 18). Y

Fig 18: PixelZoomer for chrome

ou can install it here.