The Y10 class have been sharpening their lab skills by using restriction enzymes to cut the genomic DNA of bacteriophage Lambda and analyse the sizes of the DNA fragments produced, using agarose gel electrophoresis. We refer to this as restriction mapping and it widely used in Molecular Biology to analyse genes, clone genes and to compare regions of two or more plasmids and viral genomes. The skills required include experimental planning, careful pipetting of one thousandth of a ml samples, and the loading of these samples onto agarose gels. I have reported on progress earlier. In the forthcoming class we are going to look at the analysis of data in detail. Not only shall we determine fragment sizes on gels, we shall also look for patterns in the data, as we assemble the restriction digests into a linear order. In addition we shall use the formulae developed by Archimedes over 2000 years ago, to calculate the volume of a genome and the theoretical space occupied by viruses in their host.

Assembling the lambda genome from restriction mapping data can be frustrating, owing to the difficulties in sizing DNA fragments on agarose gels. The problem is that whilst short DNA fragments do migrate at a faster rate than larger fragments, the relationship breaks down over the range of fragment sizes we wish to analyse (see left). You can plot the distance migrated by a group of fragment of DNA on a gel and you will notice the relationship is non-linear. Simply, small, adjacent fragments appear to be better separated than large adjacent fragments (look at the fragments 1371 and 1264, compared with the bands at the top of the gel). As the size of the DNA increases, the separation achieved by conventional electrophoresis becomes less effective. For this reason, size standards that match the DNA fragment size under investigation are used. Alternatively, in order to overcome this problem, the use of sophisticated power supplies, which pulse the electrical field may be used.

The lambda genome contains just under 50 000 base pairs and since DNA can be approximated to a cylinder, it is therefore possible to calculate the volume of the genome (let's forget the charged surface for now and assume it is a simple cylinder) using Watson and Crick values for the diameter of the duplex and the number of base pairs in a repeating unit. We also know from the pioneering electron microscopy work in the 1950s, the dimensions of the phage head, or capsid and the volume of a typical cell (let's assume both can be represented by regular spheres of 60 and 1000nm respectively). So if the diameter of a DNA duplex is 2nm, 10 base pairs repeat every 3.4nm, we only need the equation for the volume of a cylinder (and it is still pi week!). We might then calculate the volume of the capsid and cell and think about how the DNA is packaged and the maximum number of phage particles that can be squeezed into a bacterial cell (for this you will need the formula for the volume of a sphere).

The first thing I realised is that the restriction digests are still proving to be a little demanding (compare Lanes 1 (perfect), 2 (partial) and 3 (uncut) across the whole class, with some notable successes (see left) and some problems still persisting. The partial is a result of insufficient enzyme, incomplete incubation or inaccurate addition of water/buffer. The uncut DNA is more worrying, but I suspect resulted from a failure to add the enzyme. The lesson here is to take more care over assembling reaction mixtures and if you are unsure about using any equipment, please ask first! On the positive side, we are getting nice gels and the experiment is probably working for 50% of the groups. Take a look at your lanes on the class data for today (Innovation Portal) and make sure you note whether your sample gave the predicted pattern and comment on whether the reaction went to completion of not.

I was pleased to see that the maths part of the session went so well. I realised that graph plotting and the use of logs and log graph paper is completely new to you, but the number of students who elected to use semi log paper was very satisfying. I think we are starting to see evidence emerging of the value in thinking about the best way to plot data and your ability to observe trends in data (here it was the non-linear migration of DNA fragments in agarose gels). The 2 cycle semi log paper might be improved on if we use 2 cycle on both axes next week. I also decided to stretch you on the volumetric calculations: determining the volume of the cylinder that best describes the linear lambda genome of 48,500 bp. You solved this pretty quickly and I could see that you then found the calculations of the volumes of phage capsids and bacterial cells (assuming they are regular spheres) was then straight forward. In the end, I felt that we had come away with an appreciation that some numerical relationships in Biology are best described in non-linear terms and that there is significant value in being able to calculate lengths and volumes in order to firm up your understanding of size relationships as we consider the molecular and cellular basis of phenomena phage and viral infection mechanisms.

Assembling the lambda genome from restriction mapping data can be frustrating, owing to the difficulties in sizing DNA fragments on agarose gels. The problem is that whilst short DNA fragments do migrate at a faster rate than larger fragments, the relationship breaks down over the range of fragment sizes we wish to analyse (see left). You can plot the distance migrated by a group of fragment of DNA on a gel and you will notice the relationship is non-linear. Simply, small, adjacent fragments appear to be better separated than large adjacent fragments (look at the fragments 1371 and 1264, compared with the bands at the top of the gel). As the size of the DNA increases, the separation achieved by conventional electrophoresis becomes less effective. For this reason, size standards that match the DNA fragment size under investigation are used. Alternatively, in order to overcome this problem, the use of sophisticated power supplies, which pulse the electrical field may be used.

The lambda genome contains just under 50 000 base pairs and since DNA can be approximated to a cylinder, it is therefore possible to calculate the volume of the genome (let's forget the charged surface for now and assume it is a simple cylinder) using Watson and Crick values for the diameter of the duplex and the number of base pairs in a repeating unit. We also know from the pioneering electron microscopy work in the 1950s, the dimensions of the phage head, or capsid and the volume of a typical cell (let's assume both can be represented by regular spheres of 60 and 1000nm respectively). So if the diameter of a DNA duplex is 2nm, 10 base pairs repeat every 3.4nm, we only need the equation for the volume of a cylinder (and it is still pi week!). We might then calculate the volume of the capsid and cell and think about how the DNA is packaged and the maximum number of phage particles that can be squeezed into a bacterial cell (for this you will need the formula for the volume of a sphere).

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I was pleased to see that the maths part of the session went so well. I realised that graph plotting and the use of logs and log graph paper is completely new to you, but the number of students who elected to use semi log paper was very satisfying. I think we are starting to see evidence emerging of the value in thinking about the best way to plot data and your ability to observe trends in data (here it was the non-linear migration of DNA fragments in agarose gels). The 2 cycle semi log paper might be improved on if we use 2 cycle on both axes next week. I also decided to stretch you on the volumetric calculations: determining the volume of the cylinder that best describes the linear lambda genome of 48,500 bp. You solved this pretty quickly and I could see that you then found the calculations of the volumes of phage capsids and bacterial cells (assuming they are regular spheres) was then straight forward. In the end, I felt that we had come away with an appreciation that some numerical relationships in Biology are best described in non-linear terms and that there is significant value in being able to calculate lengths and volumes in order to firm up your understanding of size relationships as we consider the molecular and cellular basis of phenomena phage and viral infection mechanisms.

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