Maths for A Level Biology - updated edition

As the radius of the worm gets bigger the fraction 2 r gets smaller, so with increasing diameter, worms have a decreasing surface area : volume ratio. As a worm gets fatter, there will be a particular radius above which it will be too fat for diffusion to be efficient at allowing it to absorb or remove all it needs. To be fatter, the worm will need to have another mechanism for getting molecules and ions around, such as a blood circulatory system for transporting what has been absorbed, which is what the earthworm does. It still has to absorb oxygen across its surface, so the area puts a limit on how much can be absorbed. This is why there are no giant worms. In the Carboniferous and Permian periods, when the oxygen concentration in the atmosphere was higher, oxygen diffusion would have been more efficient. This suggests that worms may have been bigger then. 2.2.2 DNA replication Another example of a situation where proportions are significant is in analysing DNA samples to demonstrate their mode of replication. DNA replicates semi-conservatively, which means that in each double helix, there is one original strand from its parent molecule and one newly synthesised daughter strand. If the parental, original molecules are labelled with heavy nitrogen, 15 N, they will sediment at a lower level than DNA containing light DNA, with 14 N. Any DNA molecule that contains one strand of each has an intermediate density and will sediment between the two. So the position of the band shows whether the DNA molecule has two heavy strands, two light strands or one of each. The thickness of the bands as drawn in the diagrams suggests how much DNA is present. If one band has half the thickness of another, this indicates that it has half the number of molecules of DNA. So from the depth of each band and the thickness as it is drawn in a diagram, it is possible to make deductions about relative amounts and composition of the DNA. Parental generation: Here is tube of sedimented DNA which contains parent molecules labelled with 15 N in both strands: Two strands labelled with heavy nitrogen. Heavy DNA 15 N 15 N Depth shows relative density of DNA Thickness drawn to suggest relative number of molecules QUICKFIRE 2.6 a) Calculate the surface area : volume ratio for two cylinders of the same length and of diameter 2mm and 4mm. b) If these represented worms in the same habitat, which is likely to be more active. Mathematics for Biology 40