This set of problems will exercise your use of units and metric conversions. To make sense of the data, you only need think of a DNA molecule as a twisted ladder: each rung on the ladder corresponds to a nucleotide pair. The genome of an organism is the number of nucleotide pairs needed to hold the information necessary to reproduce the organism.
Given the following information:
| Organism | Shape | Diameter (mm) | Length (mm) | Genome Size |
|---|---|---|---|---|
| T4 bacteriophage | cylinder | .05 | .1 | 1.7 x 105 |
| E. Coli cell | cylinder | 1 | 2 | 3.5 x 106 |
| plant palisade cell | cylinder | 20 | 35 | 9 x 109 |
| human liver cell | sphere | 20 | 3 x 109 |
A nucleotide pair in a DNA molecule can be thought of as a cylinder with a diameter of 1.58 x 10-3 microns and a length of 3.34 x 10-4 microns:
The density of human tissue is approximately 1.071 g / cc, and the molecular weight of a nucleotide pair is about 660 (6.02 x 1023 nucleotide pairs weighs 660 g).
1. Compute the volumes of the organisms.
2. What is the volume ratio of a 70 kg person to each of the organisms?
3. What percentage (by volume) of each of the organisms is taken up by its DNA?
4. What is the ratio of DNA length to organism length for each of the organisms?
5. Which of the quantities do you feel best characterizes each of the organism's complexity: volume, % DNA by volume (problem #10) or ratio of DNA length to organism length (problem #11)? Why? Think in terms of searching for additional meaning in a set of numbers; look at order as well as scale. What effect would the presence of repeated or unused segments in the genome have on this question?
6. Compute the average molecular weight of human tissue (look up the elemental composition of the human body and the atomic weights of the elements involved).
7. Compute the density of DNA. Now consider the question: can you use tissue density to obtain an estimate of the percent of a human body that is water? Pretend that human tissue is made solely of water and DNA.
Hint: If the fraction of your body that is water is x, the fraction that is DNA is 1 - x.
Why is the value you would get from the quantity inaccurate? Will the value be too large or too small? Try using molecular weight instead of density, and evaluate the result.
8. E. Coli DNA duplicates itself during cell division in 20 minutes. To do this, each group of 10 pairs must unwind one full turn. What rate of rotation is necessary for this? What is the linear speed of movement of the unwinding pairs (how fast is the outside of a pair moving) ?
