The diameter of a typical human cell nucleus is approximately 6 μm. Human chromosome 2 consists of approximately 243 million contiguous base pairs. Calculate the length of chromosome 2 if it were extended in a relaxed B-form structure (refer to structural parameters provided in Figure 6-17). How does this compare with the diameter of the nucleus?

What is the superhelical density (σ) of a closed-circular DNA with a length of 4,200 bp and a linking number (Lk) of 374? What is the superhelical density (σ) of the same DNA when Lk = 412? In each case, is the molecule negatively or positively supercoiled?

The T4-like bacteriophage JS98 has a DNA of molecular weight 1.11 × 10⁸ contained in a head about 100 nm long.

The base composition of phage M13 DNA is A, 23%; T, 36%; G, 21%; C, 20%. What does this tell you about the DNA structure of phage M13?

The complete genome of the simplest bacterium known, Mycoplasma genitalium, is a circular DNA molecule with 580,070 bp. Calculate the molecular weight (assume the molecular weight of a nucleotide pair is 650) and contour length (when relaxed) of this molecule. What is Lk₀ for this Mycoplasma chromosome? If σ = −0.06, what is Lk?

A closed-circular DNA molecule in its relaxed form has an Lk of 500. Approximately how many base pairs are in this DNA? How does the linking number change (increases, decreases, doesn’t change, becomes undefined) in each of the following situations?

In the presence of a eukaryotic condensin and a type II topoisomerase, the Lk of a relaxed closed-circular DNA molecule does not change. However, the DNA becomes highly knotted, as shown in the figure below. The formation of knots requires breakage of the DNA, passage of a segment of DNA through the break, and religation by the topoisomerase. Given that every reaction of the topoisomerase would be expected to result in a change in linking number, how can Lk remain the same?

Bacteriophage λ infects E. coli by integrating its DNA into the bacterial chromosome. The success of this recombination depends on the topology of the E. coli DNA. When the superhelical density (σ) of the E. coli DNA is greater than −0.045, the probability of integration is <20%; when σ is less than −0.06, the probability is >70%. Plasmid DNA isolated from an E. coli culture is found to have a length of 13,800 bp and an Lk of 1,222. Calculate σ for the plasmid DNA (which reflects the superhelical density of all DNA in the cell, plasmid and chromosome), and predict the likelihood that bacteriophage λ will be able to infect this culture.

Explain how the underwinding of a B-DNA helix might facilitate or stabilize the formation of Z-DNA.

YACs are used to clone large pieces of DNA in yeast cells. What three types of DNA sequence are required to ensure proper replication and propagation of a YAC in a yeast cell, and what is the function of each?

When DNA is subjected to electrophoresis in an agarose gel, shorter molecules migrate faster than longer ones. Closed-circular DNAs of the same size but with different linking numbers can also be separated on an agarose gel; topoisomers that are more supercoiled, and thus more condensed, migrate faster through the gel. In the gel shown below, purified plasmid DNA has migrated from top to bottom. There are two bands, with the faster band much more prominent.

As in the experiment described in Problem 13, gels are run to separate closed-circular DNAs of the same size but different linking number. The new gels include two different concentrations of the dye chloroquine:

Chloroquine intercalates between base pairs and stabilizes a more underwound DNA structure. When the dye binds to a relaxed, closed-circular DNA, the DNA is underwound where the dye binds, and unbound regions take on positive supercoils to compensate. In the experiment shown below, topoisomerases were used to make preparations of the same closed-circular DNA with different superhelical densities (σ). Completely relaxed DNA migrated to the position labeled N (nicked), and highly supercoiled DNA (above the limit where individual topoisomers can be distinguished) migrated to the position labeled X.

328

In the early electron microscopy experiments of Vinograd and colleagues (see this chapter’s How We Know section), the polyoma virus DNA was clearly circular in both form I and form II. However, the DNA in form II tended to be spread out on the electron microscope grid, whereas the DNA in form I tended to twist on itself, often repeatedly. Explain these observations.

A small plasmid DNA is isolated, and one negatively supercoiled topoisomer is purified (see this chapter’s How We Know section). A small amount of bacterial topoisomerase III or topoisomerase II (DNA gyrase) plus ATP is added to the plasmid DNA in two separate experiments, allowing only limited reaction of the topoisomers. The experiments yield the DNA banding patterns shown below. Which pattern is produced by DNA topoisomerase III, and which by DNA gyrase?

If bacterial topoisomerase I is inactivated by mutating the gene (topA) encoding it, will the superhelical density of the cell’s chromosomal DNA increase or decrease? When such mutations are introduced into the topA gene, compensating mutations appear rapidly in another gene, which serve to partly ameliorate the deleterious cellular effects of the topA mutations. Which gene is likely to be the site of the new mutations, and why?