Missing genes. Predict the effects of deleting the following regions of DNA:

Minimal concentration. Calculate the concentration of lac repressor, assuming that one molecule is present per cell. Assume that each E. coli cell has a volume of 10⁻¹² cm³. Would you expect the single molecule to be free or bound to DNA?

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Counting sites. Calculate the expected number of times that a given 8-base-pair DNA site should be present in the E. coli genome. Assume that all four bases are equally probable. Repeat for a 10-base-pair site and a 12-base-pair site.

The same but not the same. The lac repressor and the pur repressor are homologous proteins with very similar three-dimensional structures, yet they have different effects on gene expression. Describe two important ways in which the gene-regulatory properties of these proteins differ.

The opposite direction. Some compounds called anti-inducers bind to repressors such as the lac repressor and inhibit the action of inducers; that is, transcription is repressed and higher concentrations of inducer are required to induce transcription. Propose a mechanism of action for anti-inducers.

Inverted repeats. Suppose that a nearly perfect 20-base-pair inverted repeat is observed in a DNA sequence. Provide two possible explanations.

Broken operators. Consider a hypothetical mutation in O_R2 that blocks both λ repressor and Cro binding. How would this mutation affect the likelihood of bacteriophage λ entering the lytic phase?

Promoters. Compare the −10 and −35 sequences for the λ repressor and Cro genes in the right operator. How many differences are there between these sequences?

Positive and negative feedback. What is the effect of an increased Cro concentration on the expression of the gene for the λ repressor? Of an increased concentration of λ repressor on the expression of the Cro gene? Of an increased concentration of λ repressor on the expression of the λ repressor gene?

Leaderless. The mRNA for the λ repressor begins with 5′-AUG-3′, which encodes the methionine residue that begins the protein. What is unusual about this beginning? Would it cause the mRNA to translate efficiently or not?

Quorum count. Suppose you have a series of compounds that you wish to test for the autoinducer activity in Vibrio fischeri. Propose a simple assay, assuming that you can grow V. fischeri cultures at low cell densities.

Codon utilization. There are four codons that encode threonine. Consider the leader sequence in Figure 31.22A What codons are used and with what frequency?

Follow the stereochemistry. The hydrolysis of lactose is catalyzed by β-galactosidase. Does the overall reaction proceed with retention or inversion of configuration? Given that each step likely proceeds with inversion of configuration, what does the overall change in stereochemistry suggest about the mechanism? A key residue in the reaction has been identified to be Glu 537. Propose an overall mechanism for the hydrolysis of lactose.

Leaving tracks. A powerful method for examining protein–DNA interactions is called DNA footprinting. In this method, a DNA fragment containing a potential binding site is radiolabeled on one end. The labeled DNA is then treated with a DNA-cleaving agent such as DNase I such that each DNA molecule within the population is cut only once. The same cleavage process is carried out in the presence of the DNA-binding protein. The bound protein protects some sites within the DNA from cleavage. The patterns of DNA fragments in the cleaved pool of DNA molecules are then examined by electrophoresis followed by autoradiography (a).

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This method is applied to a DNA fragment containing a single binding site for the λ repressor in the presence of different concentrations of the λ repressor. The results are shown below (b):

Estimate the dissociation constant for the λ repressor–DNA complex and the standard free energy of binding.