1. Effect of mRNA and Protein Stability on Regulation E. coli cells are growing in a medium with glucose as the sole carbon source. After the sudden addition of tryptophan, the cells continue to grow and divide every 30 min. Describe (qualitatively) how the amount of tryptophan synthase activity in the cells changes with time under each condition:

1. The trp mRNA is stable (degrades slowly over many hours).
2. The trp mRNA degrades rapidly, but tryptophan synthase is stable.
3. The trp mRNA and tryptophan synthase both degrade rapidly.

2. The Lactose Operon A researcher engineers a lac operon on a plasmid but inactivates all parts of the lac operator (lacO) and the lac promoter, replacing them with the binding site for the LexA repressor (which acts in the SOS response) and a promoter regulated by LexA. She then introduces the plasmid into E. coli cells that have a lac operon with an inactive lacZ gene. Under what conditions will these transformed cells produce β-galactosidase?

3. Negative Regulation Describe the probable effects on gene expression in the lac operon of each mutation:

1. Mutation in the lac operator that deletes most of
2. Mutation in the lacI gene that eliminates binding of repressor to operator
3. Mutation in the promoter near position that increases its similarity to the E. coli consensus sequence
4. Mutation in the lacI gene that eliminates binding of repressor to lactose
5. Mutation in the promoter near position that decreases its similarity to the E. coli consensus sequence

4. Specific DNA Binding by Regulatory Proteins A typical bacterial repressor protein discriminates between its specific DNA-binding site (operator) and nonspecific DNA by a factor of to . About 10 molecules of repressor per cell are sufficient to ensure a high level of repression. Assume that a very similar repressor existed in a human cell, with a similar specificity for its binding site. How many copies of the repressor would a human cell require to elicit a level of repression similar to that in the bacterial cell? (Hint: The E. coli genome contains about 4.6 million bp; the human haploid genome has about 3.2 billion bp.)

5. Repressor Concentration in E. coli The dissociation constant for a particular repressor-operator complex is very low, about . An E. coli cell contains 10 copies of the repressor. Calculate the cellular concentration of the repressor protein. How does this value compare with the dissociation constant of the repressor-operator complex? What is the significance of this answer?

6. Catabolite Repression E. coli cells are growing in a medium that contains lactose but no glucose. Indicate whether each of the following changes or conditions would increase, decrease, or not change the expression of the lac operon. It may be helpful to draw a model depicting what is happening in each situation.

1. Addition of a high concentration of glucose
2. A mutation that prevents dissociation of the Lac repressor from the operator
3. A mutation that completely inactivates β-galactosidase
4. A mutation that completely inactivates galactoside permease
5. A mutation that prevents binding of CRP to its binding site near the lac promoter

7. Transcription Attenuation How would each manipulation of the leader region of the trp mRNA affect transcription of the E. coli trp operon?

1. Increasing the distance (number of bases) between the leader peptide gene and sequence 2
2. Increasing the distance between sequences 2 and 3
3. Removing sequence 4
4. Changing the two Trp codons in the leader peptide gene to His codons
5. Eliminating the ribosome-binding site for the gene that encodes the leader peptide
6. Changing several nucleotides in sequence 3 so that it can base-pair with sequence 4 but not with sequence 2

8. Repressors and Repression How would a mutation in the lexA gene that prevents autocatalytic cleavage of the LexA protein affect the SOS response in E. coli?

9. Regulation by Recombination In the phase variation system of Salmonella, what would happen to the cell if the Hin recombinase became more active and promoted recombination (DNA inversion) several times in each cell generation?

10. Initiation of Transcription in Eukaryotes A biochemist discovers a new RNA polymerase activity in crude extracts of cells derived from an exotic fungus. The RNA polymerase initiates transcription only from a single, highly specialized promoter. As the biochemist purifies the polymerase, its activity declines, and the purified enzyme is completely inactive unless he adds crude extract to the reaction mixture. Suggest an explanation for these observations.

11. Functional Domains in Regulatory Proteins A biochemist replaces the DNA-binding domain of the yeast Gal4 protein with the DNA-binding domain from the Lac repressor and finds that the engineered protein no longer regulates transcription of the GAL genes in yeast. Draw a diagram of the different functional domains you would expect to find in the Gal4 protein and in the engineered protein. Why does the engineered protein no longer regulate transcription of the GAL genes? What might be done to the DNA-binding site recognized by this chimeric protein to make it functional in activating transcription of GAL genes?

12. Nucleosome Modification during Transcriptional Activation To prepare genomic regions for transcription, cells acetylate and methylate certain histones in the resident nucleosomes at specific locations. Once transcription is no longer needed, cells need to reverse these modifications. In mammals, peptidylarginine deiminases (PADIs) reverse the methylation of Arg residues in histones. The reaction promoted by these enzymes does not yield unmethylated arginine. Instead, it produces citrulline residues in the histone. What is the other product of the reaction? Suggest a mechanism for this reaction.

13. Gene Repression in Eukaryotes Explain why repression of a eukaryotic gene by an RNA might be more efficient than repression by a protein repressor.

14. Inheritance Mechanisms in Development A Drosophila egg that is may develop normally, but the adult fruit fly will not be able to produce viable offspring. Explain.

15. Engineering a Genetic Toggle Switch in E. coli Gene regulation is often described as an “on or off” phenomenon: a gene is either fully expressed or not expressed at all. In fact, repression and activation of a gene involve ligand-binding reactions, so genes can show intermediate levels of expression when intermediate levels of regulatory molecules are present. For example, for the E. coli lac operon, consider the binding equilibrium of the Lac repressor, operator DNA, and inducer (see Fig. 28-8). Although this is a complex, cooperative process, it can be approximately modeled by the following reaction (R is repressor; IPTG is the inducer isopropyl-β-d-thiogalactoside):

Free repressor, R, binds to the operator and prevents transcription of the lac operon; the R • IPTG complex does not bind to the operator, and thus transcription of the lac operon can proceed.

1. Using Equation 5-8, we can calculate the relative expression level of the proteins of the lac operon as a function of [IPTG]. Use this calculation to determine over what range of [IPTG] the expression level would vary from 10% to 90%.
2. Describe qualitatively the level of lac operon proteins present in an E. coli cell before, during, and after induction with IPTG. You do not need to give the amounts at exact times — just indicate the general trends.

   Gardner, Cantor, and Collins (2000) set out to make a “genetic toggle switch” — a gene-regulatory system with two key characteristics, A and B, of a light switch. (A) It has only two states: it is either fully on or fully off; it is not a dimmer switch. In biochemical terms, the target gene or gene system (operon) is either fully expressed or not expressed at all; it cannot be expressed at an intermediate level. (B) Both states are stable: although you must use a finger to flip the light switch from one state to the other, once you have flipped it and removed your finger, the switch stays in that state. In biochemical terms, exposure to an inducer or some other signal changes the expression state of the gene or operon, and it remains in that state once the signal is removed.

3. Explain how the lac operon lacks both characteristics A and B.

   To make their “toggle switch,” Gardner and coworkers constructed a plasmid from the following components:

   ori	An origin of replication
   	A gene conferring resistance to the antibiotic ampicillin
   	The operator-promoter region of the E. coli lac operon
   	The operator-promoter region of λ phage
   lacI	The gene encoding the lac repressor protein, LacI. In the absence of IPTG, this protein strongly represses ; in the presence of IPTG, it allows full expression from .
   	The gene encoding a temperature-sensitive mutant λ repressor protein, . At 37 °C, this protein strongly represses ; at 42 °C, it allows full expression from .
   GFP	The gene for green fluorescent protein (GFP), a highly fluorescent reporter protein (see Fig. 9-16)
   T	Transcription terminator

   The investigators arranged these components, as shown in the following figure, so that the two promoters were reciprocally repressed: controlled expression of , and controlled expression of lacI. The state of this system was reported by the expression level of GFP, which was also under the control of .

   

4. The constructed system has two states: GFP-on (high level of expression) and GFP-off (low level of expression). For each state, describe which proteins are present and which promoters are being expressed.
5. Treatment with IPTG would be expected to toggle the system from one state to the other. From which state to which? Explain your reasoning.
6. Treatment with heat (42 °C) would be expected to toggle the system from one state to the other. From which state to which? Explain your reasoning.
7. Why would this plasmid be expected to have characteristics A and B as described above?

   To confirm that their construct did indeed exhibit these characteristics, Gardner and colleagues first showed that, once switched, the GFP expression level (high or low) was stable for long periods of time (characteristic B). Next, they measured the GFP level at different concentrations of the inducer IPTG, with the following results.

   

   They noticed that the average GFP expression level was intermediate at concentration X of IPTG. However, when they measured the GFP expression level in individual cells at , they found either a high level or a low level of no cells showed an intermediate level.

8. Explain how this finding demonstrates that the system has characteristic A. What is happening to cause the bimodal distribution of expression levels at ?