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Shown below are relevant genes and sites from various E. coll strains. Note: + designates the wild-type gene or site that is

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Let us first stablish what each element in the operon does:

- crp: This is an inductor of promoters, it promotes transcription, and it is positive in all the strains here

- lac I: This is the sequence to produce the repressor protein, if this sequence is defective then the repressor does not exists and the transcription is constitutive

- lac O: This is the operator site that attaches to the repressor, when the repressor is attached transcription is not possible. If lacO is defective then the repressor cannot bind and transcription is constitutive

- lac Z: Encodes for the enzyme that cleaves lactose

- lac Y: Encodes for the lactose transporter into the cell

- Glucose: Its absence binds the CAP to the operon, it activates the operon

- Lactose: Its presence removes the repressor from the operator and the operon is thus transcribed

Now let us address each case:

Case CAP? lacI? Maximum?
1 Yes No Yes
2 No Yes No
3 Yes No Yes
4 No No Yes
5 No Yes No
6 No No No
7 No Yes No
8 Yes No Yes
9 No Yes No
10 Yes No No
11 Yes No No
12 No Yes No

The CAP binding depends only on the glucose presence/absence.

The lacI binding depends on both the lacI state and the lacO state, and in the presence of lactose.

The maximum transcription requires for the CAP to be bound but the lacI to not be bound, and reuires for both lac Z and lac Y to be wildtype.

The addition of a wildtype allele in a plasmid will bring the normal function of such allele.

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