Step 1: Understanding the Concept:
The *lac* operon of *Escherichia coli* is a classic model of prokaryotic gene regulation.
It coordinates the expression of genes involved in lactose transport and metabolism in response to the availability of lactose and glucose in the environment.
Step 2: Detailed Explanation:
Let us evaluate each of the statements to identify the true ones:
- Statement (A) is correct.
The *lac* operon contains three structural genes: *lacZ* (coding for $\beta$-galactosidase), *lacY* (coding for $\beta$-galactoside permease), and *lacA* (coding for $\beta$-galactoside transacetylase).
These three genes are transcribed together as a single, long polycistronic mRNA molecule under the control of a single promoter.
- Statement (B) is incorrect.
When lactose is available, it is converted into allolactose, which acts as an inducer.
Allolactose binds to the *lac* repressor protein, causing a conformational change that reduces its affinity for the operator.
The repressor dissociates from the operator, allowing RNA polymerase to transcribe the operon.
- Statement (C) is correct.
The operator sequence overlaps physically with the promoter region.
When the *lac* repressor binds to the operator, it physically blocks RNA polymerase from binding to the promoter or moving along the DNA, serving as a negative regulatory site.
- Statement (D) is correct.
The operon contains structural genes for proteins involved in lactose utilization alongside regulatory DNA elements like the promoter, the operator, and the CAP-binding site.
Therefore, statements (A), (C), and (D) are correct.
Step 3: Final Answer:
The true statements are (A), (C), and (D), corresponding to option (C).