Step 1: Understanding the Question:
This question asks us to identify which structural arrangements (schematics) of the lac operon genes and regulatory regions allow for successful negative regulation by the Lac repressor.
Step 2: Key Formula or Approach:
Negative regulation of the lac operon relies on:
1. A regulatory gene ($i$) with its own promoter to synthesize the repressor protein.
2. An operon promoter ($P$) where RNA polymerase binds.
3. An operator ($O$) situated downstream of the promoter ($P$) and upstream of the structural genes, so that repressor binding physically blocks the movement of RNA polymerase.
Step 3: Detailed Explanation:
Let's analyze each schematic individually:
• Schematic i:
- Order: $P - i - P - O - z - y - a$.
- This is the standard wild-type layout. The $i$ gene has its promoter. The structural genes ($z, y, a$) are driven by their promoter $P$, which is immediately followed by the operator $O$.
- When active repressor binds to $O$, it blocks RNA polymerase from transcribing $z, y, a$. Thus, it can be negatively regulated.
• Schematic ii:
- Order: $P - O - i - z - P - y - a$.
- Here, the promoter and operator are separated from some of the structural genes, and the gene order is completely scrambled in a way that prevents coordinated transcription from a single operator-controlled promoter. This cannot be normally regulated.
• Schematic iii:
- Order: $P - i - P - O - y - z - a$.
- In this schematic, the positions of the structural genes $z$ and $y$ are swapped ($y - z - a$ instead of $z - y - a$).
- However, the crucial regulatory elements ($P$ and $O$) remain correctly positioned upstream of the structural genes.
- RNA polymerase will still bind to $P$, and repressor binding to $O$ will still physically block transcription of the structural genes. Thus, this operon can still be negatively regulated.
• Schematic iv:
- Order: $P - O - i - P - z - y - a$.
- Here, the operator $O$ is placed upstream of the regulatory gene $i$ and far away from the promoter $P$ that drives the structural genes ($z, y, a$).
- Because there is no operator between the $P$ promoter and the $z, y, a$ structural genes, the repressor cannot bind and block RNA polymerase. Thus, negative regulation is impossible.
Step 4: Final Answer:
Schematics i and iii can both be negatively regulated, making option (A) the correct choice.