You have created a fusion between trp operon and lac operon which encodes the enzymes for tryptophan biosynthesis, under the regulatory control of the lac operator. Under which of the following conditions will tryptophan synthase be induced in the strain that carries the chimeric operator fused operons ?

Options

A. Only when both lactose and glucose are absent
B. Only when both lactose and glucose are present
C. Only when lactose is absent and glucose is present
D. Only when lactose is present and glucose is absent

Answer

To solve the question regarding the induction of tryptophan synthase in a strain with a fusion between the trp operon and lac operon, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Operons**:
- The **trp operon** is responsible for the biosynthesis of tryptophan.
- The **lac operon** is responsible for the metabolism of lactose.

2. **Identify the Regulatory Control**:
- In this scenario, the trp operon is under the regulatory control of the lac operator. This means that the expression of the trp operon (and thus tryptophan synthase) is dependent on the activity of the lac operon.

3. **Conditions for lac Operon Activation**:
- The lac operon is activated (switched on) when lactose is present and glucose is absent.
- When lactose is present, it acts as an inducer for the lac operon, allowing the enzymes necessary for lactose metabolism to be produced.

4. **Linking lac Operon to trp Operon**:
- Since the trp operon is fused to the lac operon and is under its control, the trp operon will only be expressed when the lac operon is active.
- Therefore, tryptophan synthase will be induced when the lac operon is activated.

5. **Evaluate the Options**:
- **Option A**: Only when both lactose and glucose are present - Incorrect, as the lac operon is not activated under these conditions.
- **Option B**: Only when both lactose and glucose are absent - Incorrect, as the lac operon requires lactose to be present to be activated.
- **Option C**: Only when lactose is absent and glucose is present - Incorrect, as the presence of glucose inhibits the lac operon.
- **Option D**: Only when lactose is present and glucose is absent - Correct, as this is the condition under which the lac operon is activated, leading to the induction of tryptophan synthase.

6. **Final Answer**:
- The correct condition under which tryptophan synthase will be induced is **Option D: only when lactose is present and glucose is absent**.