In E.coli, lac operon is induced by

Options

A. promoter gene
B. operator gene
C. regulator gene
D. allolactose

Answer

### Step-by-Step Solution:

1. **Understanding the Lac Operon**: The lac operon in E. coli is a model for gene regulation. It consists of three main components: the promoter, the operator, and the structural genes responsible for lactose metabolism.

2. **Role of the Inducer**: The lac operon is regulated by the presence or absence of an inducer. In this case, the inducer is allolactose, which is a derivative of lactose.

3. **Absence of Inducer**: When allolactose is absent, the repressor protein binds to the operator region of the lac operon. This binding prevents RNA polymerase from transcribing the structural genes, thus inhibiting the production of enzymes required for lactose metabolism.

4. **Presence of Inducer**: When allolactose is present, it binds to the repressor protein. This binding inactivates the repressor, causing it to detach from the operator. As a result, RNA polymerase can now bind to the promoter and transcribe the structural genes.

5. **Conclusion**: Therefore, in E. coli, the lac operon is induced by allolactose, which allows for the transcription of genes necessary for lactose utilization.

### Final Answer:
In E. coli, the lac operon is induced by allolactose.

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