This is not produced by E.coli in the lactose medium :

Options

A. `beta` galactosidase
B. Thiogalactoside transacetylase
C. Lactose dehydrogenase
D. Lactose permease

Answer

To solve the question "This is not produced by E. coli in the lactose medium," we need to analyze the options provided and understand the role of each component in the context of E. coli and the lac operon.

### Step-by-step Solution:

1. **Understand the lac operon**:
- The lac operon in E. coli is responsible for the metabolism of lactose. It consists of three structural genes: lacZ, lacY, and lacA.

2. **Identify the products of the lac operon**:
- **LacZ gene**: Codes for beta-galactosidase, which breaks down lactose into glucose and galactose.
- **LacY gene**: Codes for lactose permease, which facilitates the transport of lactose into the cell.
- **LacA gene**: Codes for beta-galactoside transacetylase (also known as thiogalactoside transacetylase), which is involved in the detoxification of certain compounds.

3. **Analyze the options**:
- **Beta-galactosidase**: Produced by the lacZ gene, so it is present in E. coli when lactose is available.
- **Lactose permease**: Produced by the lacY gene, so it is also present in E. coli in lactose medium.
- **Beta-galactoside transacetylase**: Produced by the lacA gene, thus it is present as well.
- **Lactose dehydrogenase**: This enzyme is not part of the lac operon and is not produced by E. coli in lactose medium. It is involved in different metabolic pathways and is found in many living cells but not specifically in E. coli for lactose metabolism.
- **Thiogalactoside**: This is a type of compound related to the lac operon but not a direct product of E. coli metabolism in lactose medium.

4. **Conclusion**:
- The only option that is not produced by E. coli in the lactose medium is **lactose dehydrogenase**.

### Final Answer:
**Lactose dehydrogenase** is not produced by E. coli in the lactose medium.

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