Step 1: Understanding the Concept:
The lac operon in E. coli is a classic model for gene regulation. Its expression is controlled by two main factors: the presence of lactose (the inducer) and the presence of glucose (the preferred energy source). This involves two regulatory mechanisms: negative control by the lac repressor and positive control by the Catabolite Activator Protein (CAP).
Step 2: Detailed Explanation:
We need to analyze the state of the lac operon when both glucose and lactose are present in the medium.
1. Effect of Lactose Presence:
- When lactose is present, it is converted into allolactose.
- Allolactose acts as an inducer by binding to the lac repressor protein.
- This binding causes a conformational change in the repressor, preventing it from binding to the operator region (lacO) of the operon.
- Therefore, the Repressor does not bind the lac operator. This means statement D is correct, and statement B is incorrect.
2. Effect of Glucose Presence (Catabolite Repression):
- The lac operon is also subject to positive control by the CAP protein. However, CAP can only bind to the promoter and activate transcription when it is complexed with cyclic AMP (cAMP).
- The level of cAMP in the cell is inversely proportional to the level of glucose.
- When glucose is present (and at a high level), the level of cAMP is low.
- Without sufficient cAMP, the CAP protein cannot bind to the CAP-binding site in the lac promoter.
- Therefore, the CAP protein does not bind the lac promoter. This means statement C is correct, and statement A is incorrect.
Step 3: Final Answer:
Based on the analysis, when both glucose and lactose are present:
- The CAP protein does not bind the promoter (Statement C).
- The repressor does not bind the operator (Statement D).
The combination of correct statements is C and D. This corresponds to option (B). The result is that transcription of the lac operon occurs, but only at a very low, basal level because the positive activation by CAP is absent.