Step 1: Understanding the lac repressor mechanism.
The lac repressor is a protein expressed from the lacI gene that regulates the lac operon, which controls the metabolism of lactose in bacteria. It works by binding to the lac operator, preventing transcription of the lac genes unless an inducer (e.g., allolactose) is present to relieve repression.
Step 2: Analyzing the options.
- (A) Correct: The lac repressor is indeed allosterically controlled. It binds to the lac operator region on the DNA and prevents the transcription of the lac operon unless an inducer like allolactose is present. The binding of the inducer changes the shape of the repressor, reducing its affinity for the operator and allowing transcription.
- (B) Incorrect: The lacI gene is in the 'trans' configuration with respect to the lac operon. The lac repressor is a diffusible molecule that can act on any lac operon in the cell, regardless of whether it is on the same DNA molecule as the lacI gene. It does not act 'cis' (on the same DNA molecule).
- (C) Incorrect: The presence of glucose actually weakens the effect of the lac repressor, but through a different mechanism, involving catabolite repression. When glucose levels are high, the levels of cyclic AMP (cAMP) are low, leading to reduced activation of the lac operon. However, this is separate from the direct action of the lac repressor.
- (D) Correct: The lac repressor regulates gene expression 'in trans', meaning it can act on any lac operon in the cell, even if the lacI gene and the lac operon are on different DNA molecules. This allows the lac repressor to regulate genes that are not on the same chromosome.
Final Answer:
\[
\boxed{\text{(A) and (D) are correct.}}
\]