Final answer:
A mutation affecting the lac I gene's DNA-binding site leads to constitutive transcription of the lac operon, as the repressor can no longer inhibit transcription. This results in continuous expression of genes involved in lactose metabolism, even when lactose is not present.
Step-by-step explanation:
A mutation in the lac I gene that affects the DNA-binding site of the protein would lead to constitutive transcription of the operon's genes, because the repressor can no longer bind to the operator and inhibit transcription. Normally, the lac operon is an inducible system that only transcribes the genes lacZ, lacY, and lacA in the presence of lactose when glucose levels are low. The repressor protein, produced by the lacI gene, binds to the operator sequence to prevent transcription in the absence of lactose. When lactose is present, it is converted into allolactose, which acts as an inducer by binding to the repressor and preventing its binding to the operator, thereby allowing the RNA polymerase to initiate transcription. Thus, failure of the repressor binding due to such a mutation leads to continuous, unregulated transcription, even in the absence of lactose.
In cases where a mutation occurs in one of the structural genes (lacZ, lacY, or lacA) of the lac operon, the specific enzyme coded for by that gene may be altered or inactivated, compromising the bacteria's ability to metabolize lactose.