Final answer:
A loss-of-function mutation in the lacI gene or a mutation in the operator that inhibits repressor binding would lead to increased synthesis of lactose-utilizing proteins because the operon would be constitutively expressed.
Step-by-step explanation:
The effect of either a loss-of-function mutation in the lacI gene or a mutation in the operator that prevents repressor binding would both lead to increased synthesis of lactose-utilizing proteins. This outcome occurs because the lacI gene encodes the repressor protein, which binds to the operator and prevents transcription of the lac operon genes when lactose is not present. A loss-of-function mutation in lacI or a mutation in the operator that inhibits repressor binding would prevent repression, allowing for the continuous expression of the lac operon, even in the absence of lactose, leading to the production of lactose-utilizing proteins like β-galactosidase.
Moreover, when lactose is available, it is converted into allolactose. Allolactose binds to the repressor, causing a conformational change that reduces its affinity for the operator, thus derepressing the operon. If the repressor or operator is mutated in such a way that repressor binding is impaired, the operon is constitutively expressed, regardless of lactose presence.