Final answer:
When both glucose and lactose are present, the lac operon exhibits limited transcription due to glucose's inhibition of cAMP production and therefore CAP binding. However, the presence of allolactose allows for a low level of lac operon transcription by preventing the lac repressor from binding to the operator. Full operon activation requires low glucose levels, which is not the case in this scenario.
Step-by-step explanation:
When both glucose and lactose are present, the regulation of the lac operon in E. coli is subject to intricate control. Glucose's presence inhibits the lac operon because E. coli prefers to use glucose over lactose. However, lactose triggers a different mechanism. The metabolite allolactose, which is derived from lactose, binds to the lac repressor, changing its shape and preventing it from binding to the operator site. This change allows for a low level of transcription of the lac operon even when glucose is present. However, the operon is not fully activated because the presence of glucose prevents the production of cyclic AMP (cAMP), which is necessary for the binding of the catabolite activator protein (CAP) to the promoter. Without the cAMP-CAP complex, the operon's transcription isn't dramatically increased.
In effect, under these conditions, the lac operon is transcribed at a reduced rate, producing a small number of enzymes necessary for lactose processing. The cell remains primed for the utilization of lactose without committing to the full expression of the lac operon unless glucose levels become sufficiently depleted to elevate cAMP levels and activate CAP, leading to the full activation of the operon. This regulation ensures the efficient use of energy resources by E. coli.