Final answer:
In the presence of both glucose and lactose, the lac operon is typically off. When glucose levels are low or absent and lactose is present, the lac operon is turned on. This is controlled by the binding of cyclic AMP (cAMP) to the catabolite activator protein (CAP) and the binding of allolactose to the lac repressor protein.
Step-by-step explanation:
The lac operon is only activated when two conditions are met: the level of glucose must be low or non-existent, and lactose must be present. The lac operon is a set of genes that encode the proteins necessary for lactose metabolism. In the presence of both lactose and glucose, the lac operon is typically off because glucose is the preferred energy source for the bacterial cell. When glucose levels are low or absent, cyclic AMP (cAMP) accumulates in the cell and binds to the catabolite activator protein (CAP) to promote transcription of the lac operon. Additionally, allolactose, a metabolite of lactose, binds to the lac repressor protein, preventing it from binding to the operator site and allowing RNA polymerase to transcribe the lac operon genes.