Final answer:
Maximal expression of the lac operon occurs in the presence of lactose, which generates allolactose to inactivate the repressor, and in the absence of glucose, which allows for the activation of CAP, leading to high levels of transcription.
Step-by-step explanation:
The condition that leads to maximal expression of the lac operon is the presence of lactose and the absence of glucose. When glucose is not available in the environment, the cellular levels of cAMP increase, which in turn, activate CAP (catabolite activator protein). This activated CAP, along with the presence of allolactose (a form of lactose), induces the transcription of the lac operon. Lactose is required as it is converted into allolactose, which binds to the lac repressor, preventing it from binding to the operator and thus allowing transcription to occur. Conversely, when glucose levels are high, it suppresses the activation of the lac operon.
In summary, maximal expression of the lac operon occurs in the presence of lactose and the absence of glucose, as this condition leads to both the derepression of the operon through the inactivation of the lac repressor and the activation of transcription by the cAMP-CAP complex.