OpenStax Biology 2e
The third type of gene regulation in prokaryotic cells occurs through inducible operons, which have proteins that bind to activate or repress transcription depending on the local environment and the needs of the cell. The lac operon is a typical inducible operon. E. coli is able to use other sugars as energy sources when glucose concentrations are low. One such sugar source is lactose. The lac operon encodes the genes necessary to acquire and process the lactose from the local environment. The Z gene of the lac operon encodes beta-galactosidase, which breaks lactose down to glucose and galactose.
However, for the lac operon to be activated, two conditions must be met. First, the level of glucose must be very low or non-existent. Second, lactose must be present. Only when glucose is absent and lactose is present will the lac operon be transcribed. In the absence of glucose, the binding of the CAP protein makes transcription of the lac operon more effective. When lactose is present, its metabolite, allolactose, binds to the lac repressor and changes its shape so that it cannot bind to the lac operator to prevent transcription. This combination of conditions makes sense for the cell, because it would be energetically wasteful to synthesize the enzymes to process lactose if glucose was plentiful or lactose was not available. It should be mentioned that the lac operon is transcribed at a very low rate even when glucose is present and lactose absent.
If glucose is present, then CAP fails to bind to the promoter sequence to activate transcription. If lactose is absent, then the repressor binds to the operator to prevent transcription. If either of these conditions is met, then transcription remains off. Only when glucose is absent and lactose is present is the lac operon transcribed.
Clark, M., Douglas, M., Choi, J. Biology 2e. Houston, Texas: OpenStax. Access for free at: https://openstax.org/details/books/biology-2e