Final answer:
When glucose is scarce, cAMP binds to CAP, and the cAMP-CAP complex increases the lac operon's affinity to RNA polymerase, promoting lactose metabolism in bacteria.
Step-by-step explanation:
When glucose is depleted in a bacterial cell, cyclic AMP (cAMP) is the molecule that needs to bind to CRP (cAMP Receptor Protein) or CAP (catabolite activator protein) to increase the affinity of the lac operon to RNA polymerase. As glucose levels fall, cAMP concentration rises and binds to CAP, activating it. This cAMP-CAP complex then binds to the promoter region of the lac operon.
The presence of lactose and its metabolite - allolactose, which is formed from lactose, removes the lac repressor protein from the operator site, allowing RNA polymerase to transcribe the genes required for lactose metabolism.