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LacI binds the operator, which overlaps the promoter, and prevents RNA polymerase from initiating transcription. Allolactose—the physiological inducer—binds LacI and reduces its affinity for DNA, allowing transcription. IPTG acts as a synthetic, non-metabolizable mimic of allolactose and is used in recombinant protein expression. Lactose metabolism supports induction because β-galactosidase can convert lactose to allolactose. Induction alone does not make the operon fully active: the cAMP-CAP complex also binds upstream when glucose is low. Mutations distinguish these controls: lacI⁻ removes functional repression, lacIˢ prevents inducer response, and Oᶜ prevents repressor binding at the operator. Together, these mechanisms make the lac operon a model of negative inducible regulation.