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When lactose is present, allolactose binds to the lac repressor, causing an allosteric change in its shape. In its changed state, the lac repressor is unable to bind tightly to its cognate operator. This effect is referred to as induction, because it induces, rather than represses, expression of the metabolic genes.
Bottom: The gene is turned on. Lactose is inhibiting the repressor, allowing the RNA polymerase to bind with the promoter, and express the genes, which synthesize lactase. Eventually, the lactase will digest all of the lactose, until there is none to bind to the repressor.