How does extracellular glucose inhibit transcription of the lac operon?

The lac operon is a set of genes in bacteria (E.coli) involved in lactose metabolism. The genes are expressed when lactose is present and glucose is absent.

There are two regulators of the operon: the lac repressor and catabolite activator protein (CAP). The lac repressor is a lactose sensor which usually blocks transcription of the operon. When lactose is present the repressor stops acting as a repressor. Another regulator is metabolite activator protein (CAP) which is a glucose sensor. It activates transcription of the operon when glucose levels are low. When glucose levels are low, cAMP is produced. cAMP binds to CAP which then binds to DNA and promotes transcription. When the glucose levels are high, there is no cAMP and CAP cannot bind to DNA-low transcription (or no transcription, depending on lactose).

it provides an alternative energy pathway for the reaction to proceed.

a catalyst is a substance that speeds up the rate of a chemical reaction but is not consumed during the course of the reaction.

catalysts increase the rate of reaction without being used up. they do this by lowering the activation energy needed. with a catalyst, more collisions result in a reaction, so the rate of reaction increases. different reactions need different catalysts.

a catalyst works by providing an alternative reaction pathway to the reaction product. the rate of the reaction is increased as this alternative route has a lower activation energy than the reaction route not mediated by the catalyst.