In the presence of lactose, how long does it take for the lac operon to be expressed?

The correct option is "as long as lactose is more than glucose concentration".

To understand why this is correct, we need to look at how the lac operon is regulated in bacteria like Escherichia coli. The lac operon is an inducible operon that encodes enzymes required for the transport and metabolism of lactose. However, glucose is the preferred carbon and energy source for the cell because it can enter glycolysis directly.
As a result, the cell has evolved a control mechanism called catabolite repression to ensure that it consumes glucose first before utilizing other sugars like lactose.

The regulation of the lac operon involves two primary control mechanisms:
1. Negative regulation (via the Lac repressor): In the absence of lactose, the Lac repressor binds to the operator, blocking transcription. When lactose is present, its isomer allolactose binds to the repressor, causing it to release from the operator. This acts as an "on/off" switch that permits transcription only if lactose is present.
2. Positive regulation (via cAMP and CAP): Even when the repressor is removed, transcription of the operon is very weak unless an activator protein called Catabolite Activator Protein (CAP), also known as cAMP receptor protein (CRP), is bound to its promoter site. CAP can only bind to the DNA when it is complexed with cyclic AMP (cAMP).

The concentration of cAMP inside the cell is inversely proportional to the concentration of glucose:
- When glucose concentration is high: cAMP levels are low. Therefore, CAP remains inactive and cannot bind to the promoter. Even if lactose is present and the repressor is inactive, transcription of the lac operon occurs at a negligible, basal level.
- When glucose concentration is low: cAMP levels rise. cAMP binds to CAP, activating it. The cAMP-CAP complex binds to the promoter, facilitating RNA polymerase binding and initiating high levels of transcription.

Therefore, for the lac operon to be actively and efficiently expressed, lactose must be present to remove the repressor, and glucose concentration must be low relative to lactose concentration so that cAMP levels rise and activate CAP. This condition is met as long as lactose is more than glucose concentration, allowing the cell to preferentially utilize the lactose when glucose is depleted.