Two related problems became evident as the operon model was tested. First, inducers must enter a cell if they are to bind to repressor molecules, yet lactose transport requires permease, and permease synthesis requires induction. Thus, we must explain how the inducer gets into a cell in the first place. Second, the isolated Lac repressor does not bind lactose (4-O-β-D-galactopyranosyl-D-glucose) but does bind a lactose isomer called allolactose (6-O-β-D-galactopyra-nosyl-D-glucose). Remarkably, β-galactosidase, the enzyme that catalyzes lactose hydrolysis, also converts a small proportion of lactose to allolactose. Therefore, induction of the synthesis of β-galactosidase by lactose requires that β-galactosidase be present.
Both problems are solved in the same way in the uninduced state, a small amount of lac mRNA is synthesized (roughly one mRNA molecule per cell per generation). This synthesis, called basal synthesis, occurs because the binding of repressor to the operator is never infinitely strong. Thus, even though the repressor binds very strongly to the operator, it occasionally comes off and an RNA polymerase molecule can initiate transcription during the instant that the operator is free.
We can now describe in molecular terms the sequence of events following addition of a small amount of lactose to a growing Lac+ culture. Consider bacteria growing in a medium in which the carbon source is glycerol. Each bacterium contains one or two molecules of β-galactosidase and of lactose permease. Lactose is then added. The few permease moIecules transport a few lactose molecules into the cell and the few β-galactosidase molecules convert some of these lactose molecules into allolactose. An allolactose molecule then binds to a repressor molecule that is sitting on the operator and the repressor is inactivated and falls off the operator. Synthesis of lac mRNA then begins and, from these RNA molecules, hundreds of copies of β-galactosidase and permease are made. The new permease molecules allow lactose molecules to pour into the cell. Most of the lactose molecules are cleaved to yield glucose and galactose, but many molecules are converted to allolactose molecules, which bind to and inactivate all of the intracellular repressor molecules. (Repressor is made continuously though at a very low rate, so there is usually sufficient allolactose to maintain the cell in the derepressed state.) Thus, lac mRNA is synthesized at a high rate and the concentration of permease and β-galactosidase becomes quite high. The glucose produced by the cleavage reaction is used as a source of carbon and energy. (The galactose formed by the cleavage is converted to glucose-1-phosphate by a set of enzymes, the synthesis of which is also inducible. This inducible system in which galactose is the induce, called the gal operon, is discussed in a later section of this chapter.)
Ultimately all of the lactose in the growth medium and within the cells is consumed. Then the allolactose concentration within the cell will drop so that there will not be sufficient allolactose to bind to a repressor. The repressor will bind to the operator reestablishing repression and thereby blocking further synthesis of lac mRNA. In bacteria, most mRNA molecules have a half-life of only a few minutes. Hence, in less than one generation there is little remaining lac mRNA and synthesis of β-galactosidase and permease ceases. These proteins are quite stable but are gradually diluted out as the cells divide. Note that if lactose were added again to the growth medium one generation after the original lactose had been depleted, cleavage of lactose would begin immediately because the cells would already have adequate Rmmase and β-galactosidase.
