The Lactose Paradox

The lac operon in E. coli consists of three genes (lacZ, lacY and lacA) transcribed from a single promoter. The lacZ gene encodes the enzyme β-galactosidase, an enzyme that cleaves β-galactosides. Lactose is a typical β-galactoside and the enzyme cleaves the disaccharide converting it to separate molecules of glucose and galactose. These monosacharides can enter into the metabolic pool of the cell where they can serve as the sole source of carbon.

LacY encodes a famous transporter called lactose permease. It is responsible for importing βgalactosides. The lacA gene encodes a transacetylase that is responsible for detoxifying the cell when it takes up poisonous β-galactosides.

[from The Lac Operon]

Transcription of the lac operon begins when RNA polymerase binds to the P_lac promoter. The long polycistronic mRNA (wavy line) is translated to produce the three proteins.

In the absence of lactose, transcription of the lac operon is blocked by a repressor protein that binds to two sites (O₁ and O₂) preventing RNA polymerase from transcribing the operon [Repression of the lac Operon].

When the bacteria encounter lactose, transcription of the lac operon is induced but since the operon has a weak promoter not much protein will be produced as long as glucose is present. Glucose is always the preferred carbon source. In the absence of both glucose and lactose the operon is maximally induced by the activator CRP-cAMP.

Lactose induces transcription by causing a change in the structure of the repressor so that it no longer binds to DNA. When that happens, RNA polymerase can transcribe the operon.

Here's the paradox. Lactose can't enter the cell unless it's transported across the membrane by the permease and the permease can only be made if the lac operon is transcribed. Furthermore, lactose itself doesn't bind to the lac repressor causing it to detatch from its binding sites. Instead, the actual inducer is allolactose, a modified form of lactose that can only be synthesized inside the cell by the enzyme β-galactosidase. β-galactosidase can only be synthesized if the operon is transcribed.

This is known as the "lactose paradox." It seems you can't induce the operon unless there's allolactose present and the only way to get allolactose is to take up lactose via the permease and convert it to allolactose via β-galactosidase.

The "paradox" was explained many decades ago when it was discovered that the lac operon is transcribed at least once whenever the lac repressor dissociates from its binding sites. The lac repressor is a highly specific DNA binding protein that binds very tightly to O₁ and O₂. But no protein can bind forever. When it dissociates, an mRNA is made and some permease and some β-galactosidase is synthesized. The repressor quickly re-binds and transcription is blocked.

The effect of this "escape" synthesis is that there will always be a few molecules of permease and a few molecules of β-galactosidase inside the cell. When the cell encounters lactose in the medium enough can be taken up and converted to allolactose to induce the operon.

A paper published in this week's issue of Science looked at the number of permease molecules that had to be present in order to induce transcription of the lac operon and discovered that there had to be about 300 molecules present. Some bacterial cells had fewer molecules of permease, by chance, so the repressor remained bound to DNA. Other cells had more than 300 molecules of permease so transcription of the operon was induced and many more molecules of permease were synthesized (Choi et al. 2008).

This is an interesting result but it might not be worth blogging about except for one thing. Our friendly IDiot DaveScot decided to use this paper to prove that evolution is wrong!! You can read all about it on Panda's Thumb: Scientific Vacuity of ID: Lactose Digestion in E. coli.

There's one more wrinkle to this story. Lactose is probably not the main substrate for β-galactosidase and it's quite likely that a typical E. coli cell never sees lactose. When they're not inside a human gut, E. coli cells won't ever encounter lactose. Even when they're living inside a friendly human, it will most often be an adult and throughout most of evolutionary history human adults did not consume milk. E. coli usually does not make up a significant proportion of the bacteria in nursing infants.

So, what is the real product of β-galactosidase and the real inducer of the lac operon? It's likely to be various other β-galactosides such as β-galactosyl glycerol. These are common breakdown products of plant membranes. They are transported efficiently by the permease but they can also be transported by a galactose permease that is always present in the bacteria membrane. Furthermore, β-galactosyl glycerol is a direct inducer of the lac operon. It binds directly to lac repressor so there's no need to convert it to something else (Egel, 1988).

While there may be a "lactose paradox" there is no "β-galactosyl glycerol paradox."

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Choi, P.J., Cai, L., Frieda, K., and Xie, X.S. (2008) A stochastic single-molecule event triggers phenotype switching of a bacterial cell. Science 322:442-6. [DOI: 10.1126/science.1161427]

Egel, R. (1988) The "lac" operon: an irrelevant paradox? Trends in Genetics 4:31.