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In the lower concentration of glucose, what among lactose and arabinose, when both are present in the growth medium, is more likely to be utilized by E. coli?

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It's been done.

Both are expressed.

I remember reading about lactose as a special case. The lac operon is not induced directly by lactose, but a different enzyme present in small concentration converts lactose to allolactose, and the allolactose induces the lac operon.

I vaguely remember reading an explanation, that at low lactose concentrations a fraction of cells would randomly get enough lactose to convert to allolactose to induce the lac operon. Then those cells would transport lactose. This would reduce the lactose concentration in the medium so that other cells would not start using lactose. A fraction of the population would use it up, while the rest concentrated on other energy sources. It would be less efficient for the whole population to gear up to use lactose and then use it up fast.

I don't remember where I saw that story and I don't know whether it's been refuted.

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