Abstract
The lac operon of Escherichia coli can exhibit bistability. Early studies showed that bistability occurs during growth on TMG/succinate and lactose + glucose, but not during growth on lactose. More recently, studies with lacGFP-transfected cells show bistability during growth on TMG/succinate, but not during growth on lactose and lactose + glucose. In the literature, these results are invariably attributed to variations in the destabilizing effect of the positive feedback generated by induction. Specifically, during growth on TMG/succinate, lac induction generates strong positive feedback because the permease stimulates the accumulation of intracellular TMG, which in turn, promotes the synthesis of even more permease. This positive feedback is attenuated during growth on lactose because hydrolysis of intracellular lactose by β-galactosidase suppresses the stimulatory effect of the permease. It is attenuated even more during growth on lactose + glucose because glucose inhibits the uptake of lactose. But it is clear that the stabilizing effect of dilution also changes dramatically as a function of the medium composition. For instance, during growth on TMG/succinate, the dilution rate of lac permease is proportional to its activity, e, because the specific growth rate is independent of e (it is completely determined by the concentration of succinate). However, during growth on lactose, the dilution rate of the permease is proportional to e 2 because the specific growth rate is proportional to the specific lactose uptake rate, which in turn, proportional to e. We show that: (a) This dependence on e 2 creates such a strong stabilizing effect that bistability is virtually impossible during growth on lactose, even in the face of the intense positive feedback generated by induction. (b) This stabilizing effect is weakened during growth on lactose + glucose because the specific growth rate on glucose is independent of e, so that the dilution rate once again contains a term that is proportional to e. These results imply that the lac operon is much more prone to bistability if the medium contains carbon sources that cannot be metabolized by the lac enzymes, e.g., succinate during growth on TMG/succinate and glucose during growth on lactose + glucose. We discuss the experimental data in the light of these results.
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Narang, A., Pilyugin, S.S. Bistability of the lac Operon During Growth of Escherichia coli on Lactose and Lactose + Glucose. Bull. Math. Biol. 70, 1032–1064 (2008). https://doi.org/10.1007/s11538-007-9289-7
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DOI: https://doi.org/10.1007/s11538-007-9289-7