Bistability of the lac operon during growth of Escherichia coli on lactose and lactose + glucose

TL;DR

This paper investigates the conditions under which the lac operon in E. coli exhibits bistability, revealing that growth medium composition significantly influences positive feedback and stability, with lactose alone suppressing bistability due to strong stabilizing effects.

Contribution

It demonstrates how the dependence of permease dilution rate on enzyme activity affects bistability, providing a mechanistic explanation for experimental observations.

Findings

Bistability is virtually impossible during growth on lactose alone.

Growth on lactose + glucose weakens the stabilizing effect, allowing bistability.

Dilution rate dependence on enzyme activity explains the presence or absence of bistability.

Abstract

The lac operon of Escherichia coli exhibits bistability. Early studies showed that bistability occurs during growth on TMG/succinate and lactose + glucose, but not during growth on lactose. More recent studies with lacGFP-transfected cells show bistability with TMG/succinate, but not with lactose and lactose + glucose. In the literature, these results are attributed to variations of the positive feedback generated by induction. Specifically, during growth on TMG/succinate, induction generates positive feedback because the permease stimulates the accumulation of TMG, which, in turn, promotes the synthesis of more permease. This positive feedback is attenuated during growth on lactose because hydrolysis of lactose by galactosidase suppresses the stimulatory effect of the permease. But 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 the permease is proportional to its activity, $e$, because the specific growth rate is independent of $e$. However, during growth on lactose, the permease dilution rate is proportional to $e^2$ because the specific growth rate is proportional to the specific lactose uptake rate, which in turn, proportional to $e$. Here, 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 positive feedback. (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 $e$. We discuss the experimental data in the light of these results.