Determinants of bistability in induction of the Escherichia coli lac operon

TL;DR

This study uses a mathematical model to analyze bistability in the E. coli lac operon, revealing conditions under which bistability occurs or is abolished, and questioning its biological relevance.

Contribution

The paper introduces a new mathematical model of lac operon regulation that identifies key parameters controlling bistability and compares induction by artificial inducers and lactose.

Findings

Bistability depends on two key parameters controllable in the model.

Bistability can be eliminated with high passive transport or permease export.

Bistability is unlikely in natural lactose induction under realistic conditions.

Abstract

We have developed a mathematical model of regulation of expression of the Escherichia coli lac operon, and have investigated bistability in its steady-state induction behavior in the absence of external glucose. Numerical analysis of equations describing regulation by artificial inducers revealed two natural bistability parameters that can be used to control the range of inducer concentrations over which the model exhibits bistability. By tuning these bistability parameters, we found a family of biophysically reasonable systems that are consistent with an experimentally determined bistable region for induction by thio-methylgalactoside (Ozbudak et al. Nature 427:737, 2004). The model predicts that bistability can be abolished when passive transport or permease export becomes sufficiently large; the former case is especially relevant to induction by isopropyl-beta, D-thiogalactopyranoside. To model regulation by lactose, we developed similar equations in which allolactose, a metabolic intermediate in lactose metabolism and a natural inducer of lac, is the inducer. For biophysically reasonable parameter values, these equations yield no bistability in response to induction by lactose; however, systems with an unphysically small permease-dependent export effect can exhibit small amounts of bistability for limited ranges of parameter values. These results cast doubt on the relevance of bistability in the lac operon within the natural context of E. coli, and help shed light on the controversy among existing theoretical studies that address this issue. The results also suggest an experimental approach to address the relevance of bistability in the lac operon within the natural context of E. coli.