The diffusive influx and carrier efflux have a strong effect on the bistability of the lac operon in Escherichia coli

TL;DR

This study demonstrates that both diffusive influx and carrier efflux significantly influence the bistability thresholds of the lac operon in E. coli, challenging previous models that neglected these fluxes and providing new insights for synthetic biology applications.

Contribution

The paper introduces a comprehensive model including both diffusive influx and carrier efflux, showing their profound impact on lac operon bistability thresholds, supported by experimental data comparisons.

Findings

Diffusive influx reduces the on threshold by increasing inducer accumulation.

Carrier efflux raises the off threshold by decreasing inducer levels.

Model predictions align well with IPTG data but show discrepancies with TMG data.

Abstract

In the presence of gratuitous inducers, the lac operon of Escherichia coli exhibits bistability. Most models in the literature assume that the inducer enters the cell via the carrier (permease), and exits by a diffusion-like process. The diffusive influx and carrier efflux are neglected. However, analysis of the data shows that in non-induced cells, the diffusive influx is comparable to the carrier influx, and in induced cells, the carrier efflux is 7 times the diffusive efflux. Since bistability entails the coexistence of steady states corresponding to both non-induced and induced cells, neither one of these fluxes can be ignored. Here, we formulate a model accounting for both fluxes. We show that: (a) The thresholds of bistability are profoundly affected by both fluxes. The diffusive influx reduces the on threshold by enhancing inducer accumulation in non-induced cells. The carrier efflux increases the off threshold by decreasing inducer accumulation in induced cells. (b) Simulations of the model with experimentally measured parameter values are in good agreement with the data for IPTG. However, there are discrepancies with respect to the data for TMG. They are most likely due to two features missing from the model, namely, the variation of the inducer exclusion effect and the specific growth rate with the lactose enzyme levels. (c) The steady states and thresholds obtained in the presence of both fluxes are well approximated by simple analytical expressions, which may be useful for the preliminary design of the lac genetic switch in synthetic biology.