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

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 comparable to 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. We present a model accounting for both fluxes, and show that (1) The thresholds (i.e., the extracellular inducer levels at which transcription turns on or off) are profoundly affected by both fluxes. The diffusive influx reduces the on threshold, and eliminates irreversible bistability, a phenomenon that is inconsistent with data. The carrier efflux increases the off threshold, and abolishes bistability at large permease activities, a conclusion that can be tested experimentally. (2) The thresholds are well approximated by simple analytical expressions obtained by considering two limiting cases (no carrier efflux and no diffusive influx). (3) The simulations are in good agreement with the data for isopropyl thiogalactoside (IPTG), but somewhat discrepant with respect to the data for thiomethyl galactoside (TMG). We discuss the potential sources of the discrepancy.