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In the presence of gratuitous inducers, the lac operon of Escherichia coliexhibits bistability. Most models in the literature assume that the inducerenters the cell via the carrier (permease), and exits by a diffusion-likeprocess. The diffusive influx and carrier efflux are neglected. However,analysis of the data shows that in non-induced cells, the diffusive influx iscomparable to the carrier influx, and in induced cells, the carrier efflux is 7times the diffusive efflux. Since bistability entails the coexistence of steadystates corresponding to both non-induced and induced cells, neither one ofthese fluxes can be ignored. Here, we formulate a model accounting for bothfluxes. We show that: (a) The thresholds of bistability are profoundly affectedby both fluxes. The diffusive influx reduces the on threshold by enhancinginducer accumulation in non-induced cells. The carrier efflux increases the offthreshold by decreasing inducer accumulation in induced cells. (b) Simulationsof the model with experimentally measured parameter values are in goodagreement with the data for IPTG. However, there are discrepancies with respectto the data for TMG. They are most likely due to two features missing from themodel, namely, the variation of the inducer exclusion effect and the specificgrowth rate with the lactose enzyme levels. (c) The steady states andthresholds obtained in the presence of both fluxes are well approximated bysimple analytical expressions, which may be useful for the preliminary designof the lac genetic switch in synthetic biology.

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