  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.
