We have developed a mathematical model of regulation of expression of theEscherichia coli lac operon, and have investigated bistability in itssteady-state induction behavior in the absence of external glucose. Numericalanalysis of equations describing regulation by artificial inducers revealed twonatural bistability parameters that can be used to control the range of inducerconcentrations over which the model exhibits bistability. By tuning thesebistability parameters, we found a family of biophysically reasonable systemsthat are consistent with an experimentally determined bistable region forinduction by thio-methylgalactoside (Ozbudak et al. Nature 427:737, 2004). Themodel predicts that bistability can be abolished when passive transport orpermease export becomes sufficiently large; the former case is especiallyrelevant to induction by isopropyl-beta, D-thiogalactopyranoside. To modelregulation by lactose, we developed similar equations in which allolactose, ametabolic intermediate in lactose metabolism and a natural inducer of lac, isthe inducer. For biophysically reasonable parameter values, these equationsyield no bistability in response to induction by lactose; however, systems withan unphysically small permease-dependent export effect can exhibit smallamounts of bistability for limited ranges of parameter values. These resultscast doubt on the relevance of bistability in the lac operon within the naturalcontext of E. coli, and help shed light on the controversy among existingtheoretical studies that address this issue. The results also suggest anexperimental approach to address the relevance of bistability in the lac operonwithin the natural context of E. coli.
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