Determinants of bistability in induction of the Escherichia coli lac operon

Abstract

We have developed a mathematical model of regulation of expression of the Escherichia coli lac operon, and have investigated bistability in its steady-state induction behavior in the absence of external glucose.Numerical analysis of equations describing regulation by artificial inducers revealed two natural bistability parameters that can be used to control the range of inducer concentrations over which the model exhibits bistability. By tuning these bistability parameters, we found a family of biophysically reasonable systems that are consistent with an experimentally determined bistable region for induction by thio-methylgalactoside (Ozbudak et al. Nature 427:737, 2004). The model predicts that bistability can be abolished when passive transport or permease export becomes sufficiently large; the former case is especially relevant to induction by isopropyl-β, D-thiogalactopyranoside. To model regulation by lactose, we developed similar equations in which allolactose, a metabolic intermediate in lactose metabolism and a natural inducer of lac, is the inducer. For biophysically reasonable parameter values, these equations yield no bistability in response to induction by lactose; however, systems with an unphysically small permease-dependent export effect can exhibit small amounts of bistability for limited ranges of parameter values. These results cast doubt on the relevance of bistability in the lac operon within the natural context of E. coli, and help shed light on the controversy among existing theoretical studies that address this issue. The results also suggest an experimental approach to address the relevance of bistability in the lac operon within the natural context of E. coli.

Memory and Fitness Optimization of Bacteria under Fluctuating Environments

“…To better quantify the fitness advantage of response memory in the lac operon, we adapted the established metabolic model described in [35] to fluctuating environments (see Materials and Methods). We focused exclusively on the observed memory effects and their impact on metabolic activity, and did not model the stringent response since it did not significantly affect the induction dynamics (Fig.…”

“…The lac induction dynamics of a population subjected to sudden environmental changes are modeled as described in [35], with an additional equation to account for mRNA transcription. The model assumes that LacY protein levels are proportional to LacZ levels.…”

“…The model assumes that LacY protein levels are proportional to LacZ levels. Unless otherwise noted in Table 1, refer to [35] for a complete rationalization behind each parameter's value. The set of equations are given by where , , , and are the intracellular concentrations of lactose, allolactose, mRNA and LacZ proteins, respectively (parameters are specified in Table 1).…”

“…Unless otherwise noted, refer to [35] for a description of the parameter values. The growth rate corresponds to a generation time of 60 minutes (i.e.…”

Stability analysis of a reduced model of the lac operon under impulsive and switching control

“…In [23], Chaves studied the local input-to-state stability of lac operon in E. Coli with respect to the compact set. In [24], the authors developed a mathematical model of regulation of expression of the E. Coli lac operon, and investigated bistability in its steady-state induction behavior in the absence of external glucose.…”