Determining the Transcription Rates Yielding Steady-State Production of mRNA in the Lac Genetic Switch of Escherichia coli

To elucidate the regulatory dynamics of the gene expression activation and inactivation, an in silico biochemical model of the lac circuit in Escherichia coli was used to evaluate the transcription rates that yield the steady-state mRNA production in active and inactive states of the lac circuit. This result can be used in synthetic biology applications to understand the limits of the genetic synthesis. Since most genetic networks involve many interconnected components with positive and negative feedback control, intuitive understanding of their dynamics is often difficult to obtain. Although the kinetic model of the lac circuit considered involves only a single positive feedback, the developed computational framework can be used to evaluate supported ranges of other reaction rates in genetic circuits with more complex regulatory networks. More specifically, the inducible lac gene switch in E. coli is regulated by unbinding and binding of the inducer-repressor complexes to or from the DNA operator to switch the gene expression on and off. The dependency of mRNA production at steady state on different transcription rates and the repressor complexes has been studied by computer simulations in the Lattice Microbe software. Provided that the lac circuit is in active state, the transcription rate is independent of the inducer-repressor complexes present in the cell. In inactive state, the transcription rate is dependent on the specific inducer-repressor complex bound to the operator that inactivates the gene expression. We found that the repressor complex with the largest affinity to the operator yields the smallest range of the feasible transcription rates to yield the steady state while the lac circuit is in inactive state. In contrast, the steady state in active state can be obtained for any value of the transcription rate.