Mechanistic Modeling of Genetic Circuits for ArsR Arsenic Regulation

Bioreporters are living cells that generate an easily measurable signal in the presence of a chemical compound. They acquire their functionality from synthetic gene circuits, the configuration of which defines the response signal and signal-to-noise ratio. Bioreporters based on the Escherichia coli ArsR system have raised significant interest for quantifying arsenic pollution, but they need to be carefully optimized to accurately work in the required low concentration range (1-10 μg arsenite L^-1). To better understand the general functioning of ArsR-based genetic circuits, we developed a comprehensive mechanistic model that was empirically tested and validated in E. coli carrying different circuit configurations. The model accounts for the different elements in the circuits (proteins, DNA, chemical species), and their detailed affinities and interactions, and predicts the (fluorescent) output from the bioreporter cell as a function of arsenite concentration. The model was parametrized using existing ArsR biochemical data, and then complemented by parameter estimations from the accompanying experimental data using a scatter search algorithm. Model predictions and experimental data were largely coherent for feedback and uncoupled circuit configurations, different ArsR alleles, promoter strengths, and presence or absence of arsenic efflux in the bioreporters. Interestingly, the model predicted a particular useful circuit variant having steeper response at low arsenite concentrations, which was experimentally confirmed and may be useful as arsenic bioreporter in the field. From the extensive validation we expect the mechanistic model to further be a useful framework for detailed modeling of other synthetic circuits.