Feedback Control and Sensitivity Analysis in Synthetic Gene Circuits

Synthetic gene circuits are engineered DNA sequences that control when genes turn on and how much they are expressed, alongside the regulatory machinery of cells. Many gene circuits use feedback, such that the molecules produced by a gene increase or decrease the expression of the same gene or another gene in the circuit. Feedback regulates how much of a molecule is produced and changes the timing of its production or degradation. However, how effective feedback is depends on biochemical parameters such as transcription, translation, and degradation rates, binding affinities and cooperativities, as well as cellular parameters such as plasmid copy numbers and the availability of cellular resources. All these parameters can change due to mutation, variation in the gene expression machinery, or changes in the cell's growth rate. To quantify how these changes affect the feedback regulation in a circuit, we introduce a method called sensitivity analysis, which measures how the steady-state expression level changes when each parameter is varied. Here, we explain sensitivity analysis and demonstrate its application to the negative autoregulation circuit. Sensitivity analysis can predict when a circuit's feedback will deteriorate, thus directing experiments to evaluate only the effects of the parameters predicted to be disruptive.