Fig. 5: Closed-loop operation enables the controller to achieve robustness to the local disturbance on the system.
From: In vitro implementation of robust gene regulation in a synthetic biomolecular integral controller
a, b Measured deGFP response of the controller in the presence of disturbances in the concentration of PYCtot (or \(P_{Y}^{{\mathrm{tot}}}\)) and \(P_Z^{{\mathrm{tot}}}\) (0.2–0.7 nM) for the a open-loop and b closed-loop cases while initial PX was 0.2 nM. The error bars are shown in the shaded region and were determined using the standard error of the mean of three or more repeats. c, d Summary of the deGFP slopes of the controller at 8 h for the c open-loop and d closed-loop operations. Error bars are from the SEM of at least three repeats. To disable the feedback in the open-loop case \(P_Y^{{\mathrm{tot}}}\) was replaced by \(P_{YC}^{{\mathrm{tot}}}\), which expresses a protein that cannot sequester with X. e, f Measured response of the controller when the disturbance in \(P_Y^{{\mathrm{tot}}}\) and \(P_Z^{{\mathrm{tot}}}\) was added in a step manner for the e open-loop and f closed-loop cases. Additional \(P_Y^{{\mathrm{tot}}}\) and \(P_Z^{{\mathrm{tot}}}\) were added (0.1–0.5 nM) after 4 h of the reaction in the presence of initial 0.2 nM of PX, \(P_Y^{{\mathrm{tot}}}\) and \(P_Z^{{\mathrm{tot}}}\) each. g, h Summary of the normalized deGFP slopes of the controller at 8 h for the g open-loop and h closed-loop operations. Normalization was done with respect to the first slope value for each variation in \(P_Y^{{\mathrm{tot}}}\) and \(P_Z^{{\mathrm{tot}}}\). The predicted response for each case was determined using the ODE model shown in Fig. 3b with parameters shown in Table 1. Before calculating deGFP slopes, measured deGFP responses were smoothed-out using the rloess smoothing method in MATLAB. Source data are provided as a Source Data file.
