Fig. 6: Closed-loop controller enables robustness to the global perturbation.
From: In vitro implementation of robust gene regulation in a synthetic biomolecular integral controller
a, b Measured response of the controller at three different external constant change in the reaction temperatures for the a open-loop (\(P_{YC}^{{\mathrm{tot}}}\) and \(P_Z^{{\mathrm{tot}}}\) were both 0.1 nM) and b closed-loop (\(P_Y^{{\mathrm{tot}}}\) and \(P_Z^{{\mathrm{tot}}}\) were both 1 nM each) cases while initial PX was 0.1 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 normalized 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. The responses shown in c, d were normalized with respect to the deGFP slope value recorded at 29 °C. Plate readers were calibrated at 29 °C, 33 °C, and 37 °C separately to a standard curve of GFP to ensure fluorescence variation reflects protein concentration variation (see Supplementary Fig. 24). 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.
