Fig. 2: The output follows the input signal linearly only in the closed-loop configuration.
From: In vitro implementation of robust gene regulation in a synthetic biomolecular integral controller
a, b TXTL deGFP measurement of the response of the integral controller in the a open-loop and b closed-loop configurations at different initial concentrations of PX (0.1–0.7 nM) while initial \(P_Y^{{\mathrm{tot}}}\) and \(P_Z^{{\mathrm{tot}}}\) were both 1 nM each. In the open-loop, instead of \(P_Y^{{\mathrm{tot}}}\), \(P_{YC}^{{\mathrm{tot}}}\) was added. c, d The slopes of measured deGFP responses for the c open-loop and d closed-loop operations and the corresponding summary in e and f at 8 h respectively. 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. g, h Summary of the deGFP slopes of the controller at 8 h for a step change in PX for the g open-loop and h closed-loop operations. PX was increased from 0 nM to different concentrations (0.1–0.7 nM) after 4 h of the reaction in the presence of initial 1 nM of \(P_Y^{{\mathrm{tot}}}\) and \(P_Z^{{\mathrm{tot}}}\) each. Note that the lower GFP slope values in g, h than e, f are due to the shorter active reaction time. Error are shown in the shaded region and were determined using the standard error of the mean of three or more repeats. A linear regression with zero intercept was used to fit the deGFP slopes and the corresponding R-square values are e 0.71, f 0.98, g 0.84, and h 0.98. A calibration factor was used to convert the measured deGFP fluorescent signal into the concentration. 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.
