Fig. 4: Validation of the controller model and simplification.
From: In vitro implementation of robust gene regulation in a synthetic biomolecular integral controller
a, b Predicting the a open-loop and b closed-loop controller response for a step change in PX. PX was increased from 0 nM to different concentrations (0.1–0.7 nM) after 2 h of incubation in the presence of initial 0.7 nM of \(P_Y^{{\mathrm{tot}}}\) and \(P_Z^{{\mathrm{tot}}}\) each. (Recall that fitting was done under different conditions, namely 1 nM of PYCtot (or \(P_{Y}^{\mathrm{tot}}\)) and \(P_{Z}^{\mathrm{tot}}\) each.) The ODE model shown in Fig. 3b was used to determine the response with parameters shown in Table 1. c Simplified ODE model of the controller. d Approximate analytical solution for deGFP slopes (time derivative of G) for the open and closed-loop cases. e, f Comparing the measured responses of the controller shown in Fig. 3c, d with the response determined using the approximate analytical solution for the e open-loop and f closed-loop cases respectively. The data shown in Fig. 4a, b are compared with the analytical solution results in Supplementary Fig. 15. Before calculating deGFP slopes, measured deGFP responses were smoothed-out using the rloess smoothing method in MATLAB. Error bars are from the SEM of at least three repeats. Source data are provided as a Source Data file.
