Fig. 4: Antithetic Integral Rein Controller (AIRC) in Cyberloop.
From: Rapid prototyping and design of cybergenetic single-cell controllers
a Addition of an extra reaction to the Antithetic Integral Controller (AIC) motif that incorporates a direct negative feedback from the controller species Z2 to the system output XL40. b Modification of the Cyberloop in silico setup to facilitate extra negative feedback from controller to the output. An extra molecule Y (in silico) is added to the biological system network being controlled, and is considered as the new output variable of interest. This facilitates addition of an extra negative feedback reaction involving the output variable. c Demonstration of set-point tracking by the Antithetic Integral Rein Controller motif. Left: three Cyberloop runs with different reference values (dashed lines) were performed. Thin lines indicate cumulative time averages of Y counts in individual cells, while thick lines represent the population average. Center: distribution of the average Y count per cell over the course of the experiment. Right: population average of Y count across cells as time progresses in those three experiments (Experimental parameters: \(k=0.1\,{\min }^{-1},\,\eta =5\,{\min }^{-1},\,\theta =0.02\,{\min }^{-1}\) and \(\mu =(7,14,21)\times \theta \,{\min }^{-1},\,\alpha =0.5\,{\min }^{-1},\,\delta =0.05\,{\min }^{-1}\) and \(\beta =5\,{\min }^{-1}\); Number of cells: red - 100, blue - 89, green - 73). d Two experiments, one with AIC (β = 0) motif and another with AIRC (β ≠ 0) motif having same values for the other parameters, were carried out. Top: shows the time-course evolution of average output Y abundance. Center: shows steady-state (from 180 to 240 min) distribution of Z1 and Z2 copy-numbers over all the cells. Bottom: shows the output variance as a function of time in both experiments. In these experiments, AIRC clearly displays better transient dynamics with faster settling time and lower variance compared to AIC. Furthermore, AIRC requires very low abundance of controller species Z2 to achieve set-point tracking as compared to AIC in these experiments (Experimental parameters: \(k=0.1\,{\min }^{-1},\,\eta =5\,{\min }^{-1},\,\theta =0.02\,{\min }^{-1}\) and \(\mu =14\times \theta \,{\min }^{-1},\,\alpha =0.5\,{\min }^{-1},\,\delta =0.05\,{\min }^{-1}\) and \(\beta =(0,5)\,{\min }^{-1}\); Number of cells: red - 89, blue - 122). e Two experiments with high degradation rate (\(\delta =0.5\,{\min }^{-1}\)) of output Y molecule, one with AIC (β = 0) motif and another with AIRC (β ≠ 0) motif having same values for the other parameters, were carried out. This plot shows the time-course evolution of average output Y abundance in the two experiments. Here, AIRC displays no significant improvement in the transient dynamics compared to AIC when there is large enough output degradation rate δ (Experimental parameters: \(k=0.01\,{\min }^{-1},\,\eta =5\,{\min }^{-1},\,\theta =0.02\,{\min }^{-1}\) and \(\mu =14\times \theta \,{\min }^{-1},\,\alpha =0.5\,{\min }^{-1},\,\delta =0.5\,{\min }^{-1}\) and \(\beta =(0,0.2)\,{\min }^{-1}\); Number of cells: red - 54, blue - 62). Source data are provided as a Source Data file.
