Fig. 2.

Cells can be maintained close to the target control point using a dual PI controller. a. A dual controller, in which aTc and IPTG levels were changed independently from one another, was used to reach the respective target levels of RFP and GFP. b. Control experiment in which the dual PI controller is applied to drive an E. coli cell. Temporal evolutions of the red (LacI-RFP) and green (TetR-GFP) fluorescence levels for the controlled cell are represented (top). The horizontal red and green lines are the target values of both controller branches. The controlled protein levels, although displaying marked oscillations, remains close to their target values. The ratio (orange, middle) of red and green fluorescence shows that protein expression levels remain comparable over several hours. The concentrations of the inducers applied by the dual PI controller are represented as a function of time (bottom). The parameters of the PI dual controller are ${\mathrm{K}}_{\mathrm{P}}^{\mathrm{L}}=3.310^{-2},{\mathrm{K}}_{\mathrm{I}}^{\mathrm{L}}=1.3210^{-4}{\mathrm{s}}^{-1}$, ${\mathrm{K}}_{\mathrm{P}}^{\mathrm{T}}=1.6510^{-2},{\mathrm{K}}_{\mathrm{I}}^{\mathrm{T}}=4.610^{-4}{\mathrm{s}}^{-1}$ (see “Methods” section). c In silico control experiment in which the dual PI controller is applied to drive a stochastic version of the toggle switch model. The parameters of the PI dual controller are as in (b). d Smoothed trajectory of the experimentally controlled cell in the (LacI-RFP, TetR-GFP) state space. The controlled cell remains close to the target control point and at some distance from the attractive states, where LacI or TetR dominate. e. Fluorescence images (RFP, GFP, merge) of cells under remote control shown in d, c (cell size  ~ 1 µm). The controlled cells express comparable levels of both RFP and GFP. See Fig. 3 and Supplementary Fig. 7 for additional single-cell control experiments