Fig. 4.

A cell population can be maintained in a state of balanced expression using periodic stimulations. a. Ratio of LacI-RFP and TetR-GFP levels for observed cells (n = 8). The concentrations of the inducers were varied periodically (120 min of 0.5 mM IPTG, 30 min of 50 ng ml⁻¹ aTc). In such dynamic conditions, the cells were kept in a state of balanced expression. As soon as the periodic stimulation was stopped, with aTc and IPTG set back to their reference levels, the cells were attracted to the RFP-dominant state. b In silico experiment, in which periodic stimulation was applied as in a to a simulated population of cells (n = 16) implementing a stochastic version of the toggle switch model and showing a similar behavior. c Experimental trajectory of one of the cells shown in a in the (LacI-RFP; TetR-GFP) state space. Cell probability of presence is shown for the time window (9 h < Time < 15 h). d Using the model, the vector field in the state space averaged over time during an entire period of stimulation can be computed. The vector field displays a single null point that acts like an effective global attractor (black circle). e The global localization of the cells in the state space during the oscillatory regime depends on the relative amounts of inducers. The average position of the cell population is represented for 14 different periodic stimulation experiments that differed by the total amount of IPTG and/or aTc used. The experiment depicted in (a, c has a ratio of 4 (violet circle). f Experimental periodic stabilization for a different stimulation frequency (180 min of 50 mM IPTG, 30 min of 50 ng ml⁻¹ aTc, n = 11). Cells were stabilized at a lower ratio than in a. Interestingly, when the periodic stimulation was stopped, the cell population split into two groups, each attracted by a stable equilibrium state. This demonstrates that the cell population was close to the frontier between basins of attraction. g In silico periodic stabilization of a population of cells (n = 16) for the same dynamic stimulation shown in f. See Supplementary Fig. 8 for additional experiments