Fig. 4: The model captures how resource competition and host-circuit interactions qualitatively alter circuit behavior.
a In the winner-takes-all scenario, the cell hosts two bistable switches, each consisting of a protein that, upon being allosterically modulated by an inducer molecule, cooperatively acts as a transcription factor activating its own expression. Adding the corresponding inducer to the medium causes a switch to move toward a high-expression equilibrium. For higher inducer levels, this happens on a shorter timescale (Supplementary Fig. 4a)5. b Phase plane diagram showing the two-switch system’s behavior upon simultaneous addition of inducer 1 and inducer 2 to the culture medium. Thin lines with arrowheads: the system trajectories for different concentrations of inducer 1 being added. Circles joined by a line: system’s final steady states as the concentration of inducer 1 increases from 4 nM to 800 nM with a step of 4 nM. In all cases, the concentration of inducer 2 being added is 20 nM. In line with winner-takes-all behavior, the switch with a lower inducer concentration (slower activation) is prevented from reaching a high-expression equilibrium. Co-activation is achieved when the timescales of activation are identical for both switches, i.e., f1 = f2 = 20 nM5. c A heterologous T7 RNAP transcribing its own gene exhibits non-cooperative self-activation. However, bistability arises due to the host cell growth rate’s susceptibility to resource competition and synthetic protein toxicity. Note that here the gene transcription rate does not scale with cell growth due to transcription being enabled by heterologous machinery46. d, e Depending on the initial condition, RNA polymerase concentration and cell growth rate converge to different steady-state values, indicatively of bistability. For both trajectories shown, the initial condition for heterologous mRNA levels is mt7(0 h) = 0. The parameters and ODEs used in simulations are given in Supplementary Notes S4.2.1 and S4.3.1 for (b) and (d, e), respectively. Source data are provided as a Source Data file.
