Extended Data Fig. 1: Schematic illustration of the design of the mutual repressive circuit and demonstration of bistability.

(a) This circuit consists of reciprocal transcriptional repression by TetR and LacI. mCherry and GFP serve as reporters for TetR high state and LacI high state, respectively. The addition of cTc relieves TetR repression, allowing for high expression of LacI and GFP, whereas induction with IPTG relieves the LacI repression, allowing for high expression of TetR and mCherry. (b-c) Temporal histograms of cell states under exponential growth in RDM glucose medium following prolonged culture via successive dilution to demonstrate the irreversibility of cellular states. Owing to the fluctuations in gene expression, a small population (~ 10%) of post-inducted red state cells (that is, low GFP state) was observed to spontaneously switch to the green state (that is, high GFP state) within 20 generations (as indicated in panel d). (e, f) Hysteresis experiments were carried out by measuring the dose-response curves in varying cTc concentrations under fast and slow growth conditions (see Methods). Red and green symbols represent initial red state cells and initial green state ones, respectively. (e) A large range of hysteresis was revealed in RDM glucose medium. The bifurcation diagram calculated from the deterministic model in varying inducer concentrations with a given growth rate is shown. The red curves show the ensembles of red states, the green curves show the ensembles of green states, and the black dashed lines suggest the calculated saddle points which are unstable. The appearance of bimodal distributions in the range of 0.1 to 1.0 ng/mL cTc concentration is supposed to be the gene expression fluctuations in proximity to the bifurcation point (blue arrows in the right panel). (f) A loss of bistability was confirmed in MOPS acetate medium without inducer. The hysteresis experiment shows that the bistable range is significantly reduced in the MOPS acetate medium.

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