Relatively slow stochastic gene-state switching in the presence of positive feedback significantly broadens the region of bimodality through stabilizing the uninduced phenotypic state
Fig 2
Bistability with and without stochastic operon-state switching.
(A) Deterministic bifurcation diagram for wild-type cells. There are two saddle-node bifurcations occurring around Ie = 10μM and 59μM. (B) Deterministic bifurcation diagram containing both the active transcriptional rate kM and the extracellular inducer concentration Ie. The wild-type cells exhibit deterministic bistability inside the parameter region between the blue and brown lines and exhibit monostability otherwise. (C) Deterministic bifurcation diagram of the mutant cells without positive feedback. (D)(E) Deterministic bifurcation diagrams with different association constants for the repressor bound to the operon in the absence of a DNA loop: 5 molec.−1 (D), 8 molec.−1 (E). (F) Stochastic hysteresis response of the probability of induction for wild-type cells. Initial conditions: uninduced (blue line) or fully induced (red line) cells with a period of T = 2000 min. The extracellular inducer concentration must exceed over 350μM to completely activate initially uninduced cells, whereas it must decrease below 10μM to completely deactivate the initially induced cells. See S1 Text for parameter values.