Stimulus vs. response profiles for generic bistable (A), hysteretic (B), and graded (C) gene expression switches and schematic representation of the model hysteretic gene network (D). (A) The most basic bistable expression switch enables a quasi-discontinuous expression change between two steady states. (B) Hysteretic expression switches require a stronger stimulus for quasi-discontinuous OFF-to-ON than for ON-to-OFF expression switches. (C)A graded expression switch converts increasing stimuli to increasing responses. (D) The transactivator TA induces its own expression by means of a positive feedback loop by binding to its cognate operator contained in the hybrid promoter P_hybrid. The constitutively expressed transrepressor TR also binds to P_hybrid, thereby inhibiting TA action. Interaction of TR with an antibiotic AB abolishes TR's transrepressor capacity. Varying AB concentrations result in different active transrepressor TR concentrations and can therefore be used to fine-tune the strength of the positive feedback control unit.

Parameter plot showing the dependence of the final [TA] on [AB] for different [TA]₀. [TA]₀ is crucial to determine the [AB] required to switch the system from OFF to ON. The numbers above the curve indicate for which [TA]₀ the final [TA] switches from OFF to ON. For example, a [TA]₀ of 0.08 requires an [AB] > 500 ng/ml AB for an efficient OFF-to-ON switch. Because [TA]₀ depends on the history of the system, the behavior is hysteretic.

Validation of hysteretic behavior (A) and reversibility of switching (B) of CHO-HYST₄₄. (A) CHO-HYST₄₄ populations, double transgenic for pWW198 and pBP228, were cultivated in the presence (+) and absence (-) of EM for 3 days to set SEAP expression to an ON (+EM) or an OFF (-EM) state. The cells were then reseeded under different [EM] and assessed for SEAP production after 48 h. CHO-HYST₄₄ populations with a cultivation history in EM-free medium (SEAP production OFF) required 1,000 ng/ml EM to switch SEAP production from an OFF to an ON state, whereas CHO-HYST₄₄ populations, cultivated in the presence of EM prereseeding (SEAP production ON), switched from an ON to OFF SEAP production state at 500 ng/ml EM. The simulated curves (normalized to expression data) are shown to demonstrate the accuracy of the mathematical model. The values of [TA]₀ used for the simulated profiles are 2.5 (+EM) and 0.045 (-EM). (B) CHO-HYST₄₄ populations (5 × 10⁴ cells) were cultivated in the presence (2 μg/ml EM, black diamonds, solid line) and absence (dotted line) of EM. The SEAP expression status (presence of EM, ON; absence of EM, OFF) was reversed and quantified on days 3 and 6 after culture medium exchanges.

Graphic plot of the left- and right-hand side of Eq. 4. For a given α (which indirectly represents transrepressor concentration [TR]), the fate of the hysteretic system is determined by [TA]₀. For [TA]₀ > a, the final [TA] is b; for [TA]₀ < a, the resulting [TA] is 0. For [TA]₀ = a, the resulting final TA remains at a, but small perturbations drive the system to either b or 0. (A) For very large α (corresponding to low [TR]), the stable point b is big and the unstable solution a is close to zero. (B and C) As α decreases (corresponding to an increase in [TR]), the two solutions a and b converge to coalesce into a single solution. (D) For sufficiently low α (high [TR]), the final [TA] is zero for any [TA]₀ because the line and the curve do not intersect.

Molecular configuration of the hysteretic synthetic mammalian gene network. The tetracycline-dependent transactivator tTA, a fusion of the E. coli TetR repressor and the Herpes simplex VP16 transactivation domain (TetR–VP16), binds to its cognate operator (tetO₇) and induces the P_hybrid (tetO₇-ETR₈-P_hCMVmin)-driven dicistronic expression unit encoding SEAP and tTA, which is translated by internal ribosome entry site (IRES)-mediated translation-initiation. The transrepressor E-KRAB, a fusion of the E. coli macrolide resistance operon repressor E and the human transsilencing domain KRAB (E-KRAB), is constitutively expressed (P_SV40-E-KRAB-pA) and binds to the ETR₈ operator in the absence of the regulating antibiotic EM, thereby repressing P_hybrid in a dose-dependent manner.

SEAP expression profiling of CHO-HYST₄₂ (A) and CHO-HYST₇ (B). (A) CHO-HYST₄₂ was cultivated in the presence (+) and absence (-) of EM for 3 days to set SEAP expression to an ON (+EM) or OFF (-EM) state. The cells then were reseeded under different [EM] and assessed for SEAP production after 48 h. The SEAP expression profile of CHO-HYST₄₂ shows residual hysteresis and marks a transition state from hysteretic to graded expression response. (B) CHO-HYST₇ is isogenic to CHO-HYST₄₄ yet harbors imbalanced composition of hysteretic network components. CHO-HYST₇ was cultivated in the presence (+) and absence (-) of EM for 3 days to set SEAP expression to an ON (+EM) or OFF (-EM) state. The cells then were reseeded under different [EM] and assessed for SEAP production after 48 h. Independent of their previous incubation (±EM), cells reached their maximal expression gradually, after an increase in [EM] from 0 to 2,000 ng/ml. The simulated curves (normalized to expression data, identical for + and -EM) are shown to demonstrate the accuracy of the mathematical model. The values of [TA]₀ used for the simulated curves are 62.5 (+EM) and 6.25 (-EM).