A genetic toggle switch is two genes that each repress the other (mutual repression). Protein A represses gene B; protein B represses gene A. With strong enough cooperativity, the circuit is bistable: it settles into an "A-high/B-low" or "B-high/A-low" state and stays there until strongly perturbed.
dA/dt = α / (1 + B^n) − γ·A
dB/dt = α / (1 + A^n) − γ·B
- Production rate α — maximum synthesis rate of each protein when fully de-repressed.
- Degradation rate γ — how fast each protein decays/dilutes; higher γ makes switching faster but populations smaller.
- Cooperativity n — Hill coefficient for repression; n≥2 is required for true bistability (below that, the circuit just settles to a single balanced state).
- Kick → A / Kick → B — injects a pulse of the named protein, mimicking an inducer chemical (like IPTG) that flips the switch to that state.
Real synthetic-biology toggle switches (Gardner, Cantor & Collins, 2000) work this way in engineered E. coli and are used as cellular memory elements — a foundational building block for genetic circuits and biosensors.