Bacterial Quorum Sensing — Bistable Switch

Controls

Cell density N: 200 Autoinducer threshold K: 0.5 Production rate α: 1.0 Degradation rate γ: 0.3 Hill coefficient n: 4

LuxI/LuxR model:
dA/dt = α·N·f(A) - γ·A
f(A) = Aⁿ/(Kⁿ + Aⁿ) (Hill fn)

Bistable switch: two stable fixed points (OFF/ON). The transition depends on N crossing a critical density N*.