Gardner-Collins 1999 bistable gene circuit — mutual repression and stochastic switching
Gardner, Cantor & Collins (2000, Nature 403) engineered E. coli with two mutually repressing promoters. Each gene's protein represses the other: du/dt = α/(1+(v/K)ⁿ) − δu; dv/dt = α/(1+(u/K)ⁿ) − δv. For n>1 this yields bistability — two stable fixed points separated by an unstable saddle. Noise causes rare but irreversible stochastic transitions, modeled by Langevin dynamics.