Bistable Genetic Toggle Switch
Kramers escape and noise-driven switching between attractors
Switching rate: —
The Gardner-Collins toggle switch (2000): two repressors u,v mutually inhibit.
du/dt = α/(1+v^β) - γu. Bistable for α^(1/β) > γ.
Noise (gene expression fluctuations) drives Kramers escape: k ~ exp(-ΔU/D).
The barrier height ΔU determines memory fidelity. High noise → frequent switching;
low noise → stable cell-fate commitment. The landscape is the quasi-potential U(u).