Genetic Toggle Switch: Stochastic Noise-Induced Switching (2D)

The genetic toggle switch — two mutually-repressing genes forming a synthetic-biology flip-flop (Gardner, Cantor & Collins, 2000) — is usually taught through its deterministic Hill-function ODE, which produces two permanently stable states. Real cells don't run on smooth concentrations, though: they run on discrete, small numbers of actual protein molecules being synthesized and degraded one at a time. This 2D simulator replaces the ODE integrator with a tau-leaping stochastic simulation of the underlying chemical master equation, tracking each cell's integer repressor-A and repressor-B molecule counts as an independent random walk. Adjust promoter strengths and cooperativity as before, but now also dial the system size Ω — the molecule-count scale — down to watch cells spontaneously hop between the two stable basins from pure molecular noise, or up to watch that noise vanish and the population freeze into the deterministic picture, with every spontaneous basin change tallied live.