Toggle Switch: Phase-Plane Molecule-Count Model (2D)

The 3D version of this simulator reduces the genetic toggle switch to a single order parameter rolling on a double-well landscape. This 2D counterpart instead simulates the real underlying chemistry directly: two mutually-repressing genes with true integer protein molecule counts, evolved cell-by-cell with a tau-leaping approximation of the Gillespie stochastic simulation algorithm on the actual birth-death chemical master equation. The phase plane shows every cell's live (A,B) molecule counts against the circuit's real nullclines and fixed points, and a Kramers/WKB escape-time estimate — re-derived for this discrete, shot-noise-driven model rather than reused from the continuous Langevin picture — is tracked live against the observed switching statistics as you tune molecule copy number, promoter strength and population size.