GATA1–PU.1 Toggle Switch: Phase-Plane Waddington Landscape

Conrad Waddington's 1957 epigenetic landscape pictures a stem cell as a ball rolling downhill into branching fate valleys — a beautiful metaphor, but usually drawn by hand. This 2D companion simulation builds the landscape directly in the GATA1–PU.1 phase plane: a population of virtual blood progenitors, each carrying two mutually repressing transcription factors, integrated as a stochastic gene-regulatory circuit. Their visitation statistics are converted live into a quasi-potential heatmap, and the two genes' analytic nullclines are drawn on top so you can watch the empirical basins line up with the closed-form fixed points. Tune the Hill cooperativity to switch the landscape between one basin and two, add noise to watch committed cells occasionally jump the separatrix, bias the signal to skew outcomes toward the erythroid or myeloid fate, and release a fresh progenitor cohort to watch the whole differentiation process unfold from scratch.