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

Gene-Circuit Parameters

Hill cooperativity n 4.0

Noise strength D 0.15

Signal bias (GM-CSF ↔ EPO) 0.00

Population State

Erythroid

Myeloid

Progenitor

100%

Mean GATA1

0.00

Mean PU.1

0.00

Sim. time (τ)

0.0

Cells tracked

Erythroid fate (GATA1-high) Myeloid fate (PU.1-high) Uncommitted progenitor dG/dτ = 0 nullcline dP/dτ = 0 nullcline

How it works

Each dot is a virtual blood progenitor cell, described by the levels of two mutually antagonistic transcription factors: GATA1 (drives the erythroid/red-cell fate) and PU.1 (drives the myeloid fate). Each represses the other's production through a cooperative (Hill-type) regulatory step — the classic "double-negative feedback" or genetic toggle switch:

dG/dt = a1 / (1 + (P/k)^n) − G + noise
dP/dt = a2 / (1 + (G/k)^n) − P + noise

G = GATA1, P = PU.1, k = repression threshold, n = Hill cooperativity, a1/a2 = maximum production rates. This 2D version plots the population directly in the (G, P) phase plane instead of a 3D terrain. The background colour is the same quasi-potential U = −ln(P_ss) computed live from the population's own 2D visitation histogram, rendered here as a flat heatmap rather than an extruded surface. On top of it, two curves are drawn from the closed-form nullcline equations G = a1/(1+(P/k)^n) and P = a2/(1+(G/k)^n) — the loci where each gene's rate of change is exactly zero. Where the two nullclines cross are the system's fixed points; the population's histogram basins should line up with the stable crossings, which is a direct, checkable link between the analytic phase-plane picture and the empirical landscape.

Hill cooperativity n — below roughly n≈2 the two nullclines cross only once (a single valley); raise it and a third, bistable crossing pair appears off the diagonal.
Noise strength D — the stochastic kick each cell receives every step; higher noise lets committed cells occasionally hop the separatrix between fates.
Signal bias — models an external cytokine skew (GM-CSF vs erythropoietin) that raises one production rate at the other's expense, sliding the nullclines and tilting the landscape toward one fate.
Release progenitor cohort — restarts all cells at the shared, near-symmetric progenitor state so you can watch differentiation happen live.

Quasi-potential U = −ln(density) +Committed cells