GATA1–PU.1 Toggle Switch: Building a Waddington Landscape from a Gene Circuit

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

How it works

Each of the many small spheres 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. When n is large enough this system is bistable: besides the unstable symmetric point G≈P, two stable attractors exist — high-GATA1/low-PU.1 (erythroid) and low-GATA1/high-PU.1 (myeloid). This mutual-repression motif is the well-studied core of the real GATA1–PU.1 circuit that commits hematopoietic progenitors to a lineage (Huang, Ingber and colleagues, 2007); the biological circuit adds self-activation loops that sharpen the switch further, omitted here to keep the two-variable dynamics visible.

The 3D terrain is not hand-drawn. Every simulated cell's (GATA1, PU.1) position is continuously binned into a 2D histogram; the height at each point is the quasi-potential U = −ln(P_ss), the negative log of the population's visitation density — exactly the numerical procedure used to reconstruct a real Waddington landscape from a gene-network model (Wang, Zhang & Jiao, 2011). Basins appear where cells accumulate; ridges appear where they rarely linger.

Hill cooperativity n — below roughly n≈2 the system has only one fate (a single valley); raise it and the landscape splits into two basins.
Noise strength D — the stochastic kick each cell receives every step; higher noise lets committed cells occasionally hop the ridge between fates.
Signal bias — models an external cytokine skew (GM-CSF vs erythropoietin) that raises one production rate at the other's expense, 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

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