Home▸Biology & Life▸Stem Cell Differentiation (Waddington Landscape)

🧫 Stem Cell Differentiation (Waddington Landscape)

Cells roll as particles down a Waddington epigenetic landscape under noise and gradient forces, settling into fate valleys — a physical metaphor for how gene networks commit stem cells to lineages.

Biology & Life2DModerate60 FPS

How it Works

The canvas renders a scalar height field h(x,y): a Gaussian hill near the top of the canvas represents the pluripotent stem-cell state, and several Gaussian wells arranged near the bottom represent distinct differentiated fates. Between them a gentle overall downward slope biases every cell to eventually leave the peak. Colour encodes height directly, from bright purple at the summit through the mid-tones down to warm valley floors, so the topography of the epigenetic landscape is visible at a glance.

Each cell particle obeys overdamped Langevin dynamics: its velocity is proportional to the negative gradient of the height field, estimated numerically by sampling h at nearby points, plus an independent Gaussian random kick every frame scaled by the noise slider. Because the gradient alone would send every particle down the exact same deterministic path, it is the noise term that lets genetically identical starting cells stochastically diverge into different valleys, exactly as real gene-regulatory network noise lets identical stem cells commit to different lineages. A signaling bias term adds a linear tilt to the whole landscape, mimicking a morphogen gradient that statistically favours one fate valley over the others.

h(x,y) = A_peak·G_peak(x,y) − Σ A_valley·G_i(x,y) + bias·x + slope·y
∇h ≈ ( [h(x+ε,y)−h(x−ε,y)] / 2ε , [h(x,y+ε)−h(x,y−ε)] / 2ε )
v = −mobility·∇h + noise·N(0,1)
x(t+dt) = x(t) + v·dt

About this simulation

A cluster of identical white dots is spawned at the purple summit and, frame by frame, tumbles downhill along the negative gradient of the height field while random noise jostles each one sideways. Watching two dots that started a pixel apart peel off toward completely different valleys is the whole point — it is stochastic cell-fate commitment made visible.

🔬 What it shows

An analytic height field rendered as a top-down colour map, with a pluripotent peak and 2–5 fate valleys, and particles that integrate noisy gradient-descent dynamics (Langevin motion) until they settle permanently into one basin.

🎮 How to use

Use Spawn Cells to release a fresh batch from the peak, click near the top of the canvas to drop individual cells, tune Noise, Steepness, Number of Fate Valleys and Signaling Bias, and press P/R to pause/reset.

💡 Did you know?

Conrad Waddington first drew his epigenetic landscape in 1957, decades before anyone could measure single-cell gene expression — modern single-cell RNA sequencing has since shown real cells really do move through valley-like attractor states much as his sketch predicted.

Frequently asked questions

What is the Waddington landscape?

The Waddington landscape is a metaphor introduced by biologist Conrad Waddington that pictures cell development as a ball rolling down a hilly surface from a high, pluripotent starting peak into one of several low valleys, each valley representing a stable differentiated cell fate.

Why do identical starting cells end up in different valleys?

Gene expression is noisy at the molecular level, so even genetically identical cells experience random fluctuations. In this simulation that noise is modelled as Gaussian jitter added every step, which can push otherwise identical particles into different basins of attraction on the same landscape.

What does the landscape steepness slider control?

Landscape steepness scales the height of the central peak and the depth of the fate valleys. A steeper landscape produces stronger gradient forces, so particles commit to a valley faster and are less easily knocked between basins by noise.

What does the signaling bias slider represent?

Signaling bias tilts the entire landscape toward one side, mimicking a morphogen or growth factor gradient in real development that makes certain fate valleys energetically more favourable, biasing which lineage a cell is statistically more likely to commit to.

What happens once a particle reaches a valley floor?

Once a particle's height and position match one of the valley basins near the bottom of the canvas, it is marked as settled, recolored to match that fate, and stops moving, representing a terminally differentiated cell that has committed to a stable lineage.

⚙ Under the hood

Cells roll as particles down a Waddington epigenetic landscape under noise and gradient forces, settling into fate valleys — a physical metaphor for how gene networks commit stem cells to lineages.

Canvas 2DWaddington LandscapeStem CellsCell FateLangevin Dynamics

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install