Each of the ~2,000 rendered cells is an independent cell-autonomous oscillator (its own transcription–translation feedback loop, e.g. Per/Cry) with a slightly different free-running period. Left uncoupled, individual SCN neurons drift out of phase with each other within days — exactly what happens in an SCN slice with the coupling neuropeptide VIP blocked. The model is the classic Kuramoto coupled-oscillator system:
dθ_i/dt = ω_i + K·r·sin(ψ − θ_i)
r·e^(iψ) = (1/N) Σ_j e^(iθ_j) (mean-field order parameter)
θi is each neuron's circadian phase, ωi its intrinsic angular frequency (2π / period, drawn from a normal distribution of width σ to model real cell-to-cell period variability of ~1–4 h). r ∈ [0,1] is the Kuramoto order parameter — 0 means phases are scattered uniformly (arrhythmic tissue), 1 means every neuron fires in lock-step (a sharp population rhythm). Mean-field coupling is mathematically exact for all-to-all coupling and is what lets thousands of instances update in real time.
- K — coupling strength standing in for VIP/GABA paracrine signaling between SCN neurons. Above a critical Kc ≈ 2σ the population spontaneously synchronizes; below it, noise wins and r collapses toward 0.
- σ — biological period heterogeneity across the nucleus. A wider spread needs proportionally more coupling to entrain.
- Light pulse — models retinal input via the retinohypothalamic tract: it nudges every neuron's phase a small step toward CT 0 (subjective dawn), the way light resets the master clock each morning.
- Scramble phases — models an SCN lesion / VIP-receptor knockout: phases are re-randomized so you can watch coupling re-synchronize the tissue from scratch.
Color encodes each neuron's own phase (its personal "time of day"): gold near subjective dawn, deep violet near subjective midnight. As r rises the color field visibly locks into a single sweeping band — the same desynchronization seen in aged or VIP-deficient mouse SCN explants, which lose amplitude and precision as their neurons drift apart.