The 3D version of this sim couples every neuron to the population mean phase (a mean-field Kuramoto model) — every cell instantly "hears" the average of all ~4,000 others, so the whole cluster snaps into sync almost immediately once K is high enough. Real SCN neurons don't work that way: gap junctions and VIP/GABA signalling only reach nearby cells. This 2D sim models that directly as a local (nearest-neighbor) lattice of 336 phase oscillators laid out on an actual 2D tissue grid — each cell only ever couples to its up-to-4 physical neighbors.
dθᵢⱼ/dt = ωᵢⱼ + (K/nᵢⱼ)·Σ_neighbors sin(θₙ − θᵢⱼ) + L·sin(θ_light − θᵢⱼ)
r·e^(iψ) = (1/N) Σ e^(iθₖ) ← global order parameter (whole grid)
r_loc = ⟨ |mean neighbor phasor| ⟩ ← local coherence (each cell vs. its own neighbors)
Because information can only diffuse cell-to-cell, synchrony has to spread physically across the tissue as a genuine traveling phase wave, exactly as dorsal→ventral phase waves are observed by real-time PER2::LUC bioluminescence imaging of the SCN. This also means the two readouts on the left tell a different story: local coherence rises fast (neighboring cells lock quickly), while the global order parameter can stay low for a long time even after most of the grid is locally synchronized, because separate wave-fronts/domains with different phases can coexist and take much longer to merge — verified numerically below (a domain-wall test field gives r≈0 with local coherence≈0.97).
- Neighbor coupling K — how strongly each cell pulls toward its immediate neighbors' phase; too weak and domains never merge, too strong overcomes noise fast.
- Noise σ — spread of individual free-running periods around the human average of 24.2h; higher σ slows domain growth and can pin permanent phase boundaries.
- Light entrainment — unlike coupling, this term acts on every cell directly (it models the retinohypothalamic tract reaching the whole SCN, not cell-to-cell relay), so it can synchronize the grid to the light cycle even with K = 0.
- SCN ablation — sets K = 0: neighbor relay stops, so any local domains that already existed simply free-run apart at their own periods and dissolve (global r decays toward the chance level ~1/√N).
- Jet lag — shifts the light target 8h; the grid's phase visibly lags behind the new light cycle and slowly re-entrains, cell by cell, matching real transmeridional travel.