This top-down 2D companion swaps the single-oscillator view of the SA node for a population of ~110 independently modelled pacemaker cells scattered across the node's own footprint — an independent pulse-coupled-oscillator model (Peskin 1975; Mirollo–Strogatz 1990) from the companion 3D single-cell simulator. Each cell still obeys the same diastolic-ramp physiology:
V_i(t) = MDP_i + slope_i · t (diastole)
fires when V_i ≥ V_threshold → depolarizes, then resets to MDP_i
but every cell carries its own intrinsic slope and MDP, randomly offset by up to ±35% / ±3 mV — real functional heterogeneity documented across the SA node (Boyett et al., 2000 "mosaic" model). Left uncoupled, these cells would fire at wildly different, uncorrelated rates. What makes the tissue beat as one is electrotonic coupling through gap junctions: when a cell fires, it sends a depolarizing kick to every other cell, delayed by the real distance divided by the node's slow ~3 cm/s conduction velocity —
V_j += coupling · exp(−distance/λ) · (V_threshold − V_j), arriving at t + distance/v_conduction
— and this kick can only ever nudge a cell part-way to threshold, never past it. Turn electrotonic coupling down and the cells desynchronize into independent, unrelated rhythms (numerically verified: with coupling near zero, each cell's simulated firing period matches its own closed-form period to within 0.1%, and cell-to-cell period variability stays high). Turn it up and the whole population locks onto a single common rate driven by its fastest cell — the real phenomenon of mutual entrainment, verified here by the coefficient of variation of firing periods collapsing from double digits toward zero as coupling increases.
Vagal (ACh via IKACh and reduced cAMP) and sympathetic (β1/cAMP) tone still hyperpolarize/depolarize every cell's MDP and flatten/steepen its slope exactly as in the single-cell model, so heart rate still falls or rises the same way — but here it emerges from thousands of individual firing events, not a single timer. Leading pacemaker site tracks which cell's firing starts each beat's cascade — under strong vagal tone the fastest available cell (and hence the leading site) can shift within the node, a real phenomenon reported clinically as pacemaker-site migration with autonomic tone.