Sinoatrial (SA) node pacemaker cells never sit at a stable resting potential. After each action potential they undergo a slow diastolic depolarization that autonomously drifts the membrane back up to threshold — this is cardiac automaticity, the "membrane clock".
C_m dV/dt = -(I_f + I_CaT + I_K + I_leak)
I_f = g_f · y · (V - E_f) HCN channels, activate on hyperpolarization
I_CaT = g_CaT · d∞(V) · f · (V - E_Ca) low-threshold Ca²⁺ window current
I_K = (g_K · n + g_KACh) · (V - E_K) delayed rectifier (+ vagal I_K,ACh), slow gate n
dy/dt = (y∞(V) - y) / τ_y, y∞(V) = 1 / (1 + exp((V - shift + 64)/13.5))
df/dt = (f∞(V) - f) / τ_f slow Ca²⁺ inactivation, closes the window at depolarized V
dn/dt = (n∞(V) - n) / τ_n(V) the slow gate that forces repolarization
- If ("funny current") — carried by HCN (hyperpolarization-activated cyclic-nucleotide-gated) channels. Unusually, it activates on hyperpolarization rather than depolarization and carries a small mixed Na⁺/K⁺ inward current that ramps up during diastole, pulling Vm toward threshold.
- ICa,T — a low-threshold T-type Ca²⁺ current whose fast activation and slower inactivation overlap near -40 to -20 mV, giving a window current that reinforces the ramp and then drives the regenerative upstroke once threshold is crossed.
- IK deactivation — the delayed-rectifier K⁺ current that repolarized the previous beat slowly turns off during diastole, "unmasking" the net inward current — the classic second contributor to the membrane clock alongside If.
- HCN density slider — scales gf directly, mimicking channel expression/availability.
- Sympathetic tone — noradrenaline (via cAMP) shifts If's activation curve to less negative voltages and boosts gf, steepening the ramp → faster rate (the real mechanism behind exercise/adrenaline tachycardia).
- Vagal tone — acetylcholine opens IK,ACh, an extra outward K⁺ conductance that hyperpolarizes the cell and flattens the ramp → slower rate (real vagal bradycardia).
- Ivabradine — a real clinical drug that selectively blocks HCN channels from inside the pore, cutting If and slowing heart rate without affecting contractility — used to treat inappropriate sinus tachycardia and chronic heart failure.
Gating kinetics and conductances here are a reduced, illustrative parameterization (not a full ionic model like DiFrancesco-Noble) chosen to reproduce the correct qualitative and rate-order-of-magnitude behavior of the real coupled "membrane clock" mechanism. This 2D view integrates the identical ODE system as the 3D version, plotted as a live oscilloscope trace.