The nerve's digital pulse. Push the membrane past threshold and it fires a spike that is all-or-none: full size or nothing, the same size every time, no matter how hard you push. And it regenerates — unlike a passive cable's decaying exp(−x/λ) spread, the spike rebuilds itself at constant amplitude down the whole axon, and myelin makes it leap node-to-node, far faster. Stimulus goes in, the excitable membrane decides, a proven spike comes out.
source J. Bernstein, membrane theory of the action potential (1902); A. L. Hodgkin & A. F. Huxley, A quantitative description of membrane current…, J. Physiol. 117:500–544 (1952), doi:10.1113/jphysiol.1952.sp004764. Rendered, not quoted. Biophysical model — parameters illustrative.
The membrane is not a wire; it is excitable. A recovery variable and a cubic reaction term (FitzHugh–Nagumo, the reduced Hodgkin–Huxley) give one stable rest state and a threshold. Below threshold, a nudge decays back. Above it, positive feedback (Na+ in) blows up to a fixed peak, then recovery (K+ out) drags it home — always the same excursion.
Live phases of the current spike, read off the trace:
| phase | value |
|---|
All-or-none and self-propagating at constant amplitude — unlike the passive the-cable-equation, whose signal dies as exp(−x/λ). The spike is the pulse that the-hodgkin-huxley gates generate, sped by myelin's saltatory jumps, and spaced in time by the-refractory-period.
Passive spread carries the sub-threshold vote; the action potential is the decision that survives the whole axon. Each sphere is the next one's premise.
The blue team's live check: re-derive amplitude vs. stimulus, propagated peaks, and saltatory velocity from the equations and confirm they match the known biophysics. If red makes the spike graded, this badge is where it shows.
One knob: a brief stimulus that depolarizes the membrane from rest. In model units 0 → 1, mapped to millivolts by −70 + 110·v, so rest = −70 mV, threshold ≈ −55 mV (v = 0.13), spike peak ≈ +35 mV.
The membrane sees only one question: did the stimulus cross threshold? Everything downstream is binary. That is the whole game — and it is what you feed the panel below.
Myelinated: the spike leaps node-to-node (saltatory) — far faster for the same diameter.
Membrane potential vs. time (mV). Dashed = threshold. Try any stimulus above threshold — the peak barely moves.
Move the stimulus — the spike is integrated from the equations on the spot, never looked up. Above threshold the amplitude is constant; that is the all-or-none law.
What the machine produces, proven: a spike that is all-or-none (a 4.5× stronger stimulus grows the peak by <10%), self-propagating at constant amplitude (regenerated, not decayed like exp(−x/λ)), saltatory — myelin conducts faster than a bare fibre of the same diameter — and followed by a refractory gap that caps the firing rate at 1/tref.
The blue team's witness (left) re-derives these live; the red team (right) tries to make the spike graded.
FitzHugh–Nagumo is the reduced model: it captures excitability and the limit cycle but collapses HH's four gating variables to two. It gets the phenomenology right and the exact kinetics wrong — good for the logic of the spike, not for a voltage-clamp fit.
"A bigger stimulus makes a bigger spike." Cut. That is a graded potential (dendrites, receptors). The axonal action potential is all-or-none — above threshold the peak is fixed; the engine shows <10% drift over 4.5×.
"The signal fades as it travels, so nerves must amplify." Cut. It does not fade — it regenerates. Passive spread fades (exp(−x/λ)); the AP rebuilds full amplitude at every patch.
"Myelin speeds signals by insulating a faster wire." Kept, corrected. It speeds them by letting the spike skip — regenerating only at nodes of Ranvier (saltatory), not by a lower-loss cable alone.
The red team's move: make the spike graded — amplitude proportional to the stimulus, like a passive potential. Then it is no longer all-or-none and it attenuates as it propagates. The blue team's witness (window 7) is watching.
Flip the spike to graded and two laws break at once: amplitude tracks the stimulus, and propagated peaks decay with distance. The witness re-derives, disagrees, and turns red. Nothing is faked; the attack is real and it is caught.