A battery made of ions
Inside a neuron there are lots of potassium ions K⁺, and outside lots of sodium ions Na⁺. These concentration differences are maintained by the sodium-potassium pump: for each ATP molecule it throws out 3 Na⁺ ions and pulls in 2 K⁺ ions. At rest the membrane lets through mainly K⁺, which leaks out and leaves the inside negatively charged — about −65 mV. The voltage at which a given ion stops flowing is described by the Nernst equation:
For K⁺ in the squid axon (400 mM inside, 20 mM outside) at 6.3 °C this gives about −72 mV, and for Na⁺ (50 mM and 440 mM) about +52 mV. The model uses the measured values EK = −77 mV and ENa = +50 mV.
An impulse step by step
- Threshold. The stimulus nudges the voltage up a little. The fast m gates of the sodium channels open, Na⁺ rushes in and pushes the voltage up even further — a positive feedback loop.
- Peak. For a moment the inside becomes positive (about +40 mV). The slower h gate plugs the sodium channels (inactivation).
- Repolarization. The n gates of the potassium channels open, K⁺ flows out and the voltage drops, even below the resting level.
- Refractory period. While the h gates are closed and the n gates open, a second impulse is impossible (absolute refractory period) or needs a much stronger stimulus (relative). This is why the impulse does not turn back.
All of this is described by one equation for the voltage and three for the gates:
Parameters: Cm = 1 µF/cm², ḡNa = 120 mS/cm², ḡK = 36 mS/cm², gL = 0.3 mS/cm², EL ≈ −54.4 mV, temperature 6.3 °C. We compute with the 4th-order Runge–Kutta method and a step of 0.01 ms.
All or nothing: a stimulus below the threshold gives a small bump in voltage; above it, a full impulse of almost the same height, whatever the stimulus strength. (Strictly speaking, in the HH model the threshold is extremely steep but continuous.)
Conduction in the axon
An excited patch of membrane passes current along the axon and excites its neighbor. Without myelin, speed grows roughly with the square root of the diameter (v ∼ √d) — which is why the squid has an axon as thick as 1 mm. Vertebrates came up with myelin: insulation that reduces current leakage and membrane capacitance. The impulse arises only at the nodes of Ranvier and jumps between them (saltatory conduction), and speed grows roughly in proportion to the diameter.
| Fiber | Speed |
|---|---|
| Unmyelinated C fibers (dull pain, temperature) | 0.5–2 m/s |
| Squid giant axon (18.5 °C) | about 20 m/s |
| Myelinated Aα fibers (muscle movement) | 80–120 m/s |
Synapse and summation
When an impulse reaches the axon terminal, Ca²⁺ flows into the bouton, and vesicles spill neurotransmitter into the synaptic cleft (about 20 nm). The molecules bind to receptors, which open ion channels. Glutamate lets in Na⁺ and produces an EPSP (excitation); GABA lets in Cl⁻ and produces an IPSP (inhibition). The neuron “counts” — it adds up these signals and fires only when the voltage at the axon hillock crosses the threshold.