Neuron action potential (original)

An action potential is a short spike in a neuron's membrane voltage. Signals arrive at the dendrites and add up at the soma, and if the total is big enough a spike runs down the axon to the terminals. The simulation above solves the model numerically, and this section explains what the curves mean.

Anatomy of a neuron

• Dendrites: branching inputs that receive signals from other neurons at synapses.
• Soma (cell body): holds the nucleus and adds up all incoming signals. In the diagram its color is the live membrane voltage from the model.
• Axon hillock: the trigger zone where the axon leaves the soma. It has the highest density of voltage-gated Na⁺ channels, so this is where the action potential starts.
• Axon: the long output cable that carries the spike away from the cell body.
• Myelin sheath: fatty insulation wrapped around the axon by Schwann cells (or oligodendrocytes in the brain). It stops current leaking out between gaps.
• Nodes of Ranvier: the small bare gaps between myelin segments. Channels cluster here, so the action potential is regenerated at each node and appears to jump from node to node. This is called saltatory conduction and it can be up to 100 times faster than conduction in an unmyelinated axon.
• Axon terminals and synaptic boutons: when the spike arrives, Ca²⁺ flows in and the boutons release neurotransmitter across the synaptic cleft onto the next neuron.

Resting membrane potential

At rest the inside of the neuron sits at about V = -65 mV relative to the outside (the V₀ used to initialize this simulation). This voltage is set by the resting balance of sodium (Na⁺), potassium (K⁺), and leak currents flowing across the membrane, each pulling V toward its own reversal potential (E_Na = +50 mV, E_K = -77 mV, E_L = -54.4 mV in the model used here).

Depolarization and repolarization

Depolarization: When injected current (I_ext in the Stimulus panel) pushes V up past roughly -55 mV, voltage-gated sodium channels open rapidly. Because E_Na is far above resting potential, Na⁺ rushes in and V shoots up toward +40 mV: the overshoot visible as the sharp upward spike in the V(t) plot.

Repolarization: Sodium channels inactivate almost as quickly as they opened, while the slower potassium channels finish opening. K⁺ flows out (toward E_K = -77 mV), driving V back down. This is why the gK trace in the conductance plot peaks slightly after gNa.

Gating variables: m, h, and n

This simulation implements the full Hodgkin-Huxley model, tracking three voltage-dependent gating variables alongside membrane voltage V:

• m: the sodium activation gate. Opens quickly when V rises, driving the fast Na⁺ influx.
• h: the sodium inactivation gate. Closes shortly after m opens, shutting off the Na⁺ current and preventing V from staying high.
• n: the potassium activation gate. Opens more slowly than m, delaying the K⁺ outflow that repolarizes the membrane.

Each gate relaxes toward a voltage-dependent steady state at its own rate, governed by empirically-fit rate constants α(V) and β(V):

The resulting conductances scale with these gates raised to powers matched to the number of independent subunits Hodgkin and Huxley fit experimentally. This is exactly what the middle chart (gNa(t) · gK(t)) plots:

Membrane voltage then evolves according to the full current-balance equation, which this simulator integrates with 4th-order Runge-Kutta for numerical accuracy:

Threshold and the all-or-nothing principle

Sodium activation (m) is much faster than inactivation (h) or potassium activation (n), which creates a positive feedback loop: a small depolarization opens a few more Na⁺ channels, which depolarizes the membrane further, which opens still more channels. Below roughly -55 mV this feedback loses to the restoring leak and potassium currents and V relaxes back to rest: no spike. Above that threshold, the feedback runs away and produces a full-sized spike regardless of exactly how far above threshold the stimulus was. That's the all-or-nothing property: there is no such thing as a "half" action potential.

Refractory period

Right after a spike, h is still low (sodium channels are inactivated) and n is still high (potassium channels are still open), so the membrane resists firing again: this is the absolute refractory period. As h recovers and n relaxes back toward its resting value, a stronger-than-normal stimulus can trigger another spike: the relative refractory period. You can see this directly in the simulation: try firing single pulses in quick succession and watch the m/h/n plot to see why the second spike is delayed or suppressed if it comes too soon after the first.

Turn on Continuous Stimulus with a moderate I_ext to see repetitive firing, and watch the Spikes and Freq (Hz) readouts in the Live Values panel update as the neuron settles into a steady firing rate.