The Action Potential and Conduction

In 1939 Alan Hodgkin and Andrew Huxley pushed a fine electrode down the inside of a squid giant axon and found that, at the peak of the action potential, the inside became positive.

The leading theory held that an impulse was the membrane briefly losing its selectivity, so the voltage should have stopped near zero. It overshot. Something let positive charge in faster than it could leak out, then reversed. What that something is explains threshold, refractoriness and speed.

The idea: clamp the voltage and the currents show themselves

An action potential is a loop: depolarization opens channels whose current depolarizes further. Break the loop with the voltage clamp: a feedback amplifier holds the membrane at a commanded voltage and supplies whatever current that takes, which equals the current crossing the membrane. Kenneth Cole, working with George Marmont, developed the method in the late 1940s; Hodgkin, Huxley and Bernard Katz built their own version for the squid giant axon and published their records in the Journal of Physiology in 1952.

Here Vm is inside minus outside and outward current is positive. The 1952 papers used the opposite signs for both, so flip them when you read the originals.

Step the clamp from rest to a depolarized level and the record has two parts. First comes a brief surge that charges the membrane. The bilayer is a capacitor (see membrane structure and function), and capacitive current, Cm × dV/dt, flows only while the voltage is changing. Once the voltage is steady it is gone, and what remains is ionic current. In the squid axon, steps of about 15 to 110 mV gave an early, transient inward current followed by a delayed outward current that lasted as long as the step. At constant voltage the currents still rise and fall, so the conductances change with time.

Two currents, two ions

A waveform does not say which ion carries it. Hodgkin and Huxley used two tests. In ion substitution, they replaced most of the sodium in the sea water with choline, a cation the membrane passes poorly: the early current reversed, while the delayed outward current was little affected. The reversal potential, the voltage at which a current changes sign, moved for the early current with external sodium as expected for a current carried by sodium. So the early current was assigned to Na+, and the sodium-independent delayed current to K+.

Every current here obeys one rule, met in the resting membrane and passive signals:

I_ion = g_ion × (Vm − E_ion)

The conductance g says how open the path is. The driving force, Vm − E_ion, the gap between the membrane potential and the ion’s equilibrium potential, says which way the ion is pushed and how hard. E_ion comes from the Nernst equation, derived in transport across membranes.

Worked problem. Take a model squid axon under an ideal clamp, outward current positive, E_Na = +50 mV and E_K = −77 mV (the Hodgkin-Huxley model constants once rest is placed at −65 mV). The conductances are illustrative round numbers, not readings from a published figure. Step from −65 mV to 0 mV.

Step 1: the early current. Suppose g_Na peaks at 20 mS/cm². The driving force is 0 − 50 = −50 mV, so

I_Na = 20 mS/cm² × (−50 mV) = −1000 µA/cm², inward

A millisiemens times a millivolt is a microampere, so the units are current per square centimetre.

Step 2: the late current. Suppose that at 5 ms g_K is 15 mS/cm². The driving force is 0 − (−77) = +77 mV, so

I_K = 15 mS/cm² × 77 mV = +1155 µA/cm², outward

Step 3: take the sodium away. Cut external Na+ to 10% with choline, at 6.3 °C. A tenfold fall shifts E_Na by 2.303RT/F, which at 279.45 K is 55.4 mV, so E_Na moves to −5.4 mV. Assume, as a simplification, that g_Na is unchanged. Then

I_Na = 20 mS/cm² × (0 − (−5.4) mV) = +108 µA/cm²

The early current is now outward, because 0 mV lies above the new E_Na: the reversal the choline experiments showed.

Step 4: the capacitive part. On the plateau dV/dt = 0, so all the current the clamp supplies is ionic.

The conductance model and what it predicts

Sodium conductance rose quickly and then declined during a maintained step; potassium conductance rose late and stayed up. Hodgkin and Huxley drew the membrane as a capacitor in parallel with sodium, potassium and leak conductances, and fitted the conductances with three variables:

g_Na = g_Na,max × m³ × h and g_K = g_K,max × n⁴

Each variable runs from 0 to 1 and relaxes toward a voltage-dependent value with first-order kinetics. Depolarization drives m (sodium activation) up quickly, h (the fraction of the sodium system available) down more slowly, which is inactivation, and n up slowly. The 1952 model used g_Na,max = 120 mS/cm², g_K,max = 36 mS/cm², leak 0.3 mS/cm² and Cm = 1 µF/cm², with rates for 6.3 °C scaled by 3 per 10 °C.

These are formal variables, not proposed proteins: the powers were chosen to fit the S-shaped onset of the currents, and the equations describe conductances without proving how a gate works. Voltage sensors and inactivation machinery were found later in channel proteins; see ion channels as receptors.

Now let the model run unclamped. Past threshold, m climbs, Na+ flows in, and Vm rises toward E_Na, which raises m further: the rising phase. Vm peaks short of +50 mV because h is already falling and n rising. Inactivation then shuts off the sodium current while potassium current drives Vm down: the falling phase. Because n falls slowly, g_K stays raised and pulls Vm toward E_K at −77 mV, below rest: the undershoot.

The model has no Na+/K+ pump, yet it repolarizes; the pump restores gradients over many spikes.

The equations passed tests they were not fitted to. They reproduced the squid action potential’s shape and refractoriness with fair accuracy, and for one fibre at 18.5 °C predicted conduction at 18.8 m/s against 21.2 m/s measured. That speed belongs to an axon about half a millimetre across. The model also predicts blockers: remove most of g_K and the spike broadens; remove g_Na and there is no spike, though the resting potential survives.

Threshold and refractoriness come from the sodium gates

A small depolarization opens a few sodium channels, but outward potassium and leak current wins. A larger one opens enough sodium channels that inward current exceeds outward current; then each millivolt opens more channels and the response runs away. Threshold is where net ionic current turns inward. It is not a fixed voltage. A slow depolarization inactivates sodium channels and raises g_K, so threshold rises; in conductance-based models, Platkiewicz and Brette (2010) showed that threshold can depend on stimulus history through sodium inactivation. A figure such as −55 mV belongs to one cell under one protocol.

After a spike most sodium channels are inactivated. During the absolute refractory period no stimulus, however strong, triggers a second spike, because too few sodium channels are available. As h recovers, the relative refractory period begins: a spike needs a stronger stimulus than at rest, because some channels are still inactivated and g_K is still raised. In one squid axon at 4.5 °C, Hodgkin and Huxley found sodium-current recovery roughly exponential with a time constant near 12 ms: one cold axon, not a general value.

Inactivation is not deactivation. Repolarize early in a step and the sodium current shuts off at once as m falls, leaving channels ready to reopen; inactivated channels stay unavailable until h recovers, which paired pulses at varying intervals reveal. Refractoriness also stops an impulse from turning back on itself, because the membrane just behind it cannot be re-excited; a stimulus applied mid-axon sends impulses both ways.

Propagation: diameter, myelin, blockers and demyelination

An impulse travels because its inward current spreads along the axon’s core and brings the next stretch of membrane to threshold. How far that current reaches is set by the length constant, the distance over which a steady voltage change decays to about 37% of its starting size.

A wider axon has lower internal resistance, so current spreads farther; in unmyelinated axons velocity rises roughly with the square root of diameter. Myelin, glial membrane wrapped around the axon (myelination covers how it is made), raises the resistance and lowers the capacitance of each internode, the wrapped stretch between gaps, so less current leaks and less charge is needed. At the gaps, the nodes of Ranvier, sodium channels regenerate the spike. Huxley and Robert Stämpfli found evidence for this saltatory conduction in single frog fibres in 1949. The impulse does not leap: each node drives current to the next, which fires in turn. Nor is the internode sealed: in rat cortical axons, recordings, electron microscopy and cable models support a conductive pathway beneath the myelin (Cohen and colleagues, 2020). In myelinated fibres velocity rises roughly in proportion to diameter. In mammalian nerves, conduction velocities run from about 0.6 m/s in the smallest fibres to about 115 m/s in the largest myelinated ones (Gasser), with exact values depending on species and temperature.

The squid is not every neuron. In rabbit nodes recorded at 14 °C, potassium current is almost entirely absent and leak accounts for repolarization after the brief sodium current (Chiu, Ritchie and colleagues, 1979). Tetraethylammonium (TEA) can abolish the delayed potassium current of frog nodes (dissociation constant near 0.4 mM; Hille, 1967). Tetrodotoxin (TTX) blocked the action potential of lobster giant axons while sparing the resting potential (Narahashi, Moore and Scott, 1964), with an apparent dissociation constant of about 1 nM at frog nodes (Hille, 1968).

Demyelination strips the sheath from an internode. In rabbit sciatic fibres, acute demyelination raised internodal leak conductance and capacitance (Chiu and Schwarz, 1987), so current reaches the next node late or too weak: conduction slows or blocks. It does not always block. Bostock and Sears (1978) found continuous conduction along bare internodes of rat ventral roots at 1.1 to 2.3 m/s. Multiple sclerosis damages central myelin and Guillain-Barré syndrome peripheral nerve; neurodegeneration covers disease, and synaptic transmission picks up the impulse at the terminal.

Design problem

In an invented experiment, stimulate a nerve at two sites 10 cm apart and record the compound response at a fixed electrode. The latency difference is 2.0 ms. After a 1 cm demyelinating lesion between the sites it is 7.0 ms, and the response is half as large. Find the velocity before and within the lesion, interpret the smaller response, and design a test of continuous conduction against slowed saltation.