Stub your toe and a message races up your leg to your brain. Along the way it is carried by nerve cells that can send only one kind of signal: a brief electrical blip of fixed size. A gentle touch and a hammer blow produce blips of the same height. So how does the brain tell them apart? The answer sits in a beautiful piece of physics that Alan Hodgkin and Andrew Huxley worked out in 1952.
The simulation below runs their equations for the voltage across a nerve membrane. Press Zap to give it a 1-millisecond electrical nudge, and drag the strength slider. Try a weak zap first, then a strong one, then a stronger one still.
The dashed line marks roughly where a spike takes off. Green below is sodium channels, orange is potassium.
Zaps below about 7 on the slider just make the voltage twitch and settle back. Nothing is passed on. Zaps above that all produce the same spike, rising to about +40 millivolts from a resting level near −65. In the model, a zap of 30 peaks within a few millivolts of a zap of 8. The size of the stimulus has been thrown away.
The reason is positive feedback. A neuron's membrane is studded with sodium channels that open when the voltage rises. Sodium ions pour in, which pushes the voltage up further, which opens more channels. Once the nudge is big enough to win the race against the slow leak that pulls the voltage back to rest, the process runs away on its own, like a domino chain: it does not matter whether you tipped the first domino gently or hard.
The runaway cannot last. Two things happen in the following millisecond. The sodium channels have a second gate that slowly swings shut, so they inactivate even though the voltage is still high. Meanwhile, potassium channels open late and let potassium ions flow out, dragging the voltage back down, even slightly below rest. Watch the lower graph: the green sodium burst comes first and the orange potassium wave follows.
While the sodium gates are still recovering, the neuron cannot fire again, however hard you push. This is the refractory period, and it lasts around a millisecond or two. It also stops the spike from running backwards: the patch of membrane just behind the spike is still recovering, so the signal can only travel forward.
Use the Constant push slider. A weak steady push gives one spike or none. Push harder and the neuron fires a train of identical spikes, and the harder you push, the faster they come. Strength is not written in the height of the spike but in how often it repeats. With the refractory period setting the speed limit, a typical neuron cannot sustain more than a few hundred spikes per second.
Press the toxin button, then zap with the strength at its maximum. The voltage barely lifts. Tetrodotoxin, the poison found in pufferfish, plugs voltage-gated sodium channels, so the runaway never starts. That is why it paralyses: nerves and muscles can no longer pass on their signals. Here the toxin is only a switch in the equations, but the effect it shows is the real one.
A spike has to be regenerated all along the nerve, and that takes time. In thin, bare fibres it creeps along at about a metre per second or less. Many of our nerves are wrapped in fatty myelin with small gaps, so the spike jumps from gap to gap, and the fastest reach speeds above 100 metres per second. That is the difference between feeling your toe a moment late and feeling it almost at once.
Hodgkin and Huxley studied the giant axon of the squid, a nerve fibre thick enough to push a fine electrode down its middle. By holding the voltage at fixed values and measuring the currents, they worked out how the sodium and potassium channels opened and closed, and wrote it as four coupled equations. They shared the 1963 Nobel Prize in Physiology or Medicine for this work, with John Eccles. The simulation above uses their equations (in the modern sign convention, with rest near −65 mV) and was written for this page.