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Hodgkin–Huxley equation

The Hodgkin-Huxley model is a set of equations describing how ion currents generate action potentials in neurons.
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Description

Until the 1950s, the mechanism of the nerve impulse remained a mystery. It was known that there was an electrical spike, but not how ions created it. Alan Hodgkin and Andrew Huxley experimented on the giant axon of the squid—its thickness allowed the insertion of electrodes. They measured the currents of sodium and potassium ions and built a mathematical model. It describes the membrane as a capacitor and ion channels as voltage-gated resistors. The equations include variables m, h, n—these are the 'gates' of the channels, which open and close depending on voltage. The model accurately reproduces the shape of the action potential—that very impulse. It was a breakthrough: for the first time, a biological process was described with engineering precision.

History

In 1952, British physiologists Alan Hodgkin and Andrew Huxley published a series of papers presenting a mathematical model of the nerve impulse. Working at the Plymouth Marine Laboratory, they used the giant axon of the squid Loligo forbesi. Using the voltage clamp technique, they separated the sodium and potassium currents and described their kinetics. For this discovery, they received the Nobel Prize in Physiology or Medicine in 1963 (jointly with John Eccles). The model became the foundation of computational neuroscience.

How it works

The model is used to simulate neural networks, study epilepsy, cardiac arrhythmias, and the action of anesthetics. It works for any excitable cell provided the types of ion channels are known. Limitations: the model describes only spiking activity, does not account for dendritic integration and slow metabotropic processes; accurate modeling of real neurons often requires modifications with additional currents.

In practice

The model underpins all modern neural implants and pacemakers, where the electrical response of excitable tissue must be precisely calculated.

Fun fact

Hodgkin and Huxley used the squid because it has a giant axon nearly a millimeter in diameter—hundreds of times thicker than a human's. Electrodes could be inserted without killing the cell. The squid became a star of neuroscience.

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