A Quantitative Description of Membrane Current
The nerve impulse, turned into equations: voltage-gated ions that fire an all-or-nothing spike.
Every thought, heartbeat and twitch is a tiny electrical pulse — and in 1952 two scientists wrote down the exact equations that make it fire.
The big idea
A nerve cell rests with its inside about 65 thousandths of a volt more negative than its outside, like a charged battery, held that way by unequal amounts of sodium and potassium ions on the two sides. A nerve impulse is a sudden, travelling reversal of that voltage. Hodgkin and Huxley showed it happens because the membrane carries tiny voltage-controlled gates: when the voltage climbs past a threshold, sodium gates fly open and sodium floods in, shooting the voltage upward; a moment later they snap shut and potassium gates open, letting potassium out and resetting it.
Their achievement was to measure exactly how those gates open and close, and to capture it in a handful of equations precise enough to predict the whole pulse — its height, its speed, even the brief 'dead time' before the nerve can fire again.
How it came about
The work hinged on an unlikely hero: the giant axon of the squid, a nerve fibre so thick — up to a millimetre — that wires could be threaded inside it. Working in Cambridge and at the Plymouth marine laboratory, Alan Hodgkin and Andrew Huxley, with Bernard Katz, invented the 'voltage clamp,' a feedback circuit that holds the membrane at a chosen voltage and reads off the current. The Second World War interrupted everything for years.
When they returned, they measured the sodium and potassium currents in painstaking detail, then — with no electronic computer available — spent weeks turning the handle of a mechanical desk calculator to solve their equations. The nerve impulse they computed matched the real one, down to its shape and speed. They shared the 1963 Nobel Prize.
Why it mattered
For the first time, a living signal had been reduced to mathematics you could solve and trust. It showed that biology obeys physics down to the millivolt, and it created the template for modelling any electrically active cell — neurons, heart muscle, hormone-secreting cells. Modern brain simulations, cardiac drug testing and neural prosthetics all descend from these equations.
A way to picture it
Picture a line of dominoes that can stand themselves back up. Nudge the first one — the stimulus — only gently and nothing happens; it wobbles and steadies. Tip it past a certain angle and it falls, knocking the next, which knocks the next: an unstoppable wave that is the same size no matter how hard you pushed. That is 'all-or-nothing.' The sodium gates are the falling; the potassium gates are the mechanism that stands each domino back up, ready — after a short pause — to fire again.
Where it sits
In the 1780s Galvani found that electricity moves muscle; around 1902 Bernstein guessed the impulse was an ion effect. Hodgkin and Huxley turned the guess into exact, testable equations — the same leap from description to mechanism that Watson and Crick made for heredity a year later. From here the line runs to today's atomic channel structures, to optogenetics, and to the conductance-based models behind large-scale brain simulation.
This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre (Hodgkin, Huxley & Katz, 1952; Hodgkin & Huxley, 1952 a–c). Its general object is to discuss the results of the preceding papers (Part I), to put them into mathematical form (Part II) and to show that they will account for conduction and excitation in quantitative terms (Part III).
Current can be carried through the membrane either by charging the membrane capacity or by movement of ions through the resistances in parallel with the capacity. The ionic current is divided into components carried by sodium and potassium ions (I_Na and I_K), and a small 'leakage current' (I_l) made up by chloride and other ions.