Hodgkin and Huxley

THE CLAIM

In 1952 the nerve impulse became an equation

Alan Hodgkin and Andrew Huxley wrote the law of the nerve impulse. In five papers published in The Journal of Physiology in 1952, four in volume 116 and the last in volume 117 at pages 500 to 544, they described the electrical behavior of a single nerve fiber using four coupled differential equations and roughly a dozen constants. The equations predicted the shape of the action potential, its threshold, its refractory period, and the speed at which it traveled down the fiber. Hodgkin and Huxley received the Nobel Prize in Physiology or Medicine in 1963, shared with John Eccles. Before 1952 the nerve impulse was a description. After 1952 it was a calculation.

Ask what that commits you to. If the behavior of a living membrane can be written as a system of equations whose variables are continuous, then excitability is not a switch. It is a quantity. The membrane does not sit at off and jump to on. It holds a graded, continuously adjustable configuration, and the impulse is what happens when that configuration crosses a line it was already sitting near. That is the beginning of a serious physics of the nervous system. It is also the beginning of a serious physics of tone. Hold that thought against the rest of this library. Every chapter before this one argued that the state of the nervous system governs the behavior of the body. This is the chapter where that argument acquires units.

THE ANIMAL

The whole model rests on one absurdly large nerve fiber in a squid

The squid giant axon is the single preparation that made the work possible. J. Z. Young identified it as a nerve fiber rather than a blood vessel and published the anatomy in 1936 (Young 1936). In Loligo the axon runs roughly 0.5 to 1 millimetre across, about a hundred times the diameter of an ordinary vertebrate axon, wide enough to thread a glass capillary electrode down its length without destroying it. Hodgkin and Huxley worked on Loligo forbesi at the Marine Biological Association laboratory in Plymouth, where the squid arrived by boat and the season ran short.

Notice the shape of the discovery. The general law of nerve conduction was not extracted from a typical nerve. It was extracted from an outlier, because the outlier was the only specimen large enough to be measured from the inside. This is how measurement usually enters biology. Someone finds the one case where the instrument fits, and everything learned there is then tested against the ordinary case. The squid giant axon is also a syncytium, formed by the fusion of many cells, which is worth saying because it is often described as simply a very large single neuron.

1939

The first recording from inside a nerve fiber broke the reigning theory

On 21 October 1939 Nature published a short note by Hodgkin and Huxley titled Action Potentials Recorded from Inside a Nerve Fibre (Hodgkin and Huxley 1939). It reported the membrane potential measured with an electrode inside the axon rather than on its surface. The result contradicted the standing account. Julius Bernstein had proposed in 1902 that the resting fiber maintains a potential across a membrane selectively permeable to potassium, and that the impulse is a transient breakdown of that selectivity. If Bernstein was right, the potential during the impulse should collapse toward zero and stop there.

It did not stop at zero. It went past. The measured impulse overshot the zero line and reversed the sign of the membrane potential by a margin comparable to the resting potential itself. A breakdown of selectivity cannot produce that. Only a new selectivity can, a membrane that becomes permeable to something else and is driven toward that ion equilibrium instead. The war interrupted the follow-up. Hodgkin went to radar work at the Telecommunications Research Establishment, Huxley to gunnery research for the Admiralty, and the question waited until 1945.

THE INSTRUMENT

The voltage clamp holds the membrane still so its currents can be read

The voltage clamp is a feedback circuit. It measures the membrane potential, compares it with a value the experimenter chooses, and injects whatever current is required to hold the difference at zero. The current the amplifier must supply is then an exact readout of the current the membrane is passing. Kenneth Cole and George Marmont developed the method in 1949 (Marmont 1949). Hodgkin and Huxley did not invent it, a point worth stating plainly because the credit is regularly assigned to them. They adapted it, refined it with a long internal wire electrode, and applied it to the squid axon at Plymouth in July and August of 1949.

Consider what the instrument does. A propagating impulse is a moving target. Voltage, current and time all change together, so nothing can be isolated. The clamp removes one variable by force. Hold the voltage fixed and the membrane can no longer run away, so its ionic currents appear separately and in order, a fast inward current followed by a slower sustained outward one. Regulation made the system legible. That is a general principle, and it returns later in this story at every scale of the body.

SODIUM

The impulse is carried inward by sodium and terminated outward by potassium

In 1949 Hodgkin and Bernard Katz published the sodium hypothesis in The Journal of Physiology, volume 108, pages 37 to 77 (Hodgkin and Katz 1949). Reduce the sodium in the seawater around the axon and the impulse shrinks in proportion. Raise it and the impulse grows. The rising phase of the action potential is sodium entering the fiber down its electrochemical gradient, driving the interior toward the sodium equilibrium potential, which is positive. Sodium permeability then shuts itself off while potassium permeability rises, carrying charge outward and returning the membrane toward rest.

The 1952 voltage clamp records made this quantitative. Hodgkin and Huxley separated the two currents by substituting choline for sodium in the bathing solution and subtracting the traces from each other. They could then plot sodium conductance and potassium conductance against time at every holding voltage. Two conductances, each with its own voltage dependence and its own kinetics, are the entire cast of characters. Everything else in the model is arithmetic performed on those two curves.

THE SERIES

Four papers measured the membrane and the fifth turned the measurements into law

The 1952 series appeared in The Journal of Physiology across two volumes. Volume 116 carried Measurement of Current-Voltage Relations in the Membrane of the Giant Axon of Loligo at pages 424 to 448, written with Bernard Katz (Hodgkin and Huxley 1952); Currents Carried by Sodium and Potassium Ions Through the Membrane of the Giant Axon of Loligo at pages 449 to 472 (Hodgkin and Huxley 1952); The Components of Membrane Conductance in the Giant Axon of Loligo at pages 473 to 496 (Hodgkin and Huxley 1952); and The Dual Effect of Membrane Potential on Sodium Conductance in the Giant Axon of Loligo at pages 497 to 506 (Hodgkin and Huxley 1952). Volume 117 carried the synthesis at pages 500 to 544.

The structure of the series is worth noticing. Four papers of pure measurement, then one paper of theory built from nothing but what the four had measured. No free parameters were smuggled in at the end. The constants in the final equations were read off the conductance curves of the preceding papers, at a stated temperature of 6.3 degrees Celsius, and the completed model was then asked to predict behavior it had never been shown. That order matters. A theory fitted after the fact can be arranged to agree with almost anything, while a theory that predicts a quantity it was never given has earned a different grade of trust. The 1952 series was built in the second manner from beginning to end.

THE VARIABLES

Three numbers between zero and one describe everything the membrane does

The model gives the membrane a capacitance of 1 microfarad per square centimetre and three conductance pathways in parallel: sodium with a maximum near 120 millisiemens per square centimetre, potassium near 36, and a small voltage-independent leak near 0.3. Those conductances are not fixed. Each is the maximum multiplied by gating variables that move between zero and one. Sodium conductance is written as the maximum times m cubed times h, where m rises with depolarization and h falls. Potassium conductance is the maximum times n raised to the fourth power, where n rises more slowly (Hodgkin and Huxley 1952).

The exponents are the interesting part, and the reading of them is narrower than the usual one. Three and four were chosen because those powers reproduce the sigmoid delay in the measured onset curves. They were fits, not counts of anything observed. It happens that the voltage-gated potassium channel was later shown to be a tetramer of four identical subunits, which makes the fourth power look prophetic. Hodgkin and Huxley never claimed it, and this page will not claim it on their behalf.

THE COMPUTATION

The first computational model of a neuron was solved by hand

The equations have no closed-form solution. To produce a predicted action potential the four coupled differential equations must be integrated step by step. Huxley did it on a Brunsviga, a hand-cranked mechanical calculator, because the Cambridge computer EDSAC was out of service for a major modification when the equations and constants were settled in March 1951 (Hodgkin 1992). The propagated action potential took about three weeks of turning a handle. Conduction velocity was worse still, because the equations had to be solved repeatedly with a guessed velocity until the solution stopped diverging.

The answer came out at 18.8 meters per second, close to the velocity measured in the axon that supplied the constants. That is the moment the argument becomes unanswerable. A number describing how fast a signal runs along a living nerve was produced from conductance curves alone, with no propagation data used in the fitting. The shape of the impulse, its threshold, its absolute and relative refractory periods and its speed all came out of the same small handful of constants.

THE DISCLAIMER

Hodgkin and Huxley refused to claim their equations described a mechanism

The most impressive sentence in the 1952 synthesis is a refusal. Having matched the action potential, the refractory period and the conduction velocity, they wrote that the agreement must not be taken as evidence that the equations were anything more than an empirical description of the time course of the permeability changes (Hodgkin and Huxley 1952). Earlier in the same paper they offered a physical picture of charged particles moving within the membrane, then warned in the same breath that the interpretation was unlikely to give a correct picture of the membrane.

They were right to hedge on the mechanism and right to refuse to hedge on the measurements. Erwin Neher and Bert Sakmann developed the patch clamp in the 1970s and recorded current flowing through single ion channels, work that took the 1991 Nobel Prize (Neher and Sakmann 1976). Roderick MacKinnon solved the atomic structure of a potassium channel in 1998 and took the 2003 Nobel Prize in Chemistry. The gating particles turned out to correspond to voltage sensors in real proteins. That is a vindication Hodgkin and Huxley declined to award themselves, and the discipline of the refusal is a large part of why the model survived.

THE STATE

Excitability is a state the membrane holds, not an event that happens to it

Here is the finding that matters most for tone, and it hides inside the arithmetic. At rest the gating variables are not zero. In the resting steady state of the model, sodium activation sits near 0.05, sodium inactivation near 0.6, and potassium activation near 0.32. The resting membrane is not closed and it is not idle. It holds a standing configuration of partially open conductances, balanced against each other, spending energy to stay where it is. Rest is a posture, actively maintained.

Ask what that commits you to. If threshold is set by where those variables are sitting before the stimulus arrives, then an identical stimulus is subthreshold in one state and suprathreshold in another, and the difference lives in the tissue rather than in the input. Raise resting inactivation and the fiber becomes difficult to fire. Lower it and the fiber fires at almost nothing. Hodgkin and Huxley demonstrated this in one axon in a dish at 6.3 degrees Celsius. The same logic scales upward, and that scaling is the subject of the unified model of tone.

RESONANCE

The equations oscillate, and a system that oscillates has a frequency

The Hodgkin and Huxley system is not merely excitable. It contains one fast positive feedback loop, where depolarization opens sodium and sodium depolarizes further, restrained by two slower negative processes, sodium inactivation and potassium activation. A fast loop restrained by slow loops is the standard recipe for a damped oscillator. Small subthreshold inputs make the membrane ring. Sustained current produces repetitive firing at a rate set by the constants. Slowly rising current can fail to fire the fiber at all, an effect called accommodation, because the slow variables drift to meet it. Frequency, damping and refractoriness all fall out of the same four equations.

The contribution of this page to the story is one line: Hodgkin and Huxley proved that excitability is a standing state rather than a discrete event, which turns the readiness of living tissue into a measurable quantity instead of a metaphor. They wrote about a squid axon and about nothing else. They never used the word tone, never discussed posture or tissue tension, and any extension of their equations to whole-organism regulation is our reading rather than their claim. What they supplied is the license to treat the state of excitable tissue as a number that can rise and fall. An earlier chapter, the reafference principle, showed the nervous system predicting its own consequences. This chapter shows the substrate that prediction runs on.

HODGKIN, HUXLEY AND THE MODEL

What they built into the Unified Model of Tone is the price of rest

Hodgkin and Huxley priced the impulse in ions, and the Unified Model of Tone takes the invoice for the resting state. Read their own numbers back. In the resting steady state of the 1952 model, sodium activation sits near 0.05, sodium inactivation near 0.6 and potassium activation near 0.32. Nothing there is switched off. The fiber at rest is holding a configuration, and the model reads that configuration as tone.

The model states the physiology plainly. Resting membrane potential is charge held in reserve and paid for continuously, and the readiness it represents is not neuronal alone, since astrocytes buffer potassium and recycle transmitter without ever firing. The resting substrate is loaded rather than empty, and what is loaded into it is tone. That readiness is the state that matters rather than a preparation for it, and every input the body meets is read against it.

So rest is not idling. It is a maintained, expensive readiness, and the expense is the point. Every membrane in the body is running a standing account whose balance decides what the next input will produce. Edgar Adrian had already shown that intensity travels as a rate rather than a size. Hodgkin and Huxley supplied the other half, which is the state that rate is answered from.

The model adds one coupling that the equations do not carry. A neuron membrane tension shapes how its channels gate, which is one of the couplings that makes tone at once mechanical and electrical rather than one or the other. Pull on the tissue and you have altered a term in the gating, not merely the scenery around it.

The equations are theirs. The identification of the resting state as tone is the model claim, made here and not by them.

WHAT THE RECORD SHOWS

The Hodgkin and Huxley record, in the numbers it was actually built from

• 21 October 1939. Their short note in Nature reported the potential measured from inside the axon (Hodgkin and Huxley 1939). The impulse overshot zero and reversed the sign of the membrane potential, which the 1902 breakdown account of Julius Bernstein could not produce (Bernstein 1902).
• 1949, the sodium hypothesis. Hodgkin and Bernard Katz published in The Journal of Physiology volume 108, pages 37 to 77 (Hodgkin and Katz 1949), showing that the impulse shrinks and grows in proportion to the sodium in the seawater around the fiber.
• July and August 1949. Hodgkin and Huxley applied the voltage clamp to the squid axon at Plymouth. Kenneth Cole and George Marmont developed the method that year (Marmont 1949), a credit regularly and wrongly assigned to Hodgkin and Huxley.
• 1952, five papers. Four of measurement in volume 116 and the synthesis in volume 117 at pages 500 to 544 (Hodgkin and Huxley 1952), with every constant read off the earlier conductance curves at a stated temperature of 6.3 degrees Celsius.
• The resting steady state. Sodium activation near 0.05, sodium inactivation near 0.6 and potassium activation near 0.32, which is a membrane holding a partially open configuration rather than a closed one.
• 18.8 meters per second. The predicted conduction velocity. Huxley integrated it by hand on a Brunsviga over roughly three weeks because EDSAC was out of service when the equations were settled in March 1951 (Hodgkin 1992). No propagation data went into the fit.
• 1963, then 1991 and 2003. Hodgkin and Huxley shared the Nobel Prize with John Eccles (Nobel Prize 1963). Erwin Neher and Bert Sakmann took the 1991 prize for single channel recording, and Roderick MacKinnon took the 2003 chemistry prize for the atomic structure of a potassium channel.