Electrophysiology

Johannes Müller, the leading physiologist of the day, thought nerve signals too fast ever to be timed. In 1850 his student Hermann von Helmholtz did it. He stimulated a frog's nerve at two points and measured how much longer the muscle took to twitch when the signal had further to go. The answer was about 30 metres per second. Nerve impulses were not electricity flowing through a wire, which would be millions of times faster, but some slower process in the living fibre.

What the process was remained unclear. In 1902 Julius Bernstein proposed that the membrane of a resting nerve lets through only potassium ions, which sets up a voltage, and that during an impulse the membrane briefly lets everything through. At Cambridge, Keith Lucas and then Edgar Adrian showed that a fibre fires all or nothing. In 1926 Adrian and Yngve Zotterman, using new valve amplifiers, recorded single sensory fibres and found that every impulse is the same size. Information lies in how often they come.

The answer to Bernstein's question came from the squid, whose giant axons, up to a millimetre across, control its jet escape. In 1939 Alan Hodgkin and Andrew Huxley at Plymouth slid a fine wire inside one and recorded the voltage directly. During an impulse it did not just fall to zero, as Bernstein's theory said. It overshot to about 40 millivolts positive. Then the war intervened.

Afterwards they used the voltage clamp, developed by Kenneth Cole and George Marmont, which holds the membrane voltage fixed and measures the current needed to hold it. By replacing the sodium in the seawater, they separated the current into two parts. When the voltage rises, the membrane first opens to sodium ions, which rush in and drive the voltage higher, then closes to sodium and opens to potassium, which flows out and restores it. In 1952 they fitted the measurements with four differential equations. Huxley solved them on a hand-cranked calculator, and they reproduced the shape of the action potential and predicted a speed of 18.8 metres per second against a measured 21.2.

Why is the inside of a nerve negative? The membrane separates two salt solutions of different composition. For the squid axon, the concentrations in millimoles per litre are:

Ion	Inside	Outside
Potassium, K⁺	400	20
Sodium, Na⁺	50	440
Chloride, Cl⁻	52	560

Suppose the membrane lets through only potassium. Potassium leaks out down its concentration gradient, leaving the inside negative, until the voltage pulls back as hard as the gradient pushes. The balance point is given by the Nernst equation, from the physical chemist Walther Nernst:

$$E = \frac{RT}{zF} \ln \frac{c_{\text{out}}}{c_{\text{in}}} ,$$

where $R$ is the gas constant, $T$ the absolute temperature, $F$ the charge on a mole of ions and $z$ the ion's charge. At 18 °C, $RT/F = 25.1$ millivolts, so

$$E_{\mathrm{K}} = 25.1 \ln \frac{20}{400} = -75 \text{ mV}, \qquad E_{\mathrm{Na}} = 25.1 \ln \frac{440}{50} = +55 \text{ mV} .$$

The real membrane lets several ions through, and the resting voltage is a weighted compromise, given by the Goldman equation. Hodgkin and Bernard Katz found in 1949 that at rest the membrane is 25 times less permeable to sodium than to potassium, and about half as permeable to chloride. With relative permeabilities $1 : 0.04 : 0.45$ for potassium, sodium and chloride,

$$V = 25.1 \ln \frac{1 \times 20 + 0.04 \times 440 + 0.45 \times 52}{1 \times 400 + 0.04 \times 50 + 0.45 \times 560} = 25.1 \ln \frac{61}{654} \approx -60 \text{ mV} .$$

At the peak of an impulse the sodium permeability rises to about 20 times that of potassium. The same equation then gives $25.1 \ln (8843/1652) \approx +42$ mV, close to the overshoot Hodgkin and Huxley measured. The action potential is a switch between two permeabilities.

How many ions does this take? The membrane stores about 1 microfarad per square centimetre, so a 100 millivolt swing moves $10^{-7}$ coulombs per square centimetre, about $6 \times 10^{11}$ ions. One centimetre of a half-millimetre squid axon has 0.16 cm² of membrane, so about $10^{11}$ ions cross it per impulse. The same length contains about $5 \times 10^{17}$ potassium ions. One impulse changes the inside by roughly one part in five million, which is why an axon can fire thousands of times with its pumps switched off.

The equations described currents, not the machinery that carried them. In 1976 Erwin Neher and Bert Sakmann pressed a polished glass pipette against a muscle cell and recorded the current through a single channel, a rectangular pulse of a few picoamperes that switched on and off at random. Hodgkin and Huxley's smooth currents were the average of many such pores. In 1998 Roderick MacKinnon's group solved the structure of a potassium channel and showed how it lets potassium through but not the smaller sodium ion.

How signals pass from one neuron to the next, across Sherrington's synapse, became synaptic transmission. Recording from single neurons in living animals became systems neuroscience, and the Hodgkin–Huxley equations became the first great model of computational neuroscience and a classic of dynamical systems. How a neuron keeps its mix of channels stable for a lifetime is still not understood.