The voltage clamp

The membrane is the experimenter’s enemy here: its conductances depend on voltage, and voltage depends on the currents through those conductances. Anything you do perturbs what you are trying to measure, and the action potential runs away from you.

The voltage clamp breaks the loop by closing a different one. An amplifier compares membrane potential against a command, and injects whatever current is needed to null the difference. Marmont and Kenneth Cole arrived at the method in 1947, in the same laboratory and on the same apparatus, and it is usually credited to both. Because voltage is now held, the conductances stop moving on their own — and the injected current becomes a direct read-out of the ionic current at that voltage.

Why it belongs on this site

It is a feedback amplifier used as a measuring instrument, and the reason it works is the ordinary reason feedback works: high loop gain makes the output track the command and makes the tracking insensitive to what the load is doing. Harold Black invented that idea in 1927 to make telephone repeaters behave. Two decades later it was pointed at an axon.

Black’s 1934 paper in the Bell System Technical Journal states the bargain: give the amplifier, say, 40 dB more gain than it needs, feed the output back “in such a way as to throw away the excess gain”, and the gain is set by the feedback network rather than by the tubes. In a clamp, the misbehaving part inside the loop is the axon, and the current the loop spends correcting it is the measurement.

Everything in the Hodgkin–Huxley model rests on this. The conductance curves, the gating exponents, the whole quantitative account of excitability are voltage-clamp measurements. Without an instrument that could hold voltage constant, there was no way to separate the sodium and potassium currents, and the model could not have been written.

Woods Hole, 1947

Cole came to nerve as a physicist with an alternating-current bridge. With Howard Curtis he had used it to show, in a paper of 1939, that the impulse is a large fall in membrane resistance with the capacitance, about a microfarad per square centimetre, almost unchanged. That put the action potential in a conductance, but could not say what the conductance depended on: in a travelling impulse, voltage varies in space and time at once.

In 1946 Cole took charge of a new Institute of Radiobiology and Biophysics at the University of Chicago, and George Marmont rejoined him there. Marmont built the instrument: a long internal electrode threaded along the squid giant axon, so that the potential inside was uniform over its length, fed with current under feedback control, and guard electrodes outside so that current was measured from a central stretch of membrane only. Cole added a second way of running it, controlling the electrode’s potential instead of its current. In that mode it was the first voltage clamp — a name Cole did not like.

They did not agree on which mode mattered. Marmont preferred to control current, and by John Moore’s account Cole could not persuade him otherwise; Marmont had the rig in prime time and Cole had it off-hours, switching modes at a connection block with two plug-ins. The first experiments ran in the summer of 1947 at the Marine Biological Laboratory in Woods Hole. Marmont’s 1949 paper, the only full account of them, describes a current-controlled experiment: a non-propagating action potential. Cole reported the voltage-clamp records briefly at a meeting in Paris in the spring of 1949.

Those few records showed the essential thing. There was no threshold: as the step grew, an early inward current appeared and grew smoothly, a current that would have fired an action potential had the feedback not held the voltage still. The late outward current sagged, because one axial wire both sensed the potential and carried the current, and the current density at its surface polarised it.

Cole wrote to Alan Hodgkin about the experiments later in 1947 and gave him the details the following spring. Hodgkin, who with Bernard Katz had just tied the overshoot of the action potential to external sodium, was already thinking of building a clamp; Huxley called what Cole and Marmont told him “a great help and stimulus”.

Two wires and an amplifier

The improvement Hodgkin called obvious was to separate the jobs. Hodgkin, Huxley and Katz put two wires along the axis of the fibre. One measured the potential inside against an electrode in the sea water just outside; the other passed current through the membrane to a second external electrode. The voltage wire fed an amplifier whose output drove the current wire, connected so that any accidental change of membrane potential was almost completely annulled, and the command, a rectangular pulse, entered at a second input. The valve amplifier had a voltage gain of about 400 and turned each millivolt of error into about a milliamp of correcting current, up to some 5 mA; the recorded potential followed the command to within 1–2 per cent. Only the current through the middle section of the fibre was measured, as the potential drop it made in the sea water between two more wires.

Huxley’s own summary is an engineer’s sentence: the net result is the same as a single ideal electrode inside the fibre, connected to a low-impedance source of voltage steps. That is what the feedback synthesises — a voltage source with almost no output impedance, applied to the inside of an axon, with an ammeter in series. The length of the wires does the other job: a metal conductor along the axis short-circuits the longitudinal resistance of the axoplasm, so the membrane along it behaves as one patch at one potential. First used at Plymouth in the summer of 1948 and improved over the winter, the clamp produced in 1949 the records behind five papers in The Journal of Physiology in 1952.

Taking the current apart

Step the inside of the fibre positive and, once the capacity current has passed, there is an early inward current followed by a late outward one. Huxley put the early phase plainly: if it were not for the feedback, this current would drive the inside of the fibre still more positive, “that is to say, it would produce the rising phase of an action potential”. The late outward current is the falling phase. Under the clamp the two halves of the impulse arrive as two currents, each measured at a voltage of the experimenter’s choosing.

Then came the step Cole and Marmont had not taken: change the ions. With 90 per cent of the sodium chloride in the sea water replaced by choline chloride, the early inward phase vanishes. Make the step large enough and the early current reverses; the potential at which it is zero, the sodium potential, moved with external sodium exactly as the Nernst equation requires. Huxley called that perhaps the strongest evidence for the sodium theory, and it licensed a subtraction: the total ionic current, minus the current with sodium’s share brought to zero, is the sodium current. The late outward current was potassium, and matched the efflux of radioactive potassium.

Divide each current by its driving force and you have a conductance as a function of voltage and time. Each, Hodgkin and Huxley found, jumped instantly to a value linear in the new voltage, passing through zero at its own reversal potential — a resistor in series with a battery — and then drifted to a new value over a millisecond or so. These are the ionic currents underlying the action potential, close to the title Hodgkin, Huxley and Katz gave their first report of the clamp in 1949, in the same volume of the Archives des Sciences Physiologiques as Cole’s.

Credit ran both ways. The 1947 records showed a lag before the inward current rose, which Hodgkin and Huxley first put down to instrumental delay. They later confirmed it as real, and Huxley counted it an important factor in the form their equations took.

Where the loop fights back

Black’s paper carries its own warning: feedback buys accuracy only while the phase shift around the loop is under control, or, in his word, the amplifier sings. A voltage clamp is a hard case, because its load is a capacitor. The membrane’s microfarad per square centimetre is driven through the resistance of the current electrode, and the potential is read back through an electrode with resistance and capacitance of its own — which, Huxley noted, limited the speed of Cole and Moore’s later clamp. Two lags in a high-gain loop, plus the amplifier’s own: turn up the gain for a tighter, faster clamp and the phase margin goes, first as ringing, then as oscillation.

The capacitor also sets the bill for every step. By Hodgkin’s own arithmetic it takes 0.12 μC to move a square centimetre of membrane by 120 mV, and the clamp has to deliver it at once. In Hodgkin, Huxley and Katz’s records a 40 mV step drew a surge of capacity current that peaked at 4.5 mA/cm² and decayed with a time constant of about 6 μs — 0.9 μF/cm² charging through the 7 Ω·cm² or so that lay in series with it. Speed matters because the sodium conductance switches on about ten times faster than the potassium conductance. Cole and Moore’s 1960 clamp, built from operational amplifiers, settled to within a few millivolts in 40 μs.

The subtler limit is series resistance. The clamp controls the potential where it measures it, not across the membrane, and the ionic current has to cross whatever resistance lies between the two, in the axoplasm on one side and outside the membrane on the other. So the membrane sits at

$$V_m = V_{\text{cmd}} - I_m R_s$$

where $V_{\text{cmd}}$ is the command, $I_m$ the membrane current (outward positive) and $R_s$ the series resistance. Taylor, Moore and Cole concluded in 1960 that a few ohm-square-centimetres could lead to serious errors of interpretation. At the 5–10 mA/cm² peak inward currents of Cole and Moore’s best axons, each Ω·cm² is 5–10 mV. And the error has the wrong sign: inward sodium current makes $I_m$ negative, which puts the membrane positive of the command, which opens more sodium channels — a little of the original runaway, let back in through a resistor.

The remedy is to add to the command a voltage proportional to the measured current, so the amplifier aims past the target by the expected drop. That is positive feedback inside a negative-feedback loop, and it behaves like it. Hodgkin, Huxley and Katz already used it, as “compensated feed-back”, in seven of their later experiments, set a little short of full. It made the capacity surge larger and briefer, and oscillatory; such a system, they wrote, “is liable to oscillate”, and if overset “the overall feed-back becomes positive and there is a strong probability that the membrane will be destroyed”. Moore, Hines and Harris found in 1984 that conventional compensation went unstable once about two-thirds of the error was corrected, and reached full, stable compensation by first subtracting the capacitive current with an active bridge. Patch-clamp amplifiers still carry the control, and it is still positive feedback.

Noise, notably, is not on this list. A squid axon’s currents run to milliamps per square centimetre, and the clamp’s problems were problems of control. Shrink the clamped membrane to a micrometre-scale patch and the currents fall to picoamps; then the noise floor is the whole problem.

What it cost

Space clamp. The technique assumes the whole patch of membrane sits at one potential, which requires a preparation short enough or an electrode long enough that cable properties do not spoil it — hence the squid giant axon, and hence the axial-wire geometry. Extending the idea to small cells with real dendrites took another twenty-seven years and became the patch clamp.

The wire did not make the space clamp automatic either. Notched and oscillating records — and, in Ichiji Tasaki and A. F. Bak’s 1958 report, a discrete threshold under clamp — were taken by some critics as undermining the method. Taylor, Moore and Cole traced such patterns to space-clamp failure, from axial electrodes with more than 20 Ω of surface resistance per centimetre of axon; no membrane that was genuinely given a step showed more than one inward current peak.

Nor did the patch clamp abolish the problem; it moved it. The whole-cell configuration of 1981 holds a neuron at its soma, and when Williams and Mitchell recorded from the soma and the apical dendrite of the same rat neocortical neuron at once, the somatic clamp controlled the voltage nowhere else.

The frog oocyte

From the 1980s the clamp found a second subject: the oocyte of the African clawed frog, Xenopus laevis. Gurdon and colleagues had shown in 1971 that frog oocytes translate messenger RNA injected into them, and in 1982 Barnard, Miledi and Sumikawa injected RNA from the electric organ of Torpedo and found working acetylcholine receptors in the oocyte membrane. Once channel genes were cloned, RNA transcribed from a single cDNA was enough: rat-brain sodium channels from Shosaku Numa’s group in 1986, the Shaker potassium channel in 1988.

The usual way to record from them is the two-electrode voltage clamp — two sharp microelectrodes, one to read the potential and one to pass current: Plymouth’s two wires, in a cell about a millimetre across. The measurement is the one Hodgkin and Huxley made, a family of steps and a family of currents. What changed is that the channel is now a sequence that can be edited. In 1989 Stühmer, Numa and colleagues expressed mutated sodium channels in oocytes and, recording from patches of their membrane, implicated the positive charges of the S4 segment in voltage sensing and the stretch between the third and fourth repeats in inactivation.

The old problems return in new proportions. The oocyte membrane has about six times the capacitance per unit area of a simple lipid bilayer, its cytoplasm conducts about five times worse than the bath, and the electrodes reach only about 100 μm into a cell ten times that size. Baumgartner, Islas and Sigworth showed in 1999 that this eccentric injection of current leaves the membrane potential non-uniform, with deviations decaying over time constants of up to 150 μs, which is why recordings are poor when currents are large or the membrane must be charged quickly. The cut-open oocyte clamp, built for small, fast currents, isolates only part of the membrane behind a vaseline gap and reaches the inside through the opened remainder; Stefani and Bezanilla put its time constant at 24 μs.

A squid axon needed a wire down its middle before it would behave as one patch of membrane. A frog oocyte, a sphere with no cable to speak of, still needs a hundred-odd microseconds.