Voltage clamp

The voltage clamp is a technique used to control the voltage across the membrane of a small or isopotential area of a nerve cell by an electronic feedback circuit. The voltage is normally stepped to a family of levels, matching preset command patterns, and the current supplied or absorbed by the circuit to hold the voltage at each level is measured. This current is equivalent to the ionic current flowing across the membrane in response to the voltage step.

In contrast, the current clamp circuit controls the amplitude of the injected current (e. g. via a microelectrode) and allows the voltage to vary. Injection of a depolarizing current across an excitable membrane may be sufficient to generate an action potential (also called an 'impulse' or 'spike'). Membrane voltage changes cause membrane conductance changes, due to the opening of populations of ion channels, which then lead to changes in the sodium and potassium currents through those channels. The balance or imbalance in these currents determines whether or not an impulse is generated.

## Contents

* 1 The Cole and Hodgkin-Huxley voltage clamps of axon patches
* 1.1 Why and how is a voltage clamp useful?
* 1.2 Tools that made the voltage clamp possible
* 1.2.1 Elimination of longitudinal voltage gradients by the "space clamp"
* 1.2.2 Elimination of the threshold by controlling the voltage
* 1.3 Hodgkin and Huxley exploit the voltage clamp and measure ionic conductances
* 2 Alternative forms of the voltage clamp for axons
* 2.1 Microelectrode voltage measurement
* 2.2 Sucrose Gap Technique
* 3 Newer Voltage clamping tools
* 3.1 Patch Clamp
* 3.2 Single Electrode Voltage Clamp
* 3.3 References
* 3.4 See Also

# [edit] The Cole and Hodgkin-Huxley voltage clamps of axon patches

## [edit] Why and how is a voltage clamp useful?

The voltage clamp provided a solution to the following problem: How do you understand the mechanisms involved in an action potential that is changing with voltage and time as it travels down an axon? A description of the mechanisms underlying a propagating impulse is essentially impossible to obtain by measurements of the voltage itself because this voltage is varying in both space (along the axon) and in time (at some chosen point along the axon); thus it must be described by a partial differential equation.

With the development of the tools described below (the space clamp and electronic feedback), it became possible to obtain detailed descriptions of the conductance mechanisms underlying the action potential by imposing experimental restraints, in particular:

* eliminating longitudinal (axial) currents so that the action potential occurred only at one locus, a "patch", and
* allowing membrane currents in the patch to be measured as a function of time at any given voltage.

The data obtained from these experiments were validated by mathematical reconstruction of an action potential.

## [edit] Tools that made the voltage clamp possible

### [edit] Elimination of longitudinal voltage gradients by the "space clamp"

In the 1930s, the huge axon of the squid became the favorite experimental preparation for exploring the basis of the action potential. In 1947, George Marmont (1949) invented a chamber for this axon that effectively turned a portion of the axon into a patch. There were two key components in this new tool:

* First, in a technological breakthrough, Marmont achieved isopotentiality over a region of axon by threading a wire along its interior to short-circuit the longitudinal resistance of the axoplasm. The key to this technological tour de force was to carefully chloride the surface of the silver axial wire, thereby reducing the wire's surface resistance and junction potential that would normally act as barriers to current flow into and out of the wire.

Figure 1: Marmont's space clamp with lateral guard electrodes: Diagram of squid axon and electrode arrangement for membrane controls. The axon passed through holes in the shaded insulating partitions. The central outside spiral electrode, for current and potential measurement, was between similar guard electrodes. The internal electrode, solid line, was inserted from the right to lie in the center of the axon.

The longitudinal short circuit of the axoplasm by the wire caused the potential difference across the axon's membrane in the region of the wire to approach a uniform level; in terms of its electrical properties, this decrease of the axial resistance was equivalent to a large increase of diameter in this region. This uniform potential throughout the length of axon surrounding the wire eliminated longitudinal voltage gradients and thus eliminated propagation.

* Secondly, Marmont was able to restrict current measurement to a short central segment of the axon membrane (now with uniform potential). Using state of the art electronic circuits to force the membrane potential in neighboring "guard" regions to track the central voltage, he was able to prevent flow into the central compartment of any possible longitudinal currents from action potentials in the axon outside the guards. Thus the radial membrane current measured in the central region of the axial wire was not contaminated by any longitudinal or axial current.

It is reported that Marmont, using this equipment in the 'current clamp' configuration, made numerous measurements of patch (non-propagating) action potentials under a wide variety of experimental conditions, including with anaesthetic agents in the medium. Nevertheless, he was not able to decipher the underlying mechanisms, did not publish these results, and left the field.

Cole also used the current clamp configuration to investigate the threshold for generating an action potential and found that threshold was not a particular voltage but depended on rate of rise. However he delayed publication of this data until 1955.

### [edit] Elimination of the threshold by controlling the voltage

Kenneth S. (Kacy) Cole shared a lab at the Marine Biological Laboratory in Woods Hole, MA, with Marmont, but their relationship was less than optimal. When Cole saw what Marmont could do with his space clamp and electronic feedback circuits, he recognized the unique possibility of controlling the membrane voltage and measuring the transmembrane currents responsible for the action potential. He was unable, however, to convince Marmont of the value of joining together to explore such a strategy.

Figure 2: Cole's original voltage clamp records in 1947: Squid axon membrane current densities after changes of potential from the resting potential as shown.

They compromised by having Marmont use the equipment in prime time and having Cole try electronic control of the voltage off-hours; circuit configurations were switched via a connection block with two plug-ins.

Cole was able to record a few traces in his voltage clamp experiments that demonstrated the principle that control of the amplitude and duration of a voltage step was a powerful tool, revealing threshold-free, continuous currents that indeed appeared to be those responsible for the action potential.

* A voltage step allowed the temporal separation of the brief initial current through the membrane's capacitance (during the step change in command voltage) and the slower inward and outward ionic currents.
* The usual perplexing threshold, known to separate all-or-none responses to the injection of depolarizing current into the axon, was eliminated.
* Without any hint of a threshold, the amplitude of the early inward and later outward currents changed smoothly with the level of the voltage step.
* The outward current increased with increasing depolarization but then sagged, the amount of sag roughly proportional to the peak current. This sag was later shown to be an artifact (see section below).

Cole's forte was mathematical descriptions of electrical circuits and the interpretation of his records was limited to a pair of possible circuits. He concedes "I had no theory to explain the early inward current. The steady state current continued to be the sort of thing to be attributed to potassium and I tried in many different ways to modify such a system to account for the transient behavior. Nor could I find a satisfactory and useful way to present the data." (page 263 of his memoirs "Membranes, Ions and Impulses" (1968) Univ. of California Press,)

Cole showed his results to Alan Hodgkin and Andrew Huxley, suggesting the possibility that the outward current was related to potassium but gave no explanation for the inward current. It was left to them to demonstrate that the inward and outward currents flowed through the sodium and potassium channels, respectively.

## [edit] Hodgkin and Huxley exploit the voltage clamp and measure ionic conductances

Alan Hodgkin and Andrew Huxley (now Sir Alan and Sir Andrew) had thought long and hard about an increase in sodium conductance as the probable cause of the regenerative upstroke of the action potential. With this notion, they had even done simple computations of the effect of changing the external sodium concentration on the height of the action potential overshoot of zero; these calculations had predicted the results of later experiments by Hodgkin and Katz (1949). Thus they understood that the currents observed when the membrane was held at a fixed value reflected the underlying ionic conductances and they were well prepared to carry out the remarkably few crucial experiments required to reveal and describe the ionic mechanisms underlying action potentials.

Figure 3: Hodgkin, Huxley, and Katz's dual electrode axial cannula.

They also had an extraordinary appreciation of the possible problems caused at the interface of a metal exposed to electrolyte solutions such as axoplasm; current passage can change both the potential difference between the metal and electrolyte, and the resistance of the interface (known as electrode polarization). Cole's voltage clamp used a single axial wire to measure the internal voltage and, simultaneously, to pass the current. Thus, when Cole showed Hodgkin and Huxley his voltage clamp data, they conjectured that electrode polarization might have caused the sag in the sustained outward current in Cole's records. Polarization, then, was likely to be a serious artifact that needed to be eliminated by improvements in the electrode arrangement.

With Sir Bernard Katz, they constructed an elegant voltage clamp that employed separate internal electrodes, one to measure the potential and the other to pass currents; this eliminated possible electrode polarization problems (Hodgkin et al. 1952). Whereas Cole simply tried to describe the ionic current patterns with mathematical expressions, Hodgkin and Huxley pursued the idea that ionic currents might be driven across the membrane by electrochemical gradients, and they set about developing a testable model.

Hodgkin and Huxley carried out the crucial experiments that provided a complete description of the time and voltage dependence of the ionic currents. Recognizing that the inward and outward currents were carried by different ions, they calculated the conductance of the inward sodium current as a function of voltage and time, then repeated this process for the outward potassium current and expressed their data in a set of differential equations.

From these equations they were able, by numerical integration carried out on a hand-cranked calculator, to reconstruct realistic action potentials elicited by a variety of stimuli (Hodgkin and Huxley 1952). This feat had remarkable consequences:

* The Hodgkin-Huxley channel concepts and equations became a reference standard for future descriptions of membrane channels.
* The field of computational neuroscience was launched.
* The Hodgkin-Huxley equations are so accurate and robust that they are routinely used for simulations some five decades later.
* The Nobel Prize was awarded to both men a decade later in 1963.

# [edit] Alternative forms of the voltage clamp for axons

## [edit] Microelectrode voltage measurement

Figure 4: Cole and Moore's dual electrode positions

By the 1950s, Kenneth Cole had become the Scientific Director of the Naval Medical Research Institute in Bethesda, MD. John Moore joined him there to try to build an improved voltage clamp. Cole and Moore (1960) continued to use the axial wire (with the guard ring technique) to pass current but avoided the complexity of Hodgkin-Huxley's dual-electrode axial cannula shown above. Instead, they employed the recently developed microelectrode to measure the voltage just inside the membrane. The difference between this potential and that sensed by another just outside the membrane provided an accurate measure of the voltage across it. This value of membrane potential was forced to match the voltage clamp command signals with a novel circuit composed of operational amplifiers.

Furthermore, such a circuit arrangement eliminated the voltage drop across the radial resistance (see figure to right) of the axoplasm, that between the membrane and the surface of the axial wire. The more accurate value of the membrane voltage provided a faster voltage clamp and better separation of the membrane capacitative currents from the larger ionic currents.

Figure 5: Voltage Clamp Circuit employing operational amplifiers

New electronic tools for the voltage clamp introduced by Moore included:

* an ultra-high-impedance input amplifier for the microelectrode inside the axon
* feedback compensation for any capacitance to minimize the lag in the response of the measurement of the membrane voltage
* operational amplifiers (new tools from analog computers) in the clamp circuit used for the following purposes:
* to control the membrane voltage
* to measure the membrane current
* to compensate for series resistance in the control circuit

Figure 6: Striped areas represent Lucite partitions and stippled areas represent flowing isotonic sucrose solution The axon extends through 300 micron diameter holes in each of the Lucite partitions. Between the sucrose solutions, a small "node" of axon is exposed to a continuously moving stream of sea water. Solutions in the I and V pools also flow continuously.

## [edit] Sucrose Gap Technique

Moore, with Fred Julian and David Goldman (1962) [1], adapted the "sucrose gap" method of Robert Stampfl 1968) [2]

(affectionately called 'Sugar Daddy') to make a voltage clamp. A sucrose solution has very low conductivity and thus two flowing streams of sucrose could be used as the "guard" regions in a chamber, isolating a short, central segment of bare axon (an 'artificial node') from the axon's ends. Further, each end of the axon was bathed in a pool of isotonic KCl solution to eliminate membrane potentials there.

Figure 7: Photographs of an axon in the experimental chamber taken from above. A shows the view before the sucrose solutions were turned on. Direction of flow of seawater in the central pool is from top to bottom. B shows sucrose solutions flowing. The 'node' of axon exposed to sea water is visible in the center between boundaries of sucrose solutions. Lateral junctions between sucrose solutions and solutions in I and V pools are also visible. Diameter of axon is about 100 microns.

One pool was used to measure the intracellular voltage at the 'node' (i.e. the voltage drop between the central compartment, containing extracellular saline, and the end pool, containing intracellular saline) while the other provided access for passing the axial current required for clamping the 'nodal' potential.

Flowing seawater or experimental solutions in the central chamber separated the lateral streams of sucrose; the solution flow patterns were readily visible schlieren patterns. The much greater simplicity of the sucrose gap (compared to the axial wire) has been especially expedient in studies on the giant axon of the squid. Because the total length of axon, that portion exposed to seawater at the node plus the regions of flowing sucrose, is relatively short compared to the length of the dissected axons, multiple regions of the same axon can be used sequentially by simple translation of the axon in the chamber. When a node has been damaged by a toxic agent, or over a long experimental time, the ability of having a fresh node area available allows many more experiments per axon than possible with the axial wire.

# [edit] Newer Voltage clamping tools

## [edit] Patch Clamp

The patch clamp technique is a specialized version of the voltage clamp. The patch clamp micropipette has an open tip (diameter of about one micron) with a polished surface rather than a sharp point. This patch pipette is pressed against a cell's surface and suction is applied to the inside of the pipette to pull the cell's membrane inside its tip. The suction causes the pipette to form a tight seal with the cell's membrane with an electrical resistance of several gigaohms. The patch clamp circuit uses a single operational amplifier in the 'current to voltage' configuration to control the voltage and measure the current across the patch. There are multiple patch clamp configurations for a variety of experimental observations.

Erwin Neher and Bert Sakmann developed the patch clamp in the late 1970s and early 1980s [3]. They received the Nobel Prize in Physiology or Medicine in 1991 [4] for this work.

## [edit] Single Electrode Voltage Clamp

The Single Electrode Voltage Clamp is a special purpose circuit clamping arrangement where a single microelectrode is used not only to measure the membrane voltage but also to pass the current necessary to control the voltage level. A fast electronic switch alternates the connection to the microelectrode between these two functions.

## [edit] References

Cole K.S. (1955) Ions, potentials and the nerve impulse. In Shedlovsky, T (ed.) Electrochemistry in biology ad medicine. New York, Wiley. p 121-140

Cole K.S. and Moore J.W. (1960) Ionic current measurements in the squid giant axon membrane. J. Gen Physiol. 44:123-167

Hodgkin A.L. and Katz B. (1949) The effect of sodium ions on the electrical activity of the giant axon of the squid. J. Physiol. 108(1):37-77

Hodgkin A.L., Huxley A.F., and Katz B. (1952) Measurement of current-voltage relations in the membrane of the giant axon of Loligo. J. Physiol. 115(4):424-48

Hodgkin A.L. and Huxley A.F. (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117(4):500-44

Julian F.J., Moore J.W., Goldman D.E. (1962) Membrane potentials of the lobster giant axon obtained by use of the sucrose-gap technique. J. Gen Physiol. 45:1195-216

Marmont G. (1949) Studies on the axon Membrane; a new method. J Cell Physiol. 1949 Dec;34(3):351-82.

Rouqier O., Vassort G., Stampfli R. (1968) Voltage clamp experiments on frog atrial heart muscle fibres with the sucrose gap technique. Pflugers Arch Gesamte Physiol Menschen Tiere. 301(2):91-108

Internal references

* Olaf Sporns (2007) Complexity. Scholarpedia, 2(10):1623.
* Frances K. Skinner (2006) Conductance-based models. Scholarpedia, 1(11):1408.
* Ichiji Tasaki (2007) Saltatory conduction. Scholarpedia, 2(6):3354.
* Alan Finkel (2007) Single electrode voltage clamp. Scholarpedia, 2(8):3528.

## [edit] See Also

Conductance-Based Models, Dynamic Clamp, Electrophysiology, Excitability, Hodgkin-Huxley Model, Rall Model, Saltatory Conduction