Voltage clamp

The voltage clamp operates by negative feedback. The membrane potential amplifier measures membrane voltage and sends output to the feedback amplifier; this subtracts the membrane voltage from the command voltage, which it receives from the signal generator. This signal is amplified and output is sent into the axon via the current electrode.

The voltage clamp is used by electrophysiologists to measure the ion currents across a neuronal membrane while holding the membrane voltage at a set level. Neuronal membranes contain many different kinds of ion channels, some of which are voltage gated. The voltage clamp allows the membrane voltage to be manipulated independently of the ionic currents, allowing the current-voltage relationships of membrane channels to be studied.[1]

The concept of the voltage clamp is due to Kenneth Cole[2] and George Marmount[3] in the 1940s. Cole discovered that it was possible to use two electrodes and a feedback circuit to keep the cell's membrane potential at a level set by the experimenter.

Alan Hodgkin realized that, to understand ion flux across the membrane, it was necessary to eliminate differences in membrane potential.[4] After experiments with the voltage clamp, Hodgkin and Andrew Huxley outlined the ionic causes of the action potential in 1952, for which they shared the Nobel Prize for Physiology or Medicine in 1963.[4]

## Contents

* 1 Technique
* 2 Variations of the voltage clamp technique
* 2.1 Two-electrode voltage clamp using microelectrodes
* 2.2 Single-electrode voltage clamp
* 2.3 Continuous single-electrode clamp (SEVC-c)
* 2.4 Discontinuous single-electrode voltage-clamp
* 3 References

## Technique

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The voltage clamp is a current generator with two electrodes. Transmembrane voltage is recorded through a "voltage electrode", relative to ground, and a "current electrode" passes current into the cell. The experimenter sets a "holding voltage", or "command potential", and the voltage clamp uses negative feedback to maintain the cell at this voltage. The electrodes are connected to an amplifier, which measures membrane potential and feeds the signal into a feedback amplifier. This amplifier also gets an input from the signal generator that determines the command potential, and it subtracts the membrane potential from the command potential (Vcommand \- Vm), magnifies any difference, and sends an output to the current electrode. Whenever the cell deviates from the holding voltage, the operational amplifier generates an "error signal", that is the difference between the command potential and the actual voltage of the cell. The feedback circuit passes current into the cell to reduce the error signal to zero. Thus, the clamp circuit produces a current equal and opposite to the ionic current. This can be measured, giving an accurate reproduction of the currents flowing across the membrane.

Cole developed the voltage clamp technique before the era of microelectrodes, so his two electrodes consisted of fine wires twisted around an insulating rod. Because this type of electrode could be inserted into only the largest cells, early electrophysiological experiments were conducted almost exclusively on squid axons. Squid squirt jets of water when they need to move quickly, as when escaping a predator. To make this escape as fast as possible, they have an axon that can reach 1 mm in diameter (signals propagate more quickly down large axons). The squid giant axon was the first preparation that could be used to voltage clamp a transmembrane current, and it was the basis of Hodgkin and Huxley's pioneering experiments on the properties of the action potential.

## Variations of the voltage clamp technique

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A more detailed discussion of the below techniques can be found in the Axon Guide. The book is now out of print but can be downloaded in PDF form from Axon Instruments.

#### Two-electrode voltage clamp using microelectrodes

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This works on the same principle, but the two electrodes are glass pipettes with very fine tips (smaller than 1 micrometer), allowing for clamping of cells smaller than the squid axon. However, microelectrodes are much poorer conductors than the wires used by Cole, and sometimes cannot pass current rapidly enough to compensate for cellular current. The faster the kinetics of the current (onset and offset), the more likely it is that the clamp will be unable to "follow" it faithfully. Another disadvantage involves "space clamp" issues. Cole's voltage clamp used a long wire that clamped the squid axon uniformly along its entire length. Microelectrodes can provide only a spatial point source of current that might not uniformly affect different parts of an irregularly shaped cell.

#### Single-electrode voltage clamp

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In this, an electrode is placed inside a cell, and serves both the voltage-recording and current-passing duties.

#### Continuous single-electrode clamp (SEVC-c)

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See main article patch clamp

The "patch-clamp" technique allows the study of individual ion channels. It uses an electrode with a relatively large tip (> 1 micrometer) which has a smooth surface (rather than a sharp tip). This is a "patch-clamp electrode" (as distinct from a "sharp electrode" used to impale cells). This electrode is pressed against a cell membrane and suction is applied to pull the cell's membrane inside the electrode tip. The suction causes the cell to form a tight seal with the electrode (a "gigaohm seal", as the resistance is more than a gigaohm).

SEV-c has the advantage is that you can record from small cells that would be impossible to impale with two electrodes. However:

1) Microelectrodes are imperfect conductors; they generally have a resistance of more than a million ohms. They rectify (i.e. change their resistance with voltage, often in an irregular manner), they sometimes have unstable resistance if clogged by cell contents. Thus they will not faithfully record the voltage of the cell, especially when it is changing quickly, nor will they faithfully pass current.

2) Voltage and current errors: SEV-c circuitry does not actually measure the voltage of the cell being clamped (as does a two-electrode clamp). The patch-clamp amplifier is like a two-electrode clamp, except the voltage measuring and current passing circuits are connected (in the two-electrode clamp, they are connected through the cell). The electrode is attached to a wire that contacts the current/voltage loop inside the amplifier. Thus the electrode has only an indirect influence on the feedback circuit. The amplifier reads only the voltage at the top of the electrode, and feeds back current to compensate. But, if the electrode is an imperfect conductor, the clamp circuity has only a distorted view of the membrane potential. Similarly, when the circuit passes back current to compensate for that (distorted) voltage, the current will be distorted by the electrode before it reaches the cell. To compensate for this, the electrophysiologist uses the lowest resistance electrode possible, makes sure that the electrode characteristics don't change during an experiment (so the errors will be constant), and avoids recording currents with kinetics likely to be too fast for the clamp to follow accurately. The accuracy of SEV-c goes up the slower and smaller are the voltage changes it is trying to clamp.

3) Series resistance errors: The currents passed to the cell must go to ground to complete the circuit. The voltages are recorded by the amplifier relative to ground. When a cell is clamped at its natural resting potential, there is no problem; the clamp is not passing current and the voltage is being generated only by the cell. But when clamping at a different potential, series resistance errors become a concern; the cell will pass current across its membrane in an attempt to return to its natural resting potential. The clamp amplifier opposes this by passing current to maintain the holding potential. A problem arises because the electrode is between the amplifier and the cell, i.e. the electrode is in series with the resistor that is the cell's membrane. Thus, when passing current through the electrode and the cell, Ohm's Law tells us that this will cause a voltage to form across both the cell's and the electrode's resistance. As these resistors are in series, the voltage drops will add. If the electrode and the cell membrane have equal resistances (which they usually do not), and if the experimenter command a 40mV change from the resting potential, the amplifier will pass enough current until it reads that it has achieved that 40mV change. However, in this example, half of that voltage drop is across the electrode. The experimenter thinks he or she has moved the cell voltage by 40mV, but has moved it only by 20mV. The difference is the "series resistance error". Modern patch-clamp amplifiers have circuity to compensate for this error, but these compensate only 70-80% of it. The electrophysiologist can further reduce the error by recording at or near the cell's natural resting potential, and by using as low a resistance electrode as possible.

4) Capacitance errors. Microelectrodes are capacitors, and are particularly troublesome because they are non-linear. The capacitance arises because the electrolyte inside the electrode is separated by an insulator (glass) from the solution outside. This is, by definition and function, a capacitor. Worse, as the thickness of the glass changes the farther you get from the tip, the time constant of the capacitor will vary. This produces a distorted record of membrane voltage or current whenever they are changing. Amplifiers can compensate for this, but not entirely because the capacitance has many time-constants. The experimenter can reduce the problem by keeping the cell's bathing solution shallow (exposing less glass surface to liquid) and by coating the electrode with silicone, resin, paint, or another substance that will increase the distance between the inside and outside solutions.

5) Space clamp errors. A single electrode is a point source of current. In distant parts of the cell, the current passed through the electrode will be less influential than at nearby parts of the cell. This is particularly a problem when recording from neurons with elaborate dendritic structures. There is nothing one can do about space clamp errors except to temper the conclusions of the experiment.

#### Discontinuous single-electrode voltage-clamp

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A single-electrode voltage clamp -- discontinuous, or SEVC-d, has some advantages over SEVC-c for “whole-cell” recording. In this, a different approach is taken for passing current and recording voltage. An SEVC-d amplifier oscillates between passing current and measuring voltage. One oscillation is a “duty cycle”. During a cycle, the amplifier measures the membrane potential and compares it with the holding potential. An operational amplifier measures the difference, and generates an error signal. This current is a mirror image of the current generated by the cell. The amplifier outputs feature sample and hold circuits, so each briefly sampled voltage is then held on the output until the next measurement in the next cycle. Specifically, the amplifier measures voltage in the first few milliseconds of the cycle, generates the error signal, and spends the rest of the cycle passing current to reduce that error. At the start of the next cycle, voltage is measured again, a new error signal generated, current passed etc. The experimenter sets the cycle length, and it is possible to sample every 500-333 microseconds.

For this to work, the cell capacitance must be higher than the electrode capacitance by at least an order of magnitude. Capacitance slows the kinetics (the rise and fall times) of currents. If the electrode capacitance is much less than that of the cell, then when current is passed through the electrode, the electrode voltage will change faster than the cell voltage. Thus when you inject current and then turn it off (at the end of a duty cycle), the electrode voltage will decay faster than the cell voltage. As soon as the electrode voltage asymptotes to the cell voltage, the voltage can be sampled (again) and the next bolus of current applied. Thus the frequency of the duty cycle is limited to the speed at which the electrode voltage rises and decays while passing current. The lower the electrode capacitance, the faster one can cycle.

SEVC-d has a major advantage over SEVC-c in allowing the experimenter to measure membrane potential, and as it obviates passing current and measuring voltage at the same time, there is never a series resistance error. The main disadvantages are that the time resolution is limited, and the amplifier is unstable. If it passes too much current, so that the goal voltage is over-shot, it reverses the polarity of the current in the next duty cycle. This causes it to undershoot the target voltage, so the next cycle reverses the polarity of the injected current again. This error can grow with each cycle until the amplifier oscillates out of control (“ringing”); this usually results in the destruction of the cell being recorded. The investigator wants a short duty cycle to improve temporal resolution; the amplifier has adjustable compensators that will make the electrode voltage decay faster, but if these are set too high the amplifier will ring, so the investigator is always trying to “tune” the amplifier as close to the edge of uncontrolled oscillation as possible, in which case small changes in recording conditions can cause ringing. There are two solutions: to “back off” the amplifier settings into a safe range, or to be alert for signs that the amplifier is about to ring.

## References

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1. ↑ Kandel ER, Schwartz JH, Jessell TM [2000] Principles of Neural Science, 4th ed. pp.152-153. McGraw-Hill, New York
2. ↑ Bear, Mark F. (2006-02-15) [1996]. "Chapter 4 - The Action Potential". Neuroscience: Exploring the Brain (3rd edition ed.). Philadelphia, Baltimore: Lippincott Williams & Wilkins. p. 84\. ISBN 0-7817-6003-8, Template:LCC. Unknown parameter `|coauthors=` ignored (help)CS1 maint: Extra text (link)
3. ↑ A Brief history of Computational Neuroscience Duke University. Retrieved on January 23, 2007.
4. ↑ 4.0 4.1 Huxley A (2002) From overshoot to voltage clamp Trends in Neurosciences 25:553-558

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