Voltage clamp

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Template:Cleanup-date Image:Voltage clamp.jpg The voltage clamp is used by electrophysiologists to measure the ion currents flowing across a neuron's membrane. Voltage-gated ion channels open and close as they normally do in response to positive charge within the cell, but the clamp prevents the changes in membrane current that result from causing a change in membrane potential (Kandel et al., 2002). With the voltage clamp it is possible to study ion flux across a membrane.

The concept and design of the voltage clamp apparatus is due to the pioneering work of Kenneth Cole and George Marmount [1] in the 1940s. Cole discovered that it was possible to use two electrodes and a feedback circuit to force the cell's membrane potential to remain at a set place determined by the experimenter.

Alan Hodgkin realized that,to understand ion flux across the membrane, it would be necessary to eliminate the other variable, differences in the membrane potential (Huxley, 2002). This is because the two phenomena are related, and differences in membrane potential would lead to differences in ion flux (Huxley, 2002). After experiments with the voltage clamp, Hodgkin and Andrew Huxley published a paper outlining the ionic causes of the action potential in 1952, for which they shared the Nobel Prize for Physiology or Medicine in 1963 (Huxley, 2002).

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Technique

The voltage clamp is a current generator with two electrodes attached. To clamp the voltage, both electrodes are placed inside a cell. Transmembrane voltage is recorded through one of these electrodes, the "voltage electrode", relative to an outside reference (ground). The second electrode, the "current electrode", is used for passing current into the cell.

The experimenter specifies a "holding voltage", or "command potential", that he or she wishes the cell to maintain across its membrane. The voltage clamp uses a negative feedback system to maintain the cell at this voltage. The electrodes inside and outside the cell are connected to an amplifier. This amplifier measures membrane potential, displays it on an oscilloscope, and feeds the signal into the next amplifier, the feedback amplifier. The feedback 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). It then magnifies any difference it finds and sends an output to a current electrode that runs along the length of the axon within it.

Whenever the cell deviates from the holding voltage, for example by passing an ion current across its membrane, the operational amplifier generates an "error signal". The error signal is the difference between the holding voltage specified by the experimenter and the actual voltage of the cell. The feedback circuit of the voltage clamp passes current into the cell (via the current electrode) as needed to reduce the error signal to zero. Thus, the current is applied in the polarity opposite the current that the cell is passing across its membrane, and the clamp circuit produces an electrical current that is equal and opposite to the ionic current. This "clamp current" can be easily measured, giving an accurate reproduction of the currents flowing across the cell's membrane (albeit in the opposite polarity). Thus it is not only possible to maintain the membrane potential at a desired voltage, it is also possible to record the amount of current that is necessary to keep it at that level.

Cole developed his voltage clamp before the era of microelectrodes, so his two clamp electrodes were constructed from two fine wires twisted around an insulating rod. This construction could be inserted into only the largest biological cells. This accounts for the nearly exclusive use of the squid as the animal of choice for early electrophysiological experiments. Squid squirt jets of water when they need to move quickly, as when escaping a predator. To make this escape as fast as possible, squid evolved an axon upwards of 1 mm in diameter (signals propagate more quickly down axons with larger diameters). This squid giant axon was the first preparation that could be used to voltage clamp any biological transmembrane current, and, along with the voltage clamp, served as the basis of the experiments that defined the properties of the action potential by Hodgkin and Huxley.

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Variations of the voltage clamp technique

Several variations exist to the voltage clamp technique. These arose mostly to accommodate cells that were too small to accept giant electrode assemblies used in the squid giant axon. These variations are the two-electrode voltage clamp, the continuous single-electrode voltage clamp (patch clamp), and discontinuous single-electrode voltage-clamp.

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Two-electrode voltage clamp using microelectrodes

This technique works on the same principal as Cole's "squid clamp" except the two electrodes are glass pipettes with very fine tips (less than 1 micrometer). A smaller cell such as a muscle cell is still large enough to accommodate the double impalement required for this technique.

The use of microelectrodes has the advantage of allowing for voltage clamping of cells smaller than the squid axon, but also has disadvantages. Chief among these is that microelectrodes are much less ideal conductors than the much larger wires used by Cole. Because their tips are so small, they sometimes cannot pass current rapidly enough to fully compensate for cellular current. Thus the voltage clamp may produce a distorted image of the cell's current. In general, the faster the kinetics of the current (onset and offset), the more likely it is that the voltage 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. Furthermore, microelectrodes can provide only a spacial point source of current that may not uniformly affect different parts of an irregularly shaped cell.

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Single-electrode voltage clamp

There are two basic variations of single electrode clamp. In this technique, an electrode is placed in contact with the intracellular compartment of a cell. The single electrode serves both the voltage-recording and current-passing duties that are performed by two separate electrodes in two-electrode clamp.

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Continuous single-electrode clamp (SEVC-c)

See main article patch clamp

The "patch clamp" technique, is a refinement of the voltage clamp that allows the study of individual ion channels. It uses an electrode with a relatively large diameter at its tip (over 1 micrometer), and made such that the tip forms a smooth surfaced circle (rather than a sharp tip; all tangents to this circle being perpendicular to the long axis of the electrode). This is known as a "patch clamp electrode" (as distinct from a "sharp microelectrode" used to impale cells). This electrode is pressed against a cell membrane and suction can be applied to the inside of the electrode to pull the cell's membrane inside the electrode tip. This suction causes the cell to form a tight seal with the electrode (a so-called "gigaohm seal", as the electrical resistance of that seal is in excess of a gigaohm).

As a recording system, single electrode voltage clamp has significant disadvantages compared to two-electrode voltage clamp. But an advantage is that you can record from small cells that would be impossible to impale with two electrodes. Some of the disadvantages are:

1) Microelectrodes are imperfect conductors of ion current. They generally have a resistance in excess of a million ohms. They rectify (i.e. they change their resistance with voltage, often in an irregular manner), they sometimes have unstable resistance if clogged by cell contents, membrane, or general free-floating gunk. Thus, they will not faithfully record the voltage of the cell (especially when it is changing quickly) nor will they faithfully pass the current from the voltage-clamp.

2) Voltage and current errors: A major disadvantage of continuous single-electrode voltage clamp circuity is that it does not actually measure the voltage of the cell being clamped (as does two-electrode clamp). To put it simply, the patch-clamp amplifier is identical in design to a two-electrode clamp, except that the voltage measuring and current passing circuits are connected directly to each other (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 in the amplifier. The amplifier reads only the voltage at the top of the electrode, and feeds back current to compensate for that. But, if the electrode is an imperfect conducter, the clamp circuity will have only a filtered and distorted view of the cell's membrane potential. Likewise, when the circuit passes back the current needed 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 electrical characteristics of the electrode don't change during an experiment (so the errors will be constant), and avoids recording currents that have kinetics likely to be too fast for the clamp to follow accurately. The accuracy of a continuous single electrode clamp 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 through the electrode must go to ground to complete the circuit. Ground is outside the cell. The voltage recorded by the amplifier are recorded relative to ground. When a cell is clamped right 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 attempting to clamp the cell at a potential different from its natural resting potential, series resistance errors become a concern. When clamping away from normal resting potential, the cell will pass current across its membrane in an attempt to get back to its natural resting potential. The clamp amplifier opposes this by passing current to keep the cell at the commanded holding potential. A problem arises because the electrode is located between the amplifier and the cell. Put another way, the resistor that is 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 two voltage drops will add. The experimenter is interested only in the voltage of the cell, but is seeing the voltage of the cell as well as that of the electrode. If the electrode and the cell membrane have equal resistances (which they usually do not), and if the experimenter command a 40 mV change from the cells resting potential, the amplifier will respond by passing enough current until it reads that it has achieved that 40 mV voltage change. However, in this example, half of that voltage drop is across the electrode, not the cell. The experimenter thinks he or she has moved the cell's voltage by 40 mV, but has, in fact, moved it only by 20 mV. The difference between what the experimenter thinks has been done and what has actually been done is the "series resistance error". It is particularly troublesome when trying to accurately assess the voltage-dependence of a particular ion current. If one doesn't know what the membrane potential of the cell really is, one cannot make this measurement.

All modern patch clamp amplifiers have circuity that tries to compensate for the series resistance error. These circuits compensate only 70-80% of the error, leaving significant error in the measurement. The electrophysiologist can further decrease the influence of series resistance 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. All microelectrodes act as capacitors as well as resistors. They are particularly troublesome capacitors because they are non-linear. The capacitance of an electrode arises because the electrolyte inside the electrode is separated by an insulator (glass) from the ion-containing solution outside the electrode. This is, by definition and function, a capacitor. Worse, since the thickness of the glass changes the farther you get from the tip, the time constant of the capacitor will vary. The main problem caused by this electrode capacitance is that it produces a distorted record of the membrane voltage or current any time they are changing. Amplifiers can compensate for this electrode capacitance, but not entirely because the capacitance has many time-constants. The experimenter can reduce this problem by keeping the cell's bathing solution as shallow as possible (exposing less glass surface to liquid) and by thickening the walls of the electrode, by coating the electrode with silicone, resin, paint, or another substance that will cling to the glass and make the distance between the inside and outside solutions larger.

5) Space clamp errors. Your single electrode is but a point source of current. In distant parts of the cell, the current passed through the electrode will be less influential than nearby parts of the cell. This is particularly a problem when recording from cells like neurons that have elaborate dendritic structures. There is basically nothing one can do about space clamp errors except to temper the conclusions of the experiment to account for them.

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Discontinuous single-electrode voltage-clamp

A single-electrode voltage clamp — discontinuous, or SEVC-d, is one of the most interesting and underutilized techniques in electrophysiology and has some striking advantages over continuous SEVC (SEVC-c) when doing “whole-cell” recording. In this technique a completely different electronic approach is taken for passing current and recording voltage through the same electrode. Rather than doing so simultaneously as in SEVC-c, the electrode is time-shared so the current is passed and voltage is recorded at different times. Basically, an SEVC-d amplifier oscillates between passing current and measuring voltage. One such oscillation of the amplifier is known as its “duty cycle”.

During one duty cycle, the amplifier measures the membrane potential of the cell. It compares that membrane potential to the experimenter specified “holding potential” (or command potential). An operational amplifier measures the difference between these two potentials and generates an error signal that specifies how much current needs to be passed into the cell to bring it to the command potential. This clamp current is then measured, and will be a mirror image of the current generated by the cell. In these ways SEVC-d is identical to all other forms of voltage clamping. How SEVC-d differs is that it measures the voltage and passes current each at different times during the duty cycle, and each time only briefly. The amplifier outputs feature sample and hold circuits, so that, for instance, each briefly recorded (sampled) voltage is then held on the output until the next measurement is made in the next duty cycle. More specifically, the amplifier measures voltage in the first few milliseconds of the duty cycle, generates the error signal, and then spends approximately the last 2/3 of each duty cycle passing current into the cell to reduce that error. At the beginning of the next duty cycle, voltage is measured again, a new error signal generated, current passed, and so on…

The experimenter sets the length of the duty cycle (or put another way, the frequency at which the amplifier oscillates). In a perfect world, one would set the frequency very high (say 100 kHz). This would give excellent time resolution of both the cells voltage and the amount of current passed (at 100 kHz, samples would be taken every 10 microseconds). In practice, one must set the oscillation much slower than that, usually in the 2-3 kHz range (giving a sample every 500-333 microseconds, or about half a millisecond).

This technique takes advantage of the fact that the capacitance of the electrode is usually lower than the capacitance of the cell being recorded. Capacitance has the effect of slowing the kinetics (the rise and fall times) of currents. If the capacitance of the electrode is significantly lower 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 into the cell through the electrode 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’s voltage, the voltage sample can be taken (again) and the next bolus of current applied. Thus the frequency of the duty cycle is thus 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.

The reason that this technique works at all is because the electrode can change its voltage much faster than the cell can (it is a requirement of this technique that an electrode can change its voltage faster than the cell). This way, the electrode can get a sample, pass current to move the cell’s membrane potential, but when the current is turned off at the end of the duty cycle (to allow for the next voltage measurement), the cell cannot recover from the previous cycles current injection before the next cycles current injection begins. In order for this to work, the cell capacitance must be higher than the electrode capacitance by at least an order of magnitude, and two orders of magnitude is better.

SEVC-d has the major advantage over SEVC-c in that it allows the experimenter to measure the membrane potential of the cell. Furthermore, since it obviates passing current and measuring voltage at the same time, there is never a series resistance error. The main disadvantages of this technique are that the time resolution is limited, and it takes considerably more skill to perform than SEVC-c. The main reason that SEVC-d is more difficult is that the amplifier, being an oscillator within a feedback loop, is inherently unstable. If the amplifier passes too much current such that the goal voltage is over-shot, it will reverse the polarity of the current in the next duty cycle. This will cause it to undershoot the target voltage so the next duty cycle reverses the polarity of the injected current again. This error can grow larger with each duty cycle until the amplifier is changing current polarities with each duty cycle at its maximum ability to pass current. In other words, the amplifier just oscillates out of control. This is known as “ringing” the amplifier. While ringing does no harm to the amplifier, it almost always results in the destruction of the cell being recorded.

The investigator is faced with two competing interests. First he or she wants to make the duty cycle as fast as possible to improve temporal resolution. The amplifier has a number of adjustable compensators that will make the electrode voltage decay faster. So to improve the temporal resolution as much as possible, the investigator sets these compensators at their maximum level. The trouble is, setting these compensators too high causes the amplifier to ring. So the investigator is always trying to “tune” the amplifier as close to the edge of uncontrolled oscillation as possible. The trouble with this strategy is that small changes in the recording conditions (for example, a small disturbance in the depth of the solution bathing the cells) can cause the amplifier to ring if it’s already teetering on the edge of ringing. There are two solutions to this problem. First one could “back off” the amplifier settings into a safe range. This would be analogous to asking a NASCAR driver to drive slower during a race to preserve the car. The second solution is hyper vigilance. The investigator must sit there eyes raptly glued to the oscilloscope screen looking for warnings that the amplifier is about to ring. One often gets a half second or so of warning before ringing becomes uncontrollable, so the investigator must also sit there with his or her hands actually on the knobs in order to be able to react quickly enough to save the cell. Because of this, it is one of the most mentally intense electrophysiology experiments, but also the most adrenaline-producing.

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References

fr:Patch-clamp nl:Patch-clamp techniek

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