Single electrode voltage clamp
| Alan Finkel (2007), Scholarpedia, 2(8):3528. | doi:10.4249/scholarpedia.3528 | revision #37754 [link to/cite this article] |
Contents |
Introduction
By the late 1970s the use of two microelectrodes to control the voltage in nerve and muscle cells had become a well established technique for the measurement of membrane current. However, the two-electrode voltage clamp technique faced limits in two important application areas. First, the penetration by a second electrode in small cells often caused damage that resulted in leakage of cellular contents and a large electrical conductance across the membrane. Second, in in vivo preparations the cells were commonly out of sight and it was difficult to drive the second electrode into the cell. In principle this could be done by gluing the two electrodes together or by aligning them outside the cell in a stereotaxically convergent micromanipulator pair prior to penetration but in practice the former technique was plagued by electrical interactions between the electrodes and the latter by the fact that the flexible tips of the electrodes did not track along straight lines as they penetrated the surrounding tissue.
Both of these problems can be largely overcome if the voltage clamp is implemented with a single electrode. Before discussing how this is achieved in practice it is worth giving consideration to how an ideal voltage clamp operates. In its simplest form, an ideal voltage clamp consists of a battery (Vcmd), a zero-resistance wire and an ammeter (A) to measure current. In Figure 1, the cell membrane is represented by a membrane capacitance (Cm) and a membrane resistance (Rm). The series resistance of the wire (Rs) is zero in this ideal case.
The voltage Vm at all times is exactly clamped to the battery voltage Vcmd. In practice, this ideal form of the voltage clamp cannot be implemented because of the series resistance (Rs) of the electrode that connects to the cell. As current flows through the electrode there is a voltage drop across Rs resulting in Vm being different from Vcmd by an amount proportional to the current (i) and Rs. This is commonly referred to as an IR voltage drop or a series-resistance voltage drop.
There are two ways that a single-electrode voltage clamp can be achieved.
1) Correction of series-resistance voltage error. In principle, if the series resistance is accurately known the voltage drop across it can be calculated and added instantaneously to the Vcmd signal. This technique, often used with patch-clamp electrodes, is called continuous single-electrode voltage clamp (cSEVC). In those cases where Re is very small or the membrane current is very small such that the product of the electrode resistance and the membrane current is a few millivolts or even less than a millivolt, the series-resistance voltage drop can simply be ignored.
2) Time sharing. In this approach, the electrode is rapidly switched (also known as multiplexed) between a current-passing configuration and a voltage-recording configuration, thereby separating voltage measurement from current passing. This technique is known as the discontinuous single electrode voltage clamp (dSEVC) technique.
This article describes the dSEVC technique. Although the patch clamp technique is more popular nowadays, the dSEVC technique remains an essential tool when the cell is covered in connective tissues that cannot be easily removed or pushed aside, or when the cell is deep in tissue and cannot be visualized.
The time sharing technique is complex and if not properly implemented results in a system that might be slow, noisy or inadvertently clamp a fraction of the series resistance of the electrode instead of the cell alone. This article discusses the principles of operation and operating procedures that can be used to minimize the inherent limitations of the dSEVC so that the noise and dynamic performance will be optimal.
Principles of operation
The time sharing principle was first proposed by Brennecke and Lindemann (1974) and applied to microelectrodes by Wilson and Goldner (1975). The principles were further developed and described by Finkel and Redman (1984, 1985). A block diagram and timing diagram are shown in Figures 2 and 3.
A single microelectrode penetrates the cell. The voltage recorded is the sum of the voltage drop (Ve) across the electrode and the membrane potential (Vm). The voltage is buffered by a high-impedance, low-bias-current, buffer amplifier and then applied to a sample-and-hold amplifier. The sample-and-hold amplifier preserves for the whole of the cycle interval (T1 plus T2) the value of the recorded voltage (Vms) that is present at the moment labeled sample in the figure.
Vms is compared to the command voltage (Vcmd ) in the differential amplifier. The difference voltage, ε, is amplified by the differential amplifier and applied to the current-passing input of the electronic switch.
The electronic switch alternates the input path to a voltage-controlled current source. The function of the voltage-controlled current source is to generate a specified current in the electrode. During the current passing interval (T1) the voltage-controlled current source passes a current into the electrode that is proportional to the output of the differential amplifier, with a magnitude determined by the transconductance GT . In this example, at the beginning of the cycle the current is a depolarizing current pulse.
The square pulse of current in the electrode causes the electrode voltage to rise at a rate determined in a non-simple fashion by the series resistance of the electrode, the input impedance (mostly capacitance) of the cell, the capacitance through the wall of the electrode, stray capacitances to ground and the capacitance at the input to the buffer amplifier. For the sake of simplicity, the change in the electrode voltage is shown as if it were a simple exponential.
The current pulse interval is normally a few electrode time constants but, importantly, it is much shorter than the membrane time constant. There is no need for the voltage on the electrode during the current pulse to reach steady state and in most cases in order to maximize the switching rate the current pulse is terminated before steady-state conditions are reached.
Because the duration of the current pulse is much shorter than the time constant of the cell the Vm change shown in Figure 3 appears linear.
During the zero-current interval (T2) the command input of the voltage-controlled current source is zero (i.e., connected to ground) thus its output current is zero. During T2, the value of Ve decays towards zero and given sufficient time the buffer amplifier records Vm alone. In practice, the T2 interval must be sufficiently long for the residual value of Ve to fall to a fraction of a millivolt. Given that at the start of the T2 recording interval the value of Ve might be several volts, a large number of electrode time constants must be allowed for Ve to decay sufficiently.
The polarity of the differential amplifier is such that the closed loop performance tends to drive ε towards a small value. Under steady-state conditions, Vms moves in small increments about the mean value (Vms,ave). The difference between Vms,ave and Vcmd is the steady-state error, ε. This error exists because in order to maintain stability the open-loop gain of the voltage clamp amplifier must be finite. The open-loop gain is the product of the voltage gain of the differential amplifier and the transconductance, GT, of the voltage-controlled current source.
For a detailed discussion of the equations that describe the operation of the dSEVC see Finkel and Redman 1984 and 1985.
Practical considerations
Proper operation of a dSEVC is non trivial and depends on the correct adjustment of several parameters and experimental conditions.
Open-Loop Gain
Although the open-loop gain of the dSEVC depends on the product of both the voltage-controlled current source and the differential amplifier, because their product is linear only one of the two needs to be adjusted. In order to minimize the steady state error, ε, the operator should use the maximum possible gain consistent with stability.
Duty Cycle
The duty cycle can in principle be varied but in practice there is little to be gained by using current-passing intervals (T1) shorter or longer than 25% or 30% of the total interval.
Electrode Resistance
It is essential that the electrode resistance be stable or at worse change slowly during the period that voltage clamping is imposed on the cell and that the electrode response time be as fast as possible. Both of these goals are approached by using electrodes with the lowest practical tip resistance. This may be achieved by using the most rapid taper and largest tip orifice consistent with the size and accessibility of the cell, or by grinding the tip to increase the surface area of its orifice.
Electrode Capacitance – Fabrication
The time constant of the electrode is crucially important. There are many things that can be done to improve the speed of the electrode response.
1) If the electrode is immersed deep in tissue or bath solution consider providing a driven shield to electronically minimize the dynamic impact of the transmural capacitance (Finkel and Redman, 1983). Shielding is very effective from the dynamic performance point of view but it increases the background noise.
2) Minimize the actual transmural capacitance either by using thick-walled glass or by coating the outside of the electrode with silicone.
3) If solution creeps up the surface of the non-immersed part of the electrode it will increase the capacitance to ground. This can be prevented by dipping the electrode in a hydrophobic coating such as mineral oil (Axon Guide, 1993)
Electrode Capacitance – Electronics
The capacitance neutralization control in the dSEVC is critically important to the performance of the clamp. The capacitance neutralization circuit inside the buffer amplifier uses an electronic circuit to provide the charging current for the electrode capacitance that would otherwise be provided from the output of the voltage-controlled current source. The magnitude of the capacitance neutralization control is set by the operator. To determine the correct setting the operator should constantly monitor the output of the buffer amplifier and adjust the Vm + Ve waveform so that during the voltage recording interval, T1, the signal decays as fast as possible without overshooting. It is normal practice to make adjustments to this control from minute to minute during the voltage clamp session. These adjustments are necessary to correct for slow drift in the value of the electrode resistance.
Although it is beyond the control of the operator, it is worth noting that the electromechanical design of the buffer amplifier should minimize its input capacitance. Techniques to achieve this are described in the Axon Guide (1993).
Switching Frequency
The switching frequency is the inverse of the sum of the switching intervals T1 and T2. The usual operating range is about 1 kHz to 10 kHz but higher or lower values may be used. The goal is to use the fastest rate possible because this minimizes the excursions in the membrane potential, thereby improving the quality of the voltage control at the membrane and also minimizing instability. Once the capacitance neutralization control has been optimized, the switching frequency can be maximized. If the switching frequency is too high, the dSEVC will oscillate and the cell might be destroyed. To avoid inadvertently setting the switching frequency too high the operator should observe the output of the buffer amplifier and ensure that there is adequate time allowed for Vm + Ve to decay to steady state, equal to Vm.
Anti-Aliasing Filter
The noise in a dSEVC is inherently worse than in a two-electrode voltage clamp because the bandwidth of the electrode and buffer amplifier must be maximized in order to enable rapid settling of the electrode voltage after each current pulse. The broadband noise is aliased by the sampling process so that it appears as noise in the recording bandwidth.
If the response of the electrode were ideal, that is an exponential response determined by the resistance of the electrode in series with all of the various capacitances lumped together as a single capacitor at the tip of the electrode, optimum noise performance would be achieved by increasing the sampling frequency to the maximum possible value prior to the onset of instability.
In practice, the electrode response is not nearly so ideal and most electrodes tend to settle with both a fast and a slow response. The noise is more related to the fast phase. The noise at the output of the buffer amplifier can be reduced by inserting a lowpass, anti-aliasing filter that is adjusted to cut the speed of the fast phase but not so much that it increases the settling time that is ordinarily dominated by the slow phase.
Lowpass Output Filter
The noise at the current and voltage outputs of the dSEVC can be reduced by inserting a lowpass filter between these outputs and the recording device. The cutoff frequency of the lowpass filter should be set to severalfold less than the sampling frequency. Typically, it will be fivefold lower.
Clamping the Electrode
If the operator does not constantly monitor the output of the buffer amplifier and adjust the capacitance neutralization and ensure that the switching frequency is not so fast that Vms fails to decay to steady state it is possible for the dSEVC to clamp not just Vm alone but the sum of Vm and the electrode voltage drop, Ve. Ordinarily, this would cause the dSEVC to go unstable and oscillate, however there are certain combinations of the anti-alias filter setting, the lowpass output filter and the capacitance neutralization control that will guarantee stability despite the fact that the electrode voltage drop is being clamped. This problem and ways to avoid it are discussed in Finkel and Redman (1984, 1985) and the Axon Guide (1993).
Performance Compared with TEVC Technique
Advantages
The dSEVC technique is superior to a two-electrode voltage clamp (TEVC) in several ways.
1) Less cell injury occurs because the cell is penetrated by one electrode instead of two.
2) The dSEVC is practical to use on cells that cannot be visualized.
3) Current does not flow when the membrane potential is being measured, so errors due to voltage drop across the cytoplasmic series resistance are avoided.
4) Instability of the negative feedback control circuit due to capacitive coupling between the two electrodes is avoided.
Disadvantages
On the other hand, the dSEVC technique is not as good as a TEVC in several ways.
1) Speed. It takes longer for the dSEVC to reach the new membrane potential after a step change in the command voltage. Similarly, the dSEVC is not as fast at following changes in the membrane conductance.
2) Noise. The dSEVC recordings are inherently more noisy than TEVC recordings. Basically, this is a result of a) the wider recording bandwidth necessary for the electrode to settle between current pulses and b) the aliasing that takes place in the sample and hold process.
3) Accuracy. It is normally possible to use higher open-loop gain settings in a TEVC before the onset of instability than it is possible to use in dSEVC, thus the clamp error (ε) is lower in the TEVC.
Conclusion
In those cases where it is not practical to use TEVC or patch clamp, the dSEVC is a powerful alternative.
A good dSEVC experiment will use an amplifier that is made with high-speed, low-noise electronic circuitry. The operator will set the capacitance neutralization, clamp gain and switching frequency in an orderly way, always directly monitoring the Vms signal. Most importantly, the electrode will be fabricated for fast settling, meaning that it will have the lowest practical resistance and various techniques will be used to minimize the numerous sources of parasitic capacitance.
If all these considerations are attended to, membrane conductance changes with millisecond rise times can be reliably measured and submillisecond rise times can be measured if some loss of voltage accuracy can be tolerated.
References
- The Axon Guide for Electrophysiology & Biophysics: Laboratory Techniques. 1993. http://www.moleculardevices.com/pages/instruments/axon_guide.html
- Brennecke, R. & Lindemann, B. Theory of membrane voltage clamp with discontinuous feedback through a pulsed current clamp. Rev. Sci. Instrum. 45: 184-188, 1974.
- Brennecke, R. & Lindemann, B. Design of a fast voltage clamp for biological membranes, using discontinuous feedback. Rev. Sci. Instrum. 45: 656-661, 1974.
- Finkel, A.S. & Redman, S.J. A shielded microelectrode suitable for single-electrode voltage clamping. J. Neurosci. Methods 9: 23-29, 1983
- Finkel, A.S. & Redman, S.J. Theory and operation of a single microelectrode voltage clamp. J. Neurosci. Methods 11: 101-127, 1984.
- Finkel, A.S. & Redman, S.J. Optimal Voltage Clamping with Single Microelectrode, in Voltage and Patch Clamping with Microelectrodes. Ed. T. Smith Jr. et al, Baltimore: Williams & Wilkins, 1985.
- Wilson, W.A. & Goldner, M.M. Voltage clamping with a single microelectrode. J. Neurobiol. 6: 411-432, 1975.
Internal references
- Jeff Moehlis, Kresimir Josic, Eric T. Shea-Brown (2006) Periodic orbit. Scholarpedia, 1(7):1358.
- Philip Holmes and Eric T. Shea-Brown (2006) Stability. Scholarpedia, 1(10):1838.
- John W. Moore (2007) Voltage clamp. Scholarpedia, 2(9):3060.
