SPECIAL COMMUNICATION
Switched single-electrode voltage-clamp amplifiers allow precise
measurement of gap junction conductance
Andreas
Müller1,
Melani
Lauven1,
Reinhard
Berkels1,
Stefan
Dhein1,
Hans-Reiner
Polder2, and
Wolfgang
Klaus1
1 Institute of Pharmacology,
University of Cologne, D-50931 Cologne; and
2 npi-electronic GmbH, D-71732
Tamm, Germany
 |
ABSTRACT |
Measurement of gap
junction conductance
(gj) with patch-clamp
amplifiers can, due to series resistance problems, be subject to
considerable errors when large currents are measured. Formulas developed to correct for these errors unfortunately depend on exact
estimates of series resistance, which are not always easy to obtain.
Discontinuous single-electrode voltage-clamp amplifiers (DSEVCs) were
shown to overcome series resistance problems in single whole cell
recording. With the use of two synchronized DSEVCs, the simulated
gj in a model
circuit can be measured with a maximum error of <5% in all recording
situations investigated (series resistance, 5-47 M
; membrane
resistance, 20-1,000 M
; gj, 1-100
nS). At a very low
gj of 100 pS, the
error sometimes exceeded 5% (maximum of 15%), but the error was
always <5% when membrane resistance was >100 M
. The precision
of the measurements is independent of series resistance, membrane
resistance, and gj. Consequently,
it is possible to calculate
gj directly from Ohm's law, i.e., without using correction formulas. Our results suggest that DSEVCs should be used to measure
gj if large
currents must be recorded, i.e., if cells are well coupled or if
membrane resistance is low.
voltage-clamp technique; connexins; ion channels
 |
INTRODUCTION |
DUAL-CELL VOLTAGE CLAMP IS now widely used to study
electrical gap junctional communication between cells. Although at
first two-electrode voltage-clamp amplifiers were used, i.e., each cell had to be impaled by two microelectrodes (6, 17, 18), single-electrode voltage-clamp amplifiers have been used ever since the tight seal whole
cell recording technique became available (5). Two different amplifier
designs are currently available for this kind of experiment. Patch-clamp amplifiers preset the potential at the electrode to the
command potential and continuously inject current to correct for
voltage deviations from the command potential (5, 11, 16).
"Switched" single-electrode voltage-clamp amplifiers
change at high frequency between potential measurement and current
injection (2, 31). The intracellular potential is measured at the end of the current-free period when the voltage transient occurring at the
electrode tip during injection of current has completely relaxed.
Because of the discontinuous mode of action, these amplifiers are often
referred to as discontinuous single-electrode voltage-clamp amplifiers (DSEVCs).
Up to now, patch-clamp amplifiers have been used almost exclusively in
dual-cell voltage-clamp experiments. However, when patch-clamp
amplifiers are used for the measurement of gap junction conductance
(gj), series resistance
(formed by the pipette and the broken membrane patch) can cause serious
errors in the measurement (22, 24, 28, 30). Series resistance is a
problem mainly in situations in which gap junction resistance
(Rj) and/or
membrane resistance is low, because large currents will flow. According to Ohm's law, this will result in large voltage drops across the series resistance. In those situations, errors in the measurement of
gj can become as
large as 70% (22). To correct for the errors introduced by series
resistance, several correction formulas were proposed that take into
account either series resistance alone (24, 28) or a combination of
series resistance and cell input resistance (22). All of these formulas
depend critically on an exact estimate of the series resistance, which
is not always easy to obtain (24).
As mentioned above, switched single-electrode voltage-clamp amplifiers
inject current discontinuously and measure the intracellular potential
at a time when no current flows across the pipette. Thus these
amplifiers should avoid the problem of errors caused by series
resistance. It was shown recently that DSEVCs avoid series resistance
problems in voltage-clamp measurements in single cells (4, 7, 14).
However, there are no studies on the use of DSEVCs in the measurement
of gj.
It was, therefore, the aim of this study to investigate the usefulness
of DSEVCs for gj
measurement. In most studies, electrodes with direct current
resistances of 2-5 M
are used. This will usually result in
series resistance of >5 M
(5, 11). However, series resistance can
increase considerably during the course of an experiment, and higher
values (10-20 M
) can easily result. In perforated patch
experiments, series resistance often is as high as 50 M
. Cell input
resistance (membrane resistance) depends mainly on the cell type and
electrode solution used and can vary between ~15 M
in adult
ventricular cardiomyocytes (9, 29) and >1 G
in neonatal rat heart
cells (15). Rj
can vary between 2-3 M
(26, 28) and >10 G
when single gap
junction channels are investigated (21). Using these data, we designed
model circuits with different series resistances, membrane resistances,
membrane capacitances, and
Rj to investigate
the accuracy of
gj measurements with two synchronized DSEVCs. Our results show that in all recording situations (series resistance 5-47 M
; membrane resistance
20-1,000 M
)
gj (1-100
nS) was precisely measured by the DSEVCs with a maximum error of 5%.
At a gj of 100 pS, which is well within the ranges of gap junction single-channel
conductance, the error was only <5% when membrane resistance was
>100 M
. The results strongly suggest that DSEVCs should be used
for the measurement of
gj in those
situations when either membrane resistance is low or
gj is high.
 |
METHODS |
Equivalent circuit.
The equivalent circuit we used in this study is depicted in Fig.
1. Each cell is represented by
a parallel combination of a resistor
(Rm1 or
Rm2) and a
membrane capacitance
(Cm1 or
Cm2). The
pipette resistance and the conductance connecting the two cells are
represented by resistors [series resistance
(Rs1 and Rs2) and
junctional resistance
(Rj),
respectively].

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Fig. 1.
Equivalent circuit of a dual whole cell measurement.
Cells
1 and
2, respectively, are represented by
parallel combinations of membrane resistance
(Rm1 and
Rm2) and
membrane capacitance
(Cm1 and
Cm2).
Microelectrodes are represented by series resistors
(Rs1 and
Rs2), and
cells are connected by junctional resistance
(Rj).
Ij, junctional
current; I1 and
I2, currents
measured by the two amplifiers, respectively;
Im1 and
Im2, membrane
currents of cells 1 and
2, respectively;
V1 and
V2, membrane
potential of cells 1 and
2, respectively.
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To study the influence of each of the components of the model circuit
on the outcome of the measurements, several combinations of resistances
and capacities were investigated. Specifically, the following values
were chosen for the respective components: series resistance, 5, 10, 20, and 47 M
; membrane resistance, 20, 100, 500, and 1,000 M
;
Rj, 10, 20, 100, 200, 1,000, and 10,000 M
; and
Cm, 56, 150, and
220 pF. These values cover almost the entire physiological range for
these parameters. All possible combinations of resistors were
investigated with the different cell capacitances. Resistors of <1
G
had tolerances of 5%. The other resistors had tolerances of 10%.
Because it was the goal of this study to determine the accuracy of the
measurement of Rj
and gj, we
measured the exact values of all resistors used to represent
Rj. For this
purpose, the resistors were put between the amplifier headstage and
ground. We then measured the voltage drop across the resistors in
response to an applied current of known magnitude. The resistance was
then calculated according to Ohm's law. The exact values were 9.88, 19.7, 99.8, 197, 990, and 9,578 M
, corresponding to conductances of
101.21, 50.81, 10.07, 5.09, and 1.01 nS and 100 pS, respectively.
Experimental protocol and data evaluation.
As can be seen from Fig. 1, the
Rj is
electrically isolated from ground. Therefore, any current flowing
across Rj will
not lead to a change of the sum of the currents measured by the two resistors
(I1 + I2). This
means that application of a voltage difference across
Rj will result in
junctional currents
(Ij) of equal
magnitude but opposite polarity in both cells. This principle is
exploited for the measurement of
gj. When a
voltage jump is applied to one cell, this will result in a change in
the current recorded from this cell. This current is the sum of the
Ij and the
elicited membrane current
(Im). Because
the voltage in the other cell was kept constant, the change in the
current recorded from this cell
(
I2) is
equal to
Ij.
Consequently, gj
can be calculated according to
|
(1)
|
The
membrane potentials of cells
1 and
2 (V1 and
V2, respectively)
and
I2 were
determined from the recordings, and
gj was calculated
from Eq.
1.
Throughout this paper, we will refer to the pulsed cell as
cell 1 (with
Rm1,
Rs1, and
I1) and to the
nonpulsed cell as cell 2 (with
Rm2,
Rs2, and
I2), regardless
of the actual physical situation.
The following experimental protocol was used to measure
Rj and
gj. A voltage
command of
100 mV (500 ms in duration) was applied to
cell 1 while cell
2 was held at 0 mV. Then the "cells" were switched, i.e., the same stimulus was applied to the other cell. This
protocol was repeated five times, and the resulting voltage and current
traces were averaged.
Data, the voltage and current of each amplifier, were sampled at a rate
of 5 kHz/channel after low-pass filtering at 1 kHz. The WinTida (HEKA
elektronik, Lambrecht, Germany) data acquisition system, which uses the
ITC-16 interface (Instrutech, New York, NY), was used for
data acquisition and analysis.
Amplifiers and amplifier adjustment.
Two DSEVCs were used for this study (SEC 05 and SEC 10, npi-electronic,
Tamm, Germany). DSEVCs use a time-sharing principle, i.e., they switch
between current injection and potential measurement with a high
frequency. Because the membrane potential is measured at a time when no
current flows across the electrode, series resistance problems are
totally avoided (Refs. 2, 31; for a review see Ref. 12). Both
amplifiers were used with the same (synchronized) switching frequency (fsw) by connecting
the SEC 05 system to the internal clock of the SEC 10 system. In this
way, current injection and membrane voltage sampling occurred at the
same time in both systems, thus avoiding interference. However, to
achieve complete suppression of the series resistance, the current
injection artifact must decay almost completely before the membrane
potential is sampled. To obtain a linear response from the DSEVC, the
fsw must be in
the range of tens of kilohertz (2), i.e., the current injection
artifacts must decay very rapidly (within a few microseconds). In the
amplifiers used here, this is achieved by the use of supercharging (1)
in addition to the regular feedback-based capacity compensation method
(12). Supercharging here is used not for speeding the response of the
membrane potential to a current step [as described initially by
Armstrong and Chow (1)] but to eliminate stray capacitances
around the microelectrode and to reduce the response time of the
microelectrode to brief current steps of a few microseconds. With this
approach, it is possible to compensate stray capacitances around a
microelectrode by injection of a certain amount of charge induced by a
spike superimposed on the command signal applied to the electrode.
Electronic circuits and calculations are given in detail in the papers
by Strickholm (19, 20). The increase in speed is considerable (up to
100-fold; see Refs. 19 and 20). With this approach, it was possible to
reduce the settling time of the microelectrode after a current pulse to
2-3 µs (tested and checked in many labs, e.g., see Refs. 8 and
14). From these findings, a frequency formula was derived that
describes the relationship between the electrode time constant, the
fsw of the DSEVC,
the sampling frequency of the data acquisition system (fs), the upper
cutoff frequency of the low-pass filter
(ff), and the
time constant of the cell membrane (27)
|
(2)
|
where
fe is the upper
cutoff frequency (
3 dB frequency) of the microelectrode and
fm is the upper
cutoff frequency of the membrane.
With the time constant in the range of 1-3 µs recorded for the
electrode resistances used in this study,
fe is 80-160
kHz; fsw of the
DSEVC was set to 30-50 kHz (calculated range 25-53 kHz),
fs was 5 kHz, and
ff was 1 kHz (see
below). These settings are currently used for recordings in our lab.
The fm was
calculated to be 140 Hz (membrane resistance, 20 M
;
Cm, 56 pF).
The headstage output signal (i.e., the response to the discontinuous
current injection at the electrode level) from both amplifiers was
monitored during all experiments with a separate oscilloscope. The
fsw was adjusted
to the optimal value between 30 and 50 kHz, and the electrode artifacts
decayed in 1-3 µs after optimal tuning of capacity compensation.
Thus the recording conditions satisfied the criteria for reliable
single-electrode voltage clamp.
The fast settling of the microelectrodes allows the use of high
switching frequencies (20-50 kHz), which in turn allows high voltage-clamp gains of up to 10-20 µA/V. By use of a
proportional-integral controller, it is possible to further increase
the gain to 100 µA/V without affecting the noise level or the
stability of the clamp. The proportional-integral controller yields an
instantaneous fast response to changes (proportional gain) while the
integral part increases the gain for frequencies below the (adjustable) upper cutoff frequency of the integrator (i.e., for slow signals; Ref.
14). Thus the so-called "integrator" improves voltage control considerably, allowing voltage-clamp measurements with an error <1%,
which is very important for the accuracy of the calculation of
gj. A more
detailed description of the amplifiers can be found in the publications
by Richter et al. (14) and Draguhn and co-workers (4).
The resistors Rs1
and Rs2 were
connected to the inputs of the amplifier headstages via shielded
cables. Each time the series resistance was changed (i.e., when the
Rs1 and
Rs2 resistors
were changed) the electrode capacitance was carefully canceled with the
capacity compensation circuit of the amplifiers and the voltage-clamp gain was adjusted. To do so, both cells were simultaneously subjected to voltage jumps of 40 mV. Voltage-clamp gain was adjusted to give the
fastest possible voltage responses with an overshoot of <5% (see
also Determinants of voltage
control). The
fsw was set to 32 kHz in all experiments (25% duty cycle).
Cell culture.
Human cervix carcinoma HeLa cells transfected with connexin 43 (Cx43;
kindly provided by K. Willecke, Bonn, Germany) were cultured in DMEM
supplemented with 100 µg/ml streptomycin, 100 U/ml penicillin, and
0.5 µg/ml puromycin.
Electrophysiology.
For electrophysiological experiments, the cells were grown in plastic
petri dishes on coverslips. Immediately before the experiments, the
coverslips were removed from the dishes, washed with modified Tyrode
solution, and transferred to an experimental chamber containing modified Tyrode solution (in mM: 135 NaCl, 4 KCl, 2 CaCl2, 1 MgCl2, 0.33 NaH2PO4,
10 HEPES, and 10 glucose, pH 7.4). Patch electrodes were pulled from
borosilicate glass (GC 150FT, Clark Electromedical, Pangbourne, UK)
with a microprocessor-controlled puller (P97, Sutter Instruments,
Novato, CA) and had direct current resistances of 3-4 M
when
filled with intracellular solution (in mM: 125 CsCl, 8 NaCl, 1 CaCl2, 10 EGTA, 2 Na2ATP, 3 MgATP, 0.1 Na2GTP, and 10 HEPES, pH adjusted
to 7.2 with CsOH). For the measurement of single-channel gap junction
currents, heptanol (2 mM) was added to the modified Tyrode solution to
uncouple the cells and reveal single gap junction channel events.
 |
RESULTS |
Determinants of voltage control.
For accurate measurement of
gj, it is
necessary for the voltage of the nonpulsed cell to be kept constant. To
find out which parameters and adjustments are important for exact
voltage control, we investigated different settings with respect to
voltage-clamp gain. Figure 2 illustrates
that accurate voltage control is possible only when both the
proportional and the integral parts of the voltage-clamp amplifiers
were used. With the exception of small voltage transients at the
beginning and at the end of the voltage pulse, there was no change in
the voltage of the nonpulsed cell. Employment of only the proportional
part of the amplifier did not allow clamping of the voltage in the
nonpulsed cell (Fig. 2B). Adjustment
of the proportional part of the amplifier was, however, important for
the speed of the clamp and for adjustment of the overshoot.

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Fig. 2.
Accuracy of voltage control. Current and voltage changes in both cells
in response to a voltage pulse of 100 mV applied to
cell 1. Arrows indicate zero-voltage
and zero-current levels. A:
proportional-integral controller was employed, and voltage in nonpulsed
cell remained unchanged except for small voltage transients at
beginning and end of voltage jump. B:
integrator was not used. This resulted in a loss of
voltage-control in nonpulsed cell.
Rm1 = Rm2 = 1 G ;
Rs1 = Rs2 = 47 M ;
Rj = 10 M .
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Effect of series resistance.
The effect of series resistance on the accuracy of the measurement of
gj was assessed
by using different resistors to represent Rs1 and
Rs2. In Fig.
3A, the
measured fraction of
gj is plotted vs.
gj for a
combination of resistors in which the membrane resistance amounts to 1 G
in both cells.
Rs1 was kept
constant at 5 M
and combined with different values for
Rs2. No influence
of series resistance on the accuracy of the measurements of
gj could be observed. The error was always well below 5%. Almost identical results
were obtained when
Rs1 was set to
10, 20, and 47 M
, respectively (data not shown). For technical
reasons, the error can become >5% at a
gj of 100 pS if
the membrane resistance of both cells is set to 100 or 20 M
(Fig.
3B; see Measurement
of very low gj and DISCUSSION for an explanation).

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Fig. 3.
Influence of Rs
on accuracy of measurement of junctional conductance
(gj). Measured fraction
of gj is plotted
vs. gj.
A:
Rm1 and
Rm2 were both 1 G . Rs1 was
held at 5 M , and
Rs2 was switched
to 5 M ( ), 10 M ( ), 20 M ( ), and 47 M ( ). In
all measurements, error is well below 5% (indicated by dotted lines).
B:
Rm1 and
Rm2 were both 20 M . Rs1 was
held at 5 M , and
Rs2 was switched
to 5 M ( ), 10 M ( ), 20 M ( ), and 47 M ( ). Only
at a gj of 100 pS
(0.1 nS) did error become >5% (indicated by dotted lines). See
Measurement of very low
gj and
DISCUSSION for an explanation.
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Effect of membrane resistance.
To investigate the effect of membrane resistance on the accuracy of the
measurement of
gj, we
investigated all possible combinations of
Rm1 and
Rm2. Figure
4 shows representative results obtained with Rm1 set to
20 M
and variable values of
Rm2. The
gj is accurately measured (error <4%), except when
gj is set to 100 pS (see Measurement of very low
gj and
DISCUSSION for an explanation).
Voltage control and correct assessment of
gj are possible
even if membrane resistance changes suddenly in either the stepped or
the nonstepped cell, as illustrated in Fig.
5. Changing
Rm1 from 1 G
to 500, 100, and 20 M
and back again did not lead to loss of voltage
control in either cell, nor did it affect the current recorded in the nonpulsed cell.

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Fig. 4.
Effect of Rm on
accuracy of measurement of
gj. Measured
fraction of gj is
plotted vs. gj.
Rm1 was kept
constant at 20 M , and
Rm2 was changed
to 20 M ( ), 100 M ( ), 500 M ( ), and 1,000 M ( ).
Because measurements of gap junction conductance
(gj) did not depend on
Rs, data from all
combinations of
Rs values were
averaged. Data are means ± SD of 16 measurements at each point.
Only at gj of 100 pS (0.1 nS) were errors >5%; note comparatively large variability of
measured fraction of
gj at this
gj.
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Fig. 5.
Effects of sudden changes in
Rm1.
Rm1 and
Rm2 were both set
to 1 G . V1 was
set to 100 mV, and
V2 was set to 0 mV. Rm1 was then
changed to values indicated at top.
Note that in cell
1, although
I1 changed
according to change in
Rm1, there were
no changes in V1.
More importantly, there were no changes in either
V2 or
I2 recorded from
cell 2.
Rs1 = Rs2 = 47 M ;
Rj = 10 M .
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Measurements in Cx43-transfected HeLa cells also demonstrate that
membrane resistance does not affect the measurement of
gj with two
DSEVCs. The results shown in Fig. 6 were
taken from an experiment in which one of the cells developed a large
leak current. The membrane resistances were calculated to be 320 and 46 M
for the "nonleaky" cell and the "leaky" cell,
respectively. Changing the membrane potential of the leaky cell from a
holding potential of 0 mV to
40 mV resulted in a large current
composed of the Im and the gap
junction current in this cell
(I1 in Fig.
6A) and a gap junction current of
1.83 nA in the other cell
(I2 in Fig. 6A). Application of the same voltage
jump to the nonleaky cell resulted in a much smaller current in this
cell (I1 in Fig.
6B) and a gap junction current of
1.80 nA in the leaky cell
(I2 in Fig.
6B), demonstrating that the gap
junction current was not influenced by the (different) membrane
resistances of the cells.

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Fig. 6.
Measurement of macroscopic gap junction currents with discontinuous
single-electrode voltage-clamp amplifiers (DSEVCs) under unfavorable
conditions. During experiment, cell
1 developed a considerable leak (here
called leaky cell). A: changing
voltage in leaky cell gives rise to a large current in this cell
(I1) and to a
gap junction current
(I2) of 1.83 nA
in other cell. B: changing voltage in
nonleaky cell gives rise to a much smaller current
(I1). However,
gap junction current
(I2, now measured
in leaky cell) had same amplitude as before (1.80 nA). Please note
adequate voltage control in both cells in both measurements. Delay
between measurements was ~1 min. Switching frequency was set to 48.6 kHz. Electrode resistance was 3.5 M .
Rm values were
calculated to be 320 M for nonleaky cell and 46 M for leaky cell.
Data were low-pass filtered at 500 Hz.
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Effect of Rj.
As can be seen from Figs. 3 and 4, there was no effect of
Rj on the
accuracy of its measurement (see below for an explanation for the
variability seen with
gj set to 100 pS).
It is well known that, with patch-clamp amplifiers, the error in the
measurement of gj
depends on the ratio of
Rj to series resistance
(Rj/Rs)
(30) and the ratio of series resistance to membrane resistance
(Rs/Rm)
(3, 24). We therefore analyzed the maximum error in the determination
of gj as a
function of the quotients
Rj/Rs
and
Rs/Rm,
respectively. It is evident from Fig. 7
that with DSEVCs the precision of
gj measurement
does not depend on either
Rj/Rs
or
Rs/Rm.
Measurement of very low
gj.
During measurement of very small currents (<20 pA), noise introduced
by the amplifiers and the headstages became a limiting factor for
current resolution. To overcome this obstacle, separate headstages with
a 10-fold increased current output gain and an improved signal-to-noise
ratio were tested for the measurement of small
Ij. Measurement
of very small Ij
is only possible if the membrane resistances of both cells are high,
because otherwise the membrane currents would introduce too much noise.
For this reason, we tested these headstages only with membrane
resistances of 500 M
and 1 G
;
Rj was set to
values between 200 M
and 10 G
(5 nS to 100 pS).
The results of these measurements are summarized in Fig.
8. Independent of series resistance,
gj is measured
with extreme accuracy (maximum error <4%).

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Fig. 8.
Accuracy of gj
measurement using headstages with a 10-fold increase in current output
gain. Because measurements were independent of
Rs and
Rm, measurements
with all combinations of
Rm values (500 M and 1 G ) and all combinations of
Rs values were
pooled. Data are means ± SD of 64 measurements at each point.
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To find out whether the use of these headstages allows measurement of
single Ij, we
performed the corresponding experiments in HeLa cells expressing Cx43
(Fig. 9). The results
demonstrate that high-resolution measurements of single gap junction
channel events are indeed possible with DSEVCs equipped with these
headstages. Event amplitudes calculated from an all-point histogram of
the data shown in Fig. 9 reveal transitional amplitudes of ~60 pS, which correspond very well with the results of other investigators (10,
23).

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Fig. 9.
Recordings of single gap junction channel events with synchronized
DSEVCs in connexin 43-transfected HeLa cells. Cells were uncoupled with
2 mM heptanol. Bottom: a voltage step
of 60 mV was applied to 1 cell, resulting in a sum of
Im and
Ij in this cell,
while in other cell single gap junction channel events can be detected.
Top: magnified section
of 1 trace. Scale bars correspond to 15 pA and 2.5 s for 2 traces at
bottom and to 5 pA and 1.5 s for
magnified trace at top. All traces
were low-pass filtered at 500 Hz.
Inset: an all-amplitude histogram of
magnified trace. A Gaussian fit (smooth curve) reveals peaks at
0.1, 1.8, 5.3, and 9.0 pA. From these data, single-channel
conductances of 60 pS were calculated.
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 |
DISCUSSION |
Measurement of gj
with the help of "dual whole cell voltage clamp" critically
depends on accurate voltage control in both cells of a pair. It is
therefore important to record the intracellular voltage. Continuous
feedback amplifiers (patch-clamp amplifiers) cannot measure the
intracellular voltage, and large currents and/or high series
resistances lead to large errors in the estimate of the intracellular
voltage. This was shown to cause serious errors in the measurement of
gj (22, 30).
In this study, we demonstrate that these errors can be avoided by the
use of DSEVCs. Neither series resistance nor membrane resistance had a
significant influence on the precision of
gj measurement.
The maximum error was <5% in all recording situations, except at
very high Rj
values (10 G
= 100 pS) when the error was larger (maximum 12%) for
technical reasons. The errors seen at an
Rj of 10 G
can
be explained by the fact that currents in excess of ±5 nA must be
recorded if membrane resistance is low, i.e., 20 M
. This will lead
to a very low resolution of the digitized current signal. Under the
assumption of a current recording range of ±10.24 nA and an
effective resolution of 14 bits (Instrutech ITC-16 user manual), 1 significant bit will correspond to ~1.25 pA. This amounts to
~12.5% of the expected signal of 10 pA. Together with some noise
introduced by the model circuit and the headstages, this error can
easily explain the variability in the measurement of the
gj of 100 pS seen
with low membrane resistances (cf. Fig. 4).
However, this problem was overcome by the use of headstages that, due
to higher amplification of the signal, provided an improved signal-to-noise ratio (cf. Fig. 8). Because the simulated
gj of 100 pS is
well within the range of single-channel conductances of connexins,
ranging from 270 pS for Cx37 (13) to ~26 pS for Cx45 (25), we tried
to record gap junction single-channel currents with these headstages.
We found that we could reliably record gap junction single-channel
events with two synchronized DSEVCs (Fig. 9). Amplitude resolution and
background noise were comparable to those of a combination of two
patch-clamp amplifiers.
Our data show that DSEVCs allow measurement of the transcellular
potential difference and exact, direct measurement of
Ij. These
measurements allow a very accurate calculation of
gj. With patch-clamp amplifiers, in many situations, correction formulas must be
used to calculate
gj (22, 24).
However, a very important point should be considered regarding use of
these formulas: they critically depend on exact estimates of series
resistance. With respect to this prerequisite, Veenstra and Brink (24)
demonstrated that estimation of series resistance from either the
amplitude of the whole cell capacity transient or from the product of
cell capacitance and the time constant of decay of the capacitive
transient gave rise to errors of maximally 79 and 27%, respectively.
On the other hand, Van Rijen and co-workers (22) calculated that an
error of 20% in the estimate of series resistance can give rise to
errors of up to 37% in the calculation of
gj. Another important point implicit in the use of such correction formulas is the
fact that they correct for voltage changes in both the pulsed and the
nonpulsed cell. However, because the voltage change in the nonpulsed
cell can elicit membrane currents, the current recorded from the
nonpulsed cell can contain "contaminating" currents that cannot
be distinguished from the
Ij and thus
corrupt the calculation of
gj.
We demonstrated that DSEVCs can accurately control the cellular
potential and thus the transcellular potential. This
feature might be especially useful in studies of the voltage-dependent gating behavior of gap junction channels because DSEVCs can avoid errors in voltage control and cross talk between the amplifiers. Furthermore, DSEVCs could be advantageous in studies investigating signal transduction and the pharmacology of connexins. Normally, membrane ion channels are blocked by heavy metal ions and/or other substances to increase cell input resistance (26, 28). Those substances, however, may interfere with signal transduction and thus
spoil such experiments. Because DSEVCs can accurately measure gj even when
membrane resistance is low, those interventions may not be necessary,
and interactions between channel blockers and signal transduction
processes or connexins may be avoided.
In summary, our study shows that DSEVCs with proportional-integral
voltage-clamp circuits can accurately control the voltage of two
electrically connected cells and, consequently, allow accurate determination of
gj. The accuracy
of the measurement of
gj is independent
of series resistance, membrane resistance, and
gj. Our results
strongly suggest that DSEVCs should be used in situations in which
1) membrane resistance is low,
2)
gj is large, and
3) the voltage dependence of
gj is important.
 |
FOOTNOTES |
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Address for reprint requests and all other correspondence: M. Lauven, Institute of Pharmacology, University of Cologne, Gleueler
Str. 24, D-50931 Köln, Germany (E-mail:
melani.lauven{at}uni-koeln.de).
Received 8 September 1998; accepted in final form 29 December
1998.
 |
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