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Patch-Clamp Capacitance Measurements

  • Takeshi Sakaba
  • Akaihiro Hazama
  • Yoshio Maruyama
Part of the Springer Protocols Handbooks book series (SPH)

Abstract

Not only electrical conductance but also electrical capacitance of the cell membrane can be measured by patch-clamp techniques. Exocytotic events can be detected by recording changes in membrane capacitance. The membrane capacitance, which reflects the surface area of the plasma membrane, increases during an exocytotic process by fusion of secretory granules to the plasma membrane. In this chapter, we describe the patch-clamp method for measuring capacitance.

Keywords

Direct Current Secretory Granule Series Resistance Capacitance Measurement Capacitance Change 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

17.1 Capacitance Changes Associated with Exocytosis and Endocytosis

The capacitance of the cell membrane is proportional to the surface area, with a constant of 1 μF/cm2. Therefore, changes in the membrane surface area can be monitored by measuring the cell capacitance (Fig. 17.1). Exocytosis of secretory granules results in an increase of the cell surface area that is compensated by membrane retrieval processes (e.g., endocytosis) that consequently reduce the cell surface area. Time-resolved capacitance measurements were developed by Neher and Marty (1) in 1982 to resolve the kinetics of exocytosis and endocytosis of secretory granules in a single cell. The conventional patch-clamp technique is used, in whole-cell or cell-attached configuration. Because of the low-noise and high temporal resolution, this method enables fast quantitative measurements of changes in membrane capacitance (2, 3). In addition, the intracellular solution can be potentially controlled through a measuring patch pipette.
Fig. 17.1.

Process for fusion of secretory granules to plasma membrane (top) and associated changes in capacitance (bottom). Secretory granules are transported to the plasma membrane (1–4), primed (5), fused to the plasma membrane (6) and endocytosed (8–10).

In the whole-cell voltage-clamp mode (4), capacitance can be measured in two ways, each of which relies on the fact that the capacitive transient is proportional to the differentiation (temporal changes) of the membrane potential: (1) In response to a step voltage pulse, capacitive currents can be observed at the onset and offset of the pulse. (2) When the membrane potential is changed in a sinusoidal manner, the capacitive current component exhibits a phase delay of 90°. One can extract the cell capacitance in both cases.

Capacitance of the patch pipettes can be several picofarads when the pipette is immersed in the extracellular bath solution. Changes in pipette capacitance, mainly due to a change in the fluid level, may cause artificial capacitance changes. Usually patch pipettes are coated with Sylgard or dental wax to reduce any stray capacitance. Also, care must be taken not to change the fluid level when exchanging the extracellular solution.

17.2 Patch-Clamp Capacitance Measurements

17.2.1 Using a Step Voltage Pulse

The step voltage pulse method is intuitively easy to understand. Figure 17.2a shows an electrical circuit of an electrically single compartment cell under whole-cell voltage clamp. When a square voltage pulse is applied to the cell membrane, capacitive currents can be seen (Fig. 17.2b). Membrane current I(t) following the onset of the pulse can be described as:
Fig. 17.2.

(a) Electrical circuit of the cell under whole-cell voltage-clamp. (b) Capacitance currents are elicited in response to a step voltage pulse. R m membrane resistance, C m membrane capacitance, R s series resistance, E r reversal potential, V D a step depolarizing pulse, I 0 instantaneous current, I ss steady-state current, τ time constant of the current decay.

$$ I(t)=\left({I}_{0}-{I}_{\text{ss}}\right)\mathrm{exp}\left(-t/\tau \right)+{I}_{\text{ss}}$$
where I 0 is the initial current amplitude, I ss is the steady-state current amplitude following the capacitive transient, and τ is the time constant of capacitive decay.
Immediately following the pulse, the impedance of the capacitive component C m is almost 0, and therefore described as
$$ {I}_{0}=\Delta V/{R}_{\text{s}}$$
where ΔV is the amplitude of the voltage step.
The steady-state current (I ss) following the capacitive transient is described as:
$$ {I}_{\text{ss}}=\Delta V/\left({R}_{\text{s}}+{R}_{\text{m}}\right)$$
The time constant of the capacitive current τ is described as:
$$ \tau ={R}_{\text{p}}{C}_{\text{m}}$$
where \({R}_{\text{p}}={R}_{\text{s}}{R}_{\text{m}}/\left({R}_{\text{s}}+{R}_{\text{m}}\right)\).
Then,
$${C}_{\text{m}}=\tau /{R}_{p}$$

This method of capacitance measurement is implemented in the patch-clamp software provided by Axon (Sunnyvale, USA) and HEKA (Lambrecht, Germany). Because a small voltage step is applied repetitively to monitor capacitance changes, the time ­resolution is limited to a few hundreds of milliseconds. However, the temporal resolution has increased with the development of faster computer processors. Voltage steps should be small enough not to activate any active conductance, which would otherwise violate the assumption of the analysis. Also, small capacitance changes may not be detected. This can be appreciated by closely monitoring the time course of the capacitive component on the oscilloscope in response to a 1 pF charge injection through the patch-clamp amplifier.

17.2.2 Using a Sinusoidal Voltage Command

Figure 17.3a shows a simplified electronic circuit of the cell where sinusoidal voltage commands are applied. The membrane current I(t) flows either through a resistive or a capacitive component and can be described as:
Fig. 17.3.

Equivalent circuit of the cell under whole-cell voltage-clamp. (a) Ideal circuit without series resistance (Rs). Im (membrane currents) and 1/Gm=Rm (membrane resistance) in the phase plane correspond to the real and imaginary part of the lock-in amplifier, respectively. (b) In reality, series resistance is added in addition to that in (a). Because of series resistance, conductance and capacitance changes are phase shifted, while they are orthogonal to each other.

$$ I(t)={G}_{\text{m}}V+{C}_{\text{m}}\left(\text{d}V/\text{d}t\right)$$
where V is the command voltage, G m is the membrane conductance, and the C m is the cell capacitance. When a sinusoidal voltage command, V  =  V 0 sin ωt (where ω is the frequency), is applied to the cell,
$$I(t)={G}_{\text{m}}{V}_{0}\mathrm{sin}\omega t+{C}_{\text{m}}{V}_{0}\mathrm{cos}\omega t$$
This can be also written as:
$$ Y\left(\omega \right)={G}_{\text{m}}+j\omega {C}_{\text{m}}$$
where Y(ω) is the admittance and j is the imaginary unit.

There is a phase shift of 90° between the resistive and the capacitive current components. In the phase plane, G m and C m are orthogonal to each other. Determination of these two current components is necessary to measure C m and G m. Usually lock-in amplifiers are used for this purpose, but they are also implemented in the software of the patch-clamp amplifiers (e.g., HEKA Pulse and Patchmaster).

Two outputs of the lock-in amplifiers (usually 0° and 90° of the input phase) are in principle proportional to the changes in G m and C m. However, there is a series resistance in the real circuit that causes a further phase shift. Because of the series resistance, changes in G m and C m can no longer be easily detected. In several cases, experimental conditions need to be optimized to nullify the series resistance, or else the series resistance is taken into account, as described below.

In principle, three parameters (G s, G m, C m) have to be determined experimentally (see also ref. (5)). In the Lindau–Neher method (2), three independent equations – one formulated from the direct current (DC) component of the membrane currents and the two from application of the sinusoidal voltage command – are numerically solved to estimate the three parameters. In the Neher–Marty method (1, 3), either G s or G m is assumed to be constant during the recording period. It is then possible to detect changes in the two other parameters, C m and G m or G s; but the absolute value of C m cannot be determined.

17.2.2.1 Lindau–Neher Technique

Figure 17.4a shows the system. For calculating the three parameters (G s, G m, C m), two independent outputs of the lock-in amplifier and the DC component of the current value are required. Here, the DC component is driven by the voltage command at V DC.
Fig. 4.

Schemes for the Lindau–Neher (a) and Neher–Marty (b) methods. A/D analog to digital, I out current out, LPF low-pass filter, OCS oscilloscope, PC personal computer, Stim stimulator, V out voltage out.

From two outputs of the lock-in amplifiers (A and B) and the DC current component, the following three equations are obtained.

Admittance Y can be described as:
$$Y=A+Bj$$
$$A=\left(1+{\omega }^{2}{R}_{\text{m}}{R}_{\text{p}}{C}_{\text{m}}{}^{2}\right)/\left\{{R}_{\text{t}}\left(1+{\omega }^{2}{R}_{\text{p}}{}^{2}{C}_{\text{m}}{}^{2}\right)\right\}$$
$$B=\omega {R}_{\text{m}}{}^{2}{C}_{\text{m}}/\left\{{R}_{\text{t}}{}^{2}\left(1+{\omega }^{2}{R}_{\text{p}}{}^{2}{C}_{\text{m}}{}^{2}\right)\right\}$$
where \( \begin{array}{l}{R}_{\text{t}}={R}_{\text{s}}+{R}_{\text{m}};{R}_{\text{p}}={R}_{\text{s}}{R}_{\text{m}}/\left({R}_{\text{s}}+{R}_{\text{m}}\right);\\ {R}_{\text{s}}=1/{G}_{\text{s}};\text{ and }{R}_{\text{m}}=1/{G}_{\text{m}}\end{array}\).
From the DC component, we can derive the DC current I dc as:
$$ {I}_{\text{dc}}=\left({V}_{\text{dc}}-{E}_{\text{r}}\right)/{R}_{\text{f}}$$
E r is the reversal potential of the component. As a variant of this method, a small step voltage is applied after each sampling period of the sinusoidal wave. Unknown parameters are C m, R m, and R s; the other parameters are known. By solving the equations, we obtain
$$ {R}_{\text{s}}=(A-{G}_{\text{t}})/({A}^{2}+{B}^{2}-A{G}_{\text{t}})$$
$$ {R}_{\text{m}}=\{{(A-{G}_{\text{t}})}^{2}+{B}^{2}\}/({G}_{\text{t}}{A}^{2}+{B}^{2}-A{G}_{\text{t}})$$
$$ {C}_{\text{m}}={({A}^{2}+{B}^{2}-A{G}_{\text{t}})}^{2}/\omega B\{{(A-{G}_{\text{t}})}^{2}+{B}^{2}\}$$
where \( {G}_{\text{t}}=1/{R}_{\text{t}}\).

Because computer processing gets faster with time, this method, although somewhat computationally exhaustive, allows fast measurements of capacitance. Temporal and signal resolution rather depends on the used frequencies and amplitudes of the sine wave. Because the method is integrated into commercial software, it does not require additional computation and so is more widely used today.

17.2.2.2 Neher–Marty Method

Fusion of secretory granules with a diameter of 1 μm and surface area of 0.8 μm2 would produce a capacitance increase of 80 fF. However, secretory granules can be even smaller; in the extreme case, fusion of synaptic vesicles with a diameter of 30–50 nm would produce a capacitance increase of only tens of abfarads. To capture such small capacitance changes, lock-in amplifiers are used in combination with the whole-cell patch-clamp or cell-attached mode, the latter of which increases the signal-to-noise ratio significantly. Here, we deal only with capacitance measurements in the whole-cell configuration. A sinusoidal voltage command is applied to the cell, and the output signals in-phase and out-of-phase (with a 90° delay) with the inputs isolated using lock-in amplifiers (phase-sensitive detection). With this method, the measured values are not C m itself but, rather, the change in C m would be amplified in proportion to the input frequency ω. This method requires a lock-in amplifier.

With the Neher–Marty method, the whole-cell capacitance is first canceled out by feedback compensation circuitry of the amplifier. Then, DC m is measured by the lock-in amplifier. The compensation circuitry of the patch-clamp amplifier is used for calibrating the capacitance traces. Figure 17.3b shows two orthogonal outputs of the lock-in amplifier, one mainly reflecting DC m, and the other mainly reflecting DG m. DC m and DG m project on these two outputs. As described above, DG m and DC m are not exactly at 0° and 90° in phase with the input sine wave but are shifted owing to the series resistance. The error factors associated with DG s compromise the accuracy of the measurements. By setting a phase angle of the lock-in amplifier, error factors can be minimized. To minimize the errors, four factors should be considered: (1) Cell capacitance should be compensated by the feedback circuitry of the amplifier. (2) R s itself should be low. (3) The lock-in amplifier should compensate the phase shift. (4) If possible, appropriate intracellular and extracellular solutions should be selected.

In the original method of Neher and Marty (1), C m and G m can vary whereas G s remains constant during the measurement. In the circuit of Fig. 17.3, the total admittance Y is a function of C m and G m and is described as:
$$Y\left({C}_{\text{m}},{G}_{\text{m}}\right)=\left({G}_{\text{m}}+j\omega {C}_{\text{m}}\right)B$$
where B is a function of C m, G m, ω, and
$$ B\left({C}_{\text{m}},{G}_{\text{m}},\omega \right)=1/\left\{1+{G}_{\text{m}}/{G}_{\text{s}}+j\omega {C}_{\text{m}}/{G}_{\text{s}}\right\}$$
When C m and G m are changed, B becomes a function of C m  +  DC m and G m  +  DG m.
$$\begin{array}{l}{B}^{+}=B\left({C}_{\text{m}}+\Delta {C}_{\text{m}},{G}_{\text{m}}+\Delta {G}_{\text{m}},\omega \right)\\ \text=1/\left\{1+\left({G}_{\text{m}}+\Delta {G}_{\text{m}}\right)/{G}_{\text{s}}+j\omega \left({C}_{\text{m}}+\Delta {C}_{\text{m}}\right)/{G}_{\text{s}}\right\}\end{array}$$
The change in the admittance DY is then
$$\begin{array}{l}\Delta Y=Y\left({C}_{\text{m}}+\Delta {C}_{\text{m}},{G}_{\text{m}}+\Delta {G}_{\text{m}}\right)-Y\left({C}_{\text{m}},{G}_{\text{m}}\right)\\ \text=\left\{\left({G}_{\text{m}}+\Delta {G}_{\text{m}}\right)+j\omega \left({C}_{\text{m}}+\Delta {C}_{\text{m}}\right)\right\}{B}^{+}-\left({G}_{\text{m}}+j\omega {C}_{\text{m}}\right)B\\ \text=(\Delta {G}_{\text{m}}+j\omega \Delta {C}_{\text{m}})B{B}^{+}\end{array}$$

In the experiments, C m and G s should be canceled out by using the feedback circuitry of the amplifier. If G s  >>  (G m  +  DG m), B and B+ approach 1. In reality, this is not perfectly achievable, and as a result the two outputs of the lock-in amplifier do not coincide with the exact phase of DG m and DC m. Therefore, the outputs are influenced by changes in both DG m and DC m. To track the changes of these two parameters accurately, the phase of the lock-in amplifier should be set properly. One way is to move the capacitance toggle of the patch-clamp amplifier back and forth, so DC m is simulated artificially. Then, the phase of the lock-in amplifier is adjusted such that the change at 0° of the lock-in output becomes minimal whereas the change at 90° of the lock-in output becomes maximum. The phase of the lock-in amplifier is then set such that interference due to the incorrect setting of the phase can be minimized. Error factors associated with this method are mentioned in other articles in the literature.

Figure 17.5 shows exemplar traces of the capacitance transients at a single acinar cell (6, 7, 8). These traces were obtained from whole-cell patch-clamping, and G s  D  (G m  +  DG m) as well as cancelation of G s and C m by the amplifier was correctly achieved. Because there was no baseline drift, G s should not have changed significantly during the measurement period. Acetylcholine 50 nM was applied using a local puff pipette, and care was taken not to change the fluid level. Patch pipettes were coated with Sylgard to reduce stray capacitance. At the beginning of the trace, a 200-f  F change of the capacitance was introduced through the feedback circuit of the patch-clamp amplifier, which calibrates the capacitance. If the phase is set correctly, this capacitance change does not cause any changes in the conductance trace (G m).
Fig. 17.5.

Example traces of capacitance measurement using the Neher–Marty method. Capacitance changes are in response to application of acetylcholine (ACh) at a single acinar cell.

17.3 Other Considerations

There are other variants of capacitance measurements, which are described elsewhere (5, 9, 10). Capacitance measurements are usually implemented with patch-clamp amplifier software (e.g., Patchmaster; HEKA), and the manual describes the detailed procedure. It is convenient to use such a software-based semiautomatic approach, although it makes it difficult for users to realize the drawbacks of the method, of which there are three major ones.
  • Because the method models a cell as a single electrical compartment, it may not be appropriate to apply it to cell types with complex morphology. For example, the method has been used at mossy fiber boutons in hippocampus (11), which has a small terminal with a very long axon. In this case, stimulation frequency must be optimized such that capacitance changes due to exocytosis from a terminal should be detected without any contamination from the axonal currents.

  • The Neher–Marty method assumes that the capacitance, series resistance, and conductance changes do not change considerably. Nevertheless, it is important to monitor not only the capacitance but also the conductance and the series resistance simultaneously. If two or three traces show associated changes, it may be an artifact due to cross-talk among the parameters. Also, it is important to verify capacitance changes experimentally. For example, exocytosis of synaptic vesicles should be sensitive to Ca2+ and to treatment of botulinum toxins that cleave the SNARE proteins (12).

  • Exocytosis and endocytosis may overlap. Because capacitance traces reflect net changes of the two processes, it is important to verify the amounts of exocytosis by independent methods, such as by (1) measuring excitatory postsynaptic currents, (2) visualizing labeled secretory granules using microscopy, or (3) detecting secreted materials using amperometry (13).

Despite these drawbacks, capacitance measurements allow one to monitor exocytotic and endocytotic events with high temporal resolution.

Notes

Acknowledgments

We thank Andreas Neef and Raunak Sinha for their comments.

References

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Copyright information

© Springer 2012

Authors and Affiliations

  • Takeshi Sakaba
    • 1
  • Akaihiro Hazama
    • 2
  • Yoshio Maruyama
    • 3
  1. 1.Graduate School of Brain ScienceDoshisha UniversityKizugawaJapan
  2. 2.Fukushima Medical UniversityFukushimaJapan
  3. 3.Department of PhysiologyTohoku University Graduate School of MedicineSendaiJapan

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