Patch-Clamp Capacitance Measurements
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.
KeywordsDirect Current Secretory Granule Series Resistance Capacitance Measurement Capacitance Change
17.1 Capacitance Changes Associated with Exocytosis and Endocytosis
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
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
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.
188.8.131.52 Lindau–Neher Technique
From two outputs of the lock-in amplifiers (A and B) and the DC current component, the following three equations are obtained.
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.
184.108.40.206 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 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.
17.3 Other Considerations
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.
We thank Andreas Neef and Raunak Sinha for their comments.
- 3.Gillis KD (1995) Techniques for membrane capacitance measurements. In: Sakmann B, Neher E (eds) Single channel recording, 2nd edn. Plenum Press, New York, pp 155–198Google Scholar