to the editor: Cell membrane capacitance Cm is a fundamental property of excitable cells. It scales with the cell surface area and is therefore used for cell size estimation and most important for normalizing currents and conductances. Consequently, proper knowledge of Cm is also crucial for accurate cell modeling (7). Whole cell patch-clamp technique has led to the development of elaborate methods for Cm estimation (3). Among the voltage clamp-based approaches, step response analysis is often the method of choice (Fig. 1, A and B). A mandatory requirement for accurate Cm determination during voltage-clamp steps is that changes in membrane resistance Rm are negligible (8). Accuracy also depends on the choice of the analysis method of the current transient. Considering Grubb et al. (4) and Vaidyanathan et al. (6), published in two previous issues of the American Journal of Physiology-Heart and Circulatory Physiology, and from other publications (2, 9), we want to point out that straightforward integration of the current transient and subsequent division by the commanded voltage step ΔE, as frequently used, is prone to give incorrect Cm estimates and how this can be avoided by proper approximating charge Q and membrane voltage Vm at the cell membrane. Obviously, it is still common practice to determine Cm by application of a small voltage-clamp step ΔE (Fig. 1B) and to numerically integrate the current response to the new steady state to get the charge Q under the current transient by (1) A first common simplification is to approximate Q by integrating the area under the transient relative to the steady-state current I∞ (Fig. 1C). However, this overestimates the resistive current flow and therefore underestimates Q. This has been corrected by Terracciano et al. (5) as follows: (2) where ΔI is the difference of the current before the pulse and I∞, and τ is the time constant of the decaying current transient.
Equation 1 implies a second imprecision by approximating the actual potential change at the membrane ΔVm by the command voltage step ΔE (Fig. 1B), thereby neglecting the voltage drop across the series resistance Rs. It can be shown that this deficiency can be avoided as series resistance and membrane resistance form a voltage divider in steady state: (3)
The resistances are not directly available, but the necessary scaling can be achieved by using the current values at the beginning and the end of the transient interval (1): (4)
where I0 is the instantaneous value of the current transient relative to the current at prepulse potential (Fig. 1D). With the assumption of compensated parasitic capacitances, Q/ΔVm precisely determines the value of Cm. Both above-mentioned inaccuracies are also avoided by the continuous square wave protocol “Membrane Test” implemented in pCLAMP, mostly used in conjunction with amplifiers from AXON Instruments.
In practice, discrete integration and finite setup rise time may limit the refined integration approach. Integration of the current transient can be avoided by using the following relationship: (5)
Under experimental conditions, τ and I0 can be easily approximated by single exponential fit (1). In practice, I0 is then the extrapolation of the current to the first sample point after the voltage change.
To raise awareness and to indicate the possible order of magnitude of an erroneous current transient analysis, we performed model simulations and Cm calculations of own patch-clamp data. In simulations of a discrete, sampled whole cell patch-clamp circuit consisting of Cm, Rm, and Rs, we found that the refinement of the direct integration approach (Eqs. 2 and 4) converges to the single exponential fit approach (Eqs. 4 and 5) for sufficiently high sample rates. Furthermore, using representative values for cardiac cells with our model, we found that the refined integration method and the exponential fit method both reproduce the exact Cm value, whereas the still widely used straight-forward approach yields significantly underestimated values (e.g., by ∼10 pF for a cell of 140 pF). Analyzing our own patch-clamp experiments on ventricular guinea pig cells, we found continuous underestimation up to 20 pF compared with that found in the exponential fit method.
Therefore, to improve the accuracy of Cm estimations from a single voltage step experiment, we recommend using the exponential fit or the refined integration method.
Besides the above-mentioned, time-domain techniques, frequency-domain approaches complement the methods for high-resolution measurement of Cm. In principle, these methods use the time shift between a sinusoidal voltage stimulus and the corresponding sinusoidal current response (3). The observed phase shift is caused by the capacitance of the system and can be measured reliably by electronic phase detector circuitry (also termed “lock-in amplifier”). This method is implemented as “lock-in extension” in the software Patchmaster, used in conjunction with HEKA amplifiers.
No conflicts of interest, financial or otherwise, are declared by the author(s).
D.P. and K.Z.-P. conception and design of research; D.P. and K.Z.-P. performed experiments; D.P. and K.Z.-P. analyzed data; D.P. and K.Z.-P. interpreted results of experiments; D.P. and K.Z.-P. prepared figures; D.P. and K.Z.-P. drafted manuscript; D.P. and K.Z.-P. edited and revised manuscript; D.P. and K.Z.-P. approved final version of manuscript.
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