Accuracy considerations for capacitance estimation by voltage steps in cardiomyocytes

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Abstract

Electrophysiologists routinely use simple voltage steps to evaluate cell membrane capacitance derived from corresponding current responses. Frequently, the resting membrane voltage Vrest is employed as holding potential for the subsequent command voltage step and more or less accurate methods are utilised to analyse the transient current. Another choice as holding potential is the peak of the “quasi steady-state” current to voltage relationship, Vpeak. The aim of this study is the systematic evaluation of capacitance estimation accuracy from voltage step experiments depending on the choice of holding potential and analysis method. In this paper, a simulation approach is employed to analyse the current response of a model patch-clamp circuit. Four commonly accepted methods are implemented, utilizing different aspects of the transient current (charge, membrane time constant, and influence of the series resistance) in various combinations and with various degrees of refinement. This simulation study indicates an acceptable accuracy of the elaborated methods for capacitance estimation at holding potentials Vrest and Vpeak over a broad range of capacitance as well as series resistance values.

Simple integration of the current transient provides sufficient accuracy at holding potentials, which effectively minimizes changes in resistive membrane current flow during command voltage steps (particularly around Vpeak). However, biphasic command protocols performed at Vpeak activate voltage dependent sodium channels, thereby possibly leading to the threshold voltage for an action potential. Compared to Vrest, all methods utilizing monophasic step protocols, gain additional accuracy, when applied at Vpeak as holding potential.

Introduction

Cell membrane capacitance Cm is routinely measured during whole-cell patch-clamp of cardiomyocytes. This is usually done to account for cell-size dependent variations of ion currents, since Cm scales with cell surface area. Another important application lies in the study of vesicular events (Neher and Marty, 1982). Whereas the latter demands high-resolution methods for Cm measurement using methods based on square or sine waves (Gillis, 2009; Hotka and Zahradnik, 2017), global cell size assessment is normally done by analysing the current response to voltage-clamp steps.

A prerequisite for accurate Cm measurements is that during voltage steps, membrane resistance Rm stays roughly constant, since a changing Rm produces an erroneous Cm estimation, resulting in errors up to 20% (Zaniboni et al., 2005). Consequently, the holding potential value should be selected in a way that voltage-dependent changes of Rm are negligible during stepping to the command potential. Knowledge about the “quasi steady-state” current-to-voltage relationship (I-V curve) specific for the cell type under investigation can be utilised to choose proper holding potential values. A convenient way to establish such I-V curves is by application of a voltage ramp. During a ramp clamp, the membrane voltage is altered in a continuous way from an initial potential to a final value. If the ramp is applied slowly enough, inactivating currents will be eliminated and a “quasi steady-state” I-V curve can be acquired. Mainly inward and outward potassium currents underlie the “quasi steady-state” I-V curve of cardiomyocytes, which, in ventricular cells, show a characteristic N shape. The membrane resting potential Vrest can be assessed as the first zero crossing of this I-V curve. Furthermore, predominantly, due to rectification of the inward rectifier potassium current IK1, the “quasi steady-state” I-V curve peaks positive to Vrest (i.e. the first turning point of the N shaped I-V curve, Vpeak). Usually voltage-clamp based determinations of Cm employ voltage values near Vrest (assuming constant Rm) as holding potential. However, it has been reported that this assumption does not hold, resulting in Cm estimation errors up to 20%, but that these errors can be avoided by extrapolating to zero step size from two different voltage steps near Vrest (Zaniboni et al., 2005). Vpeak is an alternative holding potential, since placing hyperpolarizing voltage steps symmetrically to Vpeak practically equalizes the steady-state current at holding and at command potential.

Series resistance Rs is a well-known challenge to proper voltage-clamp measurements and a further decisive factor of reliable Cm estimation. Rs impedes the patch-clamp amplifier from charging the membrane capacitance. Therefore, the actual membrane voltage will be smaller in amplitude (voltage error) and slower in time course (time error) than the command voltage step. On the one hand, these errors can be reduced by usage of amplifier built-in Rs compensation and proper choice of pipette resistance and on the other hand, the remaining uncompensated Rs can be estimated from patch-clamp measurements and taken into account accordingly (Marty and Neher, 2009).

Indeed, the choice of analysis method of the elicited current transient is of crucial importance for accurate Cm determination. As summarized previously (Platzer and Zorn-Pauly, 2016), simple integration of the current transient and subsequent division by the command step voltage profoundly underestimates Cm. Therefore, improved analysis methods have been suggested (Benitah et al., 1993; Terracciano et al., 2003). An alternative time-domain based approach, termed Q-method, has been introduced (Novak and Zahradnik, 2006). Commercial patch-clamp systems also provide elaborated Cm estimation, employing either time- or frequency-domain techniques (e.g. pCLAMP® and HEKA® in conjunction with AXON® and HEKA® amplifiers, respectively). However, neither the principal dependence of accurate Cm estimation on the linearity of electrical cell parameters over the command voltage range, nor the proper handling of Rs, can be circumvented in these commercial systems.

The aim of this study is the systematic accuracy evaluation of voltage step based Cm determination with respect to both the choice of holding potential (Vrest or Vpeak) and analysis method. An in silico approach allowing control of the main parameters of the whole-cell patch-clamp recording configuration (Cm, Rs and Rm), is employed to shed light on the topic.

Section snippets

Model and simulation environment

The basis of the current investigation is the execution of “virtual voltage-clamp experiments”, using an established cardiac ventricular cell model with manageable complexity, but sufficient realism to address the study questions (Luo and Rudy, 1991). Realistic values of series resistance inherent to the patch clamp method and the nonlinear time-dependent conductivities of the cell membrane current create difficult challenges to accurate Cm determination. The model equations are programmed in

Response of the model cell to employed voltage stimuli

Fig. 1A shows the equivalent model circuit representing a whole-cell patch-clamp experiment under the assumption of negligible pipette capacitance is (e.g. due to Sylgard coating). The current response of the mammalian ventricular cell model (Luo and Rudy, 1991) to a slow voltage ramp (from −100 to +60 mV and a duration of 20 s) is depicted in Fig. 1B. The N-shape of the obtained I-V curve is typical for ventricular cells and is a measure of “quasi steady-state” current (Amos et al., 1996;

Summary

Given the typical shape of the “quasi steady-state” current to voltage relationship of ventricular myocytes, one often used holding potential value is the resting membrane potential, conserving cellular resources, since no net ion current is flowing across the membrane. However, hyperpolarizing voltage steps around Vrest induce significant resistive current flow across the membrane, which creates challenges for simple integration of Ic and the neglect of series resistance for Cm determination.

Author statement

Platzer Dieter: Conceptualization, Methodology, Software, Investigation, Visualization, Writing - original draft. Zorn-Pauly Klaus: Conceptualization, Methodology, Visualization, Writing - original draft, Supervision.

Declaration of competing interest

None.

Acknowledgements

We want to express our thanks to Dr. B. Pelzmann for fruitful discussions, to Dr. Jerry Batzel for carefully reading the manuscript, and to the reviewers for their important and valuable suggestions.

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