Whole-cell patch-clamp recording and parameters

Abstract

The patch-clamp technique represents an electrophysiology type of method. This is one of several insightful approaches with five major configurations, namely a loose patch, cell-attached (also known as on-cell), whole-cell, inside-out, and outside-out modes. The patch-clamp method is more advanced compared to classical electrophysiology since it elucidates single-channel activation in a tiny portion of the membrane in addition to action potential (AP), junction potential (JP), endplate potential (EP), electrical coupling between two adjacent cells via Gap junction hemi-channels, excitatory/inhibitory postsynaptic potentials, and resting membrane potential (RMP). In fact, a malfunction of only one channel or even one component will alter AP amplitude or duration in vitro. If parameters are inferred appropriately and recordings are performed properly, the patch-clamp trace readouts and results are robust. The main hallmarks of currents via voltage-dependent calcium (Cav), hyperpolarization-activated cyclic nucleotide gated non-selective cation (HCN), inwardly rectifying potassium (Kir), voltage-dependent potassium (Kv), and voltage-dependent sodium (Nav) channels are similar and tractable among cells even when they are derived from evolutionary distinct organs and species. However, the size of the membrane area, where the functional subunits reside, and current magnitudes vary among cells of the same type. Therefore, dividing current magnitudes by cell capacitance– current density enables the estimate of functional and active channels relative to recorded cytoplasmic membrane area. Since the patch-clamp recordings can be performed in both current- and voltage-clamp modes, the action potential or spike durations can be adequately elucidated. Sometimes, optical methods are preferred to patch-clamp electrophysiology, but the obtained signals and traces are not robust. Finally, not only an alternans of AP durations, but also that of ‘action potential shape’ is observed with electrophysiology.

…the cell, therefore, acts as a condenser, which transmits the current by its capacitance…

(Christie 1928).

Introduction

For voltage-clamp experiments, the ‘first step in our analysis is to divide the total membrane current into a capacity current and an ionic current’ (Hodgkin and Huxley 1952a). The capacity current is used to estimate the capacitance of a cell—size that helps in relating the membrane current magnitude and available active α subunits—channel densities under a whole-cell patch-clamp configuration. That is, the magnitude of whole-cell currents through specific channels, often expressed in pA, is divided by cell capacitance pF to yield a current density in pA/pF. Densities of α subunits can also be estimated either from single channel conductance or binding of antagonists (Holden and Yoda 1981a). For this purpose, an experimental paradigm must be designed adequately, namely that at holding potential the channel should be fully closed and voltage steps should lead to an absolute open-state of the channel pore as a prerequisite condition. Under these conditions, the α subunits behave as an ‘ideal ion channel.’ With the ideal channel, the size of the voltage step will determine the number of channels open in the membrane rather than the conductance of each individual channel. However, the situation can be more complex if, for example, the channel exhibits sub-conductance or bursting and flickering behaviors.

During voltage-clamp recordings, there are always capacitive currents, which charge the cell or tissue membrane capacitance (C_m) (Frankenhaeuser 1962). The latter is also known as the input capacity of a membrane area (Kostyuk et al. 1981). The concept of current density is not new and was used prior to patch-clamp to describe ionic conductance as μA per cm² surface of the membrane of a giant axon—nerve fiber of the squid Loligo by considering the capacitance as μF/cm² (Hodgkin and Huxley 1952b). These parameters were analyzed in order to describe and identify ionic currents responsible for the generation of all-or-none action potential (AP) (Hodgkin and Huxley 1939).

Ionic current density estimation applies only to functional channels, which are readily activated during experimental paradigms. Therefore, e.g., the maximal K⁺ conductance that occurs during AP is considered reflective of K⁺ channel densities in the membrane (Holden and Yoda 1981b). The primary goal of current densities estimation is not to overcome the variable amplitude diapason within the group (Bébarová et al. 2020), but rather to control for cell size and the amount of functional α subunits in the cytoplasmic membrane (Maltsev et al. 1994). Thereby, e.g., the effects of dominant α subunits, which upon heteromerization turn the endogenous channels into non-functional ones, could be elucidated, as shown for the voltage-dependent K⁺ channel subfamily—Kv (Kodirov et al. 2004).

It should be noted that the method of normalizing current to capacitance has been used extensively for many years in many different situations to account not only for different cell and pipette diameters but, as importantly, to account for non-uniformities in the membrane, particularly in cardiac and skeletal muscle myocytes where the membrane infolds into transverse tubules and caveolae (Chandler and Meves 1970; Chandler et al. 1976; Schneider and Chandler 1976; Yarbrough et al. 2002). As one of the pioneering studies summarizes, ‘it was not possible to measure the membrane conductance during the first few ms, because of the current needed to charge the membrane capacity, but from 5 ms to 1 s, the conductance appeared independent of time, although it was large for inward current and small for outward current’ in fibers from the frog sartorius muscle (Adrian 1969). Note that more extensive studies are devoted to Nav channels using giant axons of the squid Loligo or CNS neurons of snails (Brenes 2022; Hodgkin and Huxley 1952b). Nevertheless, in the majority of excitable cells, a sudden depolarization leads to enhancement of capacity (I_C), I_K, I_Leak, and I_Na currents (Armstrong and Bezanilla 1974). Current density is mainly crucial in heterologous systems, as the expression of exogenous channels does not occur homogeneously in all cells. This parameter may also help to discern whether or not a channel protein reaches the cytoplasmic membrane, known as trafficking. Taken in total, the current density is applicable only for channels within the cell membrane under conditions enabling maximum conductance.

This review emphasizes the importance of the quality of patch-clamp traces. In the absence of established standards for recordings, the prevailing retrospective meta-analyses are without crucial merit. For voltage-dependent ionic currents, the original traces should be first recorded without leak subtraction and excessive filtering, though for analysis and the clarity of presentation, they could be performed later off-line. The latter may, however, depend on the relative size of the leak and the ionic current, which may vary among recordings. However, if the channel current is small compared to the leak current, the original record will provide no information apart from the size of the leak. If currents flow independently of voltage and just mimic the waveform of the pulse protocol, then the leak subtraction will be useful. The leak current in this and all other cases should be determined by the smallest voltage steps of identical magnitude, albeit with negative and positive polarities. The sufficiency is simple to manifest because the magnitudes of inward and outward currents should be nearly identical.

Note that this study concerns itself with very recent and targeted patch-clamp data accuracy and mining. As ‘data integrity means that data presented to the public accurately reflect what was actually observed’ (Rossner et al. 2008).

Methods

Detailed descriptions of the experimental study appeared previously (Kodirov et al. 2003, 2004); therefore, for this review, only crucial elements are stated.

Animals

A single dominant negative (DN) (either toward the Kv1.5 or Kv2.1) transgenic mouse model of LQT syndrome was created by overexpression of truncated Kv1.1 or Kv2.1 channels in the heart (Kodirov et al. 2003). Double DN transgenic mice were obtained by crossbreeding Kv2.1N216 C56/BL6 males with Kv1.1N206 FVB females (Kodirov et al. 2004).

Solutions

The physiological solution was composed of (in mM): 135 NaCl, 5.4 KCl, 0.33 NaH₂PO₄, 1 MgCl₂, 1 CaCl₂, 10 HEPES, and 10 glucose. The pH was adjusted to 7.35 by the gradual addition of NaOH. Activities of Kv channels were registered in the absence and presence of 2 mM CoCl₂ and 20 μM TTX in order to isolate them from Cav and Nav ones. Cells were dialyzed with a combination of (in mM): 140 KCl, 1 MgCl₂, 10 HEPES, 5 EGTA, 5 Mg₂ATP, and 0.1 NaGTP (pH = 7.2 with KOH). These compounds were produced by Sigma (St. Louis, MO, USA), while collagenase type I by Worthington Biochemical (Lakewood, NJ, USA).

Cells

Left ventricular cardiomyocytes were dissociated from isolated hearts of WT (Kv1⁺/Kv2⁺), Kv1DN, Kv2DN, and Kv1/Kv2DN mice using the Langendorff technique. The latter enabled a retrograde perfusion of the heart in order to free it from blood, to stop the heartbeat by excluding CaCl₂, and to introduce collagenase. Stepwise enzymatic digestion and mechanical isolation were performed in the absence of Ca²⁺, while the content of [K⁺]_o—extracellular (o—out) concentration of K⁺ kept constant. Reliability of enzyme was ensured by using stocks from similar batches.

Patch-clamp

Membrane currents and potentials were recorded using the whole-cell mode of the patch-clamp technique (Hamill et al. 1981). When filled with a 140 KCl solution, the microelectrode resistance was within a diapason of 0.8 − 2 MΩ. When perfused with physiological solutions, some cells exhibited all four major currents, Cav, Kir, Kv, and Nav. The latter were isolated by using either pharmacology or a voltage pre-pulse. Traces were acquired by an analog Axopatch 200B amplifier, pClamp 8.1 software, and DigiData 1322A (Axon Instruments, USA). Detailed recordings of capacitive currents were performed in a neuron for illustrative purposes and were acquired from a brain slice similar to prior studies (Kodirov et al. 2010, 2021).

Statistics

A degree of significance was determined by Student’s paired t test also in regard to Gaussian distribution of or linear fit to data points. The coefficient of correlation R is provided for dependencies between two probed parameters. Accordingly, values accompany n numbers of experiments and standard deviation or standard error of the mean (SD or SEM), respectively. Whether differences are significant or not, the P values are indicated.

Meta-analyses

Most of the referred studies will be discussed in detail and in dedicated paragraphs; therefore, all information until next citation often belongs to initial study. Importantly, an unusual approach will be undertaken by evaluating figures—the hub of published data (Kodirov 2022). That is, a meta-analysis of visualized results will be enabled. Therefore, the latter will be cited in italics, e.g., as figure 1, in order to distinguish them from those in this study and referred to as Fig. 1 and others. The same holds true for presented and referred tables. Thereby, a reader may additionally learn from corresponding figures and tables in the original studies.

Fig. 1.

General schematics of steps leading to patch-clamp electrophysiological recordings. A The basic components of the patch-clamp technique enable registration of membrane current and potential. The ideal cell for patch-clamp is spherical (B). However, it is possible to record from cardiac myocytes of snails (C) or even neurons (D) within live mammalian brain slices. Note that the ventricular cardiomyocytes of mollusks (Kodirov et al. 2022) resemble those of spindle-shaped sino-atrial nodal cells of vertebrates including the Oryctolagus cuniculus, New Zealand White rabbit (Honjo et al. 2002). Also, these are the appearance of live acute 300 μm coronal CA1 slice and neurons during actual whole-cell recording (Bonni et al. 2008). CA1—cornu ammonis region of the mouse hippocampus. Note that the patch pipette is retrospectively colored. E − H, J, K Configurations of the patch-clamp technique: cell contact—loose patch (E), cell-attached (F). F During the cell-attached mode, the portion of cell membrane is forced into the electrode opening − tight seal, ideally of at least 1 GΩ in resistance. Note the Ω-like position between the membrane and patch pipette. The physics of the equivalent electrical circuit between a glass electrode and cell body has been precisely elucidated (Neher and Lux 1969). G Thereafter, the Ω portion of the cell is ruptured, and the assembled and orchestrated activities of all ion channels, whole-cell currents are documented (H). Note non-selective inward cationic currents representing the HCN pacemaker channels. For a single-channel recording, ideally only one channel of certain α subunits is located at the Ω position. Therefore, the narrower electrode tip and either inside-out (J) or outside-out (K) configurations are preferred. Simplified based on previously established knowledge (Gerasimov et al. 1964; Hamill et al. 1981; Krishtal 2015; Neher and Lux 1969; 1973). I Spontaneous cell-attached mode to whole-cell transition. Continued recording from SLM—stratum lacunosum moleculare interneuron (#897) in cell-attached mode in artificial cerebrospinal fluid (ACSF) was planned during 60 s (Kodirov, unpublished). After 31 s, however, a spontaneous whole-cell configuration occurred at a holding potential of – 70 mV. Closed (c) and open (o) states of single channels. Only a 1.7-s portion of a 60-s patch-clamp trace is depicted (Kodirov, unpublished)

Results and discussion

Patch-clamp technique

This method enables reliable registration of membrane current and potential (Gerasimov et al. 1964; Hamill et al. 1981; Krishtal 2015; Neher and Lux 1969; 1973). The main components of the patch-clamp technique are the circuits of the pre-amplifier (headstage) and dedicated amplifier (Fig. 1A). The ideal cell for patch-clamp should be spherical (Fig. 1B). However, it is possible to record from unusually long cardiomyocytes (Fig. 1C) or even from neurons (Fig. 1D) within live brain slices (Kodirov et al. 2016, 2022). However, one needs to both navigate within the slice and approach the neurons while the glass electrode is under negative pressure, which enables a constant flow of solution out. As a result, the slice will sustain only minor damage and the tip opening will not become clogged. Note that the ventricular cardiomyocytes of mollusks resemble those of spindle-shaped (Fig. 1C) sino-atrial nodal cells of vertebrates including the Oryctolagus cuniculus, New Zealand White rabbit (Honjo et al. 2002; Kodirov et al. 2022).

There are five configurations of the patch-clamp technique: cell contact—loose patch, cell-attached, whole-cell, inside-out, and outside-out (Fig. 1 E − H, J, and K). The resistance—degree of contact between the glass electrode and cell membrane—is low at < 100 MΩ when a proper loose patch configuration is achieved. During the cell-attached mode, the portion of cell membrane is forced into the electrode opening, forming a tight seal, ideally of at least 1 GΩ. Interestingly, the latter resemble the Greek latter Ω (Fig. 1G). The physics of the equivalent electrical circuit between a glass electrode and perikarion has been precisely described (Neher and Lux 1969). Next, the Ω portion of the cell is ruptured, and the assembled and orchestrated activities of all ion channels, whole-cell, are registered (Fig. 1H).

After obtaining a cell-attached mode, sometimes a spontaneous transition to whole-cell may occur without the application of positive pressure—suction to the patch electrode (Fig. 1I). The latter is usually achieved by a very brief, yet more intense pressure compared to the prior situation during the cell-attached mode. This is exemplified by the continued recording from SLM—stratum lacunosum moleculare interneuron (#897) in cell-attached mode in artificial cerebrospinal fluid (ACSF) at a holding potential of – 70 mV. During the cell-attached mode, the closed (c) and open (o) states of single channels are observed (Kodirov, unpublished). For a precise single-channel recording, ideally only one functional channel formed by either hetero- or homomeric α subunits should be located at the Ω position of the cell membrane. Therefore, the narrower electrode tip and either inside-out or outside-out configurations are preferred.

The patch-clamp technique is applicable to any cell. The latter is independent of whether the cell lines or those of native origin are used after acute isolation. However, one of the major attentions is usually paid to ion current density. When and if the merits of current density and Gaussian distribution are plausible for certain electrophysiological parameters of channels, they are exemplified by the activities of Cav and Kv channels along with the action potentials recorded by electrophysiological and optical methods.

Configurations, modes, and parameters

Depending on recording configuration (loose patch, cell-attached, inside-out, outside-out, and whole-cell) and mode (current- and voltage-clamp), there are several main parameters to consider (Almers et al. 1984; Fischmeister et al. 1984; Hamill et al. 1981; Kononenko and Berezetskaya 2010; Krishtal 2015; Neher and Lux 1969). For the whole-cell configuration, under voltage clamp mode, the most crucial parameter is the capacitive current (Fig. 2). The latter is commonly evoked from a holding potential (HP) ranging between − 70 and − 50 mV by short, up to 10 ms pulses. Its magnitude must be as low as possible and could be set to 5 mV. Alternatively, the parameters of capacitive current can be determined using actual experiments dedicated to ion channel activation (Fig. 2A). In this case, only the initial 50 ms portion immediately after the pulse onset could be considered a starting point. In the absence of excessive electrical noise, it is straightforward to distinguish the capacitive and ionic currents. Adequate responses to steps are registered when conditions are right, and a crucial one is the pipette resistance. When it is possible, the lower the better, and ideally closer to 1 MΩ will yield the most reliable responses. The latter also depends on cell types and expected current magnitude; therefore, pipettes with appropriate tip resistances are fabricated. The geometry of the glass tip–shank along the diameter of its wall is also important (Hume and Giles 1983). Prior to recording, an analog capacitance compensation circuit of amplifier is utilized as an ultimate step.

Fig. 2.

Illustration of capacitive and ionic currents. A Membrane currents during 50 ms upon depolarization to + 60 mV and hyperpolarization to – 60 mV from a holding potential of – 50 mV in CA1 neuron. The baseline is adjusted, but the level of holding current was low at + 10 pA. B Expansion in time scale reveals components and parameters of currents. Note a sharp transition during peak reflecting the sampling frequency of 10 kHz. That is, actual amplitude of capacitive current might be slightly higher. Thus, a faster acquisition is more appropriate. C, D Often visualizing traces with dots instead of lines helps to distinguish the capacitive currents from ionic ones, as even the decaying phase of former is fast and during each 100 μs a stepwise decrease in amplitude is observed (Kodirov, unpublished)

The capacitive current is a rapid phenomenon even when recorded at room temperature (Fig. 2B). Its duration depends on the quality of the whole-cell patch-clamp configuration as defined by electrode access resistance (R_a) after rupturing the portion of the lipid bilayer within the opening of the tip of the pipette. However, the ruptured portion of the membrane is smaller than the tip opening, as it is first forced into the pipette by positive pressure. The latter is achieved in two steps. After approaching the cell, the electrode is advanced gently against the membrane, so that one observes an invagination-like change under a microscope. At this stage, one may measure up to 100 MΩ in seal resistance, a configuration that is referred to as a loose patch. Additional suction increases the tightness of contact and resistance to a GΩ range, enabling a transition to a cell-attached configuration. Thereby, the electrode opening is completely isolated from an extracellular solution, and the applied pressure targets only the portion of membrane under the opening of the tip. More pressure leads to a whole-cell configuration.

The entire cell membrane during the whole-cell configuration of a patch-clamp technique could be considered approximately as in the shape of Ω when imagined upside-down. A small –10 mV step evokes an inward transient that is prevailingly of capacitive nature (Fig. 2B). The amplitude of capacitive currents depends on the patch quality—opening of the ruptured part of the cell membrane. The bigger capacitive current reflects the shorter time in cell charging—smaller R_a and faster τ—time constant of decay. If the patch quality worsens, one will observe a decrease in capacitive currents, that is, the edges of the membrane will move and narrow the opening. Since before rupturing it, the portion of membrane was forced into the tip opening by pressure. So that a small portion of membrane is folded into a Ω shape. Therefore, occasionally after rupturing it, the two ends of the membrane may move toward each other and reconnect. The latter may be adjusted and opened by gently applying a small amount of either negative or positive pressure depending on cell types. Similar unstable whole-cell configuration may also occur because of an inadequate osmolarity gradient between extracellular and intracellular solutions.

When the capacitive current is decreased from its initial value, the τ will become slower while R_a increases. The decay of capacitive currents should occur in an absolute exponential manner until the baseline. Even if this is not the case, the automatic algorithm of software, pClamp (Axon Instruments, USA), may estimate adequate values for R_a and τ by taking into account the initial decay immediately after peak capacitive currents. Therefore, a visual inspection of capacitive currents is important, as occasionally a sharp transition is observed after the initial exponential decay.

Capacitive transients in neurons

Ideally, upon the application of small voltage steps, one should observe only capacitive transients. However, there are also − 5.5 pA ionic currents, which do not exhibit rectification during 50 ms (Fig. 2B). Therefore, those could be leak currents, which are generated by either Cl⁻ or K⁺ ions. The former is more plausible, as the recording electrode contained 120 mM CsCl. Contrary to ionic currents, capacitive transients are relatively unbiased by the pipette content of major solutions based on KCl, K⁺ gluconate, or CsCl, or other salts of these ions. A strong depolarization by a 110 mV step reveals the occurrence of leak current in time and space in the SR—stratum radiatum interneuron of cornu ammonis—CA1 area of the hippocampus (Kodirov, unpublished). The baseline is adjusted, but the level of holding current was low at + 10 pA. When the initial portion of the same trace is expanded in time, the three major components of currents are observed (Fig. 2B). Importantly, there is a clear-cut transition from capacitive to ionic currents. An instantaneous component is constituted by leak currents, while a subsequent one reflects a slow and gradual activation of delayed rectifier K channels. Take note of the sharp transition during peak, which reflects the sampling frequency of 10 kHz. That is, the actual amplitude of capacitive current might be slightly higher. Thus, a faster acquisition is more appropriate.

Polarities of pulses for capacitive current estimations vary among studies, so that the MP is either depolarized by, e.g., + 5 mV or hyperpolarized by – 5 mV pulses. However, for recordings from cardiomyocytes and neurons, it is important not to depolarize or excite cells unnecessarily. Therefore, quiescent cardiomyocytes are also chosen for patch-clamp experiments. Thus, a – 5 mV step is favorable. Besides, there are more types of major channels that activate upon depolarization (Cav, Kv, and Nav) vs. hyperpolarization (HCN and Kir).

A sudden appearance of capacitive transients reflects the transition from cell-attached to whole-cell configuration when the behavior of current is continuously monitored during the application of steps to, e.g., − 5 mV from HP and positive pressure (Fig. 3B). Since the pipette capacitance is canceled after forming a tight seal between the cell and electrode opening, i.e., the cell-attached mode, there are no transients. Subsequently, once in whole-cell mode the latter appear and the C_m—membrane capacitance, R_in or R_m—input or membrane resistance along the R_a are estimated and monitored during the course of each experiment based on the magnitude and decay of capacitive current. The R_in is also defined for electrically coupled cells via Gap junctions and is termed a network resistance (Sidorov 2012). R_a and R_in are obtained from peak and relative steady-state current amplitudes by considering R = V/I and mV/nA as units. Original units are ampere, ohm, and volt and are named after discoverers, French, German, and Italian physicists André-Marie Ampère, Georg Simon Ohm, and Alessandro Volta, respectively.

Fig. 3.

Capacitive currents during patch-clamp recordings. A Transients activated by – 5 mV 50 ms steps from HP of – 70 mV in CA1 neuron. Three traces at 0, 20, and 100 s time points are superimposed. B Expansion in amplitude and time scale reveals similitude in parameters and stability of current fluctuations. C, D Exponential fits to transients during onset and offset of step (see Table 1). E Same cell in response to − 10 and + 10 mV steps. F Initial portion of E at expanded time scale. G Decaying phase of transients as scatter plot. Data points between cursors 1 and 2 are considered for a single term exponential fit according to Chebyshev method. Interval of 49.6 ms is inadequate, as some points were not covered by fit (arrow). H, I Shorter intervals of 10 and 3 ms are more adequate for kinetic analyses. J All pairs of amplitudes as defined from fit overlap but one at 8 ms (arrow). K, L Time constants and y intercept values exhibit similar dynamics in accord to analyzed portions. The actual amplitude is more precisely reflected during initial 10 ms (Kodirov, unpublished)

The R_a does not alter in magnitude during small voltage steps and was identical, i.e., 34.45 MΩ for transients evoked by − 5 vs. – 10 mV (Fig. 3 A and B). Current values were taken from the y intercept during 3 ms and converted to nA, e.g., resulting in − 0.145 nA instead of − 145 pA (Table 1). The same procedure applies as to R_in and yields significantly different values of 403 vs. 273 MΩ, respectively, for the 10 ms portion of the current. The amount of current at cursor 2 was − 12 vs. − 37 pA. The latter substantiates that, in contrast to R_a, R_in is biased among studies. Note that for this experiment, the inward currents were not at steady-state levels during the first 10 ms, which were achieved after 20 ms of step onset. Alternatively, the corresponding values of A and C can also be used for calculations. The relative stability of the latter then ensures the quality of the patch and recordings. During off-line analyses, one can use dots instead of solid lines when visualizing the traces (Fig. 2 C and D). The latter helps to clearly distinguish the capacitive and ionic currents because of their distinct kinetics and durations. The R_in value is also reflected by the magnitude of hyperpolarization from resting membrane potential (RMP) achieved by small injected currents that will not lead to a sag in MP–HCN activation (Kodirov et al. 2014, 2021; Kodirov 2021).

Table 1.

Analysis of capacitive currents from Fig. 3

Pulse		Parameters of capacitive currents
Potential (mV)	Duration (ms)	A (pA)	tau (ms)	C (pA)	m (pA/ms)	y intercept (pA)	Cursor 1 Peak (pA)	Cursor 2 End (pA)	Correlation Coefficient	Points Fitted	Area (pAms)
− 5	50	− 114	1.4	− 16	0.1	− 130	− 130	− 13	0.92	496	880
	40	− 114	1.4	− 16	0.1	− 130	− 130	− 13	0.92	401	757
	30	− 114	1.5	− 15	− 0.003	− 129	− 129	− 15	0.92	301	623
	20	− 115	1.4	− 15	− 0.02	− 130	− 130	− 15	0.92	201	472
	10	− 109	1.0	− 29	2	− 139	-139	− 12	0.96	100	323
	9	− 109	1.0	− 30	2	− 139	− 139	− 14	0.96	91	310
	8	− 108	1.0	− 31	2	− 139	− 139	− 15	0.96	81	295
	7	− 106	0.9	− 35	3	− 140	− 140	− 16	0.97	71	278
	6	− 102	0.8	− 39	4	− 142	− 142	− 17	0.97	61	260
	5	− 98	0.8	− 45	5	− 143	− 143	− 19	0.98	50	238
	4	− 91	0.7	− 53	7	− 144	− 144	− 23	0.98	40	215
	3	− 80	0.6	− 65	12	− 145	− 145	− 29	0.98	30	187
− 10	50	− 215	1.6	− 34	0.1	− 249	− 249	− 28	0.92	496	1887
	40	− 218	1.5	− 37	0.2	− 254	− 254	− 27	0.93	401	1607
	30	− 221	1.4	− 40	0.4	− 260	− 260	− 28	0.94	301	1321
	20	− 223	1.2	− 48	1	− 270	− 270	− 27	0.96	201	1020
	10	− 221	1.0	− 55	2	− 275	− 275	− 27	0.96	101	701
	9	− 220	1.0	− 56	2	− 276	− 276	− 28	0.96	91	663
	8	− 217	1.0	− 62	3	− 278	− 278	− 28	0.97	81	622
	7	− 212	0.9	− 68	4	− 280	-280	− 28	0.97	71	581
	6	− 202	0.8	− 81	7	− 283	− 283	− 39	0.97	61	538
	5	− 194	0.8	− 92	10	− 285	− 285	− 43	0.98	51	494
	4	− 177	0.6	− 111	16	− 288	− 288	− 49	0.99	41	445
	3	− 167	0.6	− 123	20	− 290	− 290	− 61	0.99	31	387
+ 10	50	217	1.7	26	− 0.2	243	243	17	0.89	496	1462
	40	220	1.6	28	− 0.3	248	248	17	0.90	401	1283
	30	225	1.4	35	− 1	259	259	16	0.93	301	1083
	20	226	1.2	41	− 1	267	267	19	0.94	201	889
	10	220	1.0	58	− 3	278	278	25	0.96	101	646
	9	217	0.9	62	− 4	279	279	26	0.96	91	617
	8	214	0.9	68	− 5	282	282	28	0.97	81	585
	7	210	0.8	74	− 6	283	283	30	0.97	71	553
	6	205	0.8	81	-8	285	285	34	0.98	61	518
	5	196	0.7	92	− 11	288	288	39	0.98	51	479
	4	190	0.7	99	− 13	289	289	48	0.98	41	434
	3	174	0.6	117	− 20	291	291	58	0.99	31	378

In order to illustrate the properties of capacitive current, the near-perfect whole-cell configuration in neurons is analyzed (Fig. 3A). The pipette tip resistance was 6 MΩ with 120 mM CsCl as the main salt. Note that during the application of negative pressure, the latter value will increase. The pressure allows for easy navigation within the slice, and the pipette will not get clogged. Also, because of the physics of internal solutions, the same pipette will have different monitored resistances. This can be demonstrated by using KCl and K⁺ gluconate as main ingredients, with the former having a convincingly lower resistance and, thereby, a true readout of the tip opening.

Responses in neurons (Fig. 3A) are more robust than in cardiomyocytes, but they are still not ideal for patch-clamp recording, as they are not absolutely round and are integrated with all processes within a 300 μm slice. The capacitive current remained similar when repeatedly evoked three times, 20 and 100 s apart (Fig. 3B). The transient current decays exponentially, and the same is true for an off response upon termination of a 50 ms step (Fig. 3 C and D).

An exponential function with a sloping baseline was applied to estimate the kinetics behavior of currents, which is integrated into pClamp (Axon Instruments, USA) software:

$$f\left(t\right)=\sum _{i=1}^n{A}_i{e}^{-t/{\tau }_i}+mc+C$$

where A is the peak amplitude, C is the amplitude of relative steady-state current, i is the components of currents (for capacitive one it is always i = 1), τ is the time constant, and m is the slope of the fitted curve after Chebyshev method. When the magnitude of the pulse was increased to – 10 mV, the amplitude of the current increased accordingly to − 290 vs. − 145 pA at – 5 mV (Fig. 3E). This will not significantly influence the readout of τ at respective 594 vs. 580 μs as measured for the initial 3 ms (Table 1). Thus, the C_M remains comparable. The C_M of this cell was estimated to be 53 pF by the pClamp software (Axon Instruments, USA) algorithm immediately after the first rupture. Since patch quality rapidly worsened and the whole-cell configuration transited back to the cell-attached state, a second rupture was again achieved by suction without changing the electrode position in the cell membrane. This time, the C_M was 48 pF, as identical conditions never occur with cells, especially with neurons within the slice. Thus, all parameters are not very precise, but rather relative. The C_M is more robustly calculated as capacitive transient area/test voltage (V_t) using pA ms and mV units. However, the area should indeed cover only capacitive transients (CT area). Therefore, those CT area values estimated during 6 ms will be compared, yielding 52, 53, and 51 pF for corresponding V_t of − 5, − 10, and + 10 mV (Table 1). These results confirm that ± 10 mV step is not excessive for this cell and condition. Nevertheless, the C_M of 51 vs. 52 and 53 pF is the lowest among them. The latter is logical, and as illustrated in Fig. 3E, there is less steady-state current at + 10 vs. – 10 mV. This is contaminating the capacitive currents evaluated during even 6 ms, and the CT area readouts were 518.4 vs. 538.1 pA ms, respectively (Table 1). Importantly, the CT area is the most unbiased parameter, even as patch quality worsens and the amplitude of transients decreases. In this scenario, the decay will decelerate and the duration of capacitive currents will increase. Thereby, these alterations do not crucially impact the overall CT area and initial values.

Note that there is no need for an extra protocol to elucidate the capacitive currents, as they can be measured from transient portions of any traces at lower voltages. Therefore, the trace from an original experiment is truncated at 50 ms. Upon applying + 10 mV from a HP of – 70 mV, the peak amplitude remained unaffected at − 291 pA, substantiating that transients occur upon depolarization and hyperpolarization of the same capacitive origin (Fig. 3F). However, in the former case, smaller steady-state currents are activated (Fig. 3E). The exponential fit applied to the entire 50 ms unravels + 26 vs. − 34 pA steady-state currents. This is consistently reflected by an absolutely unbiased parameter, CT area at 1462 vs. 1887 (Table 1). Since I_Leak—leak currents are voltage-independent, the underlying contributors could be HCN and Kir upon hyperpolarization (see above). An observed difference proves that applying steps of more than both 5 mV magnitude and 10 ms duration is unnecessary in this specific situation.

This was also confirmed by the y intercept of the curve by analyzing current behavior within 3, 10, and 50 ms after the onset of transients (Fig. 3G − I). A wider and more detailed range of diapasons for analyses revealed that a 10 ms pulse is optimal to elucidate the capacitive currents (Fig. 3J − L). Details of these analyses are provided (Table 1). Only the values of one pair of peak amplitudes upon depolarization and hyperpolarization were significantly apart at + 190 ± 3 vs. − 177 ± 2 pA when an exponential fit was targeted to the initial 4 ms portion (Fig. 3J). For compression of absolute values, their amplitude polarities are not considered. Note that the algorithms in Clampfit (pClamp, Axon Instruments, USA) are easy to follow, and all these digits are automatically calculated at once. One needs only to record traces of adequate quality and choose the right portion for each designated function. Although the presented digits in two columns for y intercept and peak amplitude values are identical (Table 1), they are not. Differences are very small and in decimals, e.g., corresponding values at – 5 mV within 8 ms after transient onset are − 139.464 vs. − 139.467 pA. Importantly, since the sampling interval was 100 μs, the total number of 81 points that were used for exponential fit approximates the duration of 8 ms. The values of the y intercept within 20 − 50 ms (− 143 vs. − 130 pA) are significantly different from the actual peak current amplitude. Despite the overlap, the superimposed values of the y intercept at 259 vs. 260 pA upon depolarization and hyperpolarization for the 30 ms portion of activated currents are different (Fig. 3L, and ). Similar respective patterns and values are estimated when data points are read with respect to the position of cursor 1 at start of the fit (Fig. 3L, and ). The close correlation of the values of the y intercept with those at cursor 1 substantiates that the latter was placed adequately. Note that since the rising phase of capacitive current is ~ 0.5 ms, the decay kinetics were obtained for 496 points, that is, 49.6 ms, but designated as the 50 ms group (Table 1).

This particular whole-cell patch is near ideal, as the tau of capacitive current decay was 560 ± 31 μs when measured for a 3 ms period at − 5 mV (Table 1). This value for a cell model with a defined electronic circuit was 348 μs in the same patch-clamp setup. The R_in was 467 MΩ, which approximates the expected value of 500 MΩ of the whole-cell electronic circuit. Thus, even the expected parameters depend on setup (the level of electrical noise within the Faraday cage and around the rig with equipment) and software settings. The R_a were 12.7 vs. 10 MΩ based on the properties of the circuit. The latter was measured with shorter – 5 mV pulses compared to 26 MΩ with longer pulse durations. This setting in Clampex (pClamp, Axon Instruments, USA) also automatically changes the sampling interval. Under these conditions, the value of tau increased to 750 μs. The C_m was less sensitive to amplifier and software settings and was 25 vs. 26 pF for both conditions. However, these values are different from the expected 33 pF. Thus, the cell model helps to properly connect the inputs and outputs between the amplifier and digitizer, to check the level of noise apart from that originating from the pipette holder and electrode filled with solution, and to set the parameters of software for optimal readouts. The latter is important for proper acquisitions, e.g., during experiments with immature or certain types of cells with high R_in exceeding 1 GΩ (Kodirov, submitted). In this case, one cannot inject high amplitude currents in order to depolarize or hyperpolarize the MP. Finally, the software settings mentioned above are required for more precise and continuous on-line monitoring to ensure cell and patch quality.

Patch-clamp traces quality

The aforementioned recordings substantiated that already during the 10 vs. 5 mV step, the magnitude of capacitive transient doubles and additional activation of ionic currents occurs. Although these transients are fast, they overlap with rapidly activating ionic currents, especially those via A type channels, at more depolarized MP. Therefore, the quality of traces and the robustness of responses are crucial in order to decipher both. From Fig. 4, it can be learned that ‘proper planning of experiments’ did not lead ‘toward more accurate data in cardiac cellular electrophysiology’ (Bébarová et al. 2020). Besides, the n = 18 for an A type channel and the n = 20 for I_Ca are not large data sets (Ismaili et al. 2020; Kula et al. 2020a).

Fig. 4.

Off-line improvement of patch-clamp trace and redundant statistics for low n numbers. A Capacitive, inward tail, and outward currents in rat right ventricular cardiomyocyte in whole-cell mode (Kula et al., 2020a). Note that the I_C is present only as inward current immediately before tail. Since the amplitude of I_C is much greater, it is truncated. The I_C should be present also upon the on-set of 50 mV pulse (see Figs. 5 , 6,  7). There is no holding current at – 85 mV hinting that the RMP of this cell was close to latter value. B Protocol. C Initial portion of traces in an expanded time scale achieved by horizontal stretch of factor 5. Thereby, the removal and replacement of I_C by a straight line is highlighted. The X denotes not properly aligned line with trace and reveals a mismatch in overlap, while the + sign mimics the un-proportional thicker line compared to a transient ( −). Subsequently, the question mark reflects the uncertainty as to originality of trace and current decay in entirety. D Absence of correlation between cell and I_t0 current size for n = 18 (Kula et al., 2020a). E Data points from the same graph after retrospective digitization (Fedorov 2002). The latter approach was adequate based on individual values (note differences in y axis) and that of linear fit in Origin yielding R of 0.037 vs. 0.04 in original study (red line). By the approach advocated by authors, the data were fitted by extrapolating through absolute 0, which did not alter the R, albeit an increase in SD to 1.9 vs. 1.8 nA (blue dashed line). Note the steepness of visual appearance of blue line, as the opposite extreme of extrapolation is not shown. Interestingly, the P value is now highly significant. Highlighted (Kula et al. 2020a)

Whether or not values indeed are different, the n numbers along the patch quality remain defining factors. Since the I_t0 is fast, its activation may overlap with capacitive currents, thereby either obscuring its rising phase or masking it all together. In Fig. 4A, the capacitive current (I_C) is present only upon termination of the step to + 50 mV from a HP of – 85 mV. Due to the fact that it is truncated, it is impossible to estimate the amount of I_C because the amplitude of A currents is higher. Since the activation phase of currents was too steep and straight, to observe the underlying data, an initial portion was expanded in time (Fig. 4B). This revealed a thicker line ( +) instead of capacitive currents. Therefore, the integrity of representative I_t0—the best recording, is compromised. That is why the patch-clamp trace quality should be favored for estimations, especially meta-statistics.

In an isolated mouse left ventricular cardiomyocyte, the capacitive, inward, and outward currents can be elucidated during a single whole-cell patch-clamp experiment. As the pulse protocol designed to determine the I-V curve enables activation of I_K1 along the Kv and Nav channels (Fig. 5A). Since pulse duration is 4 s and inactivation of A channels is fast, one cannot appreciate the time course of outward currents. This is enabled by a simple switch from a linear to a log10 time scale (Fig. 5B). Under these conditions, the bidirectional I_C and inactivation of I_K1 currents are also visualized. The phenotype of fast inward transients—I_Na is resolved in the Logit time scale, which expands and highlights the initial portion of traces (Fig. 5C). The Logit scale obeys the equation: logit = ln(Y/(100-Y)), where ln is the natural log scale. Thus, each component of currents has a distinct amplitude and kinetics, as revealed for I_Na (the thick black trace), I_t0 (blue), and I_K1 (red). These components can be deciphered by estimating the I-V relationship. Peak values of outward (blue) and steady-state currents (red) change as expected for Kv channels in a voltage-dependent manner (Fig. 5D). Figure 5B shows that a 20 mV step activates more I_K1 than 130 mV needed for I_SS activation (− 552 vs. 488 pA, respectively), which is substantiated by normalizing the data in Fig. 5D to the maximum amplitude of outward currents at + 60 mV (Fig. 5E). Note that the amplitude of peak I_K1 is even higher at − 759 pA (Fig. 5C). The behavior of I_K1 is opposite to that of HCN (I_f or I_h), as the former activates rapidly upon the onset of a pulse and immediately starts to inactivate gradually, while the latter gradually starts to activate upon the onset of hyperpolarizing steps. Next, the activation of HCN progresses gradually over seconds without inactivation. The unique activation pattern of I_Na in the I-V curve reflects that the patch quality was not ideal, at least for Nav (Fig. 5F). As the activation of fast I_Na inward currents—transient type (I_Na−T) is not proportionally gradual between − 50 and – 30 mV. However, this is a common phenomenon in other cells as well (Kodirov, submitted).

Fig. 5.

Simultaneous activation of major currents in cardiomyocyte. A Capacitive, inward, and outward currents in mouse left ventricular cardiomyocyte in whole-cell mode of patch-clamp technique. A simple single step protocol enables activation of I_K1 along Kv and Nav channels. B Same recording in Log 10 time scale. Note the bidirectional I_C and inactivation of I_K1 currents. C Initial portion of traces in Logit scale. One of each trace is highlighted for I_Na (thick black), I_t0 (blue), and I_K1 (red). D I-V relationship of currents upon the on-set (blue) and immediately before the off-set of pulses in (A). E Same data are normalized to maximum amplitude at + 60 mV. Note un-proportional bigger I_K1 during a small 10 and 20 mV hyperpolarization. F Same steady-state currents as in (D) are superimposed with current polarities during the time in (C) (Kodirov, unpublished). Amplitude scale in (B) identically applies to (A and C), while different timing in ms is indicated by respective linear, base 10, and Logit logarithmic x axis (Kodirov, unpublished)

Thus, a clear differentiation of capacitive currents is also possible when a rapid I_Na is present upon the onset of steps (Fig. 5 B and C). Note that the time course of I_Na is faster than that of I_t0. Similar distinctions between capacitive currents and the occasional conductance occurring selectively upon repolarization led to a pioneering and precise description of ion channels in mammalian Purkinje strands (Noble and Tsien 1968). Capacitive currents occur distinctly prior to the fast activation of cloned Kv4.1 and Kv4.3 when expressed in Xenopus oocytes (DeSimone et al. 2011).

Besides, even in the absence of off-line trace processing, that is, in raw traces, the inward and outward currents along the capacitive transients are easily distinguishable and could be compared after the actions of inhibitors (Fig. 6A). Note that the activation of distinct channels and capacitive current are observed in a single mouse left ventricular cardiomyocyte during application of the same protocol and voltage steps in whole-cell mode. Therefore, there is no need for prior elucidations dedicated to capacitive currents, which may not be constant during the entire course of experiments. Since the cell was isolated from a double dominant-negative Kv1/Kv2 mouse, both components of I_K−Slow are absent. Currents were adjusted to ± 0 pA by defining the amplitude immediately before the off-set of pulses as a baseline (Kodirov, unpublished). In this case, it was insightful to present the same recording on the Log 10 time scale (Fig. 6B). It is worth noting that the capacitive currents I_C are bidirectional, and that the fast inactivation of I_Ca and I_t0 occur within similar time diapason. The marginal I_K could be the slower component of I_t0. Subsequently, 5 mM Co²⁺ obliterated the I_Ca when tested in the same cell (Fig. 6C). Blockade of Cav channels augmented I_t0 and decreased I_ss currents while I_K remained unaffected (Fig. 6D). The I_Na currents were inactivated by the pre-pulse to – 20 mV. Effects of Co²⁺ are visualized in corresponding I-V curves for I_Ca and I_t0 before and after application (black and blue, Fig. 6 E and F). Co²⁺ not only augmented the amplitude of I_t0, but also shifted the threshold for activation of K currents to the right.

Fig. 6.

Simultaneous activation of major currents in cardiomyocyte. A Recording is conducted under identical conditions as in Fig. 5, in mouse left ventricular cardiomyocyte in whole-cell mode of patch-clamp technique. Since the cell was isolated from double dominant-negative Kv1/Kv2 mouse, both components of I_K−Slow are absent. Currents were adjusted to ± 0 pA by defining the amplitude immediately before the off-set of pulses as a baseline. B Same recording in Log 10 time scale. Note the bidirectional I_C and fast inactivation of I_Ca and I_t0 currents. The marginal I_K might be the slower component of I_t0. This baseline adjustment could also be considered as a simple method to exclude minor leak currents (Kodirov, submitted). C Same cell in A in the presence of 5 mM Co²⁺. D Blockade of Cav channels augmented I_t0 and decreased I_ss currents, while I_K remained unaffected. The I_Na are inactivated by pre-pulse to – 20 mV. E, F Corresponding I-V relationship of I_Ca and I_t0 before (black) and after Co.²⁺ (blue). Amplitude scale in B identically applies to (A, C and D), while different timing in ms is indicated by respective linear and base 10 logarithmic x axis (Kodirov, unpublished)

Capacitive currents are present after each voltage change and also during multi-step protocols (Fig. 7A). These recordings were conducted under identical conditions as in Fig. 6 by using the same pulse protocol (Fig. 7B). The capacitive transients during a near optimal whole-cell patch are fast in mouse left ventricular cardiomyocytes recorded at 35 °C. Transients are complete in less than 2 ms (an interval between the pre-pulse of – 20 mV and the test voltage of + 60 mV, Fig. 7C, red trace) and do not interfere with the activation of I_t0 (Barry et al. 1998). The lower amplitude of capacitive currents is linked to a sampling interval of 500 μs. Despite longer sampling intervals, the resolution of I_t0 was sufficient to appreciate the activation and subsequent inactivation (Fig. 7C). Recording was conducted in con-current presence of Co²⁺ and TTX. It is possible that the TTX did not completely inhibit the fast I_Na in this cell, as smaller inward currents (0.6 vs. 8.7 nA under control conditions) are present upon the onset of the pre-pulse to – 20 mV from a holding potential (HP) of – 70 mV. Nonetheless, the purpose of the pre-pulse was fulfilled, as the fast I_Na were absent during test voltages, leading to the activation of outward currents. However, for clarity, capacitive currents preceding the I_t0 are Lowpass filtered (Gaussian, − 3 dB cutoff at 50 Hz, Clampfit (pClamp, Axon Instruments, USA), since the P/N subtraction protocol (see further) was not used on-line. Note that the amount of leak current was negligible in this experiment.

Fig. 7.

Amplitude heterogeneity is unaffected by considering the current density. A Outward currents in left ventricular cardiomyocyte in whole-cell mode of patch-clamp technique. The temperature in recording chamber was set to 35 °C. Cells were isolated from double dominant-negative Kv1/Kv2 mice. B Protocol with pre-pulse that enables inactivation of Nav channels. C The I_t0 portion of outward currents from (A). The exemplary raw trace is evoked by + 60 mV (red) and all are Lowpass filtered (blue, Gaussian, − 3 dB cutoff at 50 Hz, Clampfit (pClamp, Axon Instruments, USA). D Differential magnitude of I_t0 (n = 28). There are only two outsider cells with a slight higher I_t0 (green and orange) and one with depolarized E_rev—reversal potential (pink). E Arithmetical average (blue) of currents in 28 cells were normalized to maximum amplitude of 4.6 ± 1.7 nA at + 60 mV. Identical approach was applied to current density values (red) revealing marginal decrease in SD. Amplitude scale in (C) identically applies to (A), while different timing is indicated. Modified (Kodirov et al. 2004). F Capacitive transient and leak current subtraction protocol of Clampfit software (pClamp, Axon Instruments, USA)

This procedure removed some data points, resulting in smoother transitions around the – 20 mV pre-pulse (Fig. 7C, blue vs. red trace). Thereby, it decelerated the activation and lowered the peak amplitude without affecting the current decay, as it is a much slower process.

Therefore, any filtering and manipulation will diminish the quality and outcomes, though often the recurrent electrical noise has to be filtered out. The amplitude of currents should be estimated in the absence of filtering, but the interference of noise should be inspected visually and excluded. Since the n numbers are always low, the automatic analyses performed by additional software are unnecessary. If responses are robust, the tendency will persist for all cells and also with regard to I_t0 (n = 28, Fig. 7D). The superimposed values revealed two outsiders (green and orange) with slightly higher I_t0 and one with depolarized E_rev—reversal potential (pink). The pattern of voltage-dependent activation is also appreciable for mean values (Fig. 7E). The latter remained unaltered when the arithmetical average (blue) of currents in 28 cells was normalized to a maximum amplitude of 4.6 ± 1.7 nA at + 60 mV. When the current density (red) was considered, mean normalized values remained unaffected, albeit the decrease in SD, e.g., 0.755 ± 0.258 pA/pF vs. 0.755 ± 0.272 pA at + 40 mV.

Also, the P/N leak subtraction method may not be advised for traces revealing the activities of voltage-dependent ion channels. Because the latter protocol not only corrects the traces for leak but also removes capacitive currents. The protocol is based on the following formula:

$$\mathrm{Corrected}\mathrm{trace}=\mathrm{Original}-\frac{\mathrm{Stimulus}\mathrm{Waveform}}{\mathrm{CF}\times \mathrm{Resistance}}$$

where CF is the conversion factor, which is equal to 1 or 0.001 for current in pA or nA and voltage in mV. The passive leak resistance of the cell is measured in MΩ. The formula is simple, but the waveform is not (Fig. 7F). The P/N protocol is used in voltage-clamp experiments and is a ‘series of scaled-down versions of the command waveform is generated, and the responses are measured, accumulated, and subtracted from the data. Scaled-down versions of the waveform are used to prevent active currents from being generated by the cell. The number of these scaled-down waveforms is entered as the number of subsweeps (N). The waveform (pulse P) is scaled down by a factor of 1/N, and this is applied N times to the cell. Since leakage current has a linear response, the accumulated responses of the subsweeps approximate the leakage current for the actual waveform’ (pClamp, Axon Instruments, USA). The number of subsweeps may equal four hence sometimes the P/-4 protocol is referred to (Fig. 7F). The polarity of subsweeps depends on the properties of channels, namely that for those activating upon depolarization, it is negative, while upon hyperpolarization, a positive sign is assigned.

Current density

The method of normalizing current to capacitance - current density has been used also to account for membrane infolds into caveolae and transverse tubules in cardiomyocytes and skeletal muscle cells. The capacitance of the t–tubule membrane has been estimated in isolation and shown to be voltage-dependent with values of 6 vs. 7 μF/cm² at − 120 vs. – 64 mV for fibers of 44 μm in radius (Schneider and Chandler 1976). The caveolae are also invaginations in the cytoplasmic membrane, and their structure exhibits similarity to the letter Ω. They regulate Nav channel functioning, but only the caveolin-3 antibody at 100 μg/ml prevents the increase of I_Na usually observed after application of 10 μM isoproterenol (Yarbrough et al. 2002). In fibers from the frog sartorius muscle, the disproportional amounts of current are normalized as μA/cm² (Adrian 1969). Similar normalization was applied to study the effects of depolarization on charge movement in isolated squid axons of about 850 μm (Chandler and Meves 1970). The latter authors explicitly state that the ‘total current flow was 5 μA which would correspond to a current density of about 20 μA/cm² if it flowed only across the membrane opposite the internal current wire,’ because the axon membrane is not intact (in comparison to a single cell) and contains an experimentally cut region to perfuse internally. The charge can also be represented as density, nC/μF, which is close to nC/cm² because the capacitance of the membrane around the T-tubule equals to ~ 0.9 μF/cm² (Chandler et al. 1976). It is fascinating that the latter pioneering study addressed precisely the current passing through electrode while it had been just immersed in the extracellular solution. If the electrodes are less than 7 MΩ in resistance, the registered currents obey an exponential solution with a τ of up to 8 μs. In this context, the authors refer to earth potential. Importantly, the recorded currents from muscle fibers are of the highest quality, and the analysis is clearly and insightfully explained: ‘difference traces, test minus control.’

Although g_Na = I_Na/(E − E_Na) is already a normalization, the conductance is further normalized by the cm² membrane area (Hodgkin and Huxley 1952b). Where E is the membrane potential and E_Na is the equilibrium potential for the sodium ion. This equally applies when the K ion movement is considered. As introduced, extensive studies are devoted to Nav channels in giant axons of the squid Loligo and CNS neurons of snails (Brenes 2022; Hodgkin and Huxley 1952b). In excitable cells, a depolarization of MP may simultaneously trigger the I_C, I_K, I_Leak, and I_Na (Armstrong and Bezanilla 1974). Also, gating currents that have a very fast outward component and occur within ~ 300 μs are normalized as μA/cm², which can be recorded in isolation from I_Na when the external solution does not contain Na⁺. The outward gating current reflects Nav channel opening and is reversibly blocked by Zn²⁺.

Independent of which method is used to calculate the J—current density, values are not finite. Contrary to recent assumptions (Kula et al. 2020a), the J is not routinely used to analyze whole-cell patch-clamp experiments (Bahring et al. 2001; Bett et al. 2012; Clay 2000). This parameter is useful when two or more components of Kv channels are activated in an overlapping manner in the same cell (Souza et al. 2002). Current density can be predicted without estimation using logic, cell size, and the amount of α subunits injected (Gordon et al. 2006). The expression of more channels not only increases the peak currents but also accelerates the activation kinetics. It was hypothesized that the endogenous ancillary subunits in the Xenopus oocyte, xMinK and xMiRP2, may decelerate the activation of exogenous Kv2.1 channels. The latter influence is presumably removed by ‘dilution’ with the increased amounts of injected Kv2.1 mRNA. It is plausible theoretically, as the ratio of β to α subunits is pre-programmed, but co-injecting MinK and MiRP along the Kv2.1 or any associated K channels will substantiate this hypothesis. Similar acceleration is commonly observed when single-channel opening and closure are achieved repeated multiple times and then the recorded traces are averaged, yielding an ensemble current. The latter resemble those recorded during whole-cell patch, and their activation kinetics are faster at the more optimal MP range for voltage-dependent channels, as is the Kv2.1. However, comparisons should be made for an equal amount of traces, considering that similar activities of a single channel were triggered each time. The latency to channel opening will determine the specific features of currents, i.e., fast or delayed activation. Finally, if those auxiliary subunits were designated for and selective for Kv2.1, then the observed acceleration could reflect a co-assembly of the channel complex. The latter, beside the α and β subunits, contains the T1 domain in between (Orlova et al. 2003). There is no physical connection between the α and β subunits. An interaction between the membranous α and intracellular β subunits of Kv channels occurs via the central 50 Å moiety—T1 domain. If this is the case, however, MinK and MiRP, whether endogenous or exogenous, should not inhibit Kv2 currents. At least there should be no dependency on the amount of Kv2.1 mRNA.

The current density depends on how the whole-cell configuration is achieved, as in the case of perforation the mean value was − 79 pA/pF vs. − 55 in ruptured cells for Nav (Okada et al. 2005). Further, it is linked to the composition of an internal solution, e.g., 500 μM GTPγS decreases the J to − 11 pA/pF. Although indirect, perhaps estimating J from active channels in a small patch of membrane is more precise. One can optimize the tip of the electrode to record the activities of only a single channel per patch. Knowing the inner diameter of the pipette, the patch membrane area will be estimated.

Direct measurements of cell size—projection area in μm² along with immunolabeling will yield more accurate results about the expression of channels, as shown for connexin in the SAN— sinoatrial node (Honjo et al. 2002). This approach may also enable answers as to whether or not the channel reaches the cytoplasmic membrane. Differential current density values correlate with α subunit expression at mRNA and protein levels (Kouranova et al. 2008).

A paradoxical increase in the cytoplasmic membrane density of WT Kv11.1 channels has been shown after stable expression in HEK293 cells (Anderson et al. 2006). Incubating the latter cells at 27 vs. 37 °C for 24 h prior to recordings increased the HERG current density to 103 vs. 83 pA/pF, which is perhaps due to effects on channel trafficking. Since the cell capacitance reflects the size of the cytoplasmic membrane area, ideally, it should not change during the course of experiments. In order to control for the variability of cell size, the individual J can be divided by the mean J value of the group data (Blaine et al. 2004). If there is no developmental change in channel expression, then the J remains constant despite a two-fold increase in cell capacitance, as shown for A type channels (Frolov and Weckström, 2014).

A type channels

Activation of A type—transient outward currents—I_t0 tightly depends on the frequency of applied steps, as its amplitude at 1 Hz is moderate, while at 2 Hz it is almost negligible even upon pulses to + 60 mV (Gomis-Tena and Saiz 2008). Similar to other channels, I_t0 has two components, fast and slow, each exhibiting unique current densities (Freeman et al. 1997). However, these components are not often separated. Moreover, the magnitude of I_t0 did not correlate with membrane capacitance in comparison to I_KACh and I_K1 (Kula et al. 2020a). If this criterion—the absence of proportionality—is correct, then all Kv channels, at least of transient types, should fall into the same category, namely Kv1.4, Kv4.1, Kv4.2, and Kv4.3 α subunits. Besides, then there would be no differences among cells in terms of functionality, as predominantly smaller types are often the specialized ones, i.e., pacemaker SAN cardiomyocytes, because of the prevailing expression of HCN channels. However, based on representative patch-clamp traces in Fig. 4 and n = 18 for I_t0, conclusions are without merit, whether or not the variability in amplitude could be diminished by considering the current densities (Kula et al. 2020a). When the polarity of the current is positive and the coefficient of correlation is marginal but also positive, why should the 95% confidence interval— CI_slope start from the non-existent negative value of − 16 pA/pF? This is especially, when the overall trend of all three fits for four components of currents is similar, whether inward or outward. Moreover, the behavior of current densities in context with statistical power and the Pearson coefficient is also comparable for all channels or components.

Thus, estimation of current densities for I_t0 cannot be avoided retrospectively, and future research will prove whether or not this recommendation stands. Based on table 5, also I_K1 analysis was already avoided, perhaps because of the lower n = 22 (Kula et al. 2020b). Current retrospective analyses of data (Kodirov et al. 2004) reveal that a correlation exists regardless of via which α subunit the currents are carried out (Fig. 8A − D). The only determinants are quality of the patch and recording along the n numbers. Among the four groups, only in Kv2 dominant-negative mouse left ventricular cardiomyocytes was no correlation between amplitude and capacitance observed, most plausibly because of n = 11 (Fig. 8B). The latter was much lower than those of double Kv1/Kv2, single Kv1 dominant-negative, and WT mice (Fig. 8 A, C, and D). Also note that in Kv2, the minimal range of capacitance was higher at 136 vs. 76, 52, and 54 pF in Kv1/Kv2, Kv1, and WT mice, respectively. The advocated ultimate goal—reduced variability was not achieved by estimating the correlation between pA/pF and pF, and on the contrary, the SD of R²—coefficient of correlation—increases by a factor of at least 5 (Fig. 8). The same data for all groups now exhibits a negative correlation, except for Kv2 dominant-negative cells, which had an R² of 0.4 ± 11.3 (Fig. 8F). Because of the artificial increase in SD to 11.3 vs. 2.2, the P is still not significant at 0.1. Besides, a significant positive correlation between pA and pF (Fig. 8 A, C, and D) is lost by this manipulation (Fig. 8 E, G, and H). It is worth noting that these complications appear in outcomes of meta-analyses even when only one component of the family of outward currents—I_t0, is considered.

Fig. 8.

Weak crucial impacts of base 10 Log transformations of actual data and absence of correlation between current densities and capacitance. A Relationship of actual amplitude of outward currents to capacitance. Data are from Fig. 7 and belong to double dominant-negative Kv1/Kv2 mice. B Kv2 dominant-negative. C Kv1 dominant-negative. D WT mice. Reanalyzed data (Kodirov et al. 2004). E − H Relationship of current density pA/pF to cell capacitance pF for each individual cell. The same data and recorded values as in (A). Note that now none of groups exhibit a degree of significance. Based on SD, this manipulation actually increased the variability by factor 5, at least. The correlation coefficients and P values have improved for (F), but differences are still statistically insignificant. Values in (E, F, G, and H) are from respective dominant-negative Kv1/Kv1, Kv2, Kv1, and WT mice. I Relationship of actual amplitude of outward currents to capacitance after Log 10 estimation (data from A − D). Log 10 refers to data point, but not to scale. Note the lower degree of significance despite of decreased variability by factor 9. J If data do not correlate, then the Log 10 will not reveal otherwise, thus the proposed meta-analyzes is redundant (Ismaili et al. 2020). K The correlation and P values may improve, but what kind of merit will have the estimated differences? L Same conclusion as in (K). Underlying actual values are from respective dominant-negative Kv1/Kv1, Kv2, Kv1, and WT mice for (A, B, C, and D). The P values are color coded with blue, while n numbers with black and coefficient of correlation along their SD with red, respectively. Meta-analysis (Kodirov et al. 2004)

It is established that in rodents, the outward currents are multi-component, and TEA alone will obliterate only one of them; therefore, additionally, 4-AP at low concentration is used (Kodirov et al. 2004). Depending on whether the α subunits tetramerize as hetero- or homo-meric complexes, the TEA, even at 100 mM concentration, may be ineffective toward outward K⁺ currents (Roeper et al. 1998). Of note, the transient component of Kv1.4 persisted in the presence of 100 mM TEA, while the steady-state currents were obliterated. Heteromeric Kv1.4 + Kv1.6 exhibit slowly inactivating outward K⁺ currents, which closely resemble the phenotype of a transient type rather than a delayed rectifier. Application of TEA has further substantiated that indeed two distinct α subunits constituting a functional channel complex were present, and prevailingly the Kv1.6 component was blocked. As subtracted TEA-sensitive currents have a similar waveform to those of Kv1.6 conducted via homomeric channels under control conditions.

It will not be clear when experimental and simulated values are very close yet not identical: 219 ± 53 vs. 218 ± 53 pF and 3488 ± 1775 vs. 3445 ± 1757 pA (Kula et al. 2020a). Under identical conditions, it is hardly possible that almost the entire inward K⁺ currents in one atrial cardiomyocyte are mediated by I_K1, while in another cell— by I_KACh channels. In addition, the background noise level in arithmetically subtracted trace—barium-sensitive currents—should not increase. A 25-mV step for the determination of cell capacitance—cF is not a subthreshold voltage, as the commonly used magnitude is ± 5 mV. Because no inward (I_f and I_K1) and outward currents (Kv family) are activated during low amplitude short steps, capacity transients upon pulse on- and off-set can be registered in isolation. If in native cells only capacitive currents are present, then any pulses can be applied, as the amplitude changes accordingly (Fig. 3 A and E). However, already at ± 10 mV pulse, the non-transient components of current differ since they are contaminated by membranous channel activation. Note that the latter portion is used for R_a estimation. Besides, it is impossible to keep a cardiomyocyte at – 110 mV (Kula et al. 2020a), at least for a longer time.

Also, the cF distribution in all atrial cells cannot start at ± 0 pF as in figure 1a (Kula et al. 2020b), since in figure 2a there is a solitary minimal value of ~ 25 pF (Kula et al. 2020a) when inward K⁺ currents were recorded. The latter can also be learned from other original figures and tables, and italics here and elsewhere prompt the reader to corresponding visual items in referred studies.

Therefore, the absence of a linear correlation between pF and pA for I_t0 is without merit (Fig. 4D). As revealed by the meta-analysis of data from figure 2b (Kula et al., 2020a), digitization (Fedorov 2002) and artificially considering the y intercept as ± 0 pA resulted in a P < 0.0001 for an identical R = 0.037, albeit with a different SEM (Fig. 4E), which was not previously mentioned. What is the meaning of this new level of significance? It accumulates more confusion, as the slopes of the lines are also significantly apart judging from their visual appearances (Fig. 4 D and E). There might only be minor differences in the original data and values after digitization, since even the coefficient of variations (CV) was comparable at 0.50 vs. 0.51. It is important to note that not all arithmetical doctrines apply to cellular cardiac electrophysiology, as there are no cells with a size close to 0 pF that could potentially contribute a ~ 0 pA current. Besides, after the exclusion of the last 1 − 3 outliers in figure 2a (Kula et al., 2020a), the linear fit will yield less significant correlations, and that is the power of statistics in biology with regard to ion channels, including the L-type.

L-type channel

The existence of Cav channels was also initially substantiated by their involvement in AP waveforms in select cells (Gerasimov et al. 1964). Already back then, it was established that Cav is permeable to Ba²⁺ (Kostyuk et al. 1974).

Another recent analytical study deals with cell capacitance in context with Cav1 − L type Ca²⁺ channels, but the unit pF is not mentioned within the article except for graphs that reflect values of this parameter for individual cardiomyocytes isolated from human and rodent hearts (Ismaili et al. 2020). Discarding cells with less than a 3 GΩ tight seal during the cell-attached mode is not a criterion of the patch-clamp standard. As the membrane ruptures sometimes spontaneously and prematuraly, the whole-cell mode may occur already at 1 GΩ, which depends on cell membrane quality and electrode tip diameter. Also, access resistance may not exceed 10 MΩ immediately after cell membrane rupture, but it will gradually increase thereafter. It is not clear whether the phrase ‘mean data are based on mean data’ means literally or whether those average values are restricted to 10 animals, including humans (Ismaili et al. 2020). The mean data cannot be based on mean data but must always be derived from several individual experiments. Otherwise, data will be processed twice, resulting in a lower SD. Actual data, namely ‘meta-statistics’ in accordance with the ‘mean of mean’, are provided as an argument in Fig. 9.

Fig. 9.

Meaningless ‘mean data based on mean data’ and data transformation. A Outward K currents in mouse left ventricular cardiomyocytes in whole-cell mode of patch-clamp technique (n = 22). The latter are separated based on origination from each four mice and color coded. B Corresponding mean values ± SD from (A). C Those of mean ± SEM. D Each conventional mean from (B) and (C) (black) is compared with those of mean of mean (magenta). Double data processing decreased the SD. However, insignificant differences persisted (Kodirov, unpublished). E The amplitudes of inward Cav currents in right atrial cardiomyocytes of humans with regular SR—sinus rhythm and those with AF—atrial fibrillation along the left ventricular cells of human, mice, and rats (HLV, MLV, and RLV). Each value is from 10 subjects (Ismaili et al. 2020). Mean ± SEM values were estimated by retrospective digitization (Fedorov 2002). F Same data as in E are normalized to individual cell capacitance to avoid effects of sell size. G Log transformation of mean values from A. H Log transformation of mean amplitude and capacitance individually with subsequent normalization. An exemplary simple math comparison of SR and AF groups reveals that a robust reduction in E and F is lost during unnecessary transformation in (G) and (H). The values of SR are taken as 100%. Altered and highlighted (Ismaili et al. 2020)

Besides, obtaining reliable n = 3 patch-clamp recordings from one animal, especially a patient, is not always possible. The latter minimal number of experiments is required to perform any statistics, including averaging for the ‘mean of mean’ (Ismaili et al. 2020). Moreover, it is very hard to obtain convincing and representative patch-clamp traces. Therefore, in the aforementioned study, not a single representative trace is presented. There is deficit in n numbers but an abundance in digits, graphs, tables, and statistics. For example, in the atrial fibrillation (AF) group, n = 29 vs. 20 were measured in the sinus rhythm (SR) one. Based on simple math and an artificial limit of analysis to only 10 experiments/samples, the n = 3 were obtained logically neither from individual human subjects nor groups of them, since 10 × 3 = 30. Comparisons are inadequate with unequal n numbers, especially when the latter is low for relatively healthier patients, the SR vs. AF group. Note that table 3 contains more N/A—not applicable and N/S—not significant notes than reliable data. Especially, the HLV vs. SR meta-statistics barely reach the P < 0.05 threshold in only 1 out of 24 sets.

The primary task of the patch-clamp technique is not to deal with meta-statistics. Nonetheless, retrospective meta-analyses reveal that when conditions are kept constant and traces are reliable, the data exhibit consistent amplitude distributions among recorded outward K currents in mouse left ventricular cardiomyocytes in the whole-cell mode of the patch-clamp technique (Fig. 9A, n = 22, black). The latter wide diapason persists when each of the four mice is analyzed individually, i.e., 22 = 6 + 4 + 7 + 5 (other colors, Fig. 9A). Corresponding mean values unravel that the SD (n = 5) in mouse 4 is the highest, but logically within the range of data points in A (Fig. 9A). The SD of all mice (black) is smaller because of the higher n = 22. A similar trend remains when the SEM is considered (Fig. 9C). Double data processing—‘mean of mean’ from B and C decreased the SD in comparison with conventional averages (black vs. magenta, Fig. 9D), with values of 3.75 ± 1.36 vs. 3.74 ± 0.66 nA. Note that the mean value was also reduced by 10 pA. In contrast, the SEM value has increased by this redundant transformation to 3.75 ± 0.28 vs. 3.74 ± 0.33 nA. One can obtain similar results by using random digits, e.g., by assuming that from 3 subjects, the values of 1, 2, 3, 4, 5, 6, 7, 8, and 9 were estimated with a mean value of 5 ± 2.7 and 5 ± 0.9 for SD and SEM, respectively. Now segregate each subject by values in a row, i.e., subjects 1 (1, 2, 3), 2 (4, 5, 6), and 3 (7, 8, 9). The mean values of the mean values of three groups will be identical at 5, but the SD and SEM will be higher at 3 vs. 2.7 and 1.7 vs. 0.9, respectively.

The retrospective analysis of Cav channels covers experiments with cardiomyocytes from humans, mice, and rats under two main conditions, i.e., either data derived from all animals or those restricted to only 10 of them. Since the ‘selection was done by drawing lots’ (Ismaili et al. 2020), it is not a biological science. Coincidentally, the latter digit is identical to another study with regard to similar statistics, as ‘data analysis indicated significant variability of I_K density between hearts. To minimize this source of variability when assessing regional differences, I_K analysis was limited to hearts in which data was obtained from a minimum of one epicardial and midmyocardial myocyte (10 hearts); this produced greater statistical power at the expense of reducing cell number’ (Gintant 1995). This selection has some logic, as at least n = 2 were eligible for inclusion in statistics targeted at 10 animals. But the rule was to have recordings from both regions of the heart of each single animal out of 10, i.e., targeted to cardiomyocytes of the epicardium and midmyocardium. It is important to note that this is not a ‘mean data are based on mean data’ statistic (Ismaili et al., 2020).

Note that in the latter study there are many statistical comparisons but not a single patch-clamp trace:

• AF vs. human LV

• AF vs. mouse LV

• AF vs. rat LV

• Human LV vs. mouse LV

• Human LV vs. rat LV

• Mouse LV vs. rat LV

• SR vs. AF

• SR vs. human LV

• SR vs. mouse LV

• SR vs. rat LV

Why should one compare humans with mice when there is a closely related pig? What is the hypothesis, and what will be gained by comparing cardiomyocytes of the atrium from patients with atrial fibrillation (AF) with those of the left ventricular (LV) and a healthy rat? Whether differences are significant or not after data manipulation, there is no logic for I_Ca comparison between a healthy patient—sinus rhythm (SR)—and that of a mouse.

The n numbers differ between the AF and SR groups in figure 1 (Ismaili et al. 2020). Furthermore, there are only two cells in SR with total currents between ~ 1.8 and 2.6 nA, and several had near + 0 pA I_Ca amplitude. In the AF group, within the cF range of ~ 200 to 340 pF, there is a solitary cardiomyocyte, thus the R² value is invalid. It is impossible that the activated Cav channels will exhibit ~ 0 pA inward currents. The same applies to representative data in figure 2.

The proposed data transformation (Ismaili et al. 2020) is not innovative, and simple math substantiates that it is also without merit (Fig. 9E). A retrospective digitization (Fedorov 2002) unravels the presented amplitude values for inward Cav currents in right atrial cardiomyocytes of humans with regular sinus rhythm (SR) and those with atrial fibrillation (AF) along the left ventricular cells of humans, mice, and rats (HLV, MLV, and RLV). Comparisons of digits derived from 10 subjects proved that plain amplitude readouts were already significantly reduced by 58% in AF vs. SR. The values of SR are taken as 100% for reference. Consistently, the trend persisted, but differences increased to 63% of SR when values were normalized to channel density to exclude effects of cell size (Fig. 9F). As opposed to assumptions and outcomes of statistics, the Log transformation of mean amplitude and capacitance obscured actual significance by exhibiting a reduction of 17 and 19%, respectively (Fig. 9 G and H). After two-step data reprocessing, a hardly significant and dogmatic P < 0.05 emerged suddenly for SR vs. HLV (Fig. 9H). It required a recommendable current density estimation and subsequent redundant Log 10 transformation. Thus, no additional doctrine is required for patch-clamp data or its readouts of cell and membrane biophysical and physiological functions, including the action potential (AP).

Action potential duration

The whole-cell patch-clamp method is more advanced compared to classical electrophysiology (impalement of fibers or tissues with a sharp electrode), since it may enable the elucidation of properties of all channels responsible for AP and resting membrane potential (RMP) in the same cells either sequentially or simultaneously. In this regard, one of the important parameters is the action potential duration (APD).

The duration of AP is modulated by many substances that target not only K⁺ channels. The APD is progressively longer up to terminal repolarization at RMP, which is considered 100 vs. 0%, i.e., the timing when the peak overshoot of AP occurs. Because of MP fluctuations, the action potential duration at 100% repolarization— APD₁₀₀ cannot always be estimated precisely, hence the APD₉₀ is measured. In more recent articles, sometimes the APD₈₀ but not the APD₉₀ are analyzed, although the APD₉₀ was established to reflect the prevailing impacts of Kv channels. The duration alone does not reflect the fate of cardiomyocytes, but the phenotype does (Thomsen et al. 2009). Therefore, during evolution, there was a need for cell diversity and distinct pacemakers, AVN and SAN—atrioventricular and sinoatrial nodes—in order to fulfill the dynamic and orchestrated functioning of the mammalian heart and four chambers.

APD₃₀ and APD₈₀ are frequently measured in rat ventricular cardiomyocytes, though no explicit rational is given. There is always a reason for measuring the APD at different time points (Fig. 10). For example, in one of the studies, it is precisely reasoned that the signal-to-noise ratio was not optimal, the speed of terminal repolarization was slow, and the ‘APD₅₀ was less sensitive to noise and filtering’ (Kondratyev et al. 2007). Therefore, the APD₅₀ was used for comparisons. The APD₅₀ in cardiomyocytes is equivalent to the half-height width of neural spikes (Mann et al. 2019). The APD₅₀ is indeed the most unbiased time point to consider for excitable cells, including cardiomyocytes, as one can easily determine it halfway between 100 and 0% repolarization, which correspond to RMP and peak overshoot, respectively (Fig. 10A). However, the APD₅₀ is not always suitable, and levels of repolarization for comparisons should be defined precisely, as is the case for this experiment after the superimposition of two previous APs (Fig. 10B). The differences in APD emerge starting at 70% repolarization. Thus, in order to decipher variations in a single cell, the APD₉₀ will be more insightful.

Fig. 10.

Action potential duration. A Two abnormal APs in LQT mouse ventricular cardiomyocyte occurred spontaneously despite acceptable RMP for patch-clamp experiments in vitro. The RMP, slow depolarization (green) around threshold, fast upstroke, and early phase up to action potential duration at 50% repolarization—APD₅₀ are comparable, while APD₁₀₀ is apart. The amplitude of 2nd AP is lower because of insufficient effective refractory period (ERP). Unchanged APD₅₀ and gradual prolongations are depicted in reference to 1st AP, i.e., the length of arrows kept identical for each conditions. B Superimposition of two sequential APs. Under this condition and for these events, measuring the APD₈₀ would be more optimal, as the velocity of upstroke is in steady-state phase. However, changes at APD₉₀ are more robust than at APD₈₀ and could be considered a better parameter for side effects of drugs on HERG. Note that the APD at each time course reflects the selective or overlapping contributions of different ion channels (Kodirov, unpublished)

A similar detailed analysis of optical signals from the hearts of rodents is challenging because they are not as robust as those during electrophysiology (Fig. 11). By analyzing optical signals in both two different preparations, regions, and species in figure 3, what is validated and what is considered a reference? It is just a method of data analysis and unlikely ‘provides a new metric for arrhythmia inducibility’ (O'Shea et al. 2020). The recordings and patterns of optical wave similarity (OWS) map are from ventricle, not ‘guinea pig heart.’ Furthermore, it is unclear why the conductance of two channels, I_K and I_K1, for simulated guinea pig APs, while for that of mouse simultaneously, the I_to, I_Kss, I_Ks, I_K1, I_Kur, should be increased or decreased by 70 and 45%, respectively. The amplitude of a family of outward currents is measured either at the onset or immediately before the termination of the pulse. Therefore, the same channel types may contribute to peak or steady-state currents, albeit the percentile differences. Currents at steady-state levels cannot be termed I_Kss in cardiomyocytes as the duration of steps always varies (Boyle and Nerbonne 1992). Outward currents activated upon + 50 mV from a HP of – 40 mV were attributed to a two-pore domain K⁺ channel, TREK-like or I_Kss, in rat atrial cardiomyocytes (Bond et al. 2014). Based on the IV curve and values of ~ 5 vs. 11 pA/pF at + 10 vs. 50 mV, the voltage dependencies of currents are not weak but rather strong. Thus, the contribution of TREK is marginal. Moreover, noradrenaline at 1 μM blocks the entire current during 500 ms rather than just the steady-state. Another hallmark of noradrenaline effects was the inhibition of noisy fluctuations that are commonly attributed to different K channels (Kodirov 2016). The waveform of noradrenaline-sensitive current resembles that longer known as I_Leak (Clay 1985).

Fig. 11.

Optical signals. A Representative activities are presumably derived from ventricular cardiomyocytes recorded by fluorescence imaging of voltage dye loaded guinea pig whole heart. Individual signals from C are superimposed. In contrary to assumption the normalization is not and cannot be achieved, at least for doublets in red. Note that signals now illogically noisier. The 2nd coupled activity is not an AP, therefore occurring even at 50% height of preceding driver signal. B Simulated action potentials in the same genus with (gray) and without 15% noise (black). C Heart of animal and ROI—region of interest. Based on siluette prevailingly ventricles are present, where the ROI at two sites is located. Continues recording during ~ 1 s reveal near normal (blue) and abnormal (red) activities. Based on reference APs in (B), the optical signals are inadequate. As a time course of a single AP (B), based on either electrophysiology or simulation thereof is not equal to that of 3 or more OAP—optical action potentials (C, cyan dashed box). It is also impossible that distinct coupled OAPs (red) may occur during proximate times as two individual and near regular OAP (C, black dashed boxes). Scale bars in A and B denote respective 50 and 200 ms. Highlighted (O'Shea et al. 2020)

In fact, a malfunction of only one channel or even one component will alter APD in vitro (Kodirov 2020). Since the simulated AP needs 1000 beats to start operating in steady-state mode (O'Shea et al. 2020), it cannot be compared to those recorded by electrophysiology. The adaptation period does not occur in native cardiomyocytes, either in vitro or in vivo, at least not for minutes. The pattern of optical action potential (OAP) in figure 1 is different compared to a simulated AP, as there are no clear diastolic intervals (O'Shea et al. 2020). The fluorescent signals underlying the OAP are always subjected to subtraction of background (pixel by pixel), filtration (in space and time), and inversion (Zaitsev et al. 2019). Therefore, alignments, OWS, and windowing (of premature APs in particular) are redundant, especially when clear signals suddenly become noisy during the algorithm (Fig. 11A). The pair of APs with an OWS of 0.91 is not aligned adequately. The APD₈₀ of guinea pig cardiomyocytes is not equal to ~ 50 ms as in figure 1a but to 300 ms as in figure 2ai. More reliable techniques helped establish much earlier that the APD₉₀ is around 236 ms (Hiraoka et al. 1986). Therefore, the APD₉₀ of ~ 600 and 120 ms in figure 6d for a guinea pig ventricle is unrealistic  (O'Shea et al., 2020). Why, in the lower panel of figure 1a, are OAPs arrhythmic? One may consider this abnormal OAP occurring around APD₅₀ of a prior AP as an ectopic one. It has been proven that an ectopic AP is usually triggered in a damaged tissue area and is linked to the physical properties of curvature in the concerned region (Teplenin et al. 2018).

The OWS is reliable only in the presence of up to 20% noise, as is the APD in conventional measurements (O'Shea et al. 2020). It is not possible to estimate the APD₈₀ when a trace is just 100% noise. Besides, figure 5 substantiates how noise should interfere, as well as when and to which phase of MP and AP it should prevail (O'Shea et al. 2020); see also Fig. 13F. Comparing the ΔAPD₈₀ as a function of noise magnitude is inadequate, as it just substantiates that one cannot reliably estimate the APD in noisy traces and, therefore, the validation of the use of OWS is invalid. Finally, both the heart region and channel malfunction-based differences in APD are evident in the optical signal traces from the laboratory of Dr. Salama. Under these conditions, there is no need for any algorithm or sorting (Brunner et al. 2003). Importantly, and as expected, there is a correlation in APD among recorded APs by patch-clamp and optical methods along the QTc from the ECG. The concept of QTc, a QT interval corrected for actual heart rate, was first used by Fridericia in 1920 (Kodirov 2015).

Fig. 13.

Action potential. A Continues recording during 60 s in whole-cell mode of patch-clamp technique from isolated mouse ventricular cardiomyocyte. B All but one spontaneous AP are superimposed (n = 124 out of 125). The excluded one was truncated at around APD₈₀ repolarization, as coincided with termination of recording at 60 s. The amplitude of this event is included in histogram. Note a big vertical noise * occurring at APD₉₀ repolarization. RMP value and overshoot range are indicated. C Distributions of amplitudes (n = 125, bin size 1 mV). Gaussian fit revealing a peak at 79.1 ± 1.9 mV (R² = 0.93, n = 125, see Table 2). D Arithmetical average (blue) of 124 traces in B along their SD (red). E Distributions of MP upon terminal repolarization (n = 124, bin size 0.2 mV). Gaussian fit revealing a peak at − 58.02 ± 0.006 mV (R² = 0.94). F Random 2 s portion of A reflecting predominant noise around RMP. Note ♪ DAD-like activities. Amplitude scale in D identically applies to A and B (Kodirov, unpublished)

Results in figure 5 prove the disadvantages of OWS in the premature atrial activity (PAA) group with values of 0.73 ± 0.03 vs. 0.77 ± 0.02 in control APs (O'Shea et al. 2020). These values were validated, but the APD₇₀ instead of the APD₈₀ was measured in a mouse left atrium, with respective values of 13.3 ± 0.02 vs. 12.9 ± 0.07 ms. Simple math enables corresponding differences of − 0.04 vs. 0.4 ms, validating the robustness of electrophysiology data (based on marginal differences and the presented trace), though it is not clear why the polarity of effects should alter. Because the latter two digits differ by a factor 10, there was no correlation between AP and OAP or APD and OWS. Subsequently, OWS mapping hardly ‘suggests that the PAAs are associated with potentially proarrhythmic periods of temporal instability,’ at best.

Also, Nav channels may contribute to APD since the magnitude of I_Na currents predicts the distinct AP waveforms, as revealed for hiPSC-CM—human induced pluripotent stem cell-derived cardiomyocytes (Goodrow et al. 2018). In this regard, a triangulation in the shape of an electrical response is considered to substantiate the ventricular-like AP in stem cells. Since distinct atrial and ventricular AP phenotypes correlate with the APD. Even those hiPSC-CM AP phenotypes that are most similar to atrial ones do not exhibit a stable RMP, though the upstroke is rapid and facilitates APD estimation. The phenotype of stem cells is discerned based on ratios of APD₅₀/APD₉₀ (Mann et al. 2019). However, it is not clear when the x-axis represents the APD₃₀ but not the APD₉₀ values during calculations of ratios as APD₃₀/APD₉₀ (Bett et al. 2013; Kane et al. 2016). Note that sometimes the ECG interval reflecting ventricular APD is also analyzed as QT₉₀ in order to consistently and precisely estimate the mean duration that is sensitive to class III antiarrhythmic agents, e.g., ibutilide (Sasaki et al. 2014; Sendra-Ferrer and Gonzalez 2019).

Alternans of action potential duration

A switch from regular APD to shorter one in two sequentially triggered APs—alternans occurs even at a constant rate of stimulation. During alternans, the diastolic interval (DI) is shorter after a longer APD and vice versa (Saitoh et al. 1988). Not only an alternans of APD, but also that of ‘action potential shape’ is observed in the ventricular fibers of an adult mongrel dog. The Cav channel antagonist nisoldipine at 2 μM abolishes APD and shape alternans while its agonist Bay K 8644 at 30 nM augments them. In contrast to Purkinje fibers of the same genus, the alternans in the ventricles were not memory- and restitution-dependent (Saitoh et al. 1988; Tolkacheva 2007).

The calculation of APD₉₀ based on available digits and traces, whether electrophysiological or optical (Zaitsev et al. 2019), is not considered optimal, and analysis engages additional algorithms and paradigms. A newcomer is an optical wave similarity (OWS) and is probed in a guinea pig ventricle by estimating the APD₈₀ alternans. Inconsequentially, at what repolarization time point was the duration calculated, why should the ΔAPD in figure 2aii (O'Shea et al. 2020) be equal to 0 ms for guinea pig or mouse cardiomyocytes? And why should the ΔAPD₈₀ increase after introducing 5 or even 100% noise that never occurs during patch-clamp experiments? Alternans in APD₈₀ are absent under simulated control conditions, whereas they are present at ~ 10 ms at pacing lengths of 90 or 100 ms in figure 6c in vitro.

In the guinea pig ventricle, a decreased rate of early repolarization results in a more positive plateau potential for regular AP in figure 2aii (O'Shea et al. 2020). During simulated rhythm at enhanced K conductance, not only APD₈₀ but also the entire duration of repolarization is increased. While a 55% decrease in K conductance does not alter the APD of the reference AP for a mouse, perhaps it is not an alternans after all but a premature beat in figure 2aii. It occurs because of the consequential shortening of DI caused by increased APD₈₀. Thereby, the refractory period is insufficient for simulated APs of a guinea pig ventricle. The mean values were 175 ms at 1 Hz vs. 149 ms at 2 Hz pacing. Also, during spontaneous excitations of hiPSC-CM, a clear correlation between the beating rate and the duration of field potentials is observed (Goineau and Castagné, 2018). The mean duration was 406 ms when corrected for the beating rate of ~ 1 Hz.

The APD alternans or its restitution depends also on a preceding DI (Saitoh et al. 1988). In order to test whether or not the same is true for ventricular cells of the LQT mouse, the APD and DI were analyzed (Fig. 12). Despite the RMP being adequate for in vitro conditions, spontaneous and recurrent excitability was observed at − 75 mV (Fig. 12A). However, an upstroke, which is normal and mediated by Nav1, was followed by multiple EADs, which prevailingly occurred around APD₅₀ (Fig. 12B). Note that the rapid phase of repolarization is intact, as it is mediated by Kv4 channels (Barry et al. 1998). This recording also substantiates that the operational range of Kv1.5 channels starts at APD₅₀ in rodents, since this α subunit was non-functional in one of the LQT models (Kodirov et al. 2003, 2004). In the absence of Kv1.5, Kv4 may exert compensatory influence in mice by repolarizing the MP up to APD₅₀. Under physiological conditions, the underlying Kv4 channels’ current, I_t0, is fast and therefore may only initiate the repolarization but not carry it up to APD₅₀ in mammals.

Fig. 12.

A new algorithm for relationship between APD and DI and vice versa. A Spontaneous excitability in LQT mouse ventricular cardiomyocytes. Blue area reflects a gradual depolarization of RMP leading to transformation of AP patterns as exemplified in C. B Analyzes approach for quasi action potential duration at 50% repolarization—APD₅₀ and diastolic interval—DI. This method is better suited for estimation of plateau duration. Nevertheless, it will not result in relatively high errors, since portions that were not considered (duration of vertical bars) are almost equally present during estimation of both APD and DI. C If the AP does not trigger EAD then this method is of use only for DI (Kodirov, unpublished). D, E Correlation based on linear regression: Y = A + B * X and n = 61. R and P values are identical. See the ‘Results and discussion’ section. The intercept of 4.06 ± 0.47 and slope of − 0.34 ± 0.16 was estimated for D, while for E these values were 2.75 ± 0.39 and − 0.19 ± 0.09. F Highlighting small differences and comparable correlations by normalization and superimposition. These analyses yield corresponding intercept of 0.31 ± 0.04 and 0.25 ± 0.03, while logically the slope values remain identical along those of R and P (Kodirov, unpublished)

Although they alternated, the APD were longer at – 75 mV and shortly after (Fig. 12B). In this cardiomyocyte, the RMP started gradually to depolarize, perhaps due to excessive excitability because of the longer depolarized states enabled by EAD. After 7 min, the MP reached − 65 mV, reducing the amount of early after depolarization (EAD) or obliterating in some of APs (Fig. 12C). Despite the insufficient amount of analyzed AP, APD is shorter during longer DI (Fig. 12D). However, this analysis proves that even after recurrent EADs resulting in an APD of 8 s, the Kv2 channels alone were able to repolarize the MP back to RMP. During intrinsic excitability and rhythm, the dependence of quasi-APD on preceding DI or that of DI on preceding APD correlates weakly, yielding an R of − 0.25 ± 1.84 and − 0.25 ± 2.48 (P = 0.04 for both fits, n = 61, Fig. 12 D and E). The negative correlations persisted even after APD and DI values were normalized to their maximums (Fig. 12F). The corresponding y intercept was 0.31 ± 0.04 vs. 0.25 ± 0.03 for the APD/DI and DI/APD relationships, respectively. As expected, the transformation of actual values by normalization does not alter the aforementioned R and P.

Additional vulnerability to arrhythmia during acute biatrial dilation (ABD) in a rat model did not alter the APD₉₀ despite an experimental increase in atrial volume to 450 vs. 280 μl in control animals (Scardigli et al. 2020). This procedure stretches the tissue, which alone leads to AF but not decelerated conduction velocity (CV). In this model, burst stimulation at 40 Hz resulted in sustained atrial tachycardia. Consistent with literature, the APs in mouse cardiomyocytes are usually evoked at 1 Hz (Kodirov et al. 2004). However, this frequency mimics the heart rate of humans but not rodents.

Whether recorded during spontaneous activities or evoked at a certain frequency (O'Shea et al. 2020), the AP, in contrast to the optical action potential (OAP), cannot be near normal and abnormal (blue and red traces, Fig. 11 A and C). Especially when optical signals underlie representative activities and presumably are originating from ventricular cardiomyocytes of a single control guinea pig heart loaded with voltage-sensitive dye (Fig. 11C). Superimposed OAPs reveal that they are not normalized but adjusted based on peak. Therefore, the diastolic levels of signals greatly fluctuate between 50 and 100%. There is no resemblance between OAP and simulated AP (Fig. 11B). The 2nd coupled activity in each pair is not an AP, therefore, it is occurring even at 50% of the height of the preceding driver signal (red, Fig. 11C). It can be an EAD, as highlighted in Fig. 12, but should not occur in control animals or under physiological conditions. Despite the distance between the two regions of interests (ROIs), based on silhouette, prevailingly the ventricles were targeted. However, both types of signals for optical mapping were handled in the same way and equally used for estimation of optical wave similarity (OWS). Based on the reference APs in Fig. 11B, the optical signal—OAP is an inadequate mimic of AP. Because at least three complete OAPs are recorded and the 4th one is generated during the time course of a single AP derived from simulation but based on electrophysiology (Fig. 11C, cyan dashed box). In OAP, an electrophysiologist will not easily recognize the phenotype of real AP (Kodirov, submitted). It is also impossible for two distinct coupled OAPs (red) to occur during the same time as two individual and near-regular OAPs (blue), as exemplified in Fig. 11C by the black dashed boxes.

The conclusion of the study was drawn based on the notion that ‘immediately after the cycle length change a substantive heterogeneity in OWS is observed between the apex and the base of the heart. Follow up studies will address the pathophysiological significance of this regional heterogeneity’ (O'Shea et al. 2020). However, it can be substantiated without OWS. For example, it has been convincingly documented that the parameters of OAP or APD in lateral LV and RV are similar in rabbits (Zaitsev et al. 2019). This is convincing, as APD remained stable for 1 h, and the drug sensitivity of both regions was also not different.

Resting membrane potential and AP

When RMP values are different from physiological, it may influence the AP amplitude and APD. An abnormality is considered to be, prevailingly, the depolarized RMP, which occurs during experimental conditions or pathological states. The impact of RMP on the duration of AP is obvious, e.g., during ischemia (Shigematsu et al. 1995). A depolarization of RMP by ~ 12 mV decreases the APD from ~ 155 to 95 ms. Also, the amplitude decreases (because of the lower overshoot range, in addition to the depolarized RMP), but the waveform of AP remains unaffected. Subsequently, the APD alone will not predict the fate of future cardiomyocytes derived from stem cells or any other source. Since the RMP of atrial and ventricular cardiomyocytes differs, the phenotypes of hiPSC-CM should also correlate based on this parameter (Giles and Noble 2016). Electrically triggered optical signals show that the RMP in hiPSC-CM is not stable, therefore the magnitude of its counterpart—MDP, was considered (Du et al. 2015). The presence of MDP reveals that hiPSC-CMs are prone to pacemaker activity and are similar to other stem cells (Bett et al. 2016). Spontaneous activities in hiPSC-CMs are also revealed with a more advanced approach termed ‘all-optical electrophysiology’ (Klimas et al. 2020). This method revealed robust AP phenotypes, prolongation of APD by 10 μM azimilide, and the presence of delayed after depolarization (DAD). The azimilide is a class III antiarrhythmic agent with a predominance of selectivity for Kv channels. Importantly, azimilide transforms the pacemaker type AP of hiPSC-CM into a ventricular one. However, even this reliable approach cannot determine the RMP, which is possible only with electrophysiology.

True RMP values during electrophysiological experiments are also not always emphasized, e.g., if a certain study is concerned with the properties of ion channels only. This shortcoming may also occur during AP recordings, as in order to control for heterogeneities in RMP values among isolated cells, the MP is held constant by injecting currents. In some studies, the RMP can be estimated retrospectively from the presented raw trace. If a certain ion channel contributes to AP, then the underlying currents should activate sufficiently within the defined range of negative and positive voltages—MP attributable for each AP types. The range between RMP and peak overshoot varies and is predetermined selectively with respect to the distinct excitability of each cardiac cell type (Denyer and Brown 1990).

Log transformation of patch-clamp data to reach Gaussian distribution

Even though in nature and science the distribution of certain values is Gaussian, those of ‘sound (decibels) and acidity’ (Ismaili et al. 2020) are very remotely related to cellular electrophysiology. Although the quality, logic, and reliability of electrophysiology traces can be appreciated even in experiments (Frankenhaeuser 1962; Neher and Lux 1969) prior to both the patch-clamp technique and sophisticated software, now more and more studies contain no raw data. In the latter field, the distribution of single channel parameters is Gaussian, especially that of an all-point amplitude histogram (Sakmann and Trube 1984).

Note that there is no need for either logarithmic data transformation or scaling in that manner, as the Gaussian distribution is applicable for many electrophysiological parameters and events, even the momentum of an experiment, when the n numbers suffice and the bin size is adequate. This is also true in the context of even minor variations in resting membrane potential (RMP) over 60 s (Fig. 13 A and E). Similar to the distribution of AP amplitude (Fig. 13C), the values of MP shortly before upstroke followed a Gaussian distribution, with a peak of − 55.7 mV (data not shown). The RMP distributions exhibited a peak of − 58.02 ± 0.006 mV (R² = 0.94, n = 124, bin size 0.2 mV). The latter also covered the majority of event numbers at 32.4 along the area of 22.6 ± 0.9 (Fig. 13E). The same is true with regard to the optimal offset value of a curve at 0.887 ± 0.488 events. Importantly, the width of the Gaussian fit was 0.55 ± 0.02 mV, and this represents the precision of patch-clamp data, the quality of traces, and the reliability of electrophysiology. The RMP was deciphered during terminal repolarization following each AP because DAD-like activity was occasionally observed (Fig. 13F). During two DADs, the MP did not reach the threshold for an AP; otherwise, one would observe 6 vs. 4 APs. This randomly chosen portion of the trace from Fig. 13A also substantiates the pattern of setup noise occurring prevailingly around RMP. Since during AP the MP changes are more rapid, the noise is not registered by the software, though it is always present. Therefore, the proposed noise patterns and the occurrence at the plateau are unrealistic (Fig. 11), though the level of noise around terminal repolarization is consistently lower.

The APD is severely prolonged (Fig. 13B), as ventricular cardiomyocytes were isolated from the heart of a mouse expressing Kv2.1DN—one of the dominant negative LQT models (Kodirov et al. 2004). In these mice, the major hallmarks of arrhythmias were present in vitro, viz., long APD, DAD, and EAD, as exemplified earlier. Importantly, AP values and their SD are not significantly apart, whether estimated from Gaussian distributions or arithmetic mean of all digits (Table 2). Results are consistent even when the entire 124 AP traces are averaged (Fig. 13B: the red trace is SD). Moreover, the Gaussian peak and median values derived from individual digits are identical at 79.1 mV (Table 2). Note that the latter is only possible when the APs are triggered with great fidelity (first and foremost the time to peak, the upstroke), especially for that amount of n number. Therefore, the desired alignments in regard to optical signals—OWS are not achieved, though fewer n numbers were chosen for representative presentation (Fig. 11a).

Table 2.

Analysis of data from Fig. 13

	Action potential amplitude (mV)
Statistic mode	Min	Max	Mean	Median	SD	SEM	CoVar	Var	n
Digits	72.8	84.2	79.02	79.1	2.3	0.2	0.02	5.3	125
Gaussian			79.1		1.9	0.1			125
Traces			77.6		7.1				124

It appears that in context with cardiomyocyte size and Cav amplitude, the above-mentioned logarithmic data re-processing was potently biased toward the fewer n numbers (Ismaili et al. 2020). Irrespective of how one normalizes the original data, the trend should not change. As established for cardiac, neuronal, and synapse electrophysiology, only two types of data meta-analyses, current density and parameter values normalization, yield unbiased results reflective of the actual trend in the raw data (Kodirov et al. 2003, 2021).

Assume that the average current in AF was ~ 0.5 nA and the density was ~ 7 pA/pF (Ismaili et al. 2020), implying a capacitance of ~ 70 pF. In contrast to pA/pF, the log · pA/log · pF cannot be applied to the IV curve, as the logarithm of base 10 is applicable to values of positive polarities only. The log transformation is artificial and will obscure the actual magnitude of differences between, e.g., 1 and 3 nA. Since the Log of 1 nA is 0, we have to transform it to 1000 vs. 3000 pA, which corresponds to Log 3 vs. 3.4 pA. Thus, the three-fold difference is transformed into only 0.15. Finally, the data are unreliable since there is no difference in the cF of human atrial and ventricular cardiomyocytes, or even that of mice.

Finally, the very last contra argument is provided with regard to unnecessary data manipulation by reanalyzing Fig. 8. The majority of values were altered (Fig. 8 I, K, and L), but a significant degree was not achieved by the Log 10 transformation for the Kv2 dominant-negative group (Fig. 8J). The corresponding correlation coefficient R² has improved to 0.16 ± 0.28 vs. 0.07 ± 2.27, while the P value has decreased to 0.6 vs. 0.8. The Log 10 transformation does not crucially help to discern differences, although it reduces the SD (Fig. 8I − L). It may decrease (Fig. 8A vs. 8I) or increase the level of significance (Fig. 8C vs. 8 K and 8D vs. 8L). If the data are not significantly different, then the same outcome will persist after unnecessary two-step transformations (Fig. 8B vs. 8 J). The same is true as to the relationship of current density pA/pF to cell capacitance pF for each individual cell (Fig. 8A − D). When the same recordings and data values from Fig. 8A − D were reanalyzed, the highly significant correlation of outward currents and cell size turned statistically insignificant (Fig. 8 E, G, and H). Thus, Fig. 8I − L proves that a possible correlation is a matter of n numbers. Data reliability should be based on the quality of recordings rather than estimates and tools.

Conclusions

Estimated current density J is not an absolute value in patch-clamp experiments, as it is based on the kinetics and magnitudes of transients reflecting capacitance charge. Since the latter is evoked at different HP and voltage steps. An accurate estimation of membrane capacitance C_m is difficult because of heterogeneity in patch quality, and therefore, values of current densities do not always adequately reflect the number of channels and size of cells. Besides, the accuracy of C_m is related to values of access resistance R_a. Drastic changes in R_a occur already within the first seconds after membrane rupture, and a stabilization period of 5 min is recommended after establishing the whole-cell configuration.

Optimal recording but not a ‘proper recognition of the statistical distribution of measured data is important for the correct selection of statistical test used to find the statically [sic] significant differences between the measured data’ (Kula et al. 2020b). Many factors may influence the J estimation. The first one is the value of HP, though it is often cell-specific because of their RMP (Platzer and Zorn-Pauly 2020). The RMP mimicking HP can be kept throughout and in between recordings, while a pre-pulse may be tailored to optimize the activation of certain channels. Second, the test pulse’s magnitude must be large enough to elicit only robust capacitative and steady-state currents. The latter is established, and ± 5 mV is commonly used. Third, the most optimal voltage for given α subunits should be applied to activate most of channels. However, as a rule, it is not the case because, e.g., of pulse duration (Gintant 1995). Fourth: temperature effects on channel activation are crucial. Fifth: influence of other subunits, and not necessarily only those of β, should be considered. Sixth: the channel trafficking can also influence the J, as expression of α subunits within the cytoplasmic bilayers depends upon. Seventh, it is also important whether the J is calculated upon maximal current activation or deactivation—tail current.

Although recent AP analyses are based on the ‘noise range observed in our experimental optical recordings from mouse atria’ (O'Shea et al. 2020), the introduction of noise that is more than 20% and subsequent OWS algorithms are irrelevant. Moreover, the parameters and physics of noise vary among experimental setups in different laboratories. Importantly, the noise is not registered consistently during the course of AP. Collectively, these analyses are divorced from both pioneering and relatively recent optical approaches, at least to some extent (Salama and Morad 1976; Zaitsev et al. 2019).

Summa summarum, as already proposed in context with the aforementioned studies, ‘we should keep high standards in our reviewing and editorial effort’ (Bébarová et al. 2020). The majority of biological studies, regardless of level of expertise of authors, cannot always result in finite conclusions, and the latter can occur in any field. There are encouraging skepticisms in the literature, such as those based on single channel recordings, as some pioneer scientists were ‘not yet sure whether the conclusions of that paper were quite right’ even after decades (Colquhoun and Sakmann 1985; Colquhoun 2007).

Abbreviations and Glossary

4-AP

Aminopyridine, blocker of Kv1.4, Kv1.5, Kv4.1, Kv4.2, Kv4.3, and other channels depending on dose

A − type

Activation and inactivation of currents resemble the capital letter A. I_A mediated by either one of Kv1.4, Kv4.1, Kv4.2, and Kv4.3 and A–type channels are transiently inactivated with the ~ 30 ms or faster—hence I_to

all-or-none

Refers to physiological phenomenon that describes the generation of AP as it either fully occurs or it fails despite the stimulus

AP

Action potential, physiological phenomenon underlying orchestrated opening and closing of ion channels and hence a bioelectricity

APD

Action potential duration, often calculated as APD₉₀—action potential duration at 90% repolarization in cardiomyocytes. APD₉₀ or half-width for neurons

Bay K 8644

Agonist of Cav1

Cav1.2

Cav1.2 voltage-dependent L-type calcium channel, and there are P/Q—Cav2.1, N—Cav2.2 and T—Cav3.1 and other α subunits

Cell-attached

That is a patch-clamp mode when > 1 GΩ tight contact between the cell membrane and pipette tip is achieved. Under these conditions, the current thru single channels are recorded. Usually the tip is narrowed down so that ideally only one channel under the electrode opening is situated

C_m

Membrane capacitance, equivalent to cell capacitance

Current density

Whole-cell current divided by cell capacitance as pA/pF

DAD

Delayed after depolarization occurs after action potential at RMP

Delayed rectifier

I_K currents via either one of Kv1.1, Kv1.2, Kv1.3, and Kv1.5 channels with no significant decay compared to I_A

Depolarization

MP value in respect to RMP that is more positive

EAD

Early after depolarization is triggered at plateau phase of action potential

E_K

Equilibrium potential for K⁺

Ensemble current

Am average of single-channel opening and closure achieved during repeated steps and reflects the phenotype of whole-cell currents

E_rev

Physiological reversal potential of currents same as E_r

HCN

Hyperpolarization-activated cyclic nucleotide gated non-selective cation channel

HERG

Human (EAG) ether-à-go-go-related gene channel

Heteromeric

When a channel tetramer consists of two or more different α subunits, e.g., Kv2 and Kv9

hiPSC-CM

Human induced pluripotent stem cell-derived cardiomyocytes

Homomeric

When all four transmembrane domains are of the same type of α subunit, e.g., only Kv2.1

HP

Holding potential, the MP that is kept constant prior and after test pulse or drug applications during voltage-clamp experimentations

Hyperpolarization

MP value in respect to RMP that is more negative

I_f

Funny current as it activates upon hyperpolarization in contrast to Ca²⁺, K⁺, and Na⁺ that were discovered earlier upon depolarization

I_h

Currents via HCN channels

I_K

K⁺ or delayed rectifier currents

I_K−tail

Tail of delayed rectifier potassium currents upon repolarization

I_Ks

Slow component of delayed rectifier K⁺ currents. Components of outward K⁺ currents in native cardiac cells are isolated using either pulse protocol—envelope test or selective blockers: E4031 for I_Kr and chromanol 293B for I_Ks

I_Kur

Ultra-rapid component of delayed rectifier K⁺ currents often observed in smooth muscle

Inside-out patch

A configuration of patch-clamp technique refers to exposed site of membrane

IV curve

Current–voltage relationship that can reveal E_rev and rectification properties of channels or its lack

Kir

Inwardly rectifying channel activated upon hyperpolarization

Kv

Voltage-dependent K⁺ channel subfamily Kv1—Kv12

Kv4.2

Channel that mediates the A − type (I_A) currents and equally known as transient outward − I_to

Loose patch

Initial lower < 100 MΩ resistance seal before achieving the cell-attached tight contact. The loose patch mode is ideal to record spike current (same as action current) in neurons

LQT

A syndrome linked to EKG QT interval prolongation

MDP

Maximum diastolic potential, unstable MP in SAN and reflects RMP

Overshoot

A range that is higher than 0 mV and is a part of upstroke phase of AP in heart or spike in neural tissue. It is physiologically relevant if it terminates at ~ 50 mV

pA/pF

Current density, estimated as pA/pF and the value indirectly reflects the total channels expressed in entire cytoplasmatic membrane of cell

PAA

Premature atrial activity

Repolarization

Return of MP value toward or back to RMP after depolarization

Retrograde perfusion

Opposite to naturally occurring anterograde blood flow descendent from heart via aorta

RMP

Resting membrane potential

Sag

Mono- or diphasic depolarization in membrane potential (MP) from a strong hyperpolarized state, e.g., − 100 mV despite constant 1 s step hyperpolarization. Upon termination of step i.e., on return to RMP, if the sag is present, the RTP and when significant then RAP occur

Tail current

Deactivation as observed after prior and sufficient activation (intensity and duration dependent) of channels predominantly at more depolarized potentials. Schwanz-Strom (German) and cлeдoвoй or xвocтoвoй тoк (Russian)

TEA

Tetraethylammonium

Triangulation

Is used to describe that the electrical response of stem cells is indeed resemble ventricular like AP

TTX

Tetrodotoxin, Nav antagonist

Whole-cell patch

Patch-clamp mode for recording activities of ion channels within the entire cytoplasmatic membrane after rupturing a portion of it under electrode opening

xMinK

Referred to a homologue of mammalian ancillary subunit in Xenopus that includes also xMiRP2

Author contribution

Kodirov analyzed results, designed research, dissociated cardiomyocytes, isolated and perfused the hearts, performed experiments, prepared brain slices, and wrote the manuscript.

Funding

Analytical inputs were supported by the Ministry of Education and Science of the Russian Federation, Federal target program ‘Research and Pedagogical Cadre for Innovative RUSSIA’ and experimental data by National Institute of Health, USA.

Data availability

All visual items, raw traces, and underlying data will be provided upon request.

Code of availability

Not applicable.

Declarations

Ethical approval

The study was performed in accordance with the guidelines of the Harvard Medical Area Standing Committee on Animals and Institutional Animal Care and Use Committee.

Consent to participate

Not applicable.

Consent to publish

Not applicable.

Conflict of interest

The author declares no conflict of interest.