Introduction

Ion current density is the membrane current value divided by the measured cell membrane capacitance (Cm). This process is usually referred to as “normalizing” current values to the obtained Cm, which serves as the consensual surrogate measure for the cell surface area. In scientific publications about cellular electrophysiology, ion current magnitudes obtained on different cell populations are expected to be reported and compared based on their ion current densities. This convention assumes linear relationships between magnitudes of ion currents, Cm, and the cell surface area. In simple terms, bigger cells are expected to generate larger currents. It is widely believed that using current densities instead of absolute current amplitudes decreases the variability of experimental results, and therefore might help in demonstrating real biological differences with statistical methods.

Transmembrane currents, Cm and cell surface area are linearly related to each other if (1) the cell membrane composition and (2) the ion channel distribution in the cell membrane is homogeneous, and if (3) Cm can be measured accurately. This concept seems to be trivial in small spheroid cells such as red and white blood cells1,2, or cells with non-articulated cell surface membrane like neuronal axons3. These assumptions, however, are not as intuitive in cardiomyocytes, which are large cells having highly articulated and compartmentalized cell surface membrane with intercalated discs and extensive axial- and transversal tubular network. In fact, the actual relations between transmembrane current, Cm and cell surface area in cardiac muscle cells are largely unknown.

Recently, Ismaili et al. studied the relationship between Cm and L-type calcium current (ICa,L) amplitude in human and rodent atrial and ventricular cardiomyocytes4, while Kula and coworkers performed similar studies with inward rectifier potassium current (IK1), acetylcholine-sensitive potassium current (IK(ACh)), and transient outward potassium current (Ito) in rat ventricular cells5,6. All these studies reported significant deviations from normal data distribution together with sometimes surprisingly low correlations between current amplitudes and Cm, with r2 ranging from 0.17 to 0.28 in4, and r values being 0.04 for Ito, 0.42 for the constitutively active-, and 0.61 for the acetylcholine-induced component of IK(ACh), while 0.84 for IK16.

Computational models and experimental studies indicate that large variations between individual cells exist in ion channel activity that may underlie electrophysiological heterogeneity within the human population7,8. Similarly, Ballouz et al. showed large variation in mRNA levels for a wide range of cardiac proteins involved in regulating cellular electrophysiological properties9, whereas Lachaud et al. have shown significant inter-cell variability in ventricular APD10. Despite these substantial variations in electrophysiological characteristics, bioelectricity of the heart can most likely be properly coordinated because of overlapping functions and certain well-defined correlations between ion currents11,12. Most recently, similar relationships in mRNA transcript levels9 and in cardiac ion channel co-translation13 have also been shown.

In this study, we systematically investigated the relationship between Cm and the major cardiac ion currents (L-type calcium current—ICa,L; late sodium current—INa,late; sodium-calcium exchange current—INCX; inward rectifier potassium current—IK1; rapid delayed rectifier potassium current—IKr; slow delayed rectifier potassium current—IKs) in canine ventricular myocytes under conventional voltage clamp (CVC) as well as action potential voltage clamp (APVC) conditions. Dogs were chosen because the electrophysiological properties of canine ventricular cells are known to be similar to those of human myocytes14,15,16. Besides investigating a broad range of ion currents, obtained under two different voltage clamp conditions, the novelties of the present study are the comprehensive statistical analyses of (1) the distribution of Cm and the ion current parameter values; (2) the relationship between Cm and the ion current parameters; and (3) the effect of “normalizing” the original membrane current parameters to Cm.

We have found generally good correlations between Cm and current amplitudes or integrals in this preparation, although correlations were occasionally limited by regional heterogeneity of ion channels and non-ideal experimental conditions.

Results

Membrane capacitance

The pooled membrane capacitance (Cm) values of all cells involved in the study (n = 639) significantly deviated from normal distribution (p < 0.001; Supplementary Fig. 1). The distribution was right-skewed (skewness = 0.533) and leptokurtic (excess kurtosis = 0.561). The arithmetic mean of Cm was 139.87 ± 1.45 pF, and median value was 139 pF. The observed effect size of the deviation from normal distribution was “small” (φ = 0.228), indicating that the magnitude of the difference between the sample distribution and the normal distribution was small. Cm values in any current groups did not deviate significantly from normal distribution, except in IKs measurements (p = 0.013; φ = 0.33; Supplementary Fig. 1J) and when all cells were pooled together in Ito1 measurements (p = 0.036; φ = 0.248; Supplementary Fig. 3A) under CVC experiments.

L-type Ca2+ current (ICa,L)

ICa,L was studied under CVC conditions in 198 myocytes (Fig. 1A). ICa,L peak current values (Fig. 1C) showed a significantly non-normal distribution, being left-skewed (towards higher current values; skewness =  − 0.546), with normal kurtosis. The absolute coefficient of variation (CV) of ICa,L peak was 0.485. The distribution of data still remained significantly non-normal after dividing peak ICa,L with Cm, although the CV significantly (p = 0.02) reduced to 0.398 after this operation (Supplementary Table 1).

Figure 1
figure 1

Correlation between Cm and ICa,L in canine ventricular myocytes. Left: representative ICa,L records obtained under CVC (A) and APVC (B) conditions, respectively. In both cases command signals are shown above the current records, dashed lines indicate zero voltage and current levels. Right: correlations between Cm and ICa,L peak amplitude measured at + 5 mV under CVC conditions (C) and under APVC conditions (D), between Cm and mid-plateau ICa,L amplitude (E), and between Cm and ICa,L integral (QCa,L; F). Here and in all subsequent figures, red lines were obtained by simple linear regression, where r or ρ indicate the respective correlation coefficient, s is slope of the line (current density or charge density, given as mean ± SEM), y0 is the intercept on y axis at Cm = 0 pF, p is significance of slope, and n is the number of cells analyzed. CVC experiments: 198 cells from 77 animals; APVC experiments: 15 cells from 7 animals.

The correlation between the amplitude of ICa,L and Cm was moderate (Spearman’s ρ =  − 0.603). The estimated current density was − 6.7 ± 0.63 pA/pF (Fig. 1C). The close to zero (− 42 ± 89 pA) value of the y intercept supports the actual linear relationship between Cm and ICa,L.

Under APVC conditions ICa,L was dissected as a 1 µM nisoldipine-sensitive current (Fig. 1B) in 15 cells. In contrast to CVC experiments, the distribution of either the ICa,L current parameters (peak current, mid-plateau current, current integral—QCa,L) or their values divided with Cm did not differ significantly from normal distribution in any case, as determined in APVC experiments (Supplementary Table 2). CVs for these parameters all reduced upon dividing the original values with Cm, however, changes in CVs did not reach statistical significance.

Pearson’s correlation coefficients were r =  − 0.74 and r =  − 0.77 for the peak and the mid-plateau values of ICa,L, as shown in Fig. 1D,E, respectively. Similarly, the charge carried by the current, indicated as QCa,L (− 75 ± 17 fC/pF) yielded a high correlation with Cm (r =  − 0.77) (Fig. 1F). These values obtained for ICa,L density and QCa,L are in a good agreement with earlier results obtained in canine ventricular myocytes16.

Late Na+ current (INa,late)

INa,late was recorded exclusively under APVC conditions as a 1 µM GS-458967-sensitive current (Fig. 2A). Since its peak often did not separate from the decaying phase of INa,early, only mid-plateau amplitudes and current integrals (QNa,late) were calculated and analyzed, as shown in Fig. 2B,C and in Supplementary Tables 3 and 6. Both the mid-plateau current values (p = 0.029, φ = 0.364) and the total charge carried by the current (p = 0.037, φ = 0.392) were significantly non-normally distributed, with medium φ effect sizes, and CVs of 0.493 and 0.447, respectively. After dividing the original values with Cm, both distributions (mid-plateau INa,late/Cm and QNa,late/Cm) became normal, with their CVs becoming non-significantly smaller (0.415 and 0.373, respectively).

Figure 2
figure 2

Correlation between Cm and INa,late (A-C), and between Cm and INCX (D-F). Left: representative INa,late (A) and INCX (D) records obtained under APVC conditions. Command action potentials are shown above the current traces, dashed lines indicate zero voltage and current levels. Right: B, E: correlations between Cm and mid-plateau currents; C, F: correlations between Cm and INa,late and INCX current integrals (QNa,late; QNCX). INa,late experiments: 24 cells from 10 animals, INCX experiments: 17 cells from 8 animals.

Bivariate distributions of Cm and mid-plateau INa,late, or Cm and QNa,late data pairs were not significantly different from the normal bivariate distribution. Pearson’s correlation coefficients were r =  − 0.475 for Cm and mid-plateau INa,late, and r =  − 0.483 for Cm and QNa,late, respectively, indicating a low linear correlation of mid-plateau INa,late, and QNa,late with Cm.

Na+/Ca2+ exchanger current (INCX)

INCX was recorded exclusively under APVC conditions as a 0.5 µM ORM-10962-sensitive current (Fig. 2D). Since its peak often did not separate well from the capacitive transient, we also present only mid-plateau current amplitudes and current integrals (QNCX) here (Fig. 2E,F; Supplementary Tables 3 and 6).

Both original current values and current densities of mid-plateau INCX were normally distributed, with CVs of 0.403 for original values, and 0.348 for current densities, respectively. QNCX was significantly non-normally distributed with a large effect size (p = 0.024, φ = 0.613), being left-skewed (towards higher current values; skewness =  − 1.274). The distribution became normal after dividing QNCX with Cm (p = 0.172), with CVs being 0.311 and 0.227, respectively.

Bivariate distribution of Cm and mid-plateau INCX data pairs was normal, whereas distribution of Cm and QNCX data pairs was significantly different from normal (p = 0.049). Correlation coefficients were r =  − 0.607 for Cm and mid-plateau INCX, and ρ =  − 0.587 for Cm and QNCX, respectively, indicating moderate linear correlation between Cm and mid-plateau INCX, and moderate monotonic correlation between Cm and QNCX.

Inward rectifier K+ current (IK1)

Both original IK1 peak (Fig. 3A) values and IK1 peak current densities showed normal distribution (with CVs being 0.309 and 0.246, respectively) under CVC conditions. The Forkman’s test showed a significantly (p = 0.0495) reduced CV after calculating IK1 peak current densities (Supplementary Table 1).

Figure 3
figure 3

Correlation between Cm and IK1. Left: representative inward IK1 current recorded at − 130 mV under CVC conditions (A) and outward IK1 record under APVC conditions (B). Command signals are shown above the current records, dashed lines indicate zero voltage and current levels. Right: correlations between Cm and IK1 amplitude, measured at the end of a 400 ms long hyperpolarization to − 130 mV under CVC conditions (C), peak amplitude of IK1 (D), mid-plateau amplitude of IK1 (E), and IK1 integral (QK1; F) under APVC conditions. CVC experiments: 88 cells from 35 animals; APVC experiments: 19 cells from 11 animals.

Bivariate distributions of Cm and IK1 peak amplitude data pairs were normal. These parameters highly correlated with each other (r =  − 0.72, Fig. 3C, Supplementary Table 4). Linear regression analysis yielded a slope of − 57.5 ± 5.9 pA/pF.

Under APVC conditions IK1 was defined as a 50 µM BaCl2-sensitive current (Fig. 3B) in 19 myocytes. IK1 current peaks as well as charges carried by IK1 (QK1) were normally distributed in all cases of original values and after dividing them with Cm. CVs were 0.27 for IK1 peak current and 0.162 for IK1 peak current density, and 0.276 for QK1 and 0.162 for QK1/Cm, respectively. Dividing original current parameters with Cm significantly reduced data variability in case of IK1 (p = 0.044 for peak current; p = 0.036 for QK1). Both the original mid-plateau IK1 values (p < 0.001) and mid-plateau IK1 densities (p = 0.016) showed significantly non-normal distribution, being right-skewed (towards larger values; skewnesses of 1.569 and 1.003, respectively), with CV values of 0.564 and 0.501, respectively. Mid-plateau IK1 densities, however, had only “medium” effect size of the non-normal distribution (φ = 0.442) compared to the “large” effect size (φ = 0.738) in case of the original mid-plateau IK1 values (Supplementary Table 3).

Bivariate distributions of Cm and IK1 peak as well as Cm and QK1 data pairs were normal, whereas the bivariate distribution of Cm and mid-plateau IK1 was significantly different from normal (p < 0.001). Correlations between Cm and IK1 peak (r = 0.785, p < 0.001), as well as Cm and QK1 (r = 0.767, p < 0.001) data pairs were high; but for Cm and mid-plateau IK1, no significant correlation was detected (see Fig. 3D–F and also Supplementary Table 6). Linear regression analysis between IK1 peak current and Cm yielded a slope of 1.5 ± 0.29 pA/pF for the regression line, a value close to what has been reported as peak IK1 current density in canine ventricular cells14,16.

Rapid delayed rectifier K+ current (IKr)

Under CVC conditions both the original IKr peak current (Fig. 4A) value and IKr peak current density distributions deviated significantly from normal distribution (p < 0.001 and p = 0.013, respectively), being right-skewed (towards larger current values; skewness values of 0.904 and 0.548, respectively), with CVs being 0.458 (absolute) and 0.378 (normalized; p = 0.075). After “normalizing” to Cm, the effect size of non-normal distribution changed from medium (φ = 0.379) to small (φ = 0.221). Similarly, bivariate distribution of Cm and IKr peak data pairs differed significantly from the normal distribution. Based on the results obtained in 120 myocytes the Spearman rank-correlation between IKr tail current amplitude and Cm was moderate (ρ = 0.628, p < 0.001; Fig. 4C). Linear regression analysis yielded a slope of 0.49 ± 0.05 pA/pF.

Figure 4
figure 4

Correlation between Cm and IKr. Left: representative IKr tail current recorded at − 40 mV under CVC conditions (A) and an IKr current trace under APVC conditions (B). Command signals are shown above the current records, dashed lines indicate zero voltage and current levels. Right: correlations between Cm and IKr tail current amplitude under CVC conditions (C), peak IKr amplitude (D), mid-plateau IKr amplitude (E), and IKr integral (QKr; F) under APVC conditions. CVC experiments: 120 cells from 54 animals; APVC experiments: 19 cells from 10 animals.

Under APVC conditions IKr peaked during terminal repolarization (Fig. 4B). Contrary to CVC results, when IKr was investigated with APVC (n = 19), all the measured parameters of the current, as well as their respective bivariate distributions with Cm followed normal distribution. The respective CV values for original and Cm “normalized” data were 0.359 and 0.266 for IKr peak; 0.632 and 0.58 for mid-plateau IKr; whereas 0.397 and 0.289 for the charge carried by IKr (QKr). Although dividing the original current parameter values with Cm reduced CVs, these changes did not reach statistical significance.

High correlations for both IKr peak amplitude (r = 0.704, p < 0.001) and for QKr (r = 0.709, p < 0.001) were obtained under these conditions (Fig. 4D,F). Similar to IK1, the mid-plateau amplitude of IKr showed no significant correlation with Cm (r = 0.312, p = 0.194, Fig. 4E). Linear regression analysis showed slope values of IKr current peak (0.49 ± 0.12 pA/pF) and QKr (40 ± 10 fC/pF) similar to the current density and charge density values reported earlier for canine ventricular cells under APVC conditions16.

Slow delayed rectifier K+ current (IKs)

In case of IKs experiments (Fig. 5A), the membrane capacitance significantly deviated from normal distribution (p = 0.013), with a medium effect size (φ = 0.33) when analyzing the results obtained from 79 myocytes under CVC conditions. The distribution was right-skewed (skewness = 0.765).

Figure 5
figure 5

Correlation between Cm and IKs. Left: representative IKs tail current recorded at − 40 mV under CVC conditions (A) and IKs current under APVC conditions (B). Command signals are shown above the current records, dashed lines indicate zero voltage and current levels. Right: correlations between Cm and IKs tail current amplitude under CVC conditions (C), peak IKs amplitude (D), mid-plateau IKs amplitude (E), and IKs integral (QKs; F) under APVC conditions. CVC experiments: 79 cells from 27 animals; APVC experiments: 18 cells from 9 animals.

Both the original and Cm “normalized” IKs peak current value distributions deviated significantly from normal distribution (p < 0.001 for both cases), being right-skewed (towards larger current values; skewness values of 1.448 and 0.886, respectively). Moreover, the absolute IKs peak values were also significantly leptokurtotic (with heavy tails; excess kurtosis = 2.544). CVs were 0.658 and 0.583, respectively. With “normalization” to Cm, the effect size of the non-normal distribution was reduced from large (φ = 0.592) to medium (φ = 0.359). Similarly, bivariate distribution of Cm and IKs peak data pairs differed significantly from the bivariate normal distribution. Based on the results obtained the Spearman rank-correlation between IKs tail current amplitude and Cm was low (ρ = 0.223, p = 0.048; Fig. 5C), with a slope of 1.04 ± 0.27 pA/pF.

Under APVC conditions, IKs rose slowly during the action potential plateau (Fig. 5B). Contrary to CVC results, when IKs was investigated with APVC (n = 18), all the measured current parameters, as well as their respective bivariate distributions with Cm followed normal distribution. The respective CV values for original and Cm “normalized” data were 0.403 and 0.354 for IKs peak; 0.561 and 0.568 for mid-plateau IKs; whereas 0.321 and 0.245 for the charge carried by IKs (QKs). Both Cm and IKs peak (r = 0.53, p = 0.024), as well as Cm and QKs (r = 0.59, p = 0.01) correlated moderately, as demonstrated in Fig. 5D,F. No significant correlation was observed between mid-plateau IKs value and Cm (Fig. 5E). Linear regression analysis yielded slopes of 0.16 ± 0.08 pA/pF for IKs peak, and 12 ± 4 fC/pF for QKs, respectively.

Transient outward K+ current (Ito1)

Ito1 was studied only under CVC conditions using myocytes (n = 108) isolated from subepicardial (EPI), subendocardial (ENDO) and midmyocardial (MID) layers of the left ventricle. During our “regular” cell isolation method there is no physical separation of the transmural layers of the myocardium, therefore we are not able to distinguish between cells originating from the different myocardial layers. Because of the quite thin EPI and ENDO tissue layers, this method dominantly yields MID cells. However, when we cut off delicate layers of tissue from the epicardial and endocardial surface of the myocardium after the enzymatic digestion process (see in Methods and in17), myocytes of known origin (documented EPI, ENDO, MID cells; n = 30, n = 15, n = 18, respectively) can be obtained.

If all 108 cells were taken into consideration, Cm significantly deviated from normal distribution (p = 0.036), being right-skewed (skewness = 0.61). However, the effect size of this deviation was small (φ = 0.248). In documented EPI, ENDO, MID as well as in presumably MID cells (all cells, except for EPI and ENDO cells), Cm followed normal distribution.

As shown in Fig. 6A, marked differences in Ito1 amplitude were observed among the cells originating from different regions—in line with the known transmural heterogeneity of Ito1 in canine ventricle18,19,20.

Figure 6
figure 6

Correlation between Cm and Ito1. (A): representative Ito1 current records obtained at + 60 mV under CVC conditions taken from a subepicardial (EPI; magenta), midmyocardial (MID; blue), and a subendocardial (ENDO, red) myocyte. The command voltage is shown above the current records, the dashed line indicates zero current level. (B–F): Correlations between Cm and peak Ito1 currents analyzed in various groups of myocytes. In panel (B), all the 108 myocytes from 41 animals were included in the analysis, independent of their origin. In panels (C, D and E) cells with documented EPI (magenta), ENDO (red), or MID (blue) origin were analyzed, respectively, while in panel F, the presumably MID (non-EPI and non-ENDO cells; black) were considered. EPI experiments: 30 cells from 14 animals; ENDO experiments: 15 cells from 10 animals; MID experiments: 18 cells from 13 animals; presumably MID experiments: 63 cells from 36 animals.

When all cells were analyzed together, both the original and the Cm “normalized” Ito1 peak current distributions deviated significantly from normal distribution (p < 0.001 for both cases), with similar “medium” effect sizes (φ = 0.334 and φ = 0.307) and CVs (0.536 and 0.526), respectively. Both distributions were right-skewed (skewness values of 0.837 and 0.752, respectively). Similarly, bivariate distribution of Cm and Ito1 peak data pairs differed significantly from the normal distribution (p < 0.001). The Spearman rank-correlation between all Ito1 peak current amplitudes and Cm was low, but statistically significant (ρ = 0.253, p = 0.008, Fig. 6B; Supplementary Table 5).

Documented ENDO and MID cells shown normal peak current and Cm normalized peak current distributions, with CVs being 0.371 vs 0.28 (ENDO) and 0.377 vs 0.226 (MID) for absolute peak currents, and for normalized peak currents, respectively.

Documented EPI cells had normal peak current, but significantly non-normal Cm “normalized” peak current (p = 0.008) distribution, with a large (φ = 0.775) effect size. CV of Ito1 peak current density was significantly smaller (0.194) than in case of original peak current magnitudes (0.323). Visualizing the data revealed that the Cm normalized peak current distribution was non-normal because of an outlier cell having Cm = 80 pF and a peak Ito1 amplitude of 4399 pA, yielding a current density of 55 pA/pF. If we omitted this outlier from the Shapiro–Wilk test, no significant deviation from the normal distribution could be detected.

Even though there was a clear trend for a reduction in CV after normalizing to Cm, this effect was only significant in case of EPI cells (p = 0.012).

Bivariate distributions of Cm and Ito1 peak data pairs were normal in case of ENDO and MID myocytes, however in case of EPI cells, it significantly deviated from normal (p = 0.01), because of the previously mentioned outlier cell. Data in cells of known origin showed strong and statistically significant correlations. Pearson’s correlation coefficients of 0.711 (p = 0.003) and 0.825 (p < 0.001) were obtained for documented ENDO and MID cells, respectively, whereas the Spearman’s correlation coefficient was 0.829 (p < 0.001) in EPI myocytes. (Fig. 6C–E).

Myocytes of presumably MID origin (all cells except for the documented EPI and ENDO cells) showed significantly non-normal peak current (p = 0.007, φ = 0.345), but normal peak current density (p = 0.081) distributions, with a significantly reduced CV (from 0.386 to 0.266; p = 0.009) after “normalization” to Cm. In these presumably MID myocytes, bivariate distribution of Cm and Ito1 peak data pairs significantly deviated from normal (p = 0.003). The correlation between Cm and Ito1 peak was also high (ρ = 0.717, p < 0.001) in these cells (Fig. 6F). Comparing Ito1 current densities obtained for the documented versus the presumably MID cells (22.6 ± 3.9 pA/pF vs 16.8 ± 2.0 pA/pF, respectively) confirms the usual assumption that most of the myocytes of undefined origin were likely digested from the midmyocardial layer.

Discussion

This is the first study to systematically investigate a broad range of ion currents, obtained under two different voltage clamp conditions in canine ventricular myocytes to provide comprehensive statistical analyses of (1) the distribution of Cm and the ion current parameter values; (2) the relationship between Cm and the ion current parameters; and (3) the effect of “normalizing” the original membrane current parameters to Cm.

The distribution of Cm of all cells involved our study was significantly non-normal, being right-skewed, similar to the findings of Kula et al.5. Cm values in case of any of the current groups did not deviate significantly from normal distribution, except in IKs measurements and when all cells were pooled together in Ito1 measurements under CVC conditions. It is worth noting, however, that all normality tests get more and more sensitive to violations of normality as the sample size gets larger21, therefore we have found multiple deviations from normal distribution in our CVC experiments where sample sizes were at least n = 79.

Absolute peak current distributions obtained under CVC conditions were significantly non-normally distributed in case of ICa,L, IKr, IKs, and if all cells were pooled together in Ito1 experiments (Supplementary Tables 1 and 2). Dividing peak current values with Cm (obtaining peak current densities) did not normalize the distributions, all of them remained significantly non-normal. However, effect sizes of the deviation from normal distribution, as well as CV values were smaller in the groups of peak current densities compared to the original peak currents. Reduction in CVs were statistically significant in cases of ICa,L, IK1, and Ito1 (in the EPI and presumably MID groups). In their recent study, Kula et al.5 also found significantly non-normal, right-skewed IK1 and IK(ACh) current magnitude distributions with the Shapiro–Wilk test, and the calculated respective current densities were also significantly non-normally distributed. Ismaili and coworkers4 studied distributions of ICa,L current peaks in various species, under different conditions. Most of their samples did not follow normal distribution and were seemingly right-skewed. When they divided ICa,L current peaks with Cm they had no consistent effect on CV, whereas in our study, the same operation significantly reduced CV in several cases. It is worth noting that in our studies, only 5 cells (less than 1% of all cells investigated) had Cm values less than 70 pF, whereas in the previously mentioned two studies4,5, a much larger proportion of the left ventricular cells had Cm values lower than 70 pF, especially in rat samples. These more frequently occurring low Cm values might lead to a greater deviation from normal distribution.

Under APVC conditions, distributions of investigated current parameters did not differ significantly from the normal distribution in most cases, with the exceptions of mid-plateau INa,late, QNa,late, QNCX and mid-plateau IK1 (Supplementary Table 3). Dividing these current parameters with Cm “normalized” mid-plateau INa,late, QNa,late and QNCX distributions, whereas distribution of the mid-plateau IK1 remained significantly non-normal, although the effect size of the deviation from non-normal distribution became much smaller (φ = 0.738 and φ = 0.442, respectively; Supplementary Table 3). In general, CVs were non-significantly reduced after dividing with Cm, however, in the cases of peak IK1 and QK1, these reductions were statistically significant (Supplementary Table 3). In conclusion, we found dividing original data with Cm values generally useful, both by reducing the effect of the sometimes originally non-normal sample distributions (even rendering them normal in certain cases), as well as by reducing CVs of the samples.

Relationships between Cm and various ion current parameters were studied using Pearson and Spearman correlations and simple linear regression analysis under both APVC and CVC conditions. In case of many ion currents, including ICa,L, IK1 and IKr, the correlation was usually high. Importantly, y intercepts of linear regression were close to zero indicating a true linear relationship between Cm and membrane current parameters (Im) for these ion currents. This is in line with the general assumption that ion current densities are constant, i.e. current amplitudes are linearly related to cell surface area. On the other hand, moderate correlation was obtained for INCX and low for INa,late and IKs.

Marked differences between individual ion currents of the same species regarding the correlation between Cm and Im is not exceptional. Good correlation was found in rat myocytes in the case of IK1 but not for Ito6—results identical to our observations in canine myocytes. Comparing the present results on canine ICa,L with those reported by Ismaili et al.4 on human ventricular ICa,L (both obtained under CVC conditions) our correlation coefficient (r =  − 0.603, r2 = 0.364) was higher than that reported by Ismaili et al. (r2 = 0.28). In that study the low correlation coefficient was attributed partially to inhomogeneous distribution of surface versus T-tubular localization of L-type Ca2+ channels22,23, which channel subpopulations might also be differently regulated24,25. This regional inhomogeneity at a cellular level may tremendously increase variability (mainly due to improper voltage control of T-tubular Ca2+ channels), however, these effects are likely similar in the cardiomyocytes of a given species.

Another possible reason for the low correlation between Cm and Im might be a limited proportionality between the cell size and Cm4,6. Although the exact level of correlation between Cm and cell surface is not known, if there was any discrepancy between them, the relationship between Cm and Im should have been affected similarly in the case of several ion currents. Furthermore, inaccurate Cm measurements26 may also contribute to the limited proportionality between Im, Cm, and cell surface area. Again, however, even if there was any inaccuracy in measuring Cm, it likely had the same systemic effect on all cells. Although we cannot completely rule out that such an inaccuracy could have disproportionally affected certain groups of cells, therefore limiting the correlation between Im and Cm.

Then, what might limit correlations between Im and Cm? Theoretically, there are at least three factors which might decrease the linear relationship between Cm and ion current amplitudes or integrals. These are: transmural and cell surface inhomogeneity of ion channel expression; small measured current values; and cell-to-cell variability of intracellular ion concentrations, especially [Ca2+]i.

Our results with Ito1 represent a good example that regional inhomogeneity of ion channel expression is likely to be a limiting factor in significant correlations between Im and Cm. Ito1 is known to be abundantly expressed in the subepicardial layer, its expression is less pronounced in mid-myocardial cells, while the current is small in the subendocardial region of the canine heart17,18,19,20. Indeed, the correlation between Ito1 and Cm vas negligible (r = 0.21) when all the cells were analyzed independently of their origin. In contrast, the correlation became much better when cells with documented origins were analyzed separately: correlation coefficients of ρ = 0.829, r = 0.711 and r = 0.825 were obtained for subepicardial, subendocardial and midmyocardial cell populations, respectively. However, transmural inhomogeneity has been reported not only for Ito1, but also for INa, INCX and IKs. More specifically, the density of INa is the highest in the mid-myocardial region and significantly lower in the subepicardial and subendocardial layers in dogs17,27,28 and marked transmural inhomogeneity was observed in the case of INCX as well29,30. Regarding IKs, the density of the current is higher in the subepicardial than in the midmyocardial region17,31. Another type of regional inhomogeneity in the density of IKs was also observed. Expression of IKs was found to be more than double in the apical than in the basal region of the canine ventricular wall32. In contrast, no transmural inhomogeneity has been observed for ICa,L, IKr or IK1 in canine ventricular myocardium17. Similarly, no apico-basal differences regarding the distribution of IK1 or IKr were demonstrated32.

Cell surface inhomogeneity of ion channel expression can also limit the correlation between certain currents and Cm. In differently sized cells, certain membrane compartments may represent different fractions of the total cell surface. For example, based on pure geometrical considerations, in short, wide cells, the relative membrane surface of intercalated discs is likely to be higher than in long, narrow ones. Therefore, the cell membrane of short, wide cells likely contains relatively more ion channels that are preferentially located in the intercalated discs (such as Nav1.5, Kir2.1 and Kir6.233) than long, narrow cells. Finding out these discrepancies, however, are well beyond the scope of the present study.

An additional source of limited correlations between Im and Cm may be the inherent inaccuracy of measurements. This error is expected to be larger when measuring currents with low amplitudes—a problem evident especially under APVC conditions. This issue is illustrated on Fig. 7, where the Pearson’s correlation coefficients obtained between Cm and certain ion current parameters are plotted as a function of their respective ion current densities. There were significant monotonic correlations between the Pearson’s correlation coefficients and their respective original current density values (Fig. 7A; ρ = 0.716, p < 0.001 for all currents; ρ = 0.833, p = 0.015 for CVC; ρ = 0.693, p = 0.026 for APVC conditions), whereas after logarithmic transformation of the current density values, significant linear relationships could be seen (Fig. 7B; r = 0.707, p = 0.001 for all conditions; r = 0.707, p = 0.0499 for CVC; r = 0.762, p = 0.01 for APVC conditions). These correlations suggest a logarithmic association between the Pearson’s correlation coefficients and their respective original current density values. This may explain the non-significant correlations between Cm and the mid-plateau amplitudes of IK1 and IKr, in sharp contrast with the significant and high correlations obtained for their peak amplitudes (r = 0.785 and r = 0.704; p < 0.001 for both) or current integrals (r = 0.767 and r = 0.709; p < 0.001 for both) under APVC conditions.

Figure 7
figure 7

Relationship between Pearson’s correlation coefficients and current densities in case of the studied currents and conditions. Open circles indicate data from conventional voltage clamp (CVC); whereas filled squares show data from action potential voltage clamp (APVC) experiments. (A): Pearson’s correlation coefficients between Cm and ion current values are plotted against their respective ion current densities yielding significant monotonic (Spearman) correlations between them. (B): Pearson’s correlation coefficients between Cm and ion current values plotted against the log10 values of their respective ion current densities. There are significant linear relationships between these data pairs, suggesting a logarithmic relationship between data pairs of correlation coefficients of Cm versus ion current values and their respective ion current densities.

Inhomogeneity of intracellular Ca2+ concentration—a possible consequence of the variable Na+ and Ca2+ loads occurring during cell isolation—may also affect the correlation in the case of some strongly Ca2+-dependent ion currents, such as ICa,L or INCX, but also INa,late34 and IKs16. Furthermore, if the turnover of ion channels in the membrane may be fast enough, the time elapsed from cell isolation to the measurement may also influence the amplitude of an ion current35. Somewhat related to this, the relatively slow, but continuous reduction of current ion magnitude over time (ion current “run-down”) may also contribute to the limited correlations between Im and Cm.

Since the experimental conditions were quite uniform in our APVC experiments, their results can be used for evaluation of effects of the above mentioned “burdens” on the correlation coefficients. This is summarized in Table 1, where all APVC experimental arrangements are included. According to these data, both regional inhomogeneity and low current amplitude are likely dominant reasons for limited proportionality between Cm and ion current amplitudes. Under APVC conditions it also must be noted that whenever the bivariate distribution of the investigated parameter and Cm was significantly (or marginally significantly) non-normal, no significant correlations were detected. These cases included the values of mid-plateau INa,late, mid-plateau INCX, mid-plateau IKr and mid-plateau IK1. These infringements of normal bivariate distributions may arise from the above mentioned “burdens”, such as regional inhomogeneity of ion channel expression, small measured current values and variability of intracellular ion concentrations.

Table 1 Burdens that might limit proportionality between ion current amplitudes and cell size under APVC conditions (+ : affected).

Our experiments performed under APVC conditions allowed the comparison of correlations found between Cm and Im with those between Cm and current integrals. From this point of view, current integrals produced correlation coefficients at least as good as those obtained for peak current amplitudes. Furthermore, correlation coefficients obtained under APVC conditions were not lower than those estimated in CVC experiments, even though the number of cells analyzed in the APVC experiments was usually much lower than those used under CVC conditions.

In summary, there is a clear tendency that dividing absolute values of ion current parameters with Cm reduces both the coefficient of variation, and the deviation from normal distribution, if there was any. In case of most currents, we found significant, moderate-to-high correlations between ion current amplitudes or integrals and Cm. However, the level of correlation between an ion current and Cm may be variable depending on the ion current studied, which must be considered when routinely evaluating ion current densities in cardiac cells.

Methods

The study is reported in accordance with ARRIVE guidelines (https://arriveguidelines.org). For details regarding experimental animals, cell isolation procedure, and specific description of electrophysiology experiments, please refer to the Supplementary Material.

Animals

Adult mongrel dogs of either sex were anesthetized with intramuscular injections of ketamine hydrochloride (10 mg/kg; Calypsol, Richter Gedeon, Hungary) and xylazine hydrochloride (1 mg/kg; Sedaxylan, Eurovet Animal Health BV, The Netherlands) according to a protocol approved by the local Animal Care Committee (license No: 2/2020/DEMÁB, 9/2015/DEMÁB). All animal procedures conformed to the guidelines from Directive 2010/63/EU of the European Parliament.

Electrophysiology

Cells were placed in a plexiglass chamber under an inverted microscope, allowing for continuous superfusion with a modified Tyrode solution by gravity flow at a rate of 1–2 ml/min. Under APVC conditions this solution contained (in mM): NaCl 121, KCl 4, CaCl2 1.3, MgCl2 1, HEPES 10, NaHCO3 25, glucose 10, while under CVC conditions it contained: NaCl, 144; KCl, 5; CaCl2, 2.5; MgCl2, 1.2; HEPES, 5; glucose, 10; both at pH = 7.35 and osmolality of 300 ± 3 mmol/kg. In all experiments, whole cell configuration of the patch clamp technique was applied36, where the bath temperature was set to 37 ºC using a temperature controller (Cell MicroControls, Norfolk, VA, USA). Electrical signals were amplified and recorded (Axopatch 200B, MultiClamp 700A or 700B; Molecular Devices, Sunnyvale, CA, USA) under the control of a pClamp 6, 9 or 10 software (Molecular Devices) following analogue–digital conversion (Digidata 1200, 1322A or 1440A, Molecular Devices). Electrodes, having tip resistances of 2–3 MΩ when filled with pipette solution (pH = 7.3 and osmolality of 285 ± 3 mmol/kg), were fabricated from borosilicate glass. The series resistance was usually between 4 and 8 MΩ, and the experiment was discarded if it changed substantially during the measurement. Cell membrane capacitance (Cm) was determined in each experiment by applying short (15 ms) hyperpolarizations from + 10 to − 10 mV.

Conventional voltage clamp (APVC)

Experimental protocols applied under CVC conditions and the components of the bathing and pipette solutions are described in the Supplementary Material.

Action potential voltage clamp (APVC)

APVC experiments were performed according to the methods described previously37,38,39. To avoid the consequences of cell-to-cell variations in AP morphology, the measurements were performed using a “canonic” AP as command signal, instead of the own AP of the cell. This canonic AP was chosen as a representative midmyocardial canine AP characterized by average parameters. Application of uniform command APs made the comparison of the individual current traces easier. In these experiments the pipette solution contained (in mM): K-aspartate 120, KCl 30, MgATP 3, HEPES 10, Na2-phosphocreatine 3, EGTA 0.01, cAMP 0.002, KOH 10 at pH = 7.3 with an osmolarity of 285 ± 3 mmol/kg. Ion currents were dissected pharmacologically by using their selective inhibitors. Accordingly, INa,late was dissected by 1 µM GS-458967, INCX by 0.5 µM ORM-10962, ICa,L by 1 µM nisoldipine, IKr by 1 µM E-4031, IKs by 0.5 µM HMR-1556, IK1 by 50 µM BaCl2, and Ito1 by 100 µM chromanol-293B applied in the presence of 0.5 µM HMR-1556. Each drug-sensitive current was obtained by subtracting the post-drug trace from the pre-drug one. The cells were superfused for 3–5 min with the inhibitor before recording its effect, which record contained 20 consecutive current traces obtained at a cycle length of 0.7 s. These traces were averaged to reduce the noise and the trace-to-trace fluctuations. The dissected currents were evaluated by determining their maximum values (peak currents), their amplitudes measured at the half-duration of the command AP (mid-plateau current values), and finally the total charge carried by the current (current integrals, Q). During the analysis, the initial 10 ms after the AP upstroke was excluded to omit the capacitive transient.

Statistics

We tested the normality of data distribution with the Shapiro–Wilk test, except for the distribution of Cm, where the D’Agostino-Pearson omnibus test was applied40,41. If there was a significant deviation from the normal distribution, the effect size of non-normality was also calculated as φ values and were categorized as negligible (φ < 0.1) small (0.1 < φ < 0.3), medium (0.3 < φ < 0.5), or large effect (φ > 0.5)41. For the description of data variance, we used the absolute value of the coefficient of variation (CV), defined as the standard deviation divided by the absolute value of the arithmetic mean. We used the F statistics proposed by Forkman42 to test if dividing the original ion current parameter values with Cm (calculating ion current densities, or “normalizing”) caused any significant differences between CVs of original and “normalized” data.

For data pairs (eg. Cm and current magnitudes or Cm and current integrals), normality of the bivariate distribution was tested with the Shapiro–Wilk test for bivariate normality. If the bivariate distribution of data pairs did not differ significantly from the bivariate normal distribution, correlation between the two variables is described with the Pearson's correlation coefficient (r) for linear association. In case of data pairs with significantly non-normal bivariate distribution, Spearman’s correlation coefficient, “rho”) for monotonic association is reported. The significance of correlation (p) was also calculated. To provide a comprehensive overview of correlation analysis, parameters for both the Pearson’s and Spearman’s correlations are reported for all investigated ion current parameters in Supplementary Tables 4, 5 and 6. For further information on correlation analysis and the bivariate normal distribution, see the Supplementary Material. Significant correlations were categorized according to the calculated coefficient: high (0.9 ≥|r|> 0.7 or 0.9 ≥|ρ|> 0.7), moderate (0.7 ≥|r|> 0.5 or 0.7 ≥|ρ|> 0.5), low (0.5 ≥|r|> 0.3, 0.5 ≥|ρ|> 0.3) or negligible (0.3 >|r| or 0.3 >|ρ|)43.

Besides correlation analysis, we also performed simple linear regression with Cm as the predictor variable, and the different current parameters (peak amplitude, mid-plateau value, current integral) being response variables. Figures show the slope of the fitted line (s) and the y intercept (y0), expressed as mean ± SEM values, whereas (n) denotes the number of myocytes studied.

For statistical analyses, we mainly used Jeffreys’s Amazing Statistics Program (JASP; version 0.16.1, Amsterdam, The Netherlands). We also used Origin 2015 (OriginLab Corporation, Northampton, MA, USA) for simple linear regression, and the Statistics Kingdom website41 for calculating the D’Agostino-Pearson omnibus test, and the effect size of non-normality (φ). Results were considered statistically significant in case of p < 0.05; in the summary tables, all p < 0.1 values are reported.