Abstract
Current density, the membrane current value divided by membrane capacitance (C_{m}), is widely used in cellular electrophysiology. Comparing current densities obtained in different cell populations assume that C_{m} and ion current magnitudes are linearly related, however data is scarce about this in cardiomyocytes. Therefore, we statistically analyzed the distributions, and the relationship between parameters of canine cardiac ion currents and C_{m}, and tested if dividing original parameters with C_{m} had any effect. Under conventional voltage clamp conditions, correlations were high for I_{K1}, moderate for I_{Kr} and I_{Ca,L}, while negligible for I_{Ks}. Correlation between I_{to1} peak amplitude and C_{m} was negligible when analyzing all cells together, however, the analysis showed high correlations when cells of subepicardial, subendocardial or midmyocardial origin were analyzed separately. In action potential voltage clamp experiments I_{K1,} I_{Kr} and I_{Ca,L} parameters showed high correlations with C_{m}. For I_{NCX}, I_{Na,late} and I_{Ks} there were lowtomoderate correlations between C_{m} and these current parameters. Dividing the original current parameters with C_{m} reduced both the coefficient of variation, and the deviation from normal distribution. The level of correlation between ion currents and C_{m} varies depending on the ion current studied. This must be considered when evaluating ion current densities in cardiac cells.
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Introduction
Ion current density is the membrane current value divided by the measured cell membrane capacitance (C_{m}). This process is usually referred to as “normalizing” current values to the obtained C_{m,} 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, C_{m}, 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, C_{m} 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) C_{m} can be measured accurately. This concept seems to be trivial in small spheroid cells such as red and white blood cells^{1,2}, or cells with nonarticulated cell surface membrane like neuronal axons^{3}. 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, C_{m} and cell surface area in cardiac muscle cells are largely unknown.
Recently, Ismaili et al. studied the relationship between C_{m} and Ltype calcium current (I_{Ca,L}) amplitude in human and rodent atrial and ventricular cardiomyocytes^{4}, while Kula and coworkers performed similar studies with inward rectifier potassium current (I_{K1}), acetylcholinesensitive potassium current (I_{K(ACh)}), and transient outward potassium current (I_{to}) in rat ventricular cells^{5,6}. All these studies reported significant deviations from normal data distribution together with sometimes surprisingly low correlations between current amplitudes and C_{m}, with r^{2} ranging from 0.17 to 0.28 in^{4}, and r values being 0.04 for I_{to}, 0.42 for the constitutively active, and 0.61 for the acetylcholineinduced component of I_{K(ACh),} while 0.84 for I_{K1}^{6}.
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 population^{7,8}. Similarly, Ballouz et al. showed large variation in mRNA levels for a wide range of cardiac proteins involved in regulating cellular electrophysiological properties^{9}, whereas Lachaud et al. have shown significant intercell variability in ventricular APD^{10}. Despite these substantial variations in electrophysiological characteristics, bioelectricity of the heart can most likely be properly coordinated because of overlapping functions and certain welldefined correlations between ion currents^{11,12}. Most recently, similar relationships in mRNA transcript levels^{9} and in cardiac ion channel cotranslation^{13} have also been shown.
In this study, we systematically investigated the relationship between C_{m} and the major cardiac ion currents (Ltype calcium current—I_{Ca,L}; late sodium current—I_{Na,late}; sodiumcalcium exchange current—I_{NCX}; inward rectifier potassium current—I_{K1}; rapid delayed rectifier potassium current—I_{Kr}; slow delayed rectifier potassium current—I_{Ks}) 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 myocytes^{14,15,16}. 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 C_{m} and the ion current parameter values; (2) the relationship between C_{m} and the ion current parameters; and (3) the effect of “normalizing” the original membrane current parameters to C_{m}.
We have found generally good correlations between C_{m} and current amplitudes or integrals in this preparation, although correlations were occasionally limited by regional heterogeneity of ion channels and nonideal experimental conditions.
Results
Membrane capacitance
The pooled membrane capacitance (C_{m}) values of all cells involved in the study (n = 639) significantly deviated from normal distribution (p < 0.001; Supplementary Fig. 1). The distribution was rightskewed (skewness = 0.533) and leptokurtic (excess kurtosis = 0.561). The arithmetic mean of C_{m} 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. C_{m} values in any current groups did not deviate significantly from normal distribution, except in I_{Ks} measurements (p = 0.013; φ = 0.33; Supplementary Fig. 1J) and when all cells were pooled together in I_{to1} measurements (p = 0.036; φ = 0.248; Supplementary Fig. 3A) under CVC experiments.
Ltype Ca^{2+} current (I_{Ca,L})
I_{Ca,L} was studied under CVC conditions in 198 myocytes (Fig. 1A). I_{Ca,L} peak current values (Fig. 1C) showed a significantly nonnormal distribution, being leftskewed (towards higher current values; skewness = − 0.546), with normal kurtosis. The absolute coefficient of variation (CV) of I_{Ca,L} peak was 0.485. The distribution of data still remained significantly nonnormal after dividing peak I_{Ca,L} with C_{m}, although the CV significantly (p = 0.02) reduced to 0.398 after this operation (Supplementary Table 1).
The correlation between the amplitude of I_{Ca,L} and C_{m} 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 C_{m} and I_{Ca,L}.
Under APVC conditions I_{Ca,L} was dissected as a 1 µM nisoldipinesensitive current (Fig. 1B) in 15 cells. In contrast to CVC experiments, the distribution of either the I_{Ca,L} current parameters (peak current, midplateau current, current integral—Q_{Ca,L}) or their values divided with C_{m} 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 C_{m}, 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 midplateau values of I_{Ca,L}, as shown in Fig. 1D,E, respectively. Similarly, the charge carried by the current, indicated as Q_{Ca,L} (− 75 ± 17 fC/pF) yielded a high correlation with C_{m} (r = − 0.77) (Fig. 1F). These values obtained for I_{Ca,L} density and Q_{Ca,L} are in a good agreement with earlier results obtained in canine ventricular myocytes^{16}.
Late Na^{+} current (I_{Na,late})
I_{Na,late} was recorded exclusively under APVC conditions as a 1 µM GS458967sensitive current (Fig. 2A). Since its peak often did not separate from the decaying phase of I_{Na,early}, only midplateau amplitudes and current integrals (Q_{Na,late}) were calculated and analyzed, as shown in Fig. 2B,C and in Supplementary Tables 3 and 6. Both the midplateau current values (p = 0.029, φ = 0.364) and the total charge carried by the current (p = 0.037, φ = 0.392) were significantly nonnormally distributed, with medium φ effect sizes, and CVs of 0.493 and 0.447, respectively. After dividing the original values with C_{m}, both distributions (midplateau I_{Na,late}/C_{m} and Q_{Na,late}/C_{m}) became normal, with their CVs becoming nonsignificantly smaller (0.415 and 0.373, respectively).
Bivariate distributions of C_{m} and midplateau I_{Na,late}, or C_{m} and Q_{Na,late} data pairs were not significantly different from the normal bivariate distribution. Pearson’s correlation coefficients were r = − 0.475 for C_{m} and midplateau I_{Na,late}, and r = − 0.483 for C_{m} and Q_{Na,late}, respectively, indicating a low linear correlation of midplateau I_{Na,late}, and Q_{Na,late} with C_{m}.
Na^{+}/Ca^{2+} exchanger current (I_{NCX})
I_{NCX} was recorded exclusively under APVC conditions as a 0.5 µM ORM10962sensitive current (Fig. 2D). Since its peak often did not separate well from the capacitive transient, we also present only midplateau current amplitudes and current integrals (Q_{NCX}) here (Fig. 2E,F; Supplementary Tables 3 and 6).
Both original current values and current densities of midplateau I_{NCX} were normally distributed, with CVs of 0.403 for original values, and 0.348 for current densities, respectively. Q_{NCX} was significantly nonnormally distributed with a large effect size (p = 0.024, φ = 0.613), being leftskewed (towards higher current values; skewness = − 1.274). The distribution became normal after dividing Q_{NCX} with C_{m} (p = 0.172), with CVs being 0.311 and 0.227, respectively.
Bivariate distribution of C_{m} and midplateau I_{NCX} data pairs was normal, whereas distribution of C_{m} and Q_{NCX} data pairs was significantly different from normal (p = 0.049). Correlation coefficients were r = − 0.607 for C_{m} and midplateau I_{NCX}, and ρ = − 0.587 for C_{m} and Q_{NCX}, respectively, indicating moderate linear correlation between C_{m} and midplateau I_{NCX}, and moderate monotonic correlation between C_{m} and Q_{NCX}.
Inward rectifier K^{+} current (I_{K1})
Both original I_{K1} peak (Fig. 3A) values and I_{K1} 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 I_{K1} peak current densities (Supplementary Table 1).
Bivariate distributions of C_{m} and I_{K1} 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 I_{K1} was defined as a 50 µM BaCl_{2}sensitive current (Fig. 3B) in 19 myocytes. I_{K1} current peaks as well as charges carried by I_{K1} (Q_{K1}) were normally distributed in all cases of original values and after dividing them with C_{m}. CVs were 0.27 for I_{K1} peak current and 0.162 for I_{K1} peak current density, and 0.276 for Q_{K1} and 0.162 for Q_{K1}/C_{m}, respectively. Dividing original current parameters with C_{m} significantly reduced data variability in case of I_{K1} (p = 0.044 for peak current; p = 0.036 for Q_{K1}). Both the original midplateau I_{K1} values (p < 0.001) and midplateau I_{K1} densities (p = 0.016) showed significantly nonnormal distribution, being rightskewed (towards larger values; skewnesses of 1.569 and 1.003, respectively), with CV values of 0.564 and 0.501, respectively. Midplateau I_{K1} densities, however, had only “medium” effect size of the nonnormal distribution (φ = 0.442) compared to the “large” effect size (φ = 0.738) in case of the original midplateau I_{K1} values (Supplementary Table 3).
Bivariate distributions of C_{m} and I_{K1} peak as well as C_{m} and Q_{K1} data pairs were normal, whereas the bivariate distribution of C_{m} and midplateau I_{K1} was significantly different from normal (p < 0.001). Correlations between C_{m} and I_{K1} peak (r = 0.785, p < 0.001), as well as C_{m} and Q_{K1} (r = 0.767, p < 0.001) data pairs were high; but for C_{m} and midplateau I_{K1}, no significant correlation was detected (see Fig. 3D–F and also Supplementary Table 6). Linear regression analysis between I_{K1} peak current and C_{m} yielded a slope of 1.5 ± 0.29 pA/pF for the regression line, a value close to what has been reported as peak I_{K1} current density in canine ventricular cells^{14,16}.
Rapid delayed rectifier K^{+} current (I_{Kr})
Under CVC conditions both the original I_{Kr} peak current (Fig. 4A) value and I_{Kr} peak current density distributions deviated significantly from normal distribution (p < 0.001 and p = 0.013, respectively), being rightskewed (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 C_{m}, the effect size of nonnormal distribution changed from medium (φ = 0.379) to small (φ = 0.221). Similarly, bivariate distribution of C_{m} and I_{Kr} peak data pairs differed significantly from the normal distribution. Based on the results obtained in 120 myocytes the Spearman rankcorrelation between I_{Kr} tail current amplitude and C_{m} was moderate (ρ = 0.628, p < 0.001; Fig. 4C). Linear regression analysis yielded a slope of 0.49 ± 0.05 pA/pF.
Under APVC conditions I_{Kr} peaked during terminal repolarization (Fig. 4B). Contrary to CVC results, when I_{Kr} was investigated with APVC (n = 19), all the measured parameters of the current, as well as their respective bivariate distributions with C_{m} followed normal distribution. The respective CV values for original and C_{m} “normalized” data were 0.359 and 0.266 for I_{Kr} peak; 0.632 and 0.58 for midplateau I_{Kr}; whereas 0.397 and 0.289 for the charge carried by I_{Kr} (Q_{Kr}). Although dividing the original current parameter values with C_{m} reduced CVs, these changes did not reach statistical significance.
High correlations for both I_{Kr} peak amplitude (r = 0.704, p < 0.001) and for Q_{Kr} (r = 0.709, p < 0.001) were obtained under these conditions (Fig. 4D,F). Similar to I_{K1}, the midplateau amplitude of I_{Kr} showed no significant correlation with C_{m} (r = 0.312, p = 0.194, Fig. 4E). Linear regression analysis showed slope values of I_{Kr} current peak (0.49 ± 0.12 pA/pF) and Q_{Kr} (40 ± 10 fC/pF) similar to the current density and charge density values reported earlier for canine ventricular cells under APVC conditions^{16}.
Slow delayed rectifier K^{+} current (I_{Ks})
In case of I_{Ks} 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 rightskewed (skewness = 0.765).
Both the original and C_{m} “normalized” I_{Ks} peak current value distributions deviated significantly from normal distribution (p < 0.001 for both cases), being rightskewed (towards larger current values; skewness values of 1.448 and 0.886, respectively). Moreover, the absolute I_{Ks} peak values were also significantly leptokurtotic (with heavy tails; excess kurtosis = 2.544). CVs were 0.658 and 0.583, respectively. With “normalization” to C_{m}, the effect size of the nonnormal distribution was reduced from large (φ = 0.592) to medium (φ = 0.359). Similarly, bivariate distribution of C_{m} and I_{Ks} peak data pairs differed significantly from the bivariate normal distribution. Based on the results obtained the Spearman rankcorrelation between I_{Ks} tail current amplitude and C_{m} was low (ρ = 0.223, p = 0.048; Fig. 5C), with a slope of 1.04 ± 0.27 pA/pF.
Under APVC conditions, I_{Ks} rose slowly during the action potential plateau (Fig. 5B). Contrary to CVC results, when I_{Ks} was investigated with APVC (n = 18), all the measured current parameters, as well as their respective bivariate distributions with C_{m} followed normal distribution. The respective CV values for original and C_{m} “normalized” data were 0.403 and 0.354 for I_{Ks} peak; 0.561 and 0.568 for midplateau I_{Ks}; whereas 0.321 and 0.245 for the charge carried by I_{Ks} (Q_{Ks}). Both C_{m} and I_{Ks} peak (r = 0.53, p = 0.024), as well as C_{m} and Q_{Ks} (r = 0.59, p = 0.01) correlated moderately, as demonstrated in Fig. 5D,F. No significant correlation was observed between midplateau I_{Ks} value and C_{m} (Fig. 5E). Linear regression analysis yielded slopes of 0.16 ± 0.08 pA/pF for I_{Ks} peak, and 12 ± 4 fC/pF for Q_{Ks}, respectively.
Transient outward K^{+} current (I_{to1})
I_{to1} 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 in^{17}), 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, C_{m} significantly deviated from normal distribution (p = 0.036), being rightskewed (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), C_{m} followed normal distribution.
As shown in Fig. 6A, marked differences in I_{to1} amplitude were observed among the cells originating from different regions—in line with the known transmural heterogeneity of I_{to1} in canine ventricle^{18,19,20}.
When all cells were analyzed together, both the original and the C_{m} “normalized” I_{to1} 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 rightskewed (skewness values of 0.837 and 0.752, respectively). Similarly, bivariate distribution of C_{m} and I_{to1} peak data pairs differed significantly from the normal distribution (p < 0.001). The Spearman rankcorrelation between all I_{to1} peak current amplitudes and C_{m} 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 C_{m} 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 nonnormal C_{m} “normalized” peak current (p = 0.008) distribution, with a large (φ = 0.775) effect size. CV of I_{to1} peak current density was significantly smaller (0.194) than in case of original peak current magnitudes (0.323). Visualizing the data revealed that the C_{m} normalized peak current distribution was nonnormal because of an outlier cell having C_{m} = 80 pF and a peak I_{to1} 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 C_{m}, this effect was only significant in case of EPI cells (p = 0.012).
Bivariate distributions of C_{m} and I_{to1} 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 nonnormal 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 C_{m}. In these presumably MID myocytes, bivariate distribution of C_{m} and I_{to1} peak data pairs significantly deviated from normal (p = 0.003). The correlation between C_{m} and I_{to1} peak was also high (ρ = 0.717, p < 0.001) in these cells (Fig. 6F). Comparing I_{to1} 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 C_{m} and the ion current parameter values; (2) the relationship between C_{m} and the ion current parameters; and (3) the effect of “normalizing” the original membrane current parameters to C_{m}.
The distribution of C_{m} of all cells involved our study was significantly nonnormal, being rightskewed, similar to the findings of Kula et al.^{5}. C_{m} values in case of any of the current groups did not deviate significantly from normal distribution, except in I_{Ks} measurements and when all cells were pooled together in I_{to1} 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 larger^{21}, 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 nonnormally distributed in case of I_{Ca,L}, I_{Kr}, I_{Ks}, and if all cells were pooled together in I_{to1} experiments (Supplementary Tables 1 and 2). Dividing peak current values with C_{m} (obtaining peak current densities) did not normalize the distributions, all of them remained significantly nonnormal. 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 I_{Ca,L}, I_{K1}, and I_{to1} (in the EPI and presumably MID groups). In their recent study, Kula et al.^{5} also found significantly nonnormal, rightskewed I_{K1} and I_{K(ACh)} current magnitude distributions with the Shapiro–Wilk test, and the calculated respective current densities were also significantly nonnormally distributed. Ismaili and coworkers^{4} studied distributions of I_{Ca,L} current peaks in various species, under different conditions. Most of their samples did not follow normal distribution and were seemingly rightskewed. When they divided I_{Ca,L} current peaks with C_{m} 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 C_{m} values less than 70 pF, whereas in the previously mentioned two studies^{4,5}, a much larger proportion of the left ventricular cells had C_{m} values lower than 70 pF, especially in rat samples. These more frequently occurring low C_{m} 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 midplateau I_{Na,late}, Q_{Na,late}, Q_{NCX} and midplateau I_{K1} (Supplementary Table 3). Dividing these current parameters with C_{m} “normalized” midplateau I_{Na,late}, Q_{Na,late} and Q_{NCX} distributions, whereas distribution of the midplateau I_{K1} remained significantly nonnormal, although the effect size of the deviation from nonnormal distribution became much smaller (φ = 0.738 and φ = 0.442, respectively; Supplementary Table 3). In general, CVs were nonsignificantly reduced after dividing with C_{m}, however, in the cases of peak I_{K1} and Q_{K1}, these reductions were statistically significant (Supplementary Table 3). In conclusion, we found dividing original data with C_{m} values generally useful, both by reducing the effect of the sometimes originally nonnormal sample distributions (even rendering them normal in certain cases), as well as by reducing CVs of the samples.
Relationships between C_{m} 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 I_{Ca,L}, I_{K1} and I_{Kr}, the correlation was usually high. Importantly, y intercepts of linear regression were close to zero indicating a true linear relationship between C_{m} and membrane current parameters (I_{m}) 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 I_{NCX} and low for I_{Na,late} and I_{Ks}.
Marked differences between individual ion currents of the same species regarding the correlation between C_{m} and I_{m} is not exceptional. Good correlation was found in rat myocytes in the case of I_{K1} but not for I_{to}^{6}—results identical to our observations in canine myocytes. Comparing the present results on canine I_{Ca,L} with those reported by Ismaili et al.^{4} on human ventricular I_{Ca,L} (both obtained under CVC conditions) our correlation coefficient (r = − 0.603, r^{2} = 0.364) was higher than that reported by Ismaili et al. (r^{2} = 0.28). In that study the low correlation coefficient was attributed partially to inhomogeneous distribution of surface versus Ttubular localization of Ltype Ca^{2+} channels^{22,23}, which channel subpopulations might also be differently regulated^{24,25}. This regional inhomogeneity at a cellular level may tremendously increase variability (mainly due to improper voltage control of Ttubular Ca^{2+} channels), however, these effects are likely similar in the cardiomyocytes of a given species.
Another possible reason for the low correlation between C_{m} and I_{m} might be a limited proportionality between the cell size and C_{m}^{4,6}. Although the exact level of correlation between C_{m} and cell surface is not known, if there was any discrepancy between them, the relationship between C_{m} and I_{m} should have been affected similarly in the case of several ion currents. Furthermore, inaccurate C_{m} measurements^{26} may also contribute to the limited proportionality between I_{m}, C_{m}, and cell surface area. Again, however, even if there was any inaccuracy in measuring C_{m}, 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 I_{m} and C_{m}.
Then, what might limit correlations between I_{m} and C_{m}? Theoretically, there are at least three factors which might decrease the linear relationship between C_{m} and ion current amplitudes or integrals. These are: transmural and cell surface inhomogeneity of ion channel expression; small measured current values; and celltocell variability of intracellular ion concentrations, especially [Ca^{2+}]_{i}.
Our results with I_{to1} represent a good example that regional inhomogeneity of ion channel expression is likely to be a limiting factor in significant correlations between I_{m} and C_{m}. I_{to1} is known to be abundantly expressed in the subepicardial layer, its expression is less pronounced in midmyocardial cells, while the current is small in the subendocardial region of the canine heart^{17,18,19,20}. Indeed, the correlation between I_{to1} and C_{m} 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 I_{to1}, but also for I_{Na}, I_{NCX} and I_{Ks}. More specifically, the density of I_{Na} is the highest in the midmyocardial region and significantly lower in the subepicardial and subendocardial layers in dogs^{17,27,28} and marked transmural inhomogeneity was observed in the case of I_{NCX} as well^{29,30}. Regarding I_{Ks}, the density of the current is higher in the subepicardial than in the midmyocardial region^{17,31}. Another type of regional inhomogeneity in the density of I_{Ks} was also observed. Expression of I_{Ks} was found to be more than double in the apical than in the basal region of the canine ventricular wall^{32}. In contrast, no transmural inhomogeneity has been observed for I_{Ca,L}, I_{Kr} or I_{K1} in canine ventricular myocardium^{17}. Similarly, no apicobasal differences regarding the distribution of I_{K1} or I_{Kr} were demonstrated^{32}.
Cell surface inhomogeneity of ion channel expression can also limit the correlation between certain currents and C_{m}. 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 Kir6.2^{33}) 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 I_{m} and C_{m} 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 C_{m} 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 nonsignificant correlations between C_{m} and the midplateau amplitudes of I_{K1} and I_{Kr}, 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.
Inhomogeneity of intracellular Ca^{2+} concentration—a possible consequence of the variable Na^{+} and Ca^{2+} loads occurring during cell isolation—may also affect the correlation in the case of some strongly Ca^{2+}dependent ion currents, such as I_{Ca,L} or I_{NCX}, but also I_{Na,late}^{34} and I_{Ks}^{16}. 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 current^{35}. Somewhat related to this, the relatively slow, but continuous reduction of current ion magnitude over time (ion current “rundown”) may also contribute to the limited correlations between I_{m} and C_{m}.
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 C_{m} and ion current amplitudes. Under APVC conditions it also must be noted that whenever the bivariate distribution of the investigated parameter and C_{m} was significantly (or marginally significantly) nonnormal, no significant correlations were detected. These cases included the values of midplateau I_{Na,late}, midplateau I_{NCX}, midplateau I_{Kr} and midplateau I_{K1}. 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.
Our experiments performed under APVC conditions allowed the comparison of correlations found between C_{m} and I_{m} with those between C_{m} 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 C_{m} reduces both the coefficient of variation, and the deviation from normal distribution, if there was any. In case of most currents, we found significant, moderatetohigh correlations between ion current amplitudes or integrals and C_{m}. However, the level of correlation between an ion current and C_{m} 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 N^{o}: 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, CaCl_{2} 1.3, MgCl_{2} 1, HEPES 10, NaHCO_{3} 25, glucose 10, while under CVC conditions it contained: NaCl, 144; KCl, 5; CaCl_{2}, 2.5; MgCl_{2}, 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 applied^{36}, 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 (C_{m}) 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 previously^{37,38,39}. To avoid the consequences of celltocell 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): Kaspartate 120, KCl 30, MgATP 3, HEPES 10, Na_{2}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, I_{Na,late} was dissected by 1 µM GS458967, I_{NCX} by 0.5 µM ORM10962, I_{Ca,L} by 1 µM nisoldipine, I_{Kr} by 1 µM E4031, I_{Ks} by 0.5 µM HMR1556, I_{K1} by 50 µM BaCl_{2}, and I_{to1} by 100 µM chromanol293B applied in the presence of 0.5 µM HMR1556. Each drugsensitive current was obtained by subtracting the postdrug trace from the predrug 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 tracetotrace fluctuations. The dissected currents were evaluated by determining their maximum values (peak currents), their amplitudes measured at the halfduration of the command AP (midplateau 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 C_{m}, where the D’AgostinoPearson omnibus test was applied^{40,41}. If there was a significant deviation from the normal distribution, the effect size of nonnormality 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 Forkman^{42} to test if dividing the original ion current parameter values with C_{m} (calculating ion current densities, or “normalizing”) caused any significant differences between CVs of original and “normalized” data.
For data pairs (eg. C_{m} and current magnitudes or C_{m} 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 nonnormal bivariate distribution, Spearman’s correlation coefficient (ρ, “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 C_{m} as the predictor variable, and the different current parameters (peak amplitude, midplateau value, current integral) being response variables. Figures show the slope of the fitted line (s) and the y intercept (y_{0}), 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 website^{41} for calculating the D’AgostinoPearson omnibus test, and the effect size of nonnormality (φ). Results were considered statistically significant in case of p < 0.05; in the summary tables, all p < 0.1 values are reported.
Data availability
Data underlying this article are available in the Open Science Framework, at https://doi.org/10.17605/OSF.IO/5X428).
Abbreviations
 C_{m} :

Membrane capacitance
 CVC:

Conventional voltage clamp
 APVC:

Action potential voltage clamp
 CV:

Coefficient of variation
 I_{K(ACh)} :

Acetylcholinesensitive potassium current
 I_{Ca} _{,L} :

Ltype Ca^{2+} current
 I_{NCX} :

Na^{+}/Ca^{2+} exchanger current
 I_{Na,late} :

Late Na^{+} current
 I_{Kr} :

Rapid delayed rectifier K^{+} current
 I_{Ks} :

Slow delayed rectifier K^{+} current
 I_{K1} :

Inward rectifier K^{+} current
 I_{to1} :

Transient outward K^{+} current
 Q_{x} :

The charge carried by ion current “x” (I_{x} integral)
 r:

Pearson’s correlation coefficient
 ρ:

Spearman’s correlation coefficient
 φ:

Effect size
 EPI:

Subepicardial cells
 ENDO:

Subendocardial cells
 MID:

Midmyocardial cells
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Acknowledgements
This work was funded by the National Research, Development and Innovation Office (NKFIHK138090 to PPN, NKFIHK142764 to NSz, NKFIHK147301 to TB and NKFIHFK128116 to BH) and by the Hungarian Academy of Sciences (János Bolyai Research Scholarship to BH). Further support was obtained from the National Research, Development and Innovation Fund of Hungary, financed under the 20204.1.1TKP2020 funding scheme (TKP2020NKA04). ZsK CsD and ZB obtained further support from the New National Excellence Program (ÚNKP233IIDE109, ÚNKP234IDE64 and ÚNKP222IDE389, respectively).
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Conceptualization: B.H., P.P.N.; Experimental design: B.H., N.S., J.M., T.B., P.P.N.; Data acquisition: B.H., Z.K., C.D., J.O., N.S., T.B., J.M., Data analysis: B.H., Z.B.; Visualization: B.H., Z.B., N.S.; Data interpretation: B.H., T.B., P.P.N.; writing—original draft preparation: B.H., C.D., Z.K.; Z.B., O.J.; writing—review and editing: J.M., T.B., P.P.N.; supervision: B.H., N.S., P.P.N.; funding acquisition: B.H., N.S., P.P.N. All persons designated as authors qualify for authorship, and all those who qualify for authorship are listed. All authors have read and approved to the submitted version of the manuscript and agreed to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.
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Horváth, B., Kovács, Z., Dienes, C. et al. Relationship between ion currents and membrane capacitance in canine ventricular myocytes. Sci Rep 14, 11241 (2024). https://doi.org/10.1038/s41598024617366
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DOI: https://doi.org/10.1038/s41598024617366
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