## ABSTRACT

The ratio between Na^{+}-Ca^{2+} exchange current densities in t-tubular and surface membranes of rat ventricular cardiomyocytes (*J*_{NaCa}-ratio) estimated from electrophysiological data published to date yields strikingly different values between 1.7 and nearly 40. Possible reasons for such divergence were analysed by Monte Carlo simulations assuming both normal and log-normal distribution of the measured data. The confidence intervals *CI*_{95} of the mean *J*_{NaCa}-ratios computed from the reported data showed an overlap of values between 1 and 3, and between 0.3 and 4.3 in the case of normal and log-normal distribution, respectively. Further analyses revealed that the published high values likely result from a large scatter of data due to transmural differences in *J*_{NaCa}, dispersion of cell membrane capacitances and variability in incomplete detubulation. Taking into account the asymmetric distribution of the measured data, the reduction of mean current densities after detubulation and the substantially smaller *CI*_{95} of lower values of the mean *J*_{NaCa}-ratio, the values between 1.6 and 3.2 may be considered as the most accurate estimates. This implies that 40 to 60% of Na^{+}-Ca^{2+} exchanger is located at the t-tubular membrane of adult rat ventricular cardiomyocytes.

## INTRODUCTION

Recent advances in experimental techniques for cardiac cell electrophysiology, as well as the elaboration of a method using osmotic shock to physically detach cardiac t-tubules from the surface membrane (a process known as ‘detubulation’), have enabled researchers to assess the density of individual ion currents in the t-tubular and surface membranes (Orchard et al., 2009). Data from adult rat ventricular cardiomyocytes published to date indicate that the mean density of Na^{+}-Ca^{2+} exchange current (*J*_{NaCa} [pA pF^{−1}]) in the t-tubular membrane (*J*_{NaCa,t}) is higher than in the surface membrane (*J*_{NaCa,s}) (Despa et al., 2003; Gadeberg et al., 2016; Thomas et al., 2003; Yang et al., 2002). However, the values of the ratio *J*_{NaCa,t}/*J*_{NaCa,s} (referred to from now on as ‘mean *J*_{NaCa}-ratio’) computed from data reported in these studies range between 1.7 and 40 (Pásek et al., 2017).

The reasons for such marked differences are unclear. They might be caused by different experimental conditions, or by differences in the properties of ventricular myocytes from animals of different ages (and therefore different weights) or from different strains of rat. However, inaccuracies in the measurement and evaluation of experimental data and their consequent scatter may also play an important role (Bébarová et al., 2020).

The assessment of the mean *J*_{NaCa}-ratio is based on the measurement of Na^{+}-Ca^{2+} exchange currents and membrane capacitances in intact and detubulated myocytes, and on the optical measurement of the fraction of t-tubules resisting detubulation. Therefore, the reliability of the assessment is dependent on the accuracy of the measurement of each of these parameters. The aim of this study was to explore: (1) whether the propagation of errors of individual parameters in the computation of the mean *J*_{NaCa}-ratio could be responsible for the reported differences; (2) what the possible sources of errors and biases in the experimental data could be; and (3) which range of values of the mean *J*_{NaCa}-ratio in adult rat cardiomyocytes might be considered plausible.

## RESULTS

### Basic experimental data

The mean values of membrane capacitance (*C*) and *J*_{NaCa} as computed from data measured in rat ventricular myocytes before (*C*_{intact,}*J*_{NaCa,intact}) and after detubulation (*C*_{detub,}*J*_{NaCa,detub}) by various groups are summarised in Table 1. Marked differences in the values of *J*_{NaCa,intact} and *J*_{NaCa,detub} reflect different experimental conditions under which the currents were measured; for example, internal or external solutions, absence or presence of exogenous intracellular Ca^{2+} buffers, different voltage clamp protocols or different temperatures (for comparison see Table 4 in Discussion).

### Calculation of mean *J*_{NaCa}-ratio in adult rat cardiomyocytes

The mean *J*_{NaCa}-ratio was calculated from Eqn 4 (see Materials and Methods) and the experimental data specified in Table 1. The fraction of t-tubules resisting detubulation (*f*_{t,res}) exhibited different values in various studies; either nearly 0, which represented almost total detubulation (Thomas et al., 2003), 0.08 (Pásek et al., 2008) or even 0.16 (Bryant et al., 2015). Therefore, in each case, the mean *J*_{NaCa}-ratio was computed for *f*_{t,res} ranging between 0 and 0.2. The traces illustrated in Fig. 1A show that the ratio increases progressively with *f*_{t,res} in all cases, but surprisingly exhibits very different values (1.7, 3.8, 5.2 and 18 for *f*_{t,res}=0, and 1.8, 5.3, 7.4 and 39.5 for *f*_{t,res}=0.16).

Our previous study (Pásek et al., 2017) showed that calculating the mean *J*_{NaCa}-ratio from the values of *J*_{NaCa,intact} and *J*_{NaCa,detub} may result in substantially different values, depending on the way *J*_{NaCa} is assessed (using the average of the current densities directly assessed in individual cells versus the ratio of the average current magnitude *I* to the average *C* for a given set of cells). To evaluate the influence of these differing methods of *J*_{NaCa} density assessment on the value of mean *J*_{NaCa}-ratio within the above mentioned span of *f*_{t,res}, comparative computations were performed based on data measured by Thomas et al. (2003) and Gadeberg et al. (2016) (Fig. 1B,C, respectively). Although the differences in the mean *J*_{NaCa}-ratios computed in both ways from data given by Thomas et al. (2003) were small (Fig. 1B), the data from Gadeberg et al. (2016) produced sizeable differences (25.9 and 57.4% at *f*_{t,res} of 0 and 0.16, respectively; Fig. 1C).

### Statistical analysis of mean *J*_{NaCa}-ratios calculated from different studies

To explore whether the different values of mean *J*_{NaCa}-ratio calculated from different studies could arise from a large scatter of experimental data, we used the statistical parameters of *C*, *J*_{NaCa}, and *f*_{t,res} (Table 1), and reconstructed the distribution of the mean *J*_{NaCa}-ratio related to each study using Monte Carlo simulations (for details see Materials and Methods). Two types of distribution of measured data, normal and log-normal, were used. The normal distribution was used because the values from the compared studies were computed within the hypothesis of normality. However, the log-normal distribution appears to be more realistic because *C* and *f*_{t,res} are always positive and *J*_{NaCa} must keep a constant sign, conditions that are not strictly observed when using the normal distribution to generate artificial data (for deeper explanation see Limpert and Stahel, 2011 and Kula et al., 2020a).

The simulations showed that, if all the measured quantities (*C*, *J*_{NaCa}, and *f*_{t,res}) were normally distributed, distributions of the mean *J*_{NaCa}-ratio were asymmetric (Fig. 2A), with medians of 24.5, 4.8, 4.3 and 1.7 (Table 2, upper) when evaluated from data measured by Gadeberg et al. (2016), Yang et al. (2002), Despa et al. (2003) and Thomas et al. (2003), respectively. If these quantities were given log-normal distribution, distributions of the mean *J*_{NaCa}-ratio were asymmetric as well (Fig. 2B); the respective medians were 17.0, 4.1, 3.2 and 1.6 (Table 2, lower).

Analysis of 95% confidence intervals of the mean *J*_{NaCa}-ratio revealed considerable differences between individual studies whenever normal or log-normal distribution were assumed (Table 2). The interval of values common for all these studies spanned from 1 to 3 in the case of normal distribution, and from 0.3 to 4.3 in the case of log-normal distribution. The latter range covers values of 1.6, 3.2 and 4.1, computed from three studies (Thomas et al., 2003; Despa et al., 2003; Yang et al., 2002). As also follows from Table 2, a large scatter of experimental data could even lead to negative values of the ratio in a considerable number of cases (expressed in percentage, *P*_{n}). It is also worth noting that the confidence interval, as well as *P*_{n}, gradually increased with an increase of the mean *J*_{NaCa}-ratio, suggesting that higher values of the mean *J*_{NaCa}-ratio (over 4.3) are less reliable than the lower ones.

This view was further supported by comparing indices *P*_{30}, which characterise probabilities that the real values of mean *J*_{NaCa}-ratio lie within ±30% from the values in Table 2. As expected, when using data from Thomas et al. (2003), Despa et al. (2003), Yang et al. (2002) and Gadeberg et al. (2016), *P*_{30} gradually decreased from 74% to 37%, 25%, and 16%, respectively, when normal distribution was assumed, and from 52% to 31%, 20%, and 10%, respectively, when log-normal distribution was assumed. Analysis of these data showed a negative correlation between the mean *J*_{NaCa}-ratio and *P*_{30} (the Pearson′s coefficients of correlation were −0.68 and −0.78, respectively, for normal and log-normal distribution of the data; not illustrated).

## DISCUSSION

The distribution of the Na^{+}-Ca^{2+} exchanger between the t-tubule and surface membranes was shown to have a marked effect on the intracellular Ca^{2+} load and Ca^{2+} transient in a model of rat ventricular cardiomyocyte (Pásek et al., 2017). In particular, these effects were dependent on the value of *J*_{NaCa}-ratio. Unfortunately, computation of the mean *J*_{NaCa}-ratio from electrophysiological data obtained in intact and detubulated rat ventricular cells (Yang et al., 2002; Despa et al., 2003; Thomas et al., 2003; Gadeberg et al., 2016; Pásek et al., 2017) results in values ranging from 1.7 to nearly 40 (Fig. 1). The discrepancy between the mean *J*_{NaCa}-ratios as evaluated from experimental data might be due to methodological differences or due to variations of the quantitative aspects related to the age/weight or the strain of rats. However, we have found that the degree of uncertainty of the mean ratio gradually increases with its value and that the values higher than 4.8 are encumbered by a considerable error resulting from very large confidence intervals, which include a considerable fraction of non-realistic negative values.

### Role of differences in experimental conditions in divergent estimates of mean *J*_{NaCa}-ratio

*J*

_{NaCa}

**-**ratio estimates (Fig. 1, Table 2). According to Eqn 4, the mean

*J*

_{NaCa}-ratio depends on five variables:

*J*

_{NaCa,intact},

*J*

_{NaCa,detub},

*C*

_{intact},

*C*

_{detub}and

*f*

_{t,res}. The differences in the mean

*J*

_{NaCa}-ratio are reflected at each value of

*f*

_{t,res}(Fig. 1), so the condition of complete detubulation (

*f*

_{t,res}=0) can be introduced in further considerations. In addition, if we introduce new variables

*j*

_{id}=

*J*

_{NaCa,intact}/

*J*

_{NaCa,detub}and

*c*

_{id}=

*C*

_{intact}/

*C*

_{detub}into Eqn 4, the mean

*J*

_{NaCa}-ratio will depend on only two variables,

*j*

_{id}and

*c*

_{id}:

The mean *J*_{NaCa}-ratio is a decreasing function of *c*_{id} and an increasing function of *j*_{id} in the whole range of values determined in the compared studies. From the results of studies by Gadeberg et al. (2016), Yang et al. (2002), Despa et al. (2003), and Thomas et al. (2003) summarized in Table 1, the following values could be calculated (for *f*_{t,res}=0): *J*_{NaCa}**-**ratio=[18, 5.2, 3.8, 1.7], *c*_{id}=[1.1649, 1.3497, 1.4717, 1.3600] and *j*_{id}=[3.3908, 2.0833, 1.9000, 1.1905], respectively. The particularly high value of the mean *J*_{NaCa}**-**ratio in the work of Gadeberg et al. (2016) results from a combination of the smallest *c*_{id} value and the largest *j*_{id} value. The dependence on *c*_{id} is less pronounced than the dependence on *j*_{id}, and in contrast to *c*_{id}, the values of *j*_{id} increase in parallel with the values of mean *J*_{NaCa}**-**ratio sorted by size.

One of the factors that could affect the value of *j*_{id} is age/weight or strain of the animals. Indeed, the highest *j*_{id} and thus *J*_{NaCa}**-**ratio corresponds to the oldest rats (25 weeks, Gadeberg et al., 2016). However, the estimated values of the mean *J*_{NaCa}**-**ratio do not correlate with age/weight at lower values of this parameter; the rats used by Thomas et al. (2003), although older than those used by Yang et al. (2002), exhibited a smaller mean *J*_{NaCa}-ratio (1.7 versus 6 according to Eqn 4). This inconsistency in age-dependency of the experimental data suggests that the mean *J*_{NaCa}**-**ratio in adult rat ventricular cardiomyocytes is affected by other factors.

Differences in the experimental conditions, particularly in intracellular and extracellular Na^{+} and Ca^{2+} concentrations, *I*_{NaCa} blockers, Ca^{2+} buffers, temperature and resistance of the pipette may also contribute to different values of assessed mean *J*_{NaCa}**-**ratio. The closest conditions (except for different *I*_{NaCa}-blocker and temperature, Table 4) were used in experiments performed by Thomas et al. (2003) and Despa et al. (2003), which might explain the closest values of mean *J*_{NaCa}-ratio (1.7 and 4.3 according to Eqn 4).

Yang et al. (2002) used higher concentrations of Ca^{2+} in perfusion solution (2.5 versus 1 mM in the other studies) and of Na^{+} in the pipette (20 versus 10 mM), but despite that, *J*_{NaCa} was 4-50× smaller than in other studies, even when assessed at the highest value of the voltage ramp (50 mV). Under these conditions, even minimal sensitivity of other currents to Ni^{2+} might affect the resulting mean *J*_{NaCa} values, which may be the reason for a higher mean *J*_{NaCa}-ratio (6 according to Eqn 4).

As for the measurement performed by Gadeberg et al., 2016, the main difference compared to the other three studies was that *I*_{NaCa} was determined at [Ca^{2+}]_{i} of 400 nM during the declining phase of Ca^{2+} transient induced by 10 mM of caffeine. The concentration of Na^{+} in the pipette was not specified in their study, which raises the question of whether the intracellular Na^{+} was well controlled during measurements on intact and detubulated cells. If not, the variation of this ion concentration might have contributed to the high dispersion of measured *I*_{NaCa} and thus to such different values of the mean *J*_{NaCa}-ratio (for explanation, see section ‘Potential causes of large scatter of experimental data’). More detailed data would be needed to assess the accuracy of this approach.

### Could scatter of experimental data explain differences in calculated values of mean *J*_{NaCa}-ratio?

To answer this question, we performed a random generation of simulated experimental data based on their statistical characteristics (Table 1) and computed the mean values of *J*_{NaCa}-ratio that could be obtained if a particular study was repeated. Having generated 50,000 sets of data, we evaluated the 95% confidence interval and the probability of negative values of the mean *J*_{NaCa}-ratio for each study (Table 2). The analysis showed that if the data measured in individual studies were distributed normally, the confidence intervals of mean *J*_{NaCa}-ratio shared values between 1 and 3. If the distribution was log-normal, the interval of common values of the ratio was between 0.3 and 4.3. Considering that the reduction of *J*_{NaCa} after detubulation (Table 1) supports values higher than 1, it is very likely that the real values of the mean *J*_{NaCa}-ratio in all four studies were between 1 and 4.3, and that values outside this interval arose from the scatter of experimental data.

### Potential causes of large scatter of experimental data

The large scatter of experimental data used to assess *J*_{NaCa} may have various causes. Firstly, transmural differences in the density and distribution of Na^{+}-Ca^{2+} exchanger between the t-tubular and surface membranes might contribute to the large dispersion of the measured *I*_{NaCa} and impaired *I*_{NaCa}-*C* proportionality, a prerequisite of a proper assessment of mean *J*_{NaCa} (Kula et al., 2020b). A transmural gradient in ventricular *J*_{NaCa} was observed in canine hearts by Zygmunt et al. (2000) and Xiong et al. (2005). Similarly, transmural differences have been reported in rat ventricles for cell size (Campbell and Gerdes, 1987) and *I*_{Ca} current properties (Volk and Ehmke, 2002). Thus, it is very likely that transmural differences in ventricular *J*_{NaCa} exist in rat. Secondly, our reconstruction of experiments performed by Gadeberg et al. (2016) using a model of rat ventricular myocyte incorporating the t-tubular system (Pásek et al., 2012) showed that the intracellular Na^{+} might have varied considerably depending on the inner diameter of the pipette tip and obstruction of its orifice after membrane rupture. The model also indicated that the Ca^{2+} and Na^{+} concentrations under the t-tubular and surface membranes might have differed from their cytosolic levels due to transmembrane Ca^{2+} and Na^{+} fluxes. Both of these factors could contribute to the high variability of *J*_{NaCa} among individual cells. As follows from Eqn 4, the high relative s.e. of *J*_{NaCa,intact} and *J*_{NaCa,detub} (∼ 30%) could then lead to values of mean *J*_{NaCa}-ratio that are higher than 1000 (e.g. if *J*_{NaCa,intact}=−0.32 pA pF^{−1} and *J*_{NaCa,detub}=−0.06 pA pF^{−1}).

Another source of scatter of experimental data could be the variability in size of the cells that were used in experiments. The larger the differences in cell size, the larger the scatter of membrane capacitances. This may substantially affect the calculated value of mean *J*_{NaCa}-ratio. For example, a change of only *C*_{intact} within s.e. from the value reported by Yang et al. (2002) (193±41 pF, *n*=25, relative s.d.=106%) could result in the mean *J*_{NaCa}-ratio to span from 4.5 up to 21.5. Furthermore, the fraction of membrane in t-tubules parallels the size of rat ventricular cells (Nakamura et al., 1986; Christé et al., 2020), with small ones having less t-tubules than large ones, which may also contribute to the scatter of *J*_{NaCa} values.

Regarding *f*_{t,res}, it may vary from cell to cell, owing to a non-homogeneous efficiency of the detubulation procedure, which may have contributed to the scatter of *f*_{t,res}. Possible biases in the estimation of *f*_{t,res} have been discussed by Pásek et al. (2008). A consequent inaccuracy in the assessed *f*_{t,res} may also contribute to the divergent mean *J*_{NaCa}-ratio among individual studies, as demonstrated in Fig. 1.

### Which way of mean current density assessment is more accurate?

To answer this question, we compared mean *J* computed from averaging the values obtained in individual cells with the values computed from the ratio of average *I* to average *C.* To achieve this, randomly generated data with normal distribution and a Monte Carlo approach were used. If the number of data was ten or more and their scatter was small (relative s.d. below 30%), the assessment of mean *J* by both ways converged to comparable values, even if both quantities were independent (Table 3, upper). Therefore, the accuracy of both ways of mean *J* assessment can be considered comparable under these conditions. However, if the scatter of data was larger (relative s.d. over 30%) and correlation of both quantities was low (Pearson coefficient of correlation between *I* and *C* below 0.6), the mean *J* assessed by both ways provided notably divergent values. In this case, the mean *J* calculated from the ratio of average *I* to average *C* was substantially more accurate (Table 3). It is also worth noting that the relative s.d. of *I* and *C* higher than 50% strongly indicates that the data are not normally distributed. If this is proved by a statistical test, their means should be calculated using the median or geometric mean (Kula et al., 2020a).

### Could a more accurate evaluation of measured data reduce the inconsistency of the mean *J*_{NaCa}-ratios assessed from different studies?

As shown in Table 2, statistical evaluation of the mean *J*_{NaCa}-ratio computed according to Eqn 4 may result in very different values and an enormous confidence interval *CI*_{95}. This might seem to be a consequence of the negative values of the input variables *C*_{intact} and *C*_{detub}, and non-real values of *J*_{intact} and *J*_{detub}, resulting from the assumption of their normal distribution. However, using the log-normal distribution that excludes the occurrence of the false values, the confidence interval even increased (Table 2, lower), as well as the probability of unrealistic negative values of the calculated mean *J*_{NaCa}-ratio.

We therefore tried to find out whether the mean *J*_{NaCa}-ratios from the compared studies could be reconciled and whether a smaller *CI*_{95} could be achieved if the mean *J*_{NaCa} was computed from the ratio of average *I*_{NaCa} to average *C.* This way of mean *J*_{NaCa} assessment would be more accurate if the original *I*_{NaCa} and *C* data were not sufficiently proportional (see section ‘Which way of mean current densities assessment is more accurate?’), which could be caused, for example, by using cells exhibiting transmural differences in *J*_{NaCa}, as reported by Zygmunt et al. (2000) and Xiong et al. (2005). The values needed to compute the mean *J*_{NaCa} from the ratio of average *I* to average *C* were only available in two cases (Thomas et al., 2003; Gadeberg et al., 2016). The Monte Carlo simulations under the assumption of log-normally distributed data then resulted in a mean *J*_{NaCa}-ratio of 1.8 and 12.9, for those two studies, respectively, thus approaching each other (see Table 2 for comparison with the former values). Interestingly, the value of the mean *J*_{NaCa}-ratio estimated from the results available in the study of Gadeberg et al. (2016) would further decrease to 6.5, and the resulting *CI*_{95} would be essentially reduced when using the less dispersed values of *C*_{intact} and *C*_{detub} measured by Bryant et al. (2015) on the same population of cells (*C*_{intact}=260±9 pF, *n*=37, and *C*_{detub}=178±9 pF, *n*=28).

These considerations lead to the conclusion that the differences between results of the compared studies are not essential and could be reduced by larger sets and more precise evaluation of the experimental data. Taking into account the asymmetric distribution of measured data (Kula et al., 2020a), the common confidence interval of the mean *J*_{NaCa}-ratio between 0.3 and 4.3, the reduction of *J*_{NaCa} after detubulation common to all compared studies (which suggests a ratio higher than 1) and the substantially smaller *CI*_{95} related to the mean ratios assessed from the data measured by Thomas et al. (2003) and Despa et al. (2003), the values from 1.6 to 3.2 appear to represent the most accurate estimates. Assuming that t-tubules are responsible for ∼30% of total membrane capacitance in rat ventricular myocytes (Brette and Orchard, 2007; Pásek et al., 2008), such values implicate that 40 to 60% of Na^{+}-Ca^{2+} exchanger proteins are located there. This range agrees well with the results of immunolabelling studies performed on rat myocytes (Kieval et al., 1992; Thomas et al., 2003; Jayasinghe et al., 2009), as well as with the approximately halved rate of decay of caffeine-induced Ca^{2+} transient in detubulated cells (Yang et al., 2002; Gadeberg et al., 2016).

## MATERIALS AND METHODS

### Assessment of mean *J*_{NaCa}-ratio from experimental data

*J*

_{NaCa}-ratio from experimentally evaluated values of

*J*

_{NaCa}and

*C*before and after detubulation was conducted using the following set of relations:where

*J*

_{NaCa,intact},

*J*

_{NaCa,detub},

*C*

_{intact},

*C*

_{detub}(measured quantities) are the densities of the Na

^{+}-Ca

^{2+}exchange current (pA pF

^{−1}) and the membrane capacitances (pF) in intact and detubulated cells, and

*J*

_{NaCa,s},

*J*

_{NaCa,t},

*C*

_{s},

*C*

_{t}(unknown quantities) stand for the densities of the Na

^{+}-Ca

^{2+}exchange current and membrane capacitances at the surface and t-tubular membranes. The

*f*

_{t,res}representing fraction of t-tubules resisting detubulation can be estimated from analysis of confocal images of intact and detubulated myocytes membrane-stained with di-8-ANEPPS (Pásek et al., 2008; Bryant et al., 2015).

*C*

_{t},

*C*

_{s},

*J*

_{NaCa,t}, and

*J*

_{NaCa,s}yields:Hence, the mean

*J*

_{NaCa}

**-**ratio can be expressed as:

### Monte Carlo simulation of experimental data

We reproduced what could be potentially obtained as a result of repeating a particular study by sampling a small number of cells out of a large population of either intact or detubulated cells. A random generation of sets of data was performed, using the published statistical parameters (average, s.e. and number of measured data) specified in Table 1. When log-normal distribution was used, the parameters of the data generator were adjusted to produce datasets with an arithmetic mean and s.e. close to those in Table 1. Thus, values were randomly generated for each of the five quantities (*C*_{intact}, *C*_{detub,}*J*_{NaCa,intact}, *J*_{NaCa,detub}, and *f*_{t,res}), and their averages were computed and stored as a dataset. For each dataset, the value of the mean *J*_{NaCa}-ratio was computed using Eqn 4. This was repeated 50,000 times. The distribution of the mean *J*_{NaCa}-ratio was reconstructed from the ensemble of these values. The whole procedure was performed using the computational software MATLAB v.7.2 (MathWorks, Natick, MA, USA).

## Footnotes

**Author contributions**

Conceptualization: M.P.; Methodology: M.P., J.S., G.C.; Software: M.P., G.C.; Formal analysis: M.P., J.S., G.C.; Writing - original draft: M.P.; Writing - review & editing: J.S., M.B., G.C.; Project administration: M.B.; Funding acquisition: M.B.

**Funding**

This study was supported by the Akademie věd České Republiky (RVO: 61388998) and the Ministerstvo Zdravotnictví Ceské Republiky (16-30571A). Georges Christé's work was supported by Université Claude Bernard Lyon 1 statutory research allowances to the EA4612 Neurocardiology Unit.

## Peer review history

The peer review history is available online at https://journals.biologists.com/jcs/article-lookup/doi/10.1242/jcs.258228

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**Competing interests**

The authors declare no competing or financial interests.