Calcium Transient and Sodium-Calcium Exchange Current in Human versus Rabbit Sinoatrial Node Pacemaker Cells

Abstract

There is an ongoing debate on the mechanism underlying the pacemaker activity of sinoatrial node (SAN) cells, focusing on the relative importance of the “membrane clock” and the “Ca²⁺ clock” in the generation of the small net membrane current that depolarizes the cell towards the action potential threshold. Specifically, the debate centers around the question whether the membrane clock-driven hyperpolarization-activated current, 𝐼_𝑓, which is also known as the “funny current” or “pacemaker current,” or the Ca²⁺ clock-driven sodium-calcium exchange current, 𝐼_NaCa, is the main contributor to diastolic depolarization. In our contribution to this journal’s “Special Issue on Cardiac Electrophysiology,” we present a numerical reconstruction of 𝐼_𝑓 and 𝐼_NaCa in isolated rabbit and human SAN pacemaker cells based on experimental data on action potentials, 𝐼_𝑓, and intracellular calcium concentration ([Ca²⁺]_𝑖) that we have acquired from these cells. The human SAN pacemaker cells have a smaller 𝐼_𝑓, a weaker [Ca²⁺]_𝑖 transient, and a smaller 𝐼_NaCa than the rabbit cells. However, when compared to the diastolic net membrane current, 𝐼_NaCa is of similar size in human and rabbit SAN pacemaker cells, whereas 𝐼_𝑓 is smaller in human than in rabbit cells.

1. Introduction

Animal studies have demonstrated that pacemaker activity of the sinoatrial node (SAN) is controlled by a complex system of “clocks” composed of voltage-dependent sarcolemmal currents—designated the “membrane clock,” “voltage clock,” or “ion channel clock”—and tightly coupled sarcoplasmic reticulum (SR) Ca²⁺ cycling molecules together with the electrogenic sodium-calcium exchanger, named the “Ca²⁺ clock” [1, 2]. There is an ongoing debate on the relative importance of the “membrane clock” and the “Ca²⁺ clock” in the generation of the small net membrane current underlying the spontaneous diastolic depolarization that drives the cell towards its action potential threshold [3–7]. This debate centers around the contribution of the hyperpolarization-activated current 𝐼_𝑓, also known as “funny current” or “pacemaker current,” as a member of the membrane clock, and the sodium-calcium exchange current 𝐼_NaCa, resulting from the electrogenic sodium-calcium exchange process and thus driven by the Ca²⁺ clock.

In contrast with the data collected in animal studies, the mechanism of SAN pacemaker activity in man is virtually unexplored. In a comprehensive study, Chandler et al. [8] characterized the “molecular architecture” of the human SAN based on messenger RNA (mRNA) levels of 120 ion channels and related proteins, and they concluded that the expression pattern was appropriate to explain pacemaking. They observed a prominent expression of HCN4 and, to a lesser extent, HCN1, which are both subunits of the 𝐼_𝑓 channel. We actually recorded 𝐼_𝑓 in voltage clamp experiments on single pacemaker cells isolated from the SAN of a patient who underwent SAN excision [9]. From these cells, we also acquired spontaneous action potentials, which showed a clear diastolic depolarization phase resulting in an intrinsic cycle length of ≈830 ms (72 beats/min). In addition, our voltage clamp experiments revealed the presence of a fast large inward current with characteristics of the Na⁺ current, 𝐼_Na [10].

Clinical data also point to a role for 𝐼_𝑓 and 𝐼_Na in human SAN pacemaker activity. Mutations in HCN4 and SCN5A, encoding pore-forming subunits of the 𝐼_𝑓 and 𝐼_Na channel, respectively, have been linked to familial sick sinus syndrome (see [11, 12] and primary references cited therein), thus suggesting that 𝐼_𝑓 and 𝐼_Na indeed contribute to human SAN pacemaker activity. A further clinical indication regarding the role of a specific ion current in human SAN pacemaker activity involves the slowly activating delayed rectifier K⁺ current (𝐼_Ks) and comes from patients who suffer from the long-QT syndrome type 1 and carry a loss-of-function mutation in the KCNQ1 (KvLQT1) gene, encoding the pore-forming α-subunit of the 𝐼_Ks channel. These patients have close-to-normal heart rates in rest [13], but their ability to increase heart rate during exercise is seriously impaired [14].

The aforementioned experimental and clinical observations all point to a role for important components of the “membrane clock” in human SAN pacemaker activity. There are also some clinical data in support of a contribution of the “Ca²⁺ clock” through patients with catecholaminergic polymorphic ventricular tachycardia (CPVT), who have an impaired Ca²⁺ clock due to mutations in the RYR2 gene (CPVT1) or the CASQ2 gene (CPVT2), encoding the cardiac ryanodine receptor isoform 2 (RyR2, responsible for Ca²⁺ release from the SR) and the cardiac calsequestrin isoform 2 protein (calsequestrin-2, responsible for calcium buffering in the SR), respectively [15]. Leenhardt et al. [16] observed a marked sinus bradycardia in a group of 21 nongenotyped CPVT patients. Sumitomo et al. [17] also reported sinus bradycardia in their group of 29 nongenotyped CPVT patients. At the time of the reports by Leenhardt et al. [16] and Sumitomo et al. [17], CPVT had not yet been associated with the RYR2 and CASQ2 genes. More recently, Postma et al. [18, 19] found a marked sinus bradycardia in both CPVT1 [18] and CPVT2 [19] patients.

Chandler et al. [8] observed various Ca²⁺-handling proteins in the human SAN, albeit less abundant than in the surrounding right atrium, including NCX1 (responsible for sodium-calcium exchange in the heart), RyR2, and SERCA2a (responsible for Ca²⁺ uptake by the SR). They constructed a mathematical model of a human SAN cell by modification of the Courtemanche et al. [20] model of a human atrial myocyte, scaling ion current densities on the basis of the relative mRNA expression level in SAN and atrium and introducing the T-type Ca²⁺ current and 𝐼_𝑓. Specifically, 𝐼_NaCa was scaled down to 74% of its value in the Courtemanche et al. [20] model. Recently, Allah et al. [21] published a study in which they used the same experimental approach as Chandler et al. [8] to determine the expression of ion channels and Ca²⁺ handling proteins in the SAN, right atrium, and left ventricle of the neonate and adult rabbit. From their Figure 6 [21], it appears that the mRNA expression level of the NCX1 gene in the adult rabbit SAN is ≈78% and ≈69% of that in right atrium and left ventricle, respectively.

When we recorded action potentials from isolated human SAN pacemaker cells and carried out voltage clamp experiments [9], we also acquired some data on the intracellular free Ca²⁺ concentration ([Ca²⁺]_𝑖) of human SAN pacemaker cells using the fluorescent Ca²⁺ indicator Indo-1. In the present study, we use these thus far unpublished experimental data in a numerical reconstruction of 𝐼_NaCa in a human SAN pacemaker cell. The thus obtained 𝐼_NaCa is compared to the net membrane current (𝐼_net) and to 𝐼_𝑓, which are also obtained through a numerical reconstruction. In addition, we present data on 𝐼_𝑓, 𝐼_NaCa, and 𝐼_net in rabbit SAN pacemaker cells, thus allowing a comparison of these currents between rabbit and human SAN pacemaker cells.

2. Materials and Methods

2.1. Cell Preparations

Single SAN cells were isolated by an enzymatic dissociation procedure as described previously [22] from New Zealand White rabbits and from a patient who underwent SAN excision because of inappropriate sinus tachycardias originating from the SAN region (see [9] for clinical details). In either case, cells were stored at room temperature for at least 45 min in modified Kraft-Brühe (KB) solution before they were put into a recording chamber on the stage of an inverted microscope and superfused with modified Tyrode’s solution at 36±0.2°C. KB solution contained (in mM) KCl 85, K₂HPO₄ 30, MgSO₄ 5.0, glucose 20, pyruvic acid 5.0, creatine 5.0, taurine 30, 𝛽-hydroxybutyric acid 5.0, succinic acid 5.0, BSA 1%, and Na₂ATP 2.0; pH was set to 6.9 with KOH. Modified Tyrode’s solution contained (in mM) NaCl 140, KCl 5.4, CaCl₂ 1.8, MgCl₂ 1.0, glucose 5.5, and HEPES 5.0; pH was set to 7.4 with NaOH. Spindle and elongated spindle-like cells displaying regular contractions were selected for measurements.

2.2. Cytosolic Ca²⁺ Measurements

Cytosolic Ca²⁺ concentration ([Ca²⁺]_𝑖) was measured in Indo-1 loaded cells as described previously [23]. In brief, cells were loaded with 5 µM of the fluorescent dye Indo-1-AM (Molecular Probes, Eugene, OR, USA) for 10 min at room temperature in KB solution and subsequently superfused with modified Tyrode’s solution for 15 min at 36±0.2°C to remove excess indicator and allow full deesterification. A rectangular adjustable slit was used to select a single cell and to reduce background fluorescence. Dual wavelength emission of Indo-1 upon excitation at 340 nm was recorded at 405–440 and 505–540 nm using photomultiplier tubes, and, after correction for background fluorescence, free [Ca²⁺]_𝑖 was calculated as described by van Borren et al. [23].

[Ca²⁺]_𝑖 transients were characterized by the minimum diastolic [Ca²⁺]_𝑖 (MDC), their amplitude (TA), their maximum rate of rise (d[Ca²⁺]_𝑖/d𝑡_max), their duration measured at 20, 50, and 90% decay (TD₂₀,TD₅₀, and TD₉₀, resp.), and their frequency. Parameter values obtained from 10 consecutive [Ca²⁺]_𝑖 transients were averaged.

2.3. Action Potential Measurements

Action potentials from rabbit and human SAN cells were recorded with the amphotericin-perforated and conventional whole-cell configuration of the patch-clamp technique, respectively, using an Axopatch 200B patch-clamp amplifier (Molecular Devices Corporation, Sunnyvale, CA, USA). For recording from rabbit SAN cells, pipettes (borosilicate glass; resistance 2–5 MΩ) were filled with solution containing (in mM) K-gluconate 120, KCl 20, NaCl 5, amphotericin B 0.22, NMDGCl (N-methyl-D-glucammonium chloride) 10, and HEPES 10; pH was set to 7.2 with KOH. For recording from human SAN cells, patch pipettes contained (in mM) K-gluconate 125, KCl 20, NaCl 5, MgCl₂ 1, MgATP 5, and HEPES 10; pH was set to 7.2 with KOH.

Action potentials were characterized by their frequency, their duration at 20, 50, and 90% repolarization (APD₂₀,APD₅₀, and APD₉₀, resp.), maximum diastolic potential (MDP), action potential amplitude (APA), maximum upstroke velocity (d𝑉_𝑚/d𝑡_max), and diastolic depolarization rate measured over the 100 ms time interval starting at MDP+1 mV (DDR₁₀₀). Parameter values obtained from 10 consecutive action potentials were averaged. All membrane potential values were corrected for the calculated liquid junction potential.

2.4. Numerical Reconstruction of Hyperpolarization-Activated Current

For the numerical reconstruction of both rabbit and human 𝐼_𝑓, we used a first-order Hodgkin and Huxley [24] type kinetic scheme. Accordingly, 𝐼_𝑓 is given by 𝐼_𝑓=𝑦×𝑔_𝑓×𝑉_𝑚−𝐸_𝑓, (1) in which 𝑔_𝑓 is the fully activated 𝐼_𝑓 conductance, 𝑉_𝑚 is the membrane potential, 𝐸_𝑓 is the 𝐼_𝑓 reversal potential, and the gating variable 𝑦, with 0≤𝑦≤1, obeys the first-order differential equation d𝑦d𝑡=𝛼×1−𝑦−𝛽×𝑦, (2) with voltage-dependent rate constants 𝛼 and 𝛽, or, equivalently, d𝑦=𝑦d𝑡^∞−𝑦𝜏, (3) with the steady-state activation 𝑦_∞ and time constant 𝜏 given by 𝑦_∞=𝛼,1𝛼+𝛽𝜏=.𝛼+𝛽 (4)(5)

For rabbit 𝐼_𝑓, we used the model by Dokos et al. [25], who based their equations on the comprehensive experimental study on rabbit 𝐼_𝑓 by van Ginneken and Giles [26], arriving at 𝑉𝛼=0.36×_𝑚+137.8exp0.066×𝑉_𝑚,𝑉+137.8−1𝛽=0.1×_𝑚+76.31−exp−0.21×𝑉_𝑚,+76.3 (6) for the rate constants 𝛼 and 𝛽, both expressed in s⁻¹. In our computations, we used a scaling factor of 0.71665 for the time constant 𝜏 (5) as a correction factor for the temperature of 30–33°C in the experiments of van Ginneken and Giles [26]. This correction factor was adopted from the SAN cell models by Kurata et al. [27] and Maltsev and Lakatta [28]. With the bath and pipette Na⁺ and K⁺ concentrations listed in Sections 2.1 and 2.3, the reversal potential of the Dokos et al. [25] model amounts to −21.0 mV. For the fully activated 𝐼_𝑓 conductance, we used a value of 0.218 pS/pF, based on the mean values of 12.0 nS and 55 pF for the fully activated conductance and membrane capacitance, respectively, reported by van Ginneken and Giles [26].

For human 𝐼_𝑓, we used the model that we developed on the basis of our voltage clamp data on human SAN cells [9]. In this model [29, 30], 𝑦_∞ and 𝜏 (in ms) are given by 𝑦_∞=0.01329+0.999211+exp𝑉_𝑚+97.134/8.1752if𝑉_𝑚𝑦<−80mV,_∞=0.0002501×exp−𝑉_𝑚12.861if𝑉_𝑚×𝑉≥−80mV,𝜏=1000×0.36_𝑚+148.8exp0.066×𝑉_𝑚×𝑉+148.8−1+0.1_𝑚+87.31−exp−0.21×𝑉_𝑚+87.3⁻¹−54, (7)(8) respectively. The fully activated 𝐼_𝑓 conductance 𝑔_𝑓 and the 𝐼_𝑓 reversal potential 𝐸_𝑓 were set to 0.075 nS/pF and −22 mV, respectively, in accordance with the fully activated 𝐼_𝑓 conductance of 75.2±3.8 pS/pF (mean±SEM, 𝑛=3) and 𝐼_𝑓 reversal potential of −22.1mV±2.4mV (mean±SEM, 𝑛=3) determined experimentally [9].

The numerical reconstruction was carried out on an Intel Xeon based workstation using Compaq Visual Fortran 6.6C and employing a simple and efficient Euler-type integration scheme with a time step of 10 µs. Simulations were run for a sufficiently long time to achieve steady-state conditions.

2.5. Numerical Reconstruction of Sodium-Calcium Exchange Current

For the numerical reconstruction of human 𝐼_NaCa on the basis of the recorded data on 𝑉_𝑚 and [Ca²⁺]_𝑖 (combined voltage and calcium clamp [31]), we adopted the 𝐼_NaCa formulation of the Courtemanche et al. [20] model for a human atrial myocyte, with 𝐼_NaCa scaled down to 74% of its control value. We thus followed the approach by Chandler et al. [8] in their construction of a mathematical model of a human SAN cell by modification of the Courtemanche et al. [20] model, as set out in the Introduction.

We used a similar approach for the numerical reconstruction of rabbit 𝐼_NaCa on the basis of the acquired data on 𝑉_𝑚 and [Ca²⁺]_𝑖. In this case, we adopted the 𝐼_NaCa formulation of the Lindblad et al. [32] model for a rabbit atrial myocyte. However, the original 𝐼_NaCa was scaled down to 78% of its control value, based on the mRNA data by Allah et al. [21], as detailed in the Introduction.

The Courtemanche et al. [20] and Lindblad et al. [32] equations not only require values for 𝑉_𝑚 and [Ca²⁺]_𝑖, but also for [Ca²⁺]_𝑒,[Na⁺]_𝑒 and [Na⁺]_𝑖, which denote the extracellular Ca²⁺ concentration, the extracellular Na⁺ concentration, and the intracellular Na⁺ concentration, respectively. For these ion concentrations, we used the bath and pipette solutions listed in Sections 2.1 and 2.3.

2.6. Statistics

Data are presented as mean±SEM. Comparisons between groups were made using an unpaired t-test. The level of significance was set at 𝑃<0.05.

3. Results

For the present study, we first characterized the action potentials and [Ca²⁺]_𝑖 transients that we recorded from single rabbit and human SAN pacemaker cells. Next, we used our experimental data for a numerical reconstruction of the hyperpolarization-activated current and the sodium-calcium exchange current associated with the recorded action potentials and [Ca²⁺]_𝑖 transients, thus allowing a comparison of these currents between rabbit and human SAN pacemaker cells.

3.1. Rabbit and Human Action Potentials

Figure 1(a) shows typical examples of the spontaneous action potentials of rabbit and human SAN pacemaker cells, recorded with the patch-clamp technique. Maximum diastolic potential (MDP) and action potential amplitude (APA) are remarkably similar, whereas the beating frequency is strikingly different, as confirmed by the mean value of 3.11±0.24 Hz for the 7 rabbit cells versus 1.21±0.02 Hz for the 3 human cells (𝑃<0.05) and illustrated in Figure 1(b).

Figure 1 

Spontaneous electrical activity of rabbit and human sinoatrial node (SAN) pacemaker cells. (a) and (b) Typical examples (a) and average characteristics (b) of action potentials. (c) and (d) Typical examples (c) and average characteristics (d) of the intracellular free Ca2+ concentration ([Ca2+]𝑖). Data are mean±SEM; 𝑛=number of cells; MDP=maximum diastolic potential; APA=action potential amplitude; DDR100=diastolic depolarization rate over the 100 ms time interval starting at MDP+1 mV; d𝑉𝑚/d𝑡max=maximal upstroke velocity; APD20,APD50, and APD90=action potential duration at 20, 50, and 90% repolarization; MDC=minimum diastolic [Ca2+]𝑖; TA=[Ca2+]𝑖 transient amplitude; d[Ca2+]𝑖/d𝑡max=maximum rate of rise of [Ca2+]𝑖 transient; TD20,TD50, and TD90=[Ca2+]𝑖 transient duration at 20, 50, and 90% decay. ∗𝑃<0.05.

Neither the action potential durations, for example, the APD₉₀ of 144±35 versus 113±6 ms, nor the diastolic depolarization rate of 49±18 versus 89±19 mV/s differ significantly between human and rabbit SAN cells, which is likely due to the low number of cells of human origin. Nevertheless, from Figure 1(a), it is indicative that the longer cycle length of the human cells (828±15 versus 337±35 ms) is importantly due to longer diastolic depolarization rather than longer action potential duration. A further difference is found in the maximum rate of rise of the action potential, which is considerably larger in the rabbit cells (13.0±1.6 versus 4.6±1.2 V/s, 𝑃<0.05; Figure 1(b)).

3.2. Rabbit and Human [Ca²⁺]_𝑖 Transients

In the 7 rabbit cells of Figure 1(b), we simultaneously recorded the membrane potential, using the perforated patch-clamp technique, and the [Ca²⁺]_𝑖 transient, using the fluorescent Ca²⁺ indicator Indo-1. A typical example of such [Ca²⁺]_𝑖 transient, recorded from the same cell and during the same period of time as used for Figure 1(a), is provided in Figure 1(c). Also shown in Figure 1(c) is the [Ca²⁺]_𝑖 transient that we were able to record from a single human SAN cell. Further attempts to acquire the [Ca²⁺]_𝑖 transient of human cells resulted in unstable recordings. Of note, no action potentials are available from the cell that we recorded the [Ca²⁺]_𝑖 transient from. So, in contrast with the rabbit data, the human data of Figures 1(a) and 1(c) are not simultaneously collected and are not from the same cell.

The minimum diastolic [Ca²⁺]_𝑖 level of the human cell is similar to that of the rabbit cells, but otherwise the [Ca²⁺]_𝑖 transients are widely different, with a smaller amplitude, longer duration, and smaller rate of rise in case of the human cell, as illustrated in Figure 1(d), in which the characteristics of the [Ca²⁺]_𝑖 transient of the human cell are compared to those of the mean characteristics in the 7 rabbit cells.

As illustrated in Figure 2(a) for the simultaneously recorded action potential (top) and [Ca²⁺]_𝑖 transient (bottom) of a rabbit SAN cell, the maximum rate of rise of the [Ca²⁺]_𝑖 transient, as determined from the time derivative of the [Ca²⁺]_𝑖 transient signal (Figure 2(b), bottom), occurs with a time lag relative to the maximum rate of rise of the associated action potential, as determined from the time derivative of the 𝑉_𝑚 signal (Figure 2(b), top). This time lag between the occurrence of d𝑉_𝑚/d𝑡_max and d[Ca²⁺]_𝑖/d𝑡_max was determined for each of the 7 rabbit SAN cells tested and amounted to 21.3±0.6 ms. The time lag ranged between 19 and 23 ms and showed no appreciable frequency dependence, as illustrated in Figure 2(c), in which the time lag is plotted versus the spontaneous beating frequency.

(a)

(b)

(c)

Figure 2 

(a), Simultaneously recorded action potential (top) and [Ca2+]𝑖 transient (bottom) of a rabbit SAN cell. (b) Time derivatives of the action potential (top) and [Ca2+]𝑖 transient (bottom) traces shown in panel (a). Arrows indicate the timing of the maximum rate of change in membrane potential (d𝑉𝑚/d𝑡max) and intracellular Ca2+ concentration (d[Ca2+]𝑖/d𝑡max). Horizontal bar indicates the time lag of ≈20 ms. (c) Time lag between the occurrence of d𝑉𝑚/d𝑡max and d[Ca2+]𝑖/d𝑡max versus beating frequency of the 7 cells measured. Solid line is the linear regression line (slope 0.1±1.1;𝑅=0.042). Note the absence of an appreciable frequency dependence of the time lag.

3.3. Numerical Reconstruction of Membrane Ionic Currents

Next, we carried out a numerical reconstruction of the hyperpolarization-activated current (𝐼_𝑓) and the sodium-calcium exchange current (𝐼_NaCa) of rabbit and human SAN pacemaker cells based on the experimental data on their action potentials and [Ca²⁺]_𝑖 transients presented in Figures 1 and 2.

3.3.1. Experimental Data

For the reconstruction of rabbit membrane ionic currents, we used a 1-s simultaneous recording of 𝑉_𝑚 and [Ca²⁺]_𝑖 of one of the 7 rabbit cells that we digitized at 10 kHz through linear interpolation of the acquired data points. This 1-s recording contained three action potentials and associated [Ca²⁺]_𝑖 transients and was turned into a continuous signal by repeating the 1-s signal. Because of the repetition of the 1-s signal, the fourth and fifth action potentials of Figure 3(a) (left) are identical to the first and second, respectively. The same holds for the associated [Ca²⁺]_𝑖 transients, which are shown in Figure 3(b) (left).

(a)

(b)

(c)

(d)

(e)

Figure 3 

Action potential and calcium transient recordings from rabbit (left) and human (right) SA nodal myocytes and associated numerical reconstructions of membrane currents. (a) Recorded membrane potential 𝑉𝑚. (b) Recorded intracellular calcium concentration ([Ca2+]𝑖). (c) Time derivative of 𝑉𝑚 (d𝑉𝑚/d𝑡). (d) Reconstructed hyperpolarization-activated inward current (𝐼𝑓). The noisy trace in gray is the net membrane current (𝐼net) computed from 𝐼net=−𝐶𝑚×d𝑉𝑚/d𝑡, where 𝐶𝑚 denotes membrane capacitance. (e) Reconstructed sodium-calcium exchange current (𝐼NaCa), with the net membrane current in gray.

A similar approach, now using a ≈1.6 s time frame, was used in case of the human cell data. However, because data on 𝑉_𝑚 and [Ca²⁺]_𝑖 were not simultaneously collected, we selected two consecutive action potentials with cycle lengths of 791 and 822 ms—human SAN pacemaker cells show a beat-to-beat fluctuation in cycle length as do rabbit cells [33]—and two consecutive [Ca²⁺]_𝑖 transients that, by coincidence, had identical cycle lengths. Furthermore, for the timing of the two signals, it was assumed that the time lag between the occurrence of d𝑉_𝑚/d𝑡_max and d[Ca²⁺]_𝑖/d𝑡_max was 21 ms, as observed in the rabbit cells (Figure 2(c)). The resulting 𝑉_𝑚 and [Ca²⁺]_𝑖 data are shown in the right panels of Figures 3(a) and 3(b).

3.3.2. Numerical Reconstruction of Net Membrane Current

As a reference for 𝐼_𝑓 and 𝐼_NaCa, we first determined the net membrane current (𝐼_net) in both rabbit and human cells. Because 𝐼_net=−𝐶_𝑚×d𝑉_𝑚/d𝑡, where 𝐶_𝑚 denotes membrane capacitance, the current density of 𝐼_net is identical to −d𝑉_𝑚/d𝑡 and thus readily follows from the time derivative of the action potential, which is shown in Figure 3(c) for the action potentials of Figure 3(a). In the diastolic voltage range, 𝐼_net is a small inward current with a density of ≈0.1 and ≈0.05 pA/pF in rabbit and human, respectively (Figures 3(d) and 3(e), gray traces), in line with the mean diastolic depolarization rate of 89±19 and 49±18 mV/s, respectively (Figure 1(b)). Figure 3(c) also confirms the data of Figure 1(b) regarding the smaller d𝑉_𝑚/d𝑡_max in human versus rabbit SAN cells.

3.3.3. Numerical Reconstruction of Hyperpolarization-Activated Current

The action potentials of Figure 3(a) were applied as a voltage clamp signal in order to reconstruct the hyperpolarization-activated current 𝐼_𝑓, as detailed in Section 2.4. The resulting 𝐼_𝑓 traces are shown in Figure 3(d). There is an almost 7-fold difference in diastolic 𝐼_𝑓 amplitude between rabbit and human, which becomes less pronounced when compared to the net membrane current, 𝐼_net, in each of the cell types. In rabbit, diastolic 𝐼_𝑓 is 2-3 times 𝐼_net, whereas diastolic 𝐼_𝑓 and 𝐼_net are of similar size in human.

3.3.4. Numerical Reconstruction of Sodium-Calcium Exchange Current

The 𝑉_𝑚 and [Ca²⁺]_𝑖 data of Figures 3(a) and 3(b) were applied as a combined voltage and calcium clamp signal in order to reconstruct the sodium-calcium exchange current 𝐼_NaCa in human and rabbit SAN cells, as detailed in Section 2.5. The resulting 𝐼_NaCa is smaller in amplitude in human than in rabbit (Figure 3(e)). However, in either case, the mid-diastolic 𝐼_NaCa amplitude is roughly twice that of 𝐼_net. The end-diastolic amplitude of 𝐼_NaCa at −45 mV is ≈0.07 pA/pF in human, which is ≈25% of the value of ≈0.28 pA/pF in rabbit.

3.3.5. Charge Carried by Individual Currents

From the current traces of Figures 3(d) and 3(e), one can compute the contribution to diastolic depolarization in terms of charge carried by 𝐼_net,𝐼_𝑓, and 𝐼_NaCa through integration of each of these currents over time. We carried out such computation for the 20 mV spontaneous depolarization from MDP+1 mV of the rabbit and human action potentials of Figure 3(a). As shown in Figure 4 (left bars), the thus computed charge carried by 𝐼_net(𝑄_net) amounts to 0.020 pC/pF for both rabbit and human, as expected from the 20 mV depolarization, which is equivalent to a charge flow of 0.02 pC/pF. The charge carried by 𝐼_𝑓(𝑄_𝑓) is 0.043 and 0.018 pC/pF for rabbit and human, respectively, whereas that carried by 𝐼_NaCa(𝑄_NaCa) amounts to 0.055 and 0.047 pC/pF, respectively (Figure 4, middle and right bars).

Figure 4 

Charge carried by net membrane current (𝑄net), reconstructed hyperpolarization-activated inward current (𝑄𝑓), and reconstructed sodium-calcium exchange current (𝑄NaCa) during 20 mV spontaneous depolarization from MDP+1 mV of the rabbit and human SA nodal action potentials of Figure 3.

4. Discussion

In the present study, we first characterized the action potentials and [Ca²⁺]_𝑖 transients that we recorded from single rabbit and human SAN pacemaker cells. Next, we used our experimental data for a numerical reconstruction of the hyperpolarization-activated current and the sodium-calcium exchange current associated with the recorded action potentials and [Ca²⁺]_𝑖 transients.

4.1. Experimental Data

Human SAN pacemaker cells have a lower beating frequency and a lower maximum upstroke velocity than rabbit SAN pacemaker cells (Figures 1(a) and 1(b)). Also, they have a considerably weaker [Ca²⁺]_𝑖 transient (Figures 1(c) and 1(d)), which may, at least in part, be a frequency effect, as observed in rabbit cells [23]. The longer cycle length of the human cells is largely due to a longer diastolic phase (Figures 1(a) and 1(b)). In this respect, the recorded action potentials differ from those that Chandler et al. [8] computed by turning the Courtemanche et al. [20] human atrial cell model into a human SAN pacemaker cell model. On the other hand, the range of the computed calcium signal (approximately 150–250 nM; Figure 8 of Chandler et al. [8]) compares reasonably well with the experimentally observed range (roughly 110–220 nM; Figures 1(c) and 1(d)).

As an important caveat, it should be noted that our data on human cells have been collected from only a small number of cells, all from a single patient who underwent SAN excision because of tachycardias [9]. Stable action potential recordings were obtained from three cells and a stable calcium transient recording from only one cell. Furthermore, although almost identical experimental methods were employed, the use of the perforated-patch configuration of the patch-clamp technique in case of the rabbit cells and the conventional whole-cell configuration in case of the human cells may have introduced deviations.

4.2. Numerical Reconstructions

In our numerical reconstruction of rabbit 𝐼_𝑓, we used the Dokos et al. [25] equations based on a reanalysis of the data by van Ginneken and Giles [26] rather than the equations provided by van Ginneken and Giles [26] themselves. In the latter equations, the 𝐼_𝑓 deactivation rate is erroneously overestimated, as set out in detail by Dokos et al. [25]. As a result, the reconstructed 𝐼_𝑓 of Figure 3(d) (left) is larger than in rabbit SAN cell models that employ the van Ginneken and Giles equations, such as the models by Kurata et al. [27] and Maltsev and Lakatta [28]. Furthermore, the more negative maximum diastolic potential of the recorded action potentials adds to the larger 𝐼_𝑓. The availability of 𝐼_𝑓 almost immediately after repolarization and its amplitude larger than that of 𝐼_net are in line with the data from action potential clamp experiments on rabbit SAN cells carried out by Zaza et al. [34]. The reconstructed human 𝐼_𝑓 trace compares well with the traces that we previously reconstructed for the other two human SAN pacemaker cells from which action potentials are available [12].

In our numerical reconstruction of 𝐼_NaCa, we used equations from rabbit and human atrial cell models—properly scaled to account for the reduced mRNA expression of NCX1 in the SAN versus the atrium, both in human [8] and in rabbit [21]—that allowed the reconstruction of 𝐼_NaCa from the experimentally recorded membrane potential and global cytosolic [Ca²⁺]_𝑖. Today, there are highly detailed models of calcium handling in (rabbit) SAN cells [28, 35], but for a reconstruction of 𝐼_NaCa, these would require experimental data on [Ca²⁺]_𝑖 in submembrane spaces rather than global cytosolic [Ca²⁺]_𝑖. In human cells, the total charge carried by 𝐼_𝑓 during spontaneous diastolic depolarization is similar to that carried by 𝐼_net, whereas in rabbit it is approximately twice (Figure 4).

Of note, the diastolic 𝐼_NaCa amplitude at −45 mV of ≈0.28 pA/pF in rabbit (Figure 3(e), left) is identical to the value of 0.28±0.03 pA/pF that Vinogradova et al. [36] observed experimentally. A highly similar amplitude is obtained (data not shown) if 𝐼_NaCa is not reconstructed from the Lindblad et al. [32] equations but from the equations for a ventricular cell provided by Faber and Rudy [37], scaled down to 69% to account for the mRNA data by Allah et al. [21].

Human 𝐼_NaCa is smaller than that of rabbit (Figure 3(e)). This is not only due to the smaller 𝐼_NaCa in the human versus the rabbit atrial cell model from which the equations were adopted for the reconstruction. What also plays a role is that the experimentally recorded [Ca²⁺]_𝑖 is smaller in human than in rabbit at all values of 𝑉_𝑚. Yet, the total charge carried by 𝐼_NaCa during spontaneous diastolic depolarization is of similar magnitude in rabbit and human (Figure 4).

5. Conclusion

Human SAN pacemaker cells have a smaller 𝐼_𝑓, a weaker [Ca²⁺]_𝑖 transient, and a smaller 𝐼_NaCa than rabbit SAN pacemaker cells. However, when compared to the diastolic net membrane current, 𝐼_NaCa is of similar size in human and rabbit cells, whereas 𝐼_𝑓 is smaller in human than in rabbit cells.

Conflict of Interests

The authors declare that they have no conflict of interests.