Diastolic Calcium Release Controls the Beating Rate of Rabbit Sinoatrial Node Cells: Numerical Modeling of the Coupling Process

Abstract

Recent studies employing Ca²⁺ indicators and confocal microscopy demonstrate substantial local Ca²⁺ release beneath the cell plasma membrane (subspace) of sinoatrial node cells (SANCs) occurring during diastolic depolarization. Pharmacological and biophysical experiments have suggested that the released Ca²⁺ interacts with the plasma membrane via the ion current (I_NaCa) produced by the Na⁺/Ca²⁺ exchanger and constitutes an important determinant of the pacemaker rate. This study provides a numerical validation of the functional importance of diastolic Ca²⁺ release for rate control. The subspace Ca²⁺ signals in rabbit SANCs were measured by laser confocal microscopy, averaged, and calibrated. The time course of the subspace [Ca²⁺] displayed both diastolic and systolic components. The diastolic component was mainly due to the local Ca²⁺ releases; it was numerically approximated and incorporated into a SANC cellular electrophysiology model. The model predicts that the diastolic Ca²⁺ release strongly interacts with plasma membrane via I_NaCa and thus controls the phase of the action potential upstroke and ultimately the final action potential rate.

INTRODUCTION

Recent studies employing Ca²⁺ indicators together with confocal microscopy demonstrate substantial cyclic intracellular Ca²⁺ changes beneath the cell plasma membrane of sinoatrial node cells (SANCs) (Bogdanov et al., 2001; Vinogradova et al., 2002). Pharmacological and biophysical experiments have suggested that those cyclic variations of submembrane Ca²⁺ are an important determinant of the pacemaker firing rate, and thus represent a critical factor determining pacemaker cell dominance, as well as for achieving the maximum possible chronotropic effect under hormonal stimulation of the heart (Lakatta et al., 2003). An important experimental finding was that part of the cyclic Ca²⁺ release occurs in the form of localized events during diastolic depolarization (CRDD). The spontaneous (voltage-independent) nature of the diastolic release has been recently demonstrated in voltage-clamp experiments and in experiments in saponin-permeabilized SANCs (Vinogradova et al., 2004). It was suggested that CRDD could accelerate the diastolic depolarization (DD) via inward current (I_NaCa) produced by Na⁺/Ca²⁺ exchanger (NCX) and thus control the SANC rate.

Until recently numerical SANC models available in the literature have not considered local [Ca²⁺] changes. Accordingly, they were unable to reproduce many recent experimental findings such as chronotropic effects of intracellular Ca²⁺ buffering and sarcoplasmic reticulum (SR) function modulation. The role of [Ca²⁺] changes in the submembrane space has been introduced in a new SANC model by Kurata et al. (2002). In contrast to previous SANC models, this model can reproduce some Ca²⁺-related phenomena including different effects of BAPTA and EGTA on the SANC beating rate. However, the model still cannot explain many experimental findings such as spontaneous Ca²⁺ release during DD and the chronotropic effect of blocking SR calcium release with ryanodine (Bogdanov et al., 2001; Li et al., 1997; Rigg and Terrar, 1996). Furthermore, quantitative intracellular Ca²⁺ concentrations ([Ca²⁺]) in the subspace of SANCs have not previously been measured. The aim of this study was to measure [Ca²⁺] and to characterize the diastolic part of the Ca²⁺ release in the subspace so that it could be approximated numerically and included in a new primary pacemaker cell model to provide numerical validation to the implied functional importance of the cyclic spontaneous Ca²⁺ release during DD for the SANC pacemaker function.

MATERIALS AND METHODS

Sinus node cell preparations and electrophysiological recordings

Single sinoatrial nodal cells were isolated from rabbit hearts as previously described (Vinogradova et al., 2000). We studied spindle-shaped sinoatrial nodal cells that exhibited spontaneous contractions in normal Tyrode solution containing 1.8 mM Ca²⁺. Perforated patch-clamp technique with 50 μM β-escin (Fan and Palade, 1998) added to the pipette solution was employed to record spontaneous action potentials (AP) with an Axopatch-200 B patch-clamp amplifier (Axon Instruments, Foster City, CA). The bath solution had the following composition (in mM): NaCl, 140; KCl, 5.4; MgCl₂, 1; HEPES, 5; CaCl₂, 1.8; Glucose, 5.5; pH, 7.4. The pipette solution contained (in mM): K-gluconate, 120; NaCl, 10; MgATP, 5; HEPES, 5; KCl, 20; pH, 7.2. The bath temperature was maintained at 35° ± 0.5°C.

Confocal Ca²⁺ imaging

Cells were placed on the stage of a Zeiss LSM-410 inverted confocal microscope (Carl Zeiss, Mannheim, Germany) and loaded for 15 min with 20 μM fluo-3 AM. Cellular fluo-3 fluorescence was recorded either in x–y (two-dimensional) or line-scan mode. In the line-scan mode the lines are plotted every 2–5 ms, and each line is added to the right of the preceding line to form the line-scan image. Image processing was performed with IDL software (Ver. 5.2, Research Systems, Boulder, CO). To identify and measure local CRDD, custom software was employed which selected them on the basis of their statistical deviation from the background noise (Cheng et al., 1999).

Ca²⁺ calibration

To identify absolute Ca²⁺ concentrations, the fluo-3 signals were calibrated using a procedure that was a modification of that we previously reported (Maltsev et al., 1994). In short, absolute [Ca²⁺] was calculated using a well-known equation (see e.g., Grynkiewicz et al., 1985),

where K_d is the dissociation constant for Ca²⁺-bound fluo-3 and is 864 nM at 37°C (Merritt et al., 1990). Maximum and minimum fluorescence (F_max and F_min) were determined offline in the images using the MetaMorph Imaging System (Universal Imaging, Downingtown, PA). Ca²⁺ ionophores such as ionomycin or 4-bromo A-23187 are usually used to obtain F_max. However, in SANCs, with the bath [Ca²⁺] being 1.8 mM, we found that application of 5 μM ionomycin to the bath solution did not saturate fluo-3 with Ca²⁺. To reach the saturation, the bath [Ca²⁺] was increased to 10 mM. F_min was calculated as described previously by Kao et al. (1989), taking into account that metal-free fluo-3 has 1/40 the fluorescence of the Ca²⁺ complex. Therefore,

where F_bkg was background cell fluorescence (autofluorescence) measured after cell lysis by digitonin (30 μM) in the presence of 10 mM EGTA and no Ca²⁺.

We used the x–y scans instead of the line-scan images for Ca²⁺ calibration to precisely monitor the subspace signals. When maximum fluorescence signal F_max was measured, ionomycin strongly increased intracellular [Ca²⁺] which, in turn, slightly changed the cell shape. With this change, in the line-scan mode it is difficult to maintain the precise close relative position (within 1–2 μm) of the scanning line with respect to the cell membrane. In other words, during calibration the scan line tends to miss the subspace and the signal becomes lost. The x–y scans obviously avoid this problem, inasmuch as the Ca²⁺ signals in subspace can be relatively easily identified and measured during the calibration.

Materials

All substances for Ca²⁺ calibration and for pipette and bath solutions were from Sigma (St. Louis, MO). Fluo-3-AM was purchased from Molecular Probes (Eugene, OR).

Computer simulations

Computer modeling studies were performed using Delphi-7 (Borland, Scotts Valley, CA) software. To model SANC electrophysiology we modified a recently published model of the primary pacemaker cell (Kurata et al., 2002) to include a phenomenological representation of CRDD, as described below. We received the original model text directly from Dr. Kurata.

RESULTS

The two phases of Ca²⁺ changes in the subspace

To illustrate the need for special consideration of Ca²⁺ signals in the subspace due to the inhomogeneity of Ca²⁺ changes within the cell, we oriented the scan line across the cell so that it crossed the longitudinal axis of the cell at approximately one-half of the cell depth (Fig. 1). It is clearly seen that during DD Ca²⁺ changes first occur in the subspace. We have previously shown that these Ca²⁺ changes are mainly contributed by local Ca²⁺ releases (Bogdanov et al., 2001; Vinogradova et al., 2002). The releases (shown by arrows) either terminate locally in the subspace or spread/propagate relatively slowly toward the cell center, inasmuch as SANCs lack t-tubules. The second part of the Ca²⁺ change, the systolic phase, comes simultaneously with the AP upstroke and occurs both in the subspace and in the cell center.

FIGURE 1.

Ca²⁺ signals across the cells as identified by line-scanning confocal microscopy. The scan line was oriented across the cell so that it crossed the longitudinal axis of the cell at approximately one-half of the cell depth (inset). Arrows on the confocal image show local Ca²⁺ releases in the submembrane space during diastolic depolarization. The blue line shows simultaneous recording of the membrane potential measured by the perforated patch-clamp technique.

Averaged Ca²⁺ signals in the subspace

To dissect the Ca²⁺ changes in subspace and to improve the signal/noise ratio, the details of the Ca²⁺ signals were further studied with the scanned line oriented along the longitudinal axis of the cell close to the plasma membrane. Examples of the line-scan images together with respective local Ca²⁺ signals in the subspace are shown in Fig. 2. The SANC model developed in the study describes the subspace [Ca²⁺] by a single variable, Ca_sub. On the other hand, the Ca²⁺ releases and related Ca²⁺ changes in the subspace occur as local stochastic events. To avoid the stochastic-related noise and to approximate Ca_sub for the SANC model, we averaged the local Ca²⁺ signals using a custom-made computer program. Spatial inhomogeneity was found to have negligible effect on the contribution of CRDD to whole-cell cellular electrophysiology, as discussed in detail in the Appendix. The SANC membrane almost instantly integrates any change in local electrical charge throughout its length. For example, for distances up to 100 μm, it needs <0.1 ms for almost complete charge integration by the cell capacitance. Thus, for determining membrane potential (V_m) changes, the spatial complexity of the diastolic Ca_sub changes does not seem to be important. Our computer program splits experimental raw Ca_sub traces into fragments and then averages them for further numeric approximation. Each fragment consists of two cycles identified by their peak positions. To avoid the phase shift due to various cycle lengths, we assign the same phase as t = 0 for the moment of maximum peak in the middle of the fragment. Fig. 3 shows Ca_sub signals recorded from four cells along with their respective averages, which reveal a characteristic bump-and-spike morphology reflecting the diastolic and systolic components (marked by D and S in Fig. 3), respectively. In the absence of hormonal stimulation, the amplitude of the average diastolic Ca²⁺ component varied from 23% to 30% of the systolic component (26.3 ± 1.75%, mean ± SE, n = 4). The duration of the diastolic Ca²⁺ component varied from 69 ms to 160 ms (100 ± 24 ms), remaining ∼18% of the total cycle length (18.0 ± 1.2%, n = 4).

FIGURE 2.

Ca²⁺ signaling identified by confocal line-scan imaging of SANCs in a subsarcolemmal space. The scanned line was oriented along to the longitudinal axis of the cell close to the plasma membrane (inset). The diastolic Ca²⁺ releases are indicated by arrows on the image. The respective trace of the average Ca²⁺ signal (in F/F₀ scale) processed from the whole image width is shown on the bottom panel.

FIGURE 3.

The two distinct components of Ca²⁺ signaling in submembrane space: D, the diastolic Ca²⁺ release and S, the systolic Ca²⁺ release (right panels), as identified by averaging the raw F/F₀ traces (superimposed, left panels) recorded by line-scanning confocal microscopy in four cells. The traces were split into two-cycle fragments by custom-made software and centered, assigning time = 0 for the peak in the middle (see dashed line marked as t = 0). Numbers of superimposed traces are 15, 9, 8, and 14 (left panels, from top to bottom).

Measurements of systolic and diastolic absolute Ca²⁺ levels

In addition to the Ca²⁺ signal shape, another important characteristic of our SANC model with the new diastolic Ca²⁺ component is a correct range of absolute [Ca²⁺] changes in the subspace. In this study we determined the systolic and diastolic absolute [Ca²⁺] levels in the subspace by calibrating the respective fluo-3 fluorescence signals. For this purpose, cellular fluo-3 fluorescence was recorded in x–y (two-dimensional) scan mode in a thin cell slice approximately in the middle of the cell height as confirmed by an additional scan image across the cell along the z axis (perpendicularly to the surface of the bath). The systolic and diastolic Ca²⁺ signals were identified on the x–y cell scans by appearance of bright and dark strips of fluo-3 fluorescence, respectively. We measured the signals in areas that were close to the image edge and thus presumed to reflect Ca²⁺ changes in the cell submembrane space. The absolute values of fluo-3 fluorescence were quantified offline using The MetaMorph Imaging System (Universal Imaging Corporation). In this set of Ca²⁺ calibration experiments, we acquired and processed three x–y images for each cell. The collected data were then calibrated using Ca²⁺ ionophore ionomycin (see Materials and Methods for calibration procedure details). We determined absolute [Ca²⁺] levels for diastolic and systolic phases in three cells. The average data for systolic and diastolic [Ca²⁺] levels were 1363 ± 394 nM and 204 ± 12 nM (mean ± SD, n = 3), respectively.

Approximation of the spontaneous Ca²⁺ release

The importance of the diastolic Ca²⁺ component for the DD phase and the SANC rate was then explored by means of computer modeling. Ca_sub changes, which are important for cell membrane potential control, are considered in the most recent SANC model by Kurata et al. (2002) (Fig. 4 A). The model presumes that j_rel, Ca²⁺ release flux from the junctional SR to subspace, is described by a simple quadratic function of Ca_sub, as

(1)

where Ca_rel is the Ca²⁺ concentration in the junctional SR, P_rel is the rate constant for Ca²⁺ release from the junctional SR, and K_rel is the half-maximal Ca_sub for Ca²⁺ release from the junctional SR. However, j_rel = f (Ca_sub)—i.e., it is an instantaneous relation between j_rel and Ca_sub that is generally not true. During Ca²⁺-induced Ca²⁺ release (CICR) the ryanodine receptor (RyR) channels become inactivated, terminating the Ca²⁺ release. Multiple mechanisms have been suggested for the release termination, e.g., via RyR regulation by luminal Ca²⁺ (Gyorke et al., 2002), by time-dependent inactivation and/or thermodynamically irreversible gating of RyR (Wang et al., 2002), or by a cytosolic Ca²⁺/calmodulin mechanism (Fruen et al., 2000). Robust CICR termination is the central problem of local Ca²⁺ control of cardiac excitation-contraction coupling (Stern, 1992) and is not solved yet. As the aim of this study was only to demonstrate the importance of the diastolic Ca²⁺ release for the SANC rate, we did not test a particular mechanism for RyR inactivation but rather developed a SANC Ca²⁺ release formulation based on a phenomenological representation. To approximate the experimental pattern of Ca²⁺ signals in the subspace (Fig. 3), we added to the release flux in the model a “spontaneous” Ca²⁺ release component, j_spont (Fig. 4 B),

(2)

P_rel,spont is the rate constant for the spontaneous Ca²⁺ release from the junctional SR and it determines the amplitude of the Ca²⁺ release. In this study we considered a wide range of possible P_rel variations from 0.5 ms⁻¹ as in the original Kurata et al. (2002) model (this value was misprinted in the original article) up to 10 ms⁻¹. Compared to Eq. 1, we also added the phasic factor (Fig. 4, blue line), which reflects the phase of Ca²⁺ release in the subspace and is described within each SANC cycle by one complete cycle of a cosine function, scaled by 0.5 and shifted by 0.5, that varies between 0 and 1 as

(3)

The variable t is time that is left after the previous Ca²⁺ transient peak. The release phase t_phase describes the moment when the spontaneous release begins. The total duration of the spontaneous Ca²⁺ release is described by t_width. The physiological significance of these phenomenological variables is that t_width would reflect the half-width of the temporal distribution of the signal mass of CRDDs, whereas the moment t = t_phase + t_width/2 would coincide with the maximum spontaneous release phase (when the signal mass from CRDDs reaches its maximum). The cosine function itself does not have any theoretical significance but was chosen as a phenomenological curve to model the Ca²⁺ cycling process in SANCs. The phasic factor, P_phase(t) described by Eq. 3, starts from 0 at the beginning of the spontaneous release phase (t = t_phase) and after reaching its peak (P_phase = 1) returns to 0. We assume that P_phase(t) = 0 before the spontaneous release begins (t < t_phase) and after the cycle is over (t > t_phase + t_width). It is important to note that our new model is a recursive computer model inasmuch as its variable t is determined for each cycle by the Ca²⁺ release phase generated by the same model on the previous cycle, thereby modeling the “resetting” of SR oscillations by the systolic Ca²⁺ release. The final Ca²⁺ transient incorporating our phenomenological model of the diastolic Ca²⁺ release is close to that which we obtained for the averaged [Ca²⁺] signals in the subspace (compare Fig. 3, Averages, and Fig. 4 B, green line).

FIGURE 4.

Increase in SANC beating rate on introduction of the spontaneous Ca²⁺ release component, j_spont, described by Eq. 2 (see text), into the model. (A) Subspace [Ca²⁺], Ca_sub, and membrane potential, V_m, generated by the original model of Kurata et al. (2002) from Eq. 1. (B) Ca_sub and V_m simulations of the same model but with introduced spontaneous Ca²⁺ release. The time course for P_phase(t), described by Eq. 3, is also shown (blue line). The beating rate increased from 195.4 bpm to 246.7 bpm with the introduction of j_spont with the following parameters: P_rel,spont = 5 ms⁻¹, t_width = 150 ms, and t_phase = 150 ms.

Electrophysiological effects of spontaneous Ca²⁺ release

Introduction of the new diastolic spontaneous Ca²⁺ release component (j_spont, Eq. 2) into the model resulted in significant increase in the AP firing rate. Fig. 4 shows an example of the strong chronotropic effect produced by the spontaneous Ca²⁺ release. The beating rate increased from 195.4 to 246.7 beats per min (bpm). With this new spontaneous release component, the AP firing rate becomes too high for a SANC in the absence of hormonal stimulation. Also, the maximum systolic [Ca²⁺] level decreased from 1815 nM (original model from Kurata et al., 2002) to 1450 nM because the diastolic Ca²⁺ release partially emptied SR before AP upstroke in the new model.

Our version of a SANC model with the diastolic Ca²⁺ release

We adjusted some of the conductances and Ca²⁺ handling parameters in the Kurata et al. (2002) model for the beating rate and the range of [Ca²⁺] changes to be in line with experimental data. Our variant of the SANC model (Fig. 5) has the spontaneous Ca²⁺ release given by P_rel,spont = 2.5 ms⁻¹, t_width = 150 ms, and t_phase = 180 ms; and the following ion conductances (in nS/pF): maximum I_CaL conductance, g_CaL = 0.464; background Na⁺ conductance, g_bNa = 0.00216; maximum I_CaT conductance, g_CaT = 0.4; and maximum I_st conductance, g_st = 0.0075. The assigned conductance values are close to those in the original model and/or to those reported in the literature. Since with these new conductances the minimum diastolic Ca²⁺ level significantly dropped (to ∼120 nM), we compensated this effect with a slight decrease of the rate constant for Ca²⁺ uptake by the Ca²⁺ pump in the network SR, P_up = 0.004 M/s, and we also included the background Ca²⁺ current I_bCa with a normalized conductance of g_bCa = 1.2 pS/pF. This current was incorporated in the previous SANC models to balance the Ca²⁺ extrusion via NCX during diastole but it was assumed to be negligible in the Kurata et al. (2002) model. The adjusted SANC model has a beating rate of 201 bpm and the Ca²⁺ systolic and diastolic levels 1384 nM and 186 nM, respectively, which fit our experimentally measured values well (see above). Other important parameters of the AP cycle produced by the model were: maximum diastolic potential = −63.4 mV; peak overshoot potential = 12.3 mV; AP amplitude = 75.7 mV; maximum dV_m/dt = 4.2 V/s; Cycle length = 298 ms; and AP duration at 50% repolarization = 102 ms.

FIGURE 5.

Our variant of SANC model with the diastolic Ca²⁺ release and adjusted membrane conductance and Ca²⁺ handling parameters to be in line with experimental data (left side marked as + Spontaneous Ca²⁺ Release) and its negative chronotropic response on the complete blockade of the spontaneous release (j_spont = 0) simulating ryanodine effect. Shown are simulated traces for subspace [Ca²⁺], Ca_sub, and membrane potential, V_m, changes. For model parameters see text. T is the action potential period; bpm is beats per min.

The parameters were basically similar to those of the previously published SANC models as well as those measured experimentally.

The phase of spontaneous Ca²⁺ release controls the phase of AP upstroke and the firing rate

In this SANC model, the blockade of spontaneous SR release results in an almost instant reduction of AP rate from 201 bpm to 148 bpm (reduction by ≈26%) that simulates ryanodine effect (j_spont = 0, Fig. 5) reported previously (Bogdanov et al., 2001; Vinogradova et al., 2002; Li et al., 1997; Rigg and Terrar, 1996). This substantial ryanodine effect was missing in the two available primary SANC models by Kurata et al. (2002) and by Zhang et al. (2000) (the latter considered intracellular [Ca²⁺] = const). To examine the importance of the phase of spontaneous Ca²⁺ release occurrence for AP period (T), we generated a family of plasma membrane responses upon an instant introduction of the j_spont component characterized by various phase, t_phase (Fig. 6). We found that the AP upstroke phase closely followed (from 280 ms to 405 ms) the phase of the Ca²⁺ release flux (j_rel) in the subspace within a wide range of t_phase from 180 ms to 400 ms (see plot T vs. t_phase in Fig. 6, inset). The next set of simulations shown in Fig. 7 illustrates the model prediction that the phase of Ca²⁺ spontaneous release can control the steady-state beating rate. The ability of the spontaneous Ca²⁺ release to control the SANC beating rate is increased as the amplitude of the release increased (see set of plots in Fig. 7 for various P_rel,spont varying from 0.5 ms⁻¹ to 10 ms⁻¹). The control becomes almost saturated for P_rel,spont > 5 ms⁻¹ (compare plots for P_rel,spont = 5 ms⁻¹ and P_rel,spont = 10 ms⁻¹). The control is lost if the spontaneous release occurs too early (t_phase < 180 ms). This happens because the junctional SR is not refilled with Ca²⁺ yet and the corresponding Ca²⁺ release is small. Interestingly, the premature Ca²⁺ release can also result in a cycle span increase. The SR leak (produced by that release) delays normal SR refilling with Ca²⁺, ultimately resulting in the prolongation of the complete SANC duty cycle.

FIGURE 6.

The AP upstroke phase follows the phase of spontaneous Ca²⁺ release (t_phase) upon introduction of spontaneous Ca²⁺ release into the model. Shown are superimposed simulated traces of [Ca²⁺] changes in subspace (Ca_sub) along with respective APs generated with varying phase of the diastolic release (t_phase, shown at peaks of Ca_sub traces). (Inset) Plot of the first AP period (T) as a function, t_phase.

FIGURE 7.

The phase and the amplitude of the diastolic Ca²⁺ release control the steady-state rate of AP firing. The family of plots shows relationships of cycle period (or respective SANC rate, right scale) versus the phase of the diastolic release (t_phase in Eq. 3) for various Ca²⁺ release amplitude determined by P_rel,spont (in ms⁻¹) in Eq. 2.

Since the spontaneous beating rate of isolated rabbit SANCs varies from ∼2–3 Hz, we also explored whether the control of the SANC rate by diastolic release was robust and could be reproduced with various membrane conductance parameter sets simulating cells with various spontaneous activity. The cell model illustrated in Fig. 7 has the range of regulation from 2.5 Hz to 3.8 Hz that covers the upper range of SANC rates. We tested if the regulation is preserved for a SANC that has an overall slower DD. To achieve this, the following parameters were changed compared to the model set illustrated in Fig. 7 (in nS/pF): g_CaL = 0.58; g_bNa = 0.00162; g_CaT = 0.229; g_bCa = 0.0006; and maximum current produced by Na⁺/K⁺ ATPase I_NaK,max = 4.32 pA/pF. We found that with P_rel,spont = 5 ms⁻¹, P_up = 0.005 M/s, and with t_phase varying from 475 ms to 225 ms, this model set generated spontaneous action potentials with the rate from 2.08 Hz to 3.18 Hz, respectively (not shown), covering essentially the entire range of spontaneous rabbit SANC activity.

Another issue related to the ryanodine effect is that ryanodine might affect sarcolemmal ion channels in some experimental conditions. However, the available data are limited and the reported effects were marginal and somewhat contradictory. In one report by Satoh (1997), ryanodine in a relatively high concentration of 10 μM produced a 45% decrease of hyperpolarization-activated current (I_f) at −90 mV, whereas others reported no significant ryanodine effect on I_f (Li et al., 1997). Satoh (1997) also observed a 10% increase of I_CaL with 1 μM ryanodine and 8% decrease with 10 μM ryanodine, whereas others found no significant effect of ryanodine on I_CaL (Li et al., 1997; Bogdanov et al., 2001). In the same report, the delayed rectifier K⁺ current (I_K) was decreased by 6% and by 26% at 1 μM and 10 μM of ryanodine, respectively. In another report by Li et al. (1997), ryanodine (10 μM) slightly decreased I_CaT by ∼17% in cultured pacemaker cells with no effect on the “background” inward current (I_bg) (Li et al., 1997). The authors did not separate whether the reported I_CaT change was due to [Ca²⁺] or a direct effect of ryanodine on T-type Ca²⁺ channels. We examined the effect of these “extreme” reductions of I_CaT (by 17%) and I_K (I_Kr + I_Ks) (by 26%) and found that they resulted in minor AP rate decreases of ∼5% and 4%, respectively (or 10%, if combined). Although the I_CaT and I_K changes modulate the AP rate in the very limited range, the diastolic Ca²⁺ release controls the rate in a wide range from 150 to 226 bpm (Fig. 7) that corresponds to the rate reductions up to 34% when the release is blocked or reduced. Thus it appears that any direct effect of ryanodine on sarcolemmal currents is a minor issue.

The key role of NCX in transduction of Ca_sub signals to the plasma membrane

The steady-state beating rate reflects the change in the phase of AP upstroke in each cycle. An important question is what is the mechanism of the AP upstroke phase change? The missing link in the mechanism is obviously a plasma membrane ion current(s) that would connect subspace Ca²⁺ changes with plasma membrane potential. The SANC model used in this study has only two ion current components, which are Ca²⁺-dependent—namely I_CaL inactivation and I_NaCa. Occurrence of CRDD are associated with inward current produced by NCX (Bogdanov et al., 2001) and thus can explain the chronotropic effects of the Ca²⁺ release phase change. On the other hand, Ca²⁺-dependent I_CaL inactivation cannot provide the link in the observed effects, inasmuch as the opposite effect is expected. Increase in Ca_sub would inactivate the Ca²⁺ channels and thus decrease the whole cell (inward) I_CaL. Also, I_CaL is very small during the initial part of DD as the pacemaker potential starts below the level of the Ca²⁺ channel activation threshold. Other Ca²⁺-dependent mechanisms of I_CaL regulation, such as modulation of I_CaL inactivation and reactivation by CaMKII (Vinogradova et al., 2000), merit examination in future studies.

Fig. 8 A shows a complete AP cycle together with simulated ion currents that have inward direction during DD. It is clearly seen that I_NaCa remains the predominant source of membrane depolarization during DD until its very late phase. Compared to other currents during DD, it is always at least two times larger than I_CaT and three times larger than I_f. The only current that becomes equal to I_NaCa is I_CaL, when the membrane potential reaches −32.8 mV (i.e., close to I_CaL activation threshold). Importantly, I_NaCa behaves very dynamically during DD: it significantly increases as NCX becomes stimulated by Ca²⁺ from spontaneous release. This I_NaCa increase results in a significantly faster DD rate (Fig. 8 B, Fast DD) and a higher frequency of AP firing. On the other hand, when spontaneous release is delayed, I_NaCa remains relatively small during the early and middle phases of DD, so that the DD rate is significantly slower inasmuch as other inward currents provide only a modest rate of depolarization of the plasma membrane (Fig. 8 B, Slow DD).

FIGURE 8.

NCX transmits Ca²⁺ signals to the plasma membrane. (A) Complete AP cycle (V_m) along with simulated ion currents that have inward direction during diastolic depolarization (DD), namely, current produced by the Na⁺/Ca²⁺ exchanger, I_NaCa; L-type Ca²⁺ current, I_CaL; T-type Ca²⁺ current, I_CaT; background Na⁺ and Ca²⁺ currents I_bNa and I_bCa; hyperpolarization-activated I_f current; and sustained inward current, I_st. I_NaCa remains the largest inward current during DD until the membrane potential reaches −32.8 mV (i.e., I_CaL activation threshold). I_CaL is shown truncated. (B) Two sets of superimposed simulations generated for normal and late spontaneous release occurrence (red and blue lines, respectively). When spontaneous release is late, I_NaCa is relatively small and DD significantly slows (Slow DD). Each set displays simulated traces of I_NaCa, membrane potential, V_m, and the phase of spontaneous Ca²⁺ release, P_phase(t), as defined by Eq. 3.

DISCUSSION

The present study for the first time provides a numerical approximation of diastolic Ca²⁺ release in SANCs. In contrast to previous models, the new SANC model that includes our Ca²⁺ release scheme reproduces the diastolic Ca²⁺ release (Figs. 3 and 4), ryanodine effect (Fig. 5), and the range of Ca²⁺ changes in the subspace. To our knowledge, this is the first report of absolute Ca²⁺ concentration measurements in the subspace of SANCs. An important result of the study is that the model predicts that NCX can provide a powerful functional link between SR and plasma membrane. Specifically, via NCX the diastolic Ca²⁺ release is able to control the AP upstroke timing and ultimately the final SANC rate in a wide and physiologically important range from 2.5 Hz to 3.8 Hz and from 2.08 Hz to 3.18 Hz, respectively, for the two model parameter sets explored in the study.

At present there is a general consensus about the importance of Ca²⁺ release for SANC rate (Lipsius and Bers, 2003). However, reports vary regarding its significance when compared to other factors contributing to pacemaking, and particularly regarding the magnitude of the ryanodine effect. Importantly, all research groups report some chronotropic effect of ryanodine in all of experimental conditions and preparations including isolated SANC and sinus-node preparations (see Lakatta et al., 2003). The extent of the ryanodine effect varies from a 20% rate decrease to a complete halt of pacemaking. Therefore, an important discussion still remains regarding intracellular Ca²⁺ as a dominant or critical factor for cardiac pacemaker cell dominance (Honjo et al., 2003 versus Lakatta et al., 2003). Part of this variability may be related to cellular heterogeneity within the sinus node, as ryanodine effect might be different within the primary and peripheral SANCs. However, our model is designed to represent the ionic currents present in primary SANCs, and the magnitude of diastolic calcium release was determined directly from localized imaging in the subspace; whole-cell measurements of Ca²⁺ release proteins may not reflect the true activity of the release machinery in this critical location. The subspace imaging combined with numerical modeling here is the first study that directly tested the hypothesis that local subspace Ca²⁺ variations could control the AP rate of a primary sinus node cell that leads the heart beat. We show here that CRDDs can control the SANC rate in a broad physiologically important range, indicating that this Ca²⁺-related mechanism is viable and can significantly contribute to the final heart rate.

Another important question concerns the pathway of β-adrenergic stimulation in SANCs via either I_f (Bucchi et al., 2003) or NCX (Vinogradova et al., 2002). One concept is that during DD the initial membrane depolarization via I_f and/or other membrane currents reaches the level of T-type (and then L-type) Ca²⁺ channel activation. The Ca²⁺ ions entering the Ca²⁺ channels induce CICR that, in turn, via NCX accelerates DD. Another concept is that the Ca²⁺ release is intrinsically spontaneous (Lakatta et al., 2003; Vinogradova et al., 2004) and under the control of β-adrenergic receptors; it has its own clock and does not need an initial push from the membrane. Accordingly, the two oscillators (one is in membrane and another is in SR) dynamically interact during the SANC duty cycle producing a variety of chronotropic effects (Lakatta et al., 2003). The present study provides theoretical support for the concept of the interacting oscillators: if such spontaneous (and cyclic) releases occur in SANCs they can effectively control the SANC rate via NCX. It was previously shown that the β-adrenergic stimulation of SANCs increased both the frequency and the amplitude of spontaneous Ca²⁺ release in the subspace (Vinogradova et al., 2002). The stimulatory effect can be analyzed using our series of plots shown in Fig. 7 depicting the model prediction for SANC rate as a function of t_phase for various P_rel,spont. As t_phase is linked to the Ca²⁺ release frequency and P_rel,spont is linked to the Ca²⁺ release amplitude, the model explains/predicts a substantial chronotropic effect of β-adrenergic stimulation apparently via an NCX effect. A further, more detailed analysis of Fig. 7 allows an additional important prediction: that increased amplitude of the release (such as under β-adrenergic stimulation) results in a wider range of rate regulation—for example, from 150 to 226 bpm for P_rel,spont = 10 ms⁻¹ but from 150 to only 185 bpm for P_rel,spont = 1.25 ms⁻¹. In other words, regulation via the phase shift of CRDD has limited capacity to alter action potential timing until the release amplitude becomes sufficiently large.

Voltage-independent Ca²⁺ release via RyRs has also been reported in other cardiac cell types (see Lakatta, 1992). For example, steady Ca²⁺ oscillations and Ca²⁺ waves occur in Ca²⁺-overloaded ventricular myocytes. In cells with increased intracellular [Ca²⁺], RyRs stay close to their activation threshold and their activation can presumably be easily provoked, leading to autooscillatory patterns, although the quantitative dynamics of RyR oscillations are by no means understood. In this study we measured a minimum diastolic [Ca²⁺] level in SANCs of ∼200 nM, twice the diastolic [Ca²⁺] level in resting ventricular myocytes. This new finding gives us a basis to speculate that the normal pacemaker SANC activity may have some similar features to the abnormal Ca²⁺ automaticity in Ca²⁺-overloaded ventricular myocytes.

APPENDIX

Consideration of possible spatial limitations

To approximate Ca_sub, we simply averaged local Ca²⁺ signals in subspace (Fig. 3). To justify the additive effect of individual CRDDs with respect to their effect on the plasma membrane potential, we considered possibilities for a nonuniform V_m distribution along the cell surface. The potential spatial heterogeneity may arise from local changes in the membrane ion permeability produced by individual CRDDs (via Ca²⁺-dependent membrane channels and transporters). Theoretically, on the one hand, the local electrical charge change (e.g., generated by NCX) would passively propagate toward cell ends (propagation effect). On the other hand, the local electric charge can be neutralized by the membrane conductance in its vicinity and thus may never reach the cell ends (space constant effect).

Propagation effect

We approximated a SANC as an infinite cable with a diameter d = 10 μm and considered its response upon an instant introduction of an excessive electrical charge at x = 0 described by a delta function, δ(t). The solution for the membrane potential V_m(x,t) is an “expanding” and decrementing Gaussian function,

with the width w(t) of the “expanding” Gaussian given as

where ρ is the resistance of intracellular medium per unit length (Ω/cm), σ is the specific membrane conductance (Ω⁻¹ × cm⁻¹), and C is the membrane capacitance per unit length (F/cm). The well-known estimates for specific membrane capacitance and resistivity of intracellular medium are C_s = 1 μF/cm² = 10⁻⁶ F/cm² and R_i = 200 Ω × cm, respectively. Accordingly,

where S is the cell cross-section area, and

Finally,

where t is given in seconds. It means that after 1 ms the “expanding” Gaussian width w could reach the distance of 1.1 cm × = 0.0348 cm = 348 μm. On the other hand, the Gaussian width will reach the cell ends (for a cell length L_cell = 100 μm) from its center after t = 0.83 w² = 0.83 s/cm² × (5 × 10⁻³ cm)² ≈ 20.8 μs. This means that the passive V_m propagation occurs almost instantly along the electric cable approximating the cell membrane.

Spatial effect: estimation for the space constant, λ

We used a well-known formula for a cable space constant λ = , where r_m is membrane resistance per unit length in the voltage range of DD. We estimated the total cell membrane resistance R_tot from the Kurata et al. (2002) model as the ratio δV_m/δI_total, where δV_m = 1 mV is an instant change of V_m induced by a switch to the voltage-clamp during DD and δI_total is the total membrane current change as the response to that change. We found that minimum R_tot is 0.25 GΩ in the range of DD from −40 mV to −20 mV. Accordingly,

and

which is still much longer than the SANC length (L_cell = 70 μm in the Kurata model). We conclude that the electrical effect of individual CRDD will be distributed instantaneously and uniformly over the surface membrane.