Synergism of coupled subsarcolemmal Ca2+ clocks and sarcolemmal voltage clocks confers robust and flexible pacemaker function in a novel pacemaker cell model

Abstract

Recent experimental studies have demonstrated that sinoatrial node cells (SANC) generate spontaneous, rhythmic, local subsarcolemmal Ca(2+) releases (Ca(2+) clock), which occur during late diastolic depolarization (DD) and interact with the classic sarcolemmal voltage oscillator (membrane clock) by activating Na(+)-Ca(2+) exchanger current (I(NCX)). This and other interactions between clocks, however, are not captured by existing essentially membrane-delimited cardiac pacemaker cell numerical models. Using wide-scale parametric analysis of classic formulations of membrane clock and Ca(2+) cycling, we have constructed and initially explored a prototype rabbit SANC model featuring both clocks. Our coupled oscillator system exhibits greater robustness and flexibility than membrane clock operating alone. Rhythmic spontaneous Ca(2+) releases of sarcoplasmic reticulum (SR)-based Ca(2+) clock ignite rhythmic action potentials via late DD I(NCX) over much broader ranges of membrane clock parameters [e.g., L-type Ca(2+) current (I(CaL)) and/or hyperpolarization-activated ("funny") current (I(f)) conductances]. The system Ca(2+) clock includes SR and sarcolemmal Ca(2+) fluxes, which optimize cell Ca(2+) balance to increase amplitudes of both SR Ca(2+) release and late DD I(NCX) as SR Ca(2+) pumping rate increases, resulting in a broad pacemaker rate modulation (1.8-4.6 Hz). In contrast, the rate modulation range via membrane clock parameters is substantially smaller when Ca(2+) clock is unchanged or lacking. When Ca(2+) clock is disabled, the system parametric space for fail-safe SANC operation considerably shrinks: without rhythmic late DD I(NCX) ignition signals membrane clock substantially slows, becomes dysrhythmic, or halts. In conclusion, the Ca(2+) clock is a new critical dimension in SANC function. A synergism of the coupled function of Ca(2+) and membrane clocks confers fail-safe SANC operation at greatly varying rates.

Fig. 1.

Interacting Ca²⁺ clock and membrane clock in our model of rabbit sinoatrial node cells (SANC): schematic illustration of the cell compartments, major functional components, and their interactions approximated by our model. The physiological (full system) Ca²⁺ clock includes both the sarcoplasmic reticulum (SR) Ca²⁺ clock and balanced sarcolemmal Ca²⁺ fluxes of L-type Ca²⁺ current (I_CaL) and Na⁺-Ca²⁺ exchanger (NCX) (bold arrows); see text for details. Ca_i, Ca²⁺ in bulk cytosol; Ca_sub, Ca²⁺ in the subspace; SERCA, SR Ca²⁺ pump; Ca_nSR, Ca²⁺ in the network SR (nSR); Ca_jSR, junctional SR (jSR); j_SRCarel, SR Ca²⁺ release rate global variable; RyR, cardiac ryanodine receptor; AP, action potential; I_Kr, rapid delayed rectifier current; I_st, sustained current; I_NCX, NCX current; I_CaT, T-type Ca²⁺ current; I_f, hyperpolarization-activated or “funny” current.

Fig. 2.

Emergence and dynamic characteristics of the isolated Ca²⁺ SR oscillator (osc.) with a simple “release-pumping-delay” mechanism in our new model of rabbit SANC (all membrane currents = 0). A: model simulations illustrating that SR can operate as a self-sustained Ca²⁺ oscillator, P_up = 20 mM/s. Note: for this and other simulations, we provide only those model parameters, which are different from our basal firing model, which is fully described in the online data supplement. B and C: results of parametric analysis for the isolated SR Ca²⁺ oscillator with simultaneously varying SR Ca²⁺ release rate and SR Ca²⁺ pumping rate are shown in terms of oscillation frequency (B) or amplitude (C). Each image shows the result of 161 × 161 = 25,921 simulations (each pixel = 5 μs⁻¹ × 0.5 mM/s) with the resultant frequency or amplitude coded by the color map shown on each image top; the parametric space yielding no sustained Ca²⁺ oscillations is shown in blue. Small green box represents the Ca²⁺ oscillator shown in A. k_s, SR Ca²⁺ release rate constant.

Fig. 3.

A major limitation (“the faster, the weaker”) of the isolated SR Ca²⁺ oscillator is its inability to sustain high-amplitude oscillations at high rates when k_s increases (A) or P_up decreases (B). C: model simulations at various k_s show that the mechanism of poor oscillator performance at high rates (i.e., decreasing amplitude) is linked to accumulation of Ca²⁺ in the submembrane space (Ca_sub, solid line). All membrane currents = 0.

Fig. 4.

Model simulations showing major dynamic interactions (vertical lines) of membrane clock and SR Ca²⁺ clock during spontaneous AP firing in rabbit SANC. Shown are simulated traces of voltage (V_m), major ion currents, Ca²⁺ concentrations, and the Ca²⁺ release flux (j_SRCarel) during 2 pacemaker cycles. Dashed lines show 0 levels; P_up = 20 mM/s. DD, diastolic depolarization.

Fig. 5.

Enhanced flexibility of the rate modulation in our model is based on mutual functional dependence of Ca²⁺ and membrane clocks. A illustrates factors that couple the 2 clocks comprising the novel pacemaker mechanism. B: damped SR Ca²⁺ release oscillations and I_NCX oscillations when membrane clock is instantly disabled by a voltage clamp to −65 mV; P_up = 20 mM/s. C: different patterns of Ca²⁺ release dynamics at different P_up of 20 and 40 mM/s in the isolated Ca²⁺ SR oscillator (all membrane currents = 0), simulated with the initial cell Ca²⁺ load of steady-state AP firing such as shown Fig. 4. The steady oscillations at 40 mM/s are shown after 40 s of simulated SR activity. D: simulations of V_m and I_NCX dynamics when Ca_sub was fixed at the maximum diastolic potential (MDP) (solid curves) or when I_CaL was completely blocked at the MDP (dotted curves), resulting in afterhyperpolarization or delayed afterdepolarization (DAD), respectively; P_up = 20 mM/s.

Fig. 6.

A: the AP firing rate is broadly and smoothly modulated by P_up, yielding a unique parametric solution for the 3-Hz basal AP rate (black circle). B: interactions of Ca²⁺ and membrane clocks result in higher amplitude Ca²⁺ oscillations at higher P_up values. Since higher P_up values result in higher AP rates (A), the system clock operates following a Bowditch-like pattern: “the faster rate, the stronger release” (inset) thus overcoming a major functional limitation of the isolated SR Ca²⁺ clock (“the faster, the weaker” in Fig. 3).

Fig. 7.

The mechanism of broad spontaneous AP rate modulation by P_up. Overlapped traces are simulations for Ca_nSR (A), Ca_jSR (B), j_SRCarel (C), I_NCX (D), and V_m (E) at various P_up (labels in B). Simulations at different P_up are shown by different colors. All traces were synchronized with the 1st AP crossing 0 mV at the same time (100 ms) and reasonably time-truncated to illustrate phase shifts. See text for details.

Fig. 8.

In contrast to Kurata model (dotted curves), our basal firing model (“Present model,” solid curves) exhibits strong increase of inward I_NCX during diastolic depolarization before activation of I_CaL. Simulated dynamics of membrane potential (V_m), I_NCX, and I_CaL at a steady-state AP firing are shown for 2 pacemaker cycles beginning at V_m = 0. The cycle lengths were 307.5 and 333 ms for Kurata model and our basal model, respectively. The vertical dash-dot line of 75% of cycle length illustrates approximate timing for I_CaL activation, i.e., when I_NCX was measured in Table 3.

Fig. 9.

Predictions of chronotropic perturbations by our basal AP firing model. A: finding the system solution (Present model, black box) for the rate reduction produced experimentally by a specific SR Ca²⁺ pump inhibition with cyclopiazonic acid (CPA) (66). Also shown: predictions of small (if any) rate modulation produced by changes in the Ca²⁺ SR pumping rate in Kyoto model (Ref. ; “Kyoto”), Zhang et al. (73) model (“Zhang”), and Kurata model. B–E: predictions of our basal model for voltage (V_m) dynamics, with instant model parameter changes (black bars) simulating various chronotropic interventions indicated by respective labels in the panels. k_NCX, scaling factor for I_NCX.

Fig. 10.

Ca²⁺ clock confers the system robustness. A: our parametric system analysis with simultaneous variations in I_CaL conductance and SR Ca²⁺ pumping rate. The image shows the result of 97 (x) × 61 (y) = 5,917 simulations (each pixel = 0.0025 nS/pF × 0.2 mM/s). The resultant AP firing rate of the system is illustrated by graded color coded by the color map on the right; areas of no firing and chaotic firing are also marked and separated by yellow line. B: simulation traces for specific points of interest in A, illustrating more robust system operation when Ca²⁺ clock is functional. C: simulations of the effect of moderate PKA inhibition by 1.7 μM PKI (represented by vector bd in A). M clock, membrane clock.

Fig. 11.

I_f increases the system robustness at low AP rates. Our parametric system analysis with simultaneous variations in I_CaL conductance and SR Ca²⁺ pumping rate was performed at 2 extreme settings: no I_f (A) and large I_f (B). The system featuring I_f has smaller areas of no firing and chaotic AP firing. The results are illustrated by images, with the size (5,917 simulations) and the pixel size (0.0025 nS/pF × 0.2 mM/s) being identical to those in Fig. 10A. Simulations for some specific points of interest within the explored parametric space are depicted on the left. g_If, I_f conductance.

Fig. 12.

The range of regulation of spontaneous (Spont.) AP firing rate by P_up substantially shrinks as g_CaL (A) or g_If (B) increases. The curves illustrate the results of our model sensitivity analysis (basal model) for spontaneous AP rate change, with P_up varying from its basal value of 12 mM/s. The respective conductance values are shown at the curves, with 2× and 3× representing their multiples.

Fig. 13.

Our model predicts extreme rate acceleration by PKA activation with cAMP increase (upon phosphodiesterase 3 inhibition with milrinone). A: finding system solution for the reported milrinone effect (47% basal rate increase) when membrane clock (I_CaL, I_f, and I_Kr) was changed according previously reported experimental data (68) and P_up was graded (“Ca & M clocks,” black box) or when only P_up was graded (“Ca clock only,” black circle) from basal state firing (“Basal”). Model predicts 12.8% rate increase when only membrane clock was changed (“M clock only”). B: simulations illustrating the mechanism of the milrinone effect. Compared are simulated traces of V_m, I_f, I_NCX, j_SRCarel, and Ca_i kinetics for basal state AP firing (“Basal,” dotted lines) vs. respective traces for the milrinone effect (“Milrinone,” solid lines), which is depicted by black box in the plot in A.