Increasing SERCA function promotes initiation of calcium sparks and breakup of calcium waves

Abstract

Waves of sarcoplasmic reticulum (SR) calcium (Ca) release can cause arrhythmogenic afterdepolarizations in cardiac myocytes. Ca waves propagate when Ca sparks at one Ca release unit (CRUs) recruit new Ca sparks at neighboring CRUs. Under normal conditions, Ca sparks are too small to recruit neighboring Ca sparks where Ca sensitivity is also low. However, under pathological conditions such as a Ca overload or ryanodine receptor (RyR) sensitization, Ca sparks can be larger and propagate more readily as macro-sparks or full Ca waves. Increasing SERCA pump activity promotes SR Ca load, which promotes RyR opening and increases driving force of the Ca release flux from SR to cytosol, promoting Ca waves. However, high SERCA activity can also decrease local cytosolic [Ca] as it approaches the next CRU, thereby reducing wave appearance and propagation. In this study, we use a physiologically detailed model of subcellular Ca cycling and experiments in phospholamban-knockout mice, to show how Ca waves are initiated and propagate and how different conditions contribute to the generation and propagation of Ca waves. We show that reducing diffusive coupling between Ca sparks by increasing SERCA activity prevents Ca waves by reducing [Ca] at the next CRU, as do Ca buffers, low intra-SR Ca diffusion, and distance between CRUs. Increasing SR Ca uptake rate has a biphasic effect on Ca wave propagation, initially it enhances Ca spark probability and amplitude and CRU-coupling, thereby promoting arrhythmogenic Ca waves propagation, but at higher levels SR Ca uptake can abort those arrhythmogenic Ca waves.

INTRODUCTION

Cardiac arrhythmia is often triggered by premature ventricular contractions (PVCs), which have been linked to early (EADs) and delayed afterdepolarizations (DADs) (Frazier et al., 1989; Gilmour & Moise, 1996; Nakajima et al., 1997; Akar & Rosenbaum, 2003; Burashnikov & Antzelevitch, 2003; Katra & Laurita, 2005; Rodriguez et al., 2005; Hirose & Laurita, 2007; Patterson et al., 2007). One cause of afterdepolarizations is transient inward current (I_ti), which is carried primarily by inward sodium-calcium exchanger (NCX) current (I_NCX) when intracellular Ca concentration ([Ca]_i) is elevated (Tseng & Wit, 1987; January & Fozzard, 1988; Lipp & Pott, 1988; Schlotthauer & Bers, 2000; Verkerk et al., 2001; Voigt et al., 2012). I_ti becomes larger when spontaneous Ca releases initiate Ca waves. Under normal (healthy) conditions, Ca sparks are isolated and Ca waves rarely occur (Cheng et al., 1996). However, under diseased conditions such as a Ca overload or ryanodine receptor (RyR) sensitization, Ca sparks recruit new Ca sparks in neighboring Ca release units (CRUs) and propagate as a wave (Cheng et al., 1996; Lukyanenko et al., 1999). As Ca wave amplitude, frequency and propagation rate increase, I_ti increases and depolarizes cell membrane. As these afterdepolarizations become larger, they can exceed the threshold of sodium (Na) channel activation and produce triggered action potentials, that at the whole heart level can manifest as premature ventricular contractions (PVCs).

The sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) pumps Ca from cytosol to the sarcoplasmic reticulum (SR) and maintains the large [Ca] gradient required for SR Ca release. During excitation-contraction (E-C) coupling SR Ca release amplifies Ca entry through L-type Ca channels. Ca released from the SR and that enters via Ca current (I_Ca; in the same cleft region) diffuses into cytosol to activate contraction. For relaxation, Ca ions are mainly removed from cytosol via SERCA or NCX (with tiny amounts removed via sarcolemmal Ca-pump and mitochondrial uniporter)(Bers, 2002). The relative Ca amounts transported by SERCA and NCX varies with species and conditions as determined by various factors such as the number of transporters, cytosolic and intra SR free Ca concentrations ([Ca]_i, [Ca]_SR), [Na]_i, membrane voltage, regulation (e.g. by phospholamban; PLN) and temperature. During normal EC coupling, ~70 % of Ca ions returns to the SR and ~25% leaves via NCX in rabbit ventricular myocytes (Bers & Bridge, 1989; Bassani et al., 1994) whereas 92% of Ca ions go back to the SR for rat and mouse ventricular myocytes (Bers & Bridge, 1989; Negretti et al., 1993; Bassani et al., 1994; Li et al., 1998; Bers, 2002).

The CRU is composed of ryanodine receptors (RyR) whose opening is sensitive to both [Ca]_i and [Ca]_SR (Gyorke & Gyorke, 1998; Gyorke et al., 2004; Zima et al., 2010; Bers, 2014). Increasing [Ca]_SR leads to higher RyR open probability and also increases Ca spark size and duration due to larger driving force for the SR Ca release flux. The refilling speed of SR Ca and the maximum [Ca]_SR depend on the SERCA activity vs. the sum of residual leak mediated by RyR and non-RyR mechanisms (Zima et al., 2010; Bers, 2014). When SERCA becomes more active, [Ca]_SR increases and thus higher SERCA activity tends to increase both Ca sparks and Ca waves. However, recent experimental and clinical studies show that increasing SERCA activity prevents Ca waves and arrhythmia (Huser et al., 1998; del Monte et al., 2004; Kawase & Hajjar, 2008; Prunier et al., 2008; Lipskaia et al., 2010; Jessup et al., 2011; Bai et al., 2013). One explanation for this could be that the increasing SERCA activity limits the propagation of Ca waves by reducing the spatiotemporal spread of local [Ca]_i release, thereby preventing spark activation at adjacent CRUs. In this study, we use physiologically detailed computational models of the subcellular Ca cycling and experimental validation in using PLN-KO mice, showing how increasing SERCA activity can both promote and reduce the propensity of Ca wave propagation in various conditions.

MATERIALS AND METHODS

Mathematical model

In order to simulate realistic Ca sparks and waves, we use a modified version of a physiologically detailed model of a rabbit ventricular myocyte used in our previous studies (Sato & Bers, 2011; Sato et al., 2012). This model is based on models by Shannon et al. (Shannon et al., 2004) and Restrepo et al (Restrepo et al., 2008). Fig 1 is the schematic illustration of the model. Near each CRU there are 5 Ca compartments; bulk cytosolic Ca ([Ca]_i), submembrane Ca ([Ca]_sm), cleft space Ca ([Ca]_Cleft), network SR Ca ([Ca]_SRN), and junctional SR Ca ([Ca]_JSR). CRUs are also coupled by Ca diffusion in cytosol and the network SR. The major difference from the previous versions of this model is Ca diffusion in submembrane space. The [Ca]_sm diffusion is primarily in a transverse vs. longitudinal direction, based on the fact that most CRUs are along transverse tubules (T-tubules) that define the internal submembrane space. The model has 4-state RyR channels, which are sensitive to both cytosolic Ca ([Ca]_i) and SR Ca ([Ca]_SR). No Ca waves are observed with normal (healthy) baseline rabbit parameters. Therefore, we increased RyR sensitivity to Ca to mimic diseased conditions such as catecholaminergic polymorphic ventricular tachycardia (CPVT) mutations. There are 19,305 CRUs (65×27×11) in the cell. One CRU contains 100 RyRs and thus there are 1,930,500 RyRs in the cell. Geometrical parameters such as the distance between CRUs and diffusion constants, for longitudinal direction and transverse direction are different based on experimental measurements. The cell model is a cuboid (65×27×11 CRUs). In order to avoid geometrical effects of the cell shape, 50×3×3 (longitudinal × transverse × transverse) and 3×50×3 cell structures are used to compare propagations of longitudinal and transverse waves. SERCA pumps are distributed equally over the cell. The maximum transport rate of the SERCA pump (v_up) is varied to mimic SERCA overexpression. Ca affinity of the SERCA pump (K_d) is also varied to mimic β-adrenergic stimulation. All parameters are given in the appendix. The program codes are written in C++ and simulated in a High-Performance Computing cluster (24 nodes, Intel Xeon E3–1270, 3.4GHz, 32GB RAM) and Amazon Web Services.

FIGURE 1. Schematic illustration of the model.

There are 5 Ca compartments. Each RyR is regulated by [Ca] at the cleft space and luminal [Ca] at the junctional SR.

In a quiescent cell, [Ca]_i is independent of the SERCA activity at the steady state. In other words, the SERCA activity does not have influence for [Ca]_i at the steady state and [Ca]_i is solely determined by the balance between transmembrane fluxes. On the other hand, [Ca]_SR is determined by the balance between the SERCA uptake flux and SR Ca leak fluxes. The SERCA pump is given by

$$I_{up}=v_{up}\left({\left(\frac{{\left[\mathrm{C}\mathrm{a}\right]}_i}{k_{\mathrm{u}\mathrm{p}}}\right)}^H-{\left(\frac{{\left[\mathrm{C}\mathrm{a}\right]}_{\mathrm{S}\mathrm{R}}}{k_{\mathrm{S}\mathrm{R}}}\right)}^H\right)/\left(1+{\left(\frac{{\left[\mathrm{C}\mathrm{a}\right]}_i}{k_{\mathrm{u}\mathrm{p}}}\right)}^H\right).$$

[Ca]_SR-dependent SR Ca leak via RyR is given by

$$I_r=J_{max}\frac{P_o\left({\left[\mathrm{C}\mathrm{a}\right]}_{\mathrm{J}\mathrm{S}\mathrm{R}}-{\left[\mathrm{C}\mathrm{a}\right]}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{f}\mathrm{t}}\right)}{v_p}.$$

The RyR channel gating model is a four-state Markovian model regulated by [Ca]_Cleft and [Ca]_jSR. Each RyR opens independently and stochastically. As shown in our previous studies (Sato & Bers, 2011; Sato et al., 2012; Xie et al., 2019), several changes to the Restrepo et al model were made, including:

1. The rates from the closed state to the open state

   $$k_{12}=\frac{K_u{\left[\mathrm{C}\mathrm{a}\right]}_{\mathrm{C}\mathrm{l}\mathrm{e}\mathrm{f}\mathrm{t}}^2}{K_{\mathrm{c}\mathrm{p}}^2+{\left[\mathrm{C}\mathrm{a}\right]}_{\mathrm{C}\mathrm{l}\mathrm{e}\mathrm{f}\mathrm{t}}^2}+w,$$

   $$k_{43}=\frac{K_b{\left[\mathrm{C}\mathrm{a}\right]}_{\mathrm{C}\mathrm{l}\mathrm{e}\mathrm{f}\mathrm{t}}^2}{K_{\mathrm{c}\mathrm{p}}^2+{\left[\mathrm{C}\mathrm{a}\right]}_{\mathrm{C}\mathrm{l}\mathrm{e}\mathrm{f}\mathrm{t}}^2}+w,$$

   where k₁₂ is the rate from state 1 to state 2, k₄₃ is the sate from state 4 to state 3, Ku, K_cp,K_b and w are constants.
2. The rates from the open state to the closed state to fit the experimental observation of the mean open times (0.7~1.9 ms) (Györke & Györke, 1998)

   $$k_{21}=0.5{\mathrm{ms}}^{-1},k_{34}=3.3{\mathrm{ms}}^{-1}$$

   The other equations are the same as that used by Restrepo et al.

   $$k_{14}=\frac{\widehat{M}\left({\left[\mathrm{C}\mathrm{a}\right]}_{\mathrm{j}\mathrm{S}\mathrm{R}}\right){\tau }_b^{-1}{B}_{CSQN}}{B_{CSQN}^0},$$

   $$k_{23}=\frac{\widehat{M}\left({\left[\mathrm{C}\mathrm{a}\right]}_{\mathrm{j}\mathrm{S}\mathrm{R}}\right){\tau }_b^{-1}{B}_{CSQN}}{B_{CSQN}^0},$$

   $$k_{41}=\frac{1}{{\tau }_u},$$

   $$k_{32}=\frac{k_{41}{k}_{12}}{k_{43}}.$$

   The total SR Ca content ([Ca]_SRT) is controlled by the balance of net SR Ca uptake by SERCA (above) and [Ca]_SR-dependent SR Ca leak via RyR (J_RyR) (above) and non-RyR leak (J_lk) as d[Ca]_SRT/dt = I_up – J_{RyR –} J_lk (see appendix). Notably, when there is no SR Ca leak, [Ca]_SR becomes the maximum value (thermodynamic limit) and given by

   $${\left[\mathrm{C}\mathrm{a}\right]}_{\mathrm{S}\mathrm{R}}=\left(\frac{k_{\mathrm{S}\mathrm{R}}}{k_{\mathrm{u}\mathrm{p}}}\right){\left[\mathrm{C}\mathrm{a}\right]}_i.$$

   This is independent of the SERCA pump strength (v_up). We use these [Ca]_i and [Ca]_SR as initial conditions and also allow the model to relax to steady state. This allows us to investigate the effect of SERCA overexpression, which changes the SERCA pump strength (v_up), and the effect of SR Ca load separately. Of note, we do not use the complex array of sarcolemmal channels and transporters to study intrinsic SR Ca handling in a focal manner.

Ethical approval

All animal protocols were performed in accordance with NIH guidelines and approved by the UC Davis Institutional Animal Care and Use Committee (IACUC). PLN knockout (PLN-KO) mice and wild type littermates were generously provided by Dr. E.G. Kranias (University of Cincinnati, OH), an animal model described in their previous work (Luo et al., 1994). Mice were group housed with ad libitum access to food and water and maintained at 22°C on a 12 h:12 h light–dark cycle. The authors understand the ethical principles under which The Journal of Physiology operates and declare that our work complies with its animal ethics checklist.

Mouse cardiac ventricular myocyte isolation

Single ventricular myocytes were enzymatically isolated as previously described from hearts of PLN-KO mice.(Li et al., 2002) Briefly, after anesthesia (isoflurane, 5%), mice were anticoagulated with intraperitoneal injection of heparin (8000 units/kg body weight). Hearts were excised and retrograde perfused on constant flow Langendorff apparatus (4 min, 37°C) with the Ca-free normal Tyrode (NT) solution, gassed with 100% O₂. Then, ventricular myocytes were digested by Liberase TM (0.075 mg/mL, Roche) and Trypsin (0.0138%, Gibco). Ventricular myocytes were dispersed mechanically and filtered through a nylon mesh and allowed to sediment for 10 min. The sedimentation is repeated three times every 10 min, while [Ca] (mmol/L) was increased stepwise, from 0.125 to 0.25 through 0.5. Finally, ventricular myocytes were kept in a 0.5 mmol/L [Ca] NT solution at room temperature.

Confocal Ca²⁺ Imaging in Intact Myocytes

Fluo-4 AM (10 μmol/L, Molecular Probes^®) was loaded into intact myocytes for 10 min in NT solution (in mmol/L): NaCl 140, KCl 4, MgCl₂ 1, CaCl₂ 1, glucose 10, HEPES 5, pH 7.4; then incubated for 30 min to allow for de-esterification. The [Ca]_o was increased stepwise from 1 to 3, and 6 mM to induce spontaneous release (Bai et al., 2013). Ca events were recorded with 6 mM [Ca]_o NT solution. Ca events were recorded at room temperature using a confocal microscope (Bio-Rad Radiance 2100 MP, 40× objective) with fluorescence excitation set at 488 nm with emission collected at wavelengths greater than 500 nm.

Statistics

Data were expressed as mean ± SD, and significance was evaluated using Student’s t-test or one-way ANOVA. p<0.05 was considered statistically significant.

RESULTS

Effects of [Ca]_SR, [Ca]_i and SERCA function alone on Ca wave Propagation

RyR gating is sensitive to [Ca]_i and [Ca]_SR. The open probability of a single RyR channel is increasing function of [Ca]_i and [Ca]_SR (Fig 2A). In the cell, RyRs are clustered in CRUs, within which RyRs interact nonlinearly through [Ca]_Cleft. When a single RyR opens, the elevation of local [Ca]_Cleft recruits openings of other RyRs within the CRU and the frequency of Ca sparks depends steeply on [Ca]_Cleft and [Ca]_SR (Fig 2B). The increase of Ca spark frequency saturates since the recovery of RyRs takes several hundred milliseconds (which depends on the refilling rate of [Ca]_SR and intrinsic properties of the channel) and RyRs must recover before the next Ca spark occurs. Ca waves propagate when Ca spark-driven Ca flux raises local [Ca]_i and [Ca]_Cleft sufficiently at neighboring CRUs to trigger a Ca spark. We measured this probability of Ca spark propagation to an adjacent CRU when inducing a first Ca spark by setting 5 RyRs open in either the longitudinal (Fig 2C) or transverse direction (Fig 2D). We use 3 RyRs opening at that second CRU as a threshold of Ca spark occurrence. Since the CRUs are more closely spaced transversely, Ca sparks propagate more easily than in the longitudinal direction. In this simulation, there was only one Ca spark to initiate the new Ca spark whereas during Ca waves, a cluster of Ca sparks supply large amount of Ca to initiate new Ca sparks. Therefore, in this simulation, relatively higher [Ca]_SR was required to initiate new Ca sparks.

FIGURE 2. Single RyR, RyR cluster (CRU), and inter-CRU properties and propagation of Ca sparks.

(A) Open probability of RyR vs [Ca]_SR at [Ca]_i = 0.1, 0.5, and 1.0 μM. (B) Spark frequency of a single CRU vs [Ca]_SR. The probability of initiation of Ca spark at the nearest CRU in longitudinal direction (C) and transverse direction (D).

Transition from isolated Ca sparks to Ca waves occurs as myocytes load with Ca. In Fig 3, we started with moderate [Ca] (relatively low [Ca] for Ca waves; [Ca]_SR=1.6 mM, [Ca]_i=0.1 μM). In this case, Ca releases from the SR generated only isolated Ca sparks (Fig 3A). The size of Ca sparks was small compared to the separation between CRUs and Ca sparks could not recruit additional neighboring sparks. There was also invisible non-spark leak (Ca quarks; <3 RyR openings). When [Ca] is increased to [Ca]_SR=1.9 mM and [Ca]_i=0.15 μM, Ca sparks were able to initiate new Ca sparks in neighboring CRUs. Ca waves propagated partially in space. These we call macro sparks if only a few Ca sparks are involved or ‘mini waves’ if the wave propagates, at least, several CRUs. This happened more often in a transverse direction (Fig 3B). When [Ca] was high enough ([Ca]_SR=2.5 mM and [Ca]_i=0.2 μM), multiple Ca waves occurred at different locations and they propagated in both longitudinal and transverse directions.

FIGURE 3. Ca waves at different [Ca].

SERCA is the same strength. Initial conditions are (A) [Ca]_SR=1.6mM and [Ca]_i=0.1μM (B) [Ca]_SR=1.9mM and [Ca]_i=0.15μM (C) [Ca]_SR=2.5mM and [Ca]_i=0.2μM.

How do structural differences in longitudinal and transverse directions affect Ca wave propagation? For Ca wave propagation, a Ca spark must recruit new Ca sparks (fire-diffuse-fire) at the neighboring CRUs. We plotted the peak [Ca]_i at the nearest CRU after the first Ca spark occurred, as a function of the SERCA pump strength (v_up: Fig 4A & B). We indicate that at 35°C the basal normal v_up (in μM/ms) is expected to be 0.212 in rabbit, 0.535 in rat and 0.85 in mouse and can be increased by PLN-KO or PKA activation (Li et al., 1998; Bers, 2001). Since SERCA removes Ca from the cytosol at all points between the 2 CRUs, it reduces [Ca]_i at both the first spark site and its neighbors. Therefore, if initial [Ca]_i and [Ca]_SR are the same, which ensures the same state of RyRs and driving force from SR to cytosol, as SERCA pumps become more active, the local [Ca]_i at the neighboring site becomes smaller and reduces the probability of new Ca sparks at that CRU. We measured probability of whole cell Ca waves when SERCA strength was varied, including longitudinal waves and transverse waves. For longitudinal waves, we used 50×3×3 (longitudinal × transverse × transverse) structure and Ca waves were initiated by stimulating the 45 (5×3×3) leftmost CRUs. To assess transverse waves, we used 3×50×3 (longitudinal × transverse × transverse) structure and Ca waves were initiated by stimulating the 45 (3×5×3) leftmost CRUs. Ca wave propagation was progressively suppressed as SR Ca uptake increases (Fig 4C–D), more dramatically in the longitudinal vs. transverse direction.

FIGURE 4. SERCA strength and Ca wave propagation.

Peak [Ca]_i at the adjacent CRU when Ca spark occurs vs SERCA strength in longitudinal direction (A) and transverse direction (B). Triangles indicate the normal v_up for rabbit (0.212 μM/ms) rat (0.535 μM/ms) and mouse (0.85 μM/ms). Probability of whole cell Ca wave vs SERCA strength in longitudinal direction (C) and transverse direction (D). The steady state [Ca]_i is 0.1478μM.

Induction of Ca waves depends biphasically on SERCA activity

We show that higher SERCA pump activity suppresses Ca wave propagation (at any fixed [Ca]_SR; Fig 4), but also that increased SERCA activity tend to increase [Ca]_SR which, by itself, promotes Ca sparks and waves (Fig 2). So, how do these opposing effects interact dynamically when the system is allowed to relax to a steady state? Fig 5D shows average [Ca]_SR vs. SERCA pump strength (v_up) at the steady state (Fig 5D right axis). The higher SERCA pump activity promotes RyR recovery, Ca sparks and raises the driving force for the SR Ca releases, but has a biphasic changes in wave frequency (three cases, depending on v_up). At lower SERCA function, Ca waves rarely occur due to lower [Ca]_SR which limits Ca spark frequency, amplitude and RyR sensitivity (Fig 5A). At intermediate SERCA activity, the increase in Ca spark frequency, amplitude and sensitivity progressive increases wave frequently (Fig 5B and peak in Fig 5D). Beyond that point, further increase in SERCA function predominantly suppress wave frequency (as in Fig 4C–D). This indicates that the reuptake-dependent curtailment of cytosolic Ca diffusion from an active CRU to any neighboring CRU suppresses propagation, despite a continued increase in Ca spark frequency and local amplitude at the active CRU (Fig 5C). That is, at very high SERCA v_up, Ca wave cannot propagate due to fast removal of [Ca]_i before it gets to the next CRU. However, Ca sparks occur more frequently. Thus, there is a window of SERCA strength where Ca wave are promoted (Fig 5D). Fig 5C indeed shows a greatly increased number of release events that are considerably more restricted in propagation (macro-sparks and mini-waves) with very few long propagating waves. A salient point here is that large and fast propagating Ca waves will cause larger and more synchronized inward I_NCX, as shown in Fig 5B, which is in the range that can trigger action potentials (Schlotthauer & Bers, 2000) and thus have arrhythmogenic impact.

FIGURE 5. Ca waves occur at the optimal range of the SERCA pump strength.

Corresponding I_ti (I_NCX) are plotted (black curves) (A) v_up=0.01 μM/ms. (B) v_up=2.16 μM/ms. (C) v_up=10 μM/ms. (D) wave frequency vs SERCA strength (v_up).

Increased Ca buffering (e.g. with EGTA) has been used by many groups to suppress Ca waves, while still measuring Ca sparks. That can be pragmatic when using Ca spark frequency to assess SR Ca leak, where occasional Ca waves can reduce [Ca]_SR cause reduced [Ca]_SR and temporarily suppress Ca sparks. Fig 6A–B shows how increasing Ca buffering also suppresses Ca wave propagation, especially in the longitudinal direction (as with increasing SERCA). If we consider increased SERCA as a spatial buffer for [Ca]_i, it makes sense that, like EGTA, it suppresses Ca wave propagation. However, the EGTA effect is monotonic suppression, because it does not increase [Ca]_SR the way SERCA enhancement does to create a window of propagating wave propensity.

FIGURE 6. Effects of EGTA and Ca diffusion in the network SR.

Probability of whole cell Ca wave vs EGTA in longitudinal direction (A) and transverse direction (B). Probability of whole cell Ca wave vs time constant of translocation of Ca between CRUs in longitudinal direction (C) and transverse direction (D). Triangle indicates a typical Ca diffusion constant in the network SR (60 μm²/s)

We also explored the effect of slowing Ca diffusion in the network SR, which Fig 6C–D shows can promote Ca waves. A typical Ca diffusion constant in the network SR is 60 μm²/s (indicated with a triangle in the figures) (Wu & Bers, 2006; Picht et al., 2011; Bers & Shannon, 2013). We infer that this effect is because if intra-SR diffusion is extremely fast, the local [Ca]_SR at the nearest CRU will be significantly depleted, resulting in reduced RyR sensitivity and Ca driving force through the RyRs in that junction. Conversely, with ultra-slow intra-SR diffusion, the neighboring CRU will have the maximal [Ca]_SR at the time the wave of cytosolic Ca arrives –making RyRs more sensitive and able to produce larger Ca release flux to drive further propagation. Thus, increased [Ca]_i buffering and fast intra-SR diffusion suppress Ca wave propagation.

Direct test of SERCA functional effects on Ca waves in intact ventricular myocytes

The high SERCA effect in Fig 5C, showing the abortion of propagated waves at high [Ca]_SR is reminiscent of prior measurements in PLN-KO mice which have very high SERCA function (Huser et al., 1998; Bai et al., 2013). To test whether the biphasic effect of graded SERCA function on propagating Ca wave frequency in Fig 5D is apparent in live ventricular myocytes we used isolated intact myocytes from PLN-KO mice, which have perhaps the highest basal SERCA activity of any native cardiac myocyte (Li et al., 1998). To induce Ca overload and robust Ca wave activity we raised [Ca]_o from 1 to at least 3 mM.

Figure 7A shows line scan confocal [Ca]_i imaging in a PLN-KO myocyte. At this initial time point (0 min) the myocyte exhibits many abortive mini-waves (Ca Waves that do not propagate the full myocyte length), but few waves that propagate through the full-cell. Then to gradually inhibit SERCA activity we added 0.3 μM cyclopiazonic acid (CPA, a selective SERCA inhibitor) and monitored Ca waves every 2 min. After 2 min exposure of CPA, the number of full propagated (cell-wide) Ca waves increased to a maximum at 2 min (Fig 7A–B) and as more SERCA pumps were progressively blocked the absolute frequency of waves decreased, but most propagated through the entire myocyte length. Indeed, as SERCA became more completely inhibited (at 8–16 min), the wave frequency declined (Fig 7B) as did the amplitude (from 4.08 ± 0.20 at 4 min to 2.17 ± 0.26 at 16 min), consistent with the expected progressive decline in [Ca]_SR.

FIGURE 7. Cyclopiazonic acid (CPA, specific SERCA inhibitor) transiently promotes fully-propagated Ca waves under Ca overload conditions in intact PLN-KO myocytes.

(A) Representative confocal images line scan images of spontaneous Ca waves for just before and at different times of exposure to .3 μM CPA. (B) The frequency of full-propagated Ca waves (# of waves/s) vs. CPA 0.3 μM exposure time (inset shows individual cell data). (C) The decay tau (in ms) of Ca waves as a function of CPA exposure time (all points are shown as well as mean ± SD). (D) Rate constants (1/tau) for [Ca]_i decline for mean values in C (□), where 95% of Ca removal is attributable to SERCA function (●), with the remainder via non-SR mechanisms (○,e.g. Na/Ca exchange; Li et al. 1998) Data are mean ± SEM of 7 cells from 2 mice.

We can infer the relative SERCA activity during the CPA exposure by measuring the time constant (τ) of [Ca]_i decline wave during each wave (at any location). Fig 7C shows the measured τ of [Ca]_i as a function of CPA exposure time as mean tau rises from 82 to 311 ms. The inverse of this τ gives a rate constant for [Ca]_i decline, which falls from 12.2 s⁻¹ at 0 min to 3.2 s⁻¹ at 16 min (Fig 7D). If we correct these rate constants by the 5% contribution of non-SERCA transporters to [Ca]_i decline in the PLN-KO myocyte under control conditions (Li et al., 1998) we can translate the SERCA-dependent uptake rate, as a percent of the maximal SERCA rate at baseline (V_max) for each time after CPA addition. (Fig 7D right ordinate scale). That allows us to plot the experimental wave frequency results as a function of maximal SERCA function (Fig 7E), for comparison with the model predictions in Fig 5D. Overall, the same biphasic response of fully-propagating wave frequency to increasing SERCA function is seen in both curves. That is, there are few waves at low SERCA activity, progressive more as SERCA activity rises, up to a peak, after which the Ca waves are more often aborted and fail to propagate effectively at the highest SERCA function level. While the experimental curve peak is a bit more right-shifted, it shows that a further 20% decrease in SERCA from the peak wave frequency suffices to prevent SERCA from aborting Ca waves.

DISCUSSION

Ca waves propagate when Ca sparks recruit new Ca sparks in neighboring CRUs. This is called fire-diffuse-fire model of Ca wave propagation (Dawson et al., 1999) and implies that diffusion, in other words, coupling between Ca sparks has a crucial role in the propagation as well as the Ca spark itself (‘fire’ in the fire-diffuse-fire model). The properties such as frequency, size, and duration, of Ca spark are substantially influenced by [Ca]. Previous studies show that stochastic openings of RyRs cause non-spark SR Ca leak (Ca quarks) when SR Ca load is low and steeply leads to Ca sparks as SR Ca load becomes higher (Zima et al., 2010; Sato & Bers, 2011; Williams et al., 2011; Bers, 2014). Further Ca loading or overloading promotes a transition from isolated Ca sparks to Ca waves occurs in the cell (Cheng et al., 1996). If the SERCA strength and Ca diffusion are unchanged, higher [Ca]_SR promotes Ca waves. This is simply understood as follows. At the single channel level, the opening of RyRs is sensitive to [Ca]_i and [Ca]_SR (Gyorke & Gyorke, 1998). Open probability becomes higher as [Ca]_i and [Ca]_SR become higher (Fig 2A). At the CRU level, more frequent Ca sparks are observed as [Ca]_SR become higher, not only due to higher open probability of RyRs but also due to higher driving force and positive feedback process of CICR (Fig 2B). As [Ca]_SR becomes higher, Ca spark becomes larger and longer. This causes higher [Ca]_i at the neighbor and initiate new sparks (Fig 4A–B).

In this study we focused more on diffusive coupling in the fire-diffuse-fire model enabling strong Ca wave propagation that is proarrhythmic. As Ca is loaded into the cell, we show how isolated Ca sparks become macro-sparks by recruiting new Ca sparks from neighboring CRUs. First, we examined the effects of initially fixing [Ca]_i and [Ca]_SR (Fig 2–3) in order to keep the same RyR states and driving force for the SR Ca release. Then, we varied the SERCA strength, revealing the intrinsic effect of more active SERCA to suppress wave propagation (Fig 4C–D), effectively reducing coupling between CRUs because SERCA progressive reduces local [Ca]_i in the space between CRUs. When we allow the system to relax to steady state it determines its own [Ca]_SR level and reveals the biphasic effect of SERCA activity on Ca waves (Fig 5).

[Ca]_SR is determined by the balance between SR Ca leak and reuptake by SERCA. Thus, increasing SERCA activity increases [Ca]_SR. Therefore, where the effect of increasing [Ca]_SR on Ca wave dominates, increasing SERCA activity promotes Ca waves. On the other hand, if the effect of decreasing [Ca]_i between CRUs dominates, waves are suppressed. In other words, increasing SERCA promotes ‘fire’ but suppresses ‘diffuse’ in the fire-diffuse-fire model. Therefore, increasing SERCA-pump function has a biphasic effect on propensity of arrhythmogenic Ca waves, but a monotonic effect to increase Ca spark frequency and amplitude.

Here, we varied the maximum transport rate of SERCA (v_up) to mimic SERCA overexpression. Increasing SERCA activity by enhancing Ca affinity (reducing k_d), which mimics β-adrenergic stimulation, PLN phosphorylation or PLN-KO also reveals an analogous biphasic effect on wave propagation (Fig 8A). Increasing RyR cluster size reduces SR Ca load, but increase Ca spark frequency (Galice et al., 2018; Xie et al., 2019). When RyR cluster size was doubled in our model, the wave frequency was increased, but then declined at higher SERCA activity (Fig 8B). Thus, this biphasic effect of SERCA enhancement on Ca wave propagation seems to be a general phenomenon.

FIGURE 8. Effects of SERCA function on Ca wave propagation.

(A) Modulating SERCA function by altering its Ca-affinity (k_d), as occurs in PLN-KO myocytes. Full Ca wave frequency shows a biphasic effect as in Fig 5 and 7. (B) RyR cluster size affects the window of the SERCA strength for maximal Ca wave propagation. Wave frequency vs SERCA strength (v_up). Faded lines are from Fig 5D. (C) Wild type mice do not exhibit a clear biphasic effect. Instead wave frequency amplitude and frequency monotonically decline with time in 0.3 μM CPA.

Our experimental results using PLN-KO mice support our simulation results (Fig 7). We note that wild type mice did not readily exhibit the biphasic effect (Fig 8C). That is, progressive inhibition of SERCA caused a monotonic decrease in Ca waves. It may thus be that the protective effect of wave suppression by SERCA enhancement can only be reached under extremely high SERCA activity, such that the more arrhythmogenic consequence is more dominant over most of the physiological rage of SERCA enhancement.

Nevertheless, while some studies show that reducing SERCA expression reduces Ca waves (Stokke et al., 2010), Davia et al. showed that SERCA overexpression reduces aftercontractions (Davia et al., 2001). A recent study by Bai et al. showed that PLN-KO in a CPVT RyR2 mutant mouse have less frequent Ca waves but more frequent Ca sparks compared to CPVT mutant mice (Bai et al., 2013). This RyR2 causes substantial increases in Ca sparks (as may also occur in other pathological states) which would amplify the amount of SR Ca release for a given [Ca]_SR and [Ca]_i, increasing waves analogous to the doubling of cluster size (Fig 8B). This emphasizes that enhancing SERCA function may also limit arrhythmogenic propagating waves that result from sensitized RyR2, whether from genetic CPVT-linked mutations or pathological states like heart failure, chronic Ca/calmodulin-dependent protein kinase II (CaMKII) activation or oxidative stress.

Another important point in our study is differences of Ca wave propagation in longitudinal and transverse directions. In ventricular myocytes, CRUs locate primarily along T-tubules with some under the surface sarcolemma and only rare RyRs in network SR. Along T-tubules CRUs are typically only 0.5–1 μm, vs. the roughly 2 μm longitudinal sarcomeric spacing. We show how much more robust transverse CRU coupling is versus longitudinal coupling, but for a more arrhythmogenic cell-wide Ca wave longitudinal coupling is essential. One can picture then how transverse CRU coupling is easier to achieve (Fig 3), but that recruitment of several transverse CRUs can provide the stronger Ca source that drives longitudinal propagation.

It has shown that sensitization of RyR ahead of Ca wave front may promote Ca waves (Keller et al., 2007; Ramay et al., 2010; Maxwell & Blatter, 2012) presumably by SERCA-dependent uptake between CRUs that raises local [Ca]_SR at the next CRU. We show here that as Ca diffusion in the network SR is decreased, Ca waves propagate more readily (Fig 6C–D), because it prevents depletion of [Ca]_SR at that next CRU that could be caused by depletion at the first CRU (if intra-SR diffusion is fast). Picht et al. measured the spatiotemporal spread of intra-SR depletion during individual Ca sparks (Picht et al., 2011). While [Ca]_SR depletion 0.8 μm from the initiating spark CRU was similar in transverse and longitudinal directions (roughly half of that at the releasing CRU), the depletion impact would be greater in the transverse direction where a neighboring CRU is at that 0.8 μm range. There was substantial variation in how diffusionally connected a particular CRU was, but for the intra-SR diffusion coefficients that matched the data, there would typically be very little depletion at a longitudinal CRU that is 2 μm away from the active CRU.

In conclusion, we have shown how increased SERCA function can both promote and suppress Ca wave propagation. For modest amounts of SERCA increase, the promotion of arrhythmogenic Ca waves predominates, but even higher SERCA enhancement can limit that Ca wave propagation. This is because enhancing SERCA activity increases SR Ca load, which promotes Ca sparks and propagation as waves, but the ability of high SERCA activity can prevent Ca from one CRU from reaching and activating a next CRU. Therefore, enhancing SERCA activity always leads to the higher Ca spark frequency but under certain conditions can lower Ca wave propensity. Lowering SERCA activities also reduces the propensity of Ca wave propagation, but at the potential cost of lower Ca transients and cardiac contraction.

KEY POINTS SUMMARY.

• Increasing SERCA pump activity enhances sarcoplasmic reticulum calcium (Ca) load, which increases both ryanodine receptor opening and driving force of Ca release flux.

• Both of these effects promote Ca spark formation and wave propagation.

• However, increasing SERCA activity also accelerates local cytosolic Ca decay as the wave front travels to the next cluster, which limits wave propagation.

• As a result, increasing SERCA pump activity has a biphasic effect on propensity of arrhythmogenic Ca waves, but a monotonic effect to increase Ca spark frequency and amplitude.