NCX-Mediated Subcellular Ca²⁺ Dynamics Underlying Early Afterdepolarizations in LQT2 Cardiomyocytes

Abstract

Long QT syndrome type 2 (LQT2) is a congenital disease characterized by loss of function mutations in hERG potassium channels (I_Kr). LQT2 is associated with fatal ventricular arrhythmias promoted by triggered activity in the form of early afterdepolarizations (EADs). We previously demonstrated that intracellular Ca²⁺ handling is remodeled in LQT2 myocytes. Remodeling leads to aberrant late RyR-mediated Ca²⁺ releases that drive forward-mode Na⁺-Ca²⁺ exchanger (NCX) current and slow repolarization to promote reopening of L-type calcium channels and EADs. Forward-mode NCX was found to be enhanced despite the fact that these late releases do not significantly alter the whole-cell cytosolic calcium concentration during a vulnerable period of phase 2 of the action potential corresponding to the onset of EADs. Here, we use a multiscale ventricular myocyte model to explain this finding. We show that because the local NCX current is a saturating nonlinear function of the local submembrane calcium concentration, a larger number of smaller-amplitude discrete Ca²⁺ release events can produce a large increase in whole-cell forward-mode NCX current without increasing significantly the whole-cell cytosolic calcium concentration. Furthermore, we develop novel insights, to our knowledge, into how alterations of stochastic RyR activity at the single-channel level cause late aberrant Ca²⁺ release events. Experimental measurements in transgenic LTQ2 rabbits confirm the critical arrhythmogenic role of NCX and identify this current as a potential target for antiarrhythmic therapies in LQT2.

Introduction

Malignant arrhythmias that result in sudden cardiac death (SCD) remain a major cause of death worldwide. Abnormally long Q wave and T wave (QT) intervals have been identified as an important risk factor for SCD in acquired cardiac diseases, including heart failure and myocardial infarction (1, 2). Mutations in 15 different genes have been associated with congenital long QT syndrome. Loss-of-function of KCNH2 encoding the rapidly activating delayed-rectifier K⁺ channel (I_Kr) is associated with long QT syndrome type 2 (LQT2), which accounts for over 30% of congenital long QT syndrome cases (2, 3) and results in a high rate of mortality. A large proportion of fatalities in LQT2 patients occur as a result of triggered ventricular tachycardia and polymorphic ventricular tachycardia (pVT) evoked by emotional stress or exercise (2, 3, 4). Features of the electrocardiogram such as triggered activity and torsade de pointes are thought to be caused by early afterdepolarizations (EADs) (4, 5), manifested as membrane voltage (V_m) oscillations at the single-myocyte level during the repolarizing phase of the action potential (AP).

To study the phenotype of human arrhythmia, we created a transgenic rabbit model of LQT2 (6) that overexpresses a pore mutant of the human gene KCNH2 (HERG-G628S) in cardiomyocytes to eliminate I_Kr currents. As a result, these rabbits exhibited prolonged QT interval and high incidence of SCD (>50% at 1 year of age) due to pVT (6). Ex vivo optical mapping used to investigate the underlying substrate of arrhythmia revealed a prominent spatial dispersion of AP duration (APD) and discordant APD alternans (6, 7). The observation of triggered activity in the form of EADs in isolated myocytes under β-adrenergic stimulation has supported the hypothesis that arrhythmia originates at the single-cell level (8, 9).

Normal Ca²⁺ cycling in cardiomyocytes is maintained by the interplay between the AP and Ca²⁺ release from the sarcoplasmic reticulum (SR) mediated by the ryanodine receptor (RyR) channels. Upon depolarization, a small amount of Ca²⁺ enters the cell through sarcolemmal L-type calcium channels (LTCCs) to activate RyR clusters that release a much larger amount of Ca²⁺ to the cytosolic compartment. The sum of those localized Ca²⁺ release events (Ca²⁺ sparks) contributes to the transient rise of the whole-cell cytosolic calcium concentration [Ca²⁺]_i (Ca²⁺ transient). Subsequent removal of intracellular Ca²⁺ by the electrogenic sarcolemmal Na⁺-Ca²⁺ exchanger (NCX) current provides additional depolarizing current and can prolong the APD, especially when RyR-mediated SR Ca²⁺ release termination is not robust. Our previous studies of LQT2 rabbit models showed that Ca²⁺-mediated communication between RyRs and other Ca²⁺ transport complexes plays a critical role in EAD formation (10, 11). We reported that the activity of RyRs in rabbit LQT2 ventricular myocytes is enhanced, resulting in a large number of late aberrant SR Ca²⁺ release events. We proposed that these protracted Ca²⁺ releases from individual RyR clusters provide a basis for an increased depolarizing NCX current, which suffices to maintain the V_m for a prolonged period of time in a window permissive for reactivation of LTCCs, thereby causing EADs. Our computational modeling validated this hypothesis by demonstrating that late aberrant Ca²⁺ releases result in a larger-magnitude NCX current during late phase 2 and early phase 3 of the AP, thereby slowing down repolarization and enabling L-type Ca²⁺ current reactivation during this vulnerable time window, which marks the onset of EADs.

Most computer modeling studies to date have associated EADs with an instability of V_m dynamics driven by reactivation of the L-type Ca²⁺ current I_Ca,L during the plateau phase of the AP (12, 13, 14, 15, 16, 17). The role of RyR-mediated Ca²⁺ release in EAD formation was also modeled in the setting of pharmacologically induced LQT2 with a generic block of I_Kr (18). This study found that reduced SR Ca²⁺ release can protect against EADs by reducing the Ca²⁺ transient amplitude and NCX current. In contrast, our previous study of transgenic LQT2 rabbits showed that stabilization of RyR activity by a CAM kinase inhibitor (KN93) increased Ca²⁺ transient amplitude while at the same time eliminating EADs (10). Our computer-modeling study of LQT2 ventricular myocytes under β-adrenergic stimulation reproduced experimental observations (10) and further showed that in the presence of RyR hyperactivity, the depolarizing NCX current can be significantly larger during late phase 2 and early phase 3 of the AP, thereby promoting reopening of LCCs and EADs. Importantly, modeling revealed that NCX current is enhanced despite SR depletion and reduced Ca²⁺ transient amplitude (i.e., reduced [Ca²⁺]_i peak during early phase 2 of the AP).

However, the mechanism by which forward-mode NCX current can be enhanced without significantly increasing the whole-cell cytosolic calcium concentration during the vulnerable period of repolarization is still not fully understood. Furthermore, the role of NCX in triggered activity in the setting of LQT2 has not been investigated experimentally. Here, we use a physiologically detailed ventricular myocyte model with spatially distributed Ca²⁺ release to further elucidate the mechanism of NCX-mediated triggered activity in LQT2 ventricular myocytes, and we validate experimentally our computer-modeling predictions.

Our modeling results show that the local NCX current is a saturating nonlinear function of the local submembrane calcium concentration. Therefore, a larger number of smaller-amplitude Ca²⁺ release events generated by hyperactive RyRs and reduced SR load can increase whole-cell forward-mode NCX about twofold as much as a smaller number of larger-amplitude Ca²⁺ release events generated by stable RyRs and normal SR load without significantly increasing calcium transient. Our modeling study further dissects the arrhythmogenic role of two different RyR channel-gating mechanisms that may underlie the increased spark rate observed in permeabilized myocyte experiments (10): increased sensitivity to cleft-calcium concentration, leading to increased RyR open probability (P_o) (19), and shortened refractoriness (20), leading to faster recovery of local RyR clusters. We find that the combination of both effects is most effective at potentiating NCX and EADs. Finally, we highlight the role of NCX in triggered activity by demonstrating computationally that partial NCX blockade eliminates EADs. To validate this prediction, we use cellular electrophysiology and confocal Ca²⁺-imaging study of ventricular myocytes derived from LQT2 hearts with pharmacologically suppressed NCX. The observations confirm the critical role of NCX in EAD initiation.

Methods

Experiments

Myocyte isolation

All procedures were approved by the Rhode Island Hospital Institutional Animal Care and Use Committee and conformed to the Guide for the Care and Use of Laboratory Animals published by the US National Institutes of Health (NIH Publication No. 85-23, revised 1996). Ventricular myocytes were isolated from the hearts of transgenic LQT2 (n = 3) female New Zealand white rabbits (3.5 kg) using standard enzymatic digestion procedures. In brief, the heart was excised from euthanized rabbits and perfused for 5–7 min with a nominally Ca²⁺-free solution containing (in mM) 140 NaCl, 4.4 KCl, 1.5 MgCl₂, 0.33 NaH₂PO₄, 16 taurine, 5 HEPES, 5 pyruvic acid, and 7.5 glucose. Next, the heart was perfused for 10–15 min with the same solution, to which 0.65% collagenase type II (Worthington Biochemical, Lakewood, NJ) and 0.1% bovine serum albumin were added. The left ventricle was minced, and the cells were dispersed with a glass pipette for 3–5 min in a solution containing (in mM) 45 KCl, 65 K-glutamate, 3 MgSO₄, 15 KH₂PO₄, 16 taurine, 10 HEPES, 0.5 EGTA, and 10 glucose and 1% bovine serum albumin (pH 7.3). The cell suspension was filtered through a 100-μm nylon mesh, plated on laminin-coated coverslips in medium M199, and used within 6–8 h.

Cell electrophysiology and Ca²⁺ imaging

APs were recorded using the whole-cell patch-clamp technique at 35 ± 2°C using an Axopatch 200B amplifier and DIGIDATA 1322A interface (Axon Instruments, Union City, CA) (10). The external solution contained (in mM) 140 NaCl, 5.4 KCl, 1.85 CaCl₂, 0.5 MgCl₂, 10 HEPES, and 5.6 glucose (pH 7.4). Patch pipettes were filled with the following solution (in mM): 90 K-aspartate, 50 KCl, 5 MgATP, 5 NaCl, 1 MgCl₂, 0.1 Tris GTP, 10 HEPES, and 0.1 Rhod-2 (Molecular Probes, Eugene, OR (pH 7.2)). APs were evoked by application of 3-ms-long voltage pulses with amplitude 20% above the threshold level. Intracellular Ca²⁺ imaging was performed using the Leica SP5 confocal system (Leica Microsystems, Buffalo Grove, IL) in a line-scan mode. Rhod-2 was excited by a 543-nm laser and the fluorescence was acquired at 560–660 nm wavelengths. Calcium transients were analyzed using Leica Software, Origin 8.2 (OriginLab, Northampton, MA), and Image J (NIH, Bethesda, MA).

Mathematical modeling

Rabbit ventricular myocyte model

We use a physiologically detailed ventricular myocyte model with Ca²⁺ cycling coupled to (V_m) dynamics (10) to investigate the ionic mechanisms of EAD formation and elimination in LQT2 myocytes under different conditions. This multiscale model, originally developed by Restrepo et al. (21, 22), bridges the submicron scale of individual Ca²⁺ release units (CRUs) and the whole cell by simulating a realistically large number of 20,000 diffusively coupled CRUs spatially distributed throughout the cell, with 4 LTCCs colocated with 100 RyRs in each CRU (Fig. S1). It accounts for the stochastic nature of Ca²⁺ releases by using a Markov description of channel kinetics for both LTCCs and RyRs. In addition, it describes the bidirectional coupling of Ca²⁺ and V_m dynamics by incorporation of a full set of sarcolemmal currents including I_Ca,L, I_NCX, I_Ks, I_to,f, I_K1, and I_NaK. We exclude I_Kr to model LQT2 myocytes. This model therefore has the unique capability to explore the effects of alteration of RyR activity at the single-channel level on EAD formation at the whole-cell level.

The model we use is a modification of Restrepo et al. (21, 22) that includes a higher spatial resolution of the diffusive coupling between CRUs, a more quantitative description of Ca²⁺ buffers, and a 16-state Markov model of LTCCs. The I_Ca,L model reduces at the whole-cell level to a Hodgkin-Huxley formulation with voltage- and Ca²⁺-dependent inactivation. This Markov model of LTCCs provides more flexibility for fitting whole-cell experimental measurements of I_Ca,L, including a larger-window V_m range of this current. We have also modified the Ca²⁺-dependent activation of the NCX current to be time dependent to account for more recent experiments showing a slower timescale of allosteric Ca²⁺ activation (23). These changes are detailed in the online supplement of Terentyev et al. (10).

To model the effect of β-adrenergic stimulation with isoproterenol (ISO), we fit the experimental data that results in an increase in the sarcoplasmic reticulumn Ca²⁺-ATPase uptake rate as well as increases in I_Ca,L and I_Ks currents. We incorporate the effect of β-adrenergic stimulation under steady-state conditions to model nontransient EADs that persist on an experimental timescale longer than the timescales of ISO-induced I_Ca,L and I_Ks phosphorylation (8).

Computer simulations were carried out by pacing myocytes at 0.25 Hz in accordance with experiments (10) until a steady state was reached. During pacing, whole-cell cytosolic and SR calcium concentrations were recorded, denoted by [Ca²⁺]_i and [Ca²⁺]_SR, respectively, along with V_m and individual sarcolemmal currents. In addition, experimental confocal line scans were emulated by recording the local [Ca²⁺]_i along a longitudinal row of CRUs passing through the center of the myocyte and parallel to its long axis.

Model of hyperactive RyRs

SR release is mediated by 100 RyRs collocated with LCCs in each CRU. Each RyR is described by a four-state model (22) (also shown in Fig. 1), which assumes that luminal Ca²⁺ regulates the sensitivity of the RyR channels via auxiliary proteins triadin/junctin (T/J) interacting with the luminal Ca²⁺ buffer calsequestrin (CSQN) (24). This mechanism is incorporated by allowing CSQN to bind to the RyR/T/J complex when Ca²⁺ is depleted in the JSR and by choosing the RyR closed-to-open transition rate in the CSQN bound state (k_p,B) to be much smaller than the one (k_p,U) in the CSQN unbound state. The reduced sensitivity in the CSQN bound state both contributes to Ca²⁺ spark termination and induces a refractory (25, 26) state whereby CSQN must unbind from RyRs before future sparks are possible. Experiments reported a large RyR unitary calcium current under near-physiological ionic conditions (0.35–0.6 pA at 1 mM [Ca²⁺]_JSR) (27, 28), which is ∼10-fold larger than the value assumed in Restrepo et al. (22). Therefore, we follow Sato et al. (29) by using RyR closed-to-open transition rates that produce a maximal open probability around 0.1 (Fig. 2 C). We also introduce an SR load dependence of the closed-to-open rates (k_p,U and k_p,B) to model the increase of RyR open probability at high [Ca²⁺]_JSR (30), which is not captured by the original Restrepo et al. model (22). In that model, luminal gating of RyR is solely mediated by CSQN binding to the RyR/T/J complex, and the RyR open probability becomes independent of SR load when all RyRs occupy the CSQN unbound state, which occurs for [Ca²⁺]_JSR larger than ∼600 μM (Fig. S2). In this model, RyRs are sensitive to luminal Ca²⁺ (in addition to being regulated by CSQN binding) as supported by a wide range of experiments (see (31) and references therein).

Figure 1.

Schematic illustration of the four-state model of RyR gating. Transition rates k_p,U and k_p,B govern the opening of the channel. The transition rate k_b, which depends on the amount of Ca²⁺ bound to CSQN, is accelerated when the load is depleted during SR Ca²⁺ release. With k_p,B much smaller than k_p,U, the refractoriness is implemented, which could be tuned by adjusting the relative magnitude of k_p,B to k_p,U. To see this figure in color, go online.

Figure 2.

Effect of altering RyR gating parameters. (A) Spark restitution curves obtained by measuring the relative magnitude of SR Ca blinks after a previous spark occurred in the same CRU for a holding membrane voltage V_m = 0 mV are shown. Blink magnitude is determined by taking the difference of the minimal [Ca²⁺]_JSR and [Ca²⁺]_JSR just before the spark begins. Blink magnitudes are binned into 20-ms intervals. The average values and standard errors are plotted as a function of time since the last spark. The blue and red lines are corresponding to $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U = 1 and $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U = 0.01, respectively, with $\overline{\text{k}}$_p,U = 4 ms⁻¹ and c^∗ = 7 μM. (B) Spark recovery time as a function of $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U is shown. The data points are extracted from a single exponential fit of spark restitution curves as in (A). (C) The steady-state open probability of RyRs for $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U = 1 and c^∗ = 20 μM (red), c^∗ = 3 μM (blue), and for high (solid lines) and low (dashed lines) [Ca²⁺]_JSR is shown. (D) The peak magnitude of I_Ca,L current (red squares) and SR Ca²⁺ release transients (blue circles) under voltage clamp steps from holding potential −80 mV to step voltages between −40 and 40 mV for c^∗ = 20 μM (solid lines) and c^∗ = 3 μM (dashed lines) is shown. I_Ca,L current peak did not differ between c^∗ = 20 μM (solid red line) and c^∗ = 3 μM (dashed red line). CICR response has a wider V_m range for c^∗ = 3 μM compared to c^∗ = 20 μM. To see this figure in color, go online.

The rates k_p,U and k_p,B (corresponding to k₁₂ and k₄₃, respectively, Restrepo et al. (22)) are given by

$$k_{p,U}=\left(\frac{{\overline{k}}_{p,U}}{1+{\left(c^{\text{∗}}/c_p\right)}^2}\right)\left(\frac{1}{1+{\left(c_{jsr}^{\text{∗}}/c_{jsr}\right)}^2}\right)$$ (1)

and

$$k_{p,B}=\left(\frac{{\overline{k}}_{p,B}}{1+{\left(c^{\text{∗}}/c_p\right)}^2}\right)\left(\frac{1}{1+{\left(c_{jsr}^{\text{∗}}/c_{jsr}\right)}^2}\right),$$ (2)

respectively, where c_p = [Ca²⁺]_cleft and c_jsr = [Ca²⁺]_JSR are the calcium concentrations in the proximal space (dyadic cleft) and junctional SR (JSR) compartment, respectively. We model RyR hyperactivity both by shifting the open probability of RyRs toward lower cleft-calcium concentration by reducing c^∗ as further explained below and by shortening RyR refractoriness. The increase in open probability is consistent with lipid bilayer studies of hyperactive RyRs (19) and the observed increased frequency of Ca²⁺ sparks in permeabilized LQT2 myocytes in which RyRs are hyperphosphorylated (10).

We can reduce refractoriness by increasing k_p,B relative to k_p,U. The ratio $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U controls the relative reduction of RyR opening rate in the CSQN bound state to the unbound state. By increasing this ratio, the channels that have transitioned to the bound state fail to keep the small opening rate and thus fail to suppress the continued sparking of the same CRU.

Refractoriness has previously been characterized by taking repeated nanoscopic measurements of SR Ca²⁺ blinks (local JSR depletions) (32). This study found that the characteristic timescale for the magnitude of subsequent SR Ca²⁺ blinks to recover to the original magnitude was much longer than the timescale of the Ca²⁺ refilling. By replicating these experiments using our model, we produce a quantitative measurement of spark restitution. Fig. 2 A shows that simulations with a larger value of $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U have reduced refractoriness. When $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U is smaller than 0.01 (0.01 corresponding to normal RyR activity), the magnitude of SR Ca²⁺ blinks recovers on a timescale determined by the rate of CSQN unbinding, whereas when $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U is larger than 0.5, the refractory state does not inhibit RyR opening, and so the magnitude of SR Ca²⁺ blinks recovers on a timescale determined by the SR refilling time. Fig. 2 B illustrates this trend for values of $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U ranging between 0.001 and 1.

To model increased Ca²⁺ sensitivity, we reduce c^∗ in Eqs. 1 and 2, which reduces the half maximal effective concentration (EC₅₀) of RyR open probability, thereby increasing the transition rate to the open state at low cleft-calcium concentration c_p. This effect is illustrated in Fig. 2 C, in which we plot the RyR open probability as a function of cleft-calcium concentration c_p for c^∗ = 3 μM and c^∗ = 20 μM. For purpose of illustration in Fig. 2 C, we restrict our attention to the limiting case $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U = 1 (corresponding to ${\overline{k}}_{p,U}={\overline{k}}_{p,B}={\overline{k}}_p$), in which the refractory state does not inhibit RyR openings and the EC₅₀ is given by

$${\text{EC}}_{50}=\frac{c^{\text{∗}}}{\sqrt{1+{\overline{k}}_p{\left[1+{\left(c_{jsr}^{\text{∗}}/c_{jsr}\right)}^2\right]}^{-1}}}.$$ (3)

By varying the EC₅₀ of RyR opening in this way, there is a measurable effect on the trend of Ca²⁺-induced-Ca²⁺-release (CICR) gain. When c^∗ is lower, the rate of spark recruitment due to I_Ca,L is increased above and below 5 mV (the peak voltage for RyR recruitment). The increase of RyR activity when c^∗ is reduced is much more potent in the voltage range of EAD onset than for the majority of the AP plateau (Fig. 2 D).

We have previously shown (10) that the mechanism for EAD initiation in this model is largely caused by downstream remodeling of cytosolic Ca²⁺ cycling, manifested by increased spark frequency in permeabilized myocytes, and has less to do with the direct effect of reduced repolarization current due to the absence of I_Kr. To investigate the effect of altered Ca²⁺ cycling, it is useful to distinguish between two extreme cases. The first corresponds to a choice of model parameters with enhanced RyR-mediated SR Ca²⁺ leak due to both increased sensitivity of RyRs to cytosolic Ca²⁺ and shortened refractoriness, referred as the “hyperactive” RyR model. This model best reproduces the experimentally observed electrophysiological phenotype of LQT2 under β-adrenergic stimulation with hyperphosphorylated RyRs. The second corresponds to a choice of parameters in which RyR activity is stabilized via Ca²⁺-calmodulin dependent protein kinase II (CaMKII) inhibitor KN93 (10), referred as the “stabilized” RyR model. We have deliberately chosen to only include the stabilizing effect of CaMKII inhibition on RyR activity. Although KN93 may potentially influence other sarcolemmal currents, we are primarily interested here in exploring the effect of abnormal Ca²⁺ handling on NCX current and EAD formation. In addition to the two above cases of stabilized and hyperactive RyRs, we investigate intermediate cases in which RyR activity is enhanced by increasing channel sensitivity to cytosolic Ca²⁺ (decreasing c^∗) or shortening the refractory period (increasing $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U). Although there is no known simple way to vary those two parameters individually in the experiment, we exploit the ability to vary them independently in the computational model to gain basic insights into the individual arrhythmogenic roles of increased RyR open probability and shortened refractoriness, which have not been clearly dissected to date.

Results

Role of RyR refractoriness and open probability on AP phenotype

Fig. 3 compares results of simulations of LQT2 myocytes under β-adrenergic stimulation for model parameters corresponding to stabilized RyRs (Fig. 3 A) and increased RyR sensitivity (Fig. 3 B), reduced RyR refractoriness (Fig. 3 C), and both increased sensitivity and reduced refractoriness, denoted as hyperactive RyRs (Fig. 3 D). For all the simulations, the intracellular sodium concentration reaches a steady-state value that varies by less than 3%.

Figure 3.

Computer modeling results of LQT2 myocytes paced at 0.25 Hz under ISO stimulation for the stabilized RyRs control condition (A), only increased Ca²⁺ sensitivity (B), only reduced refractoriness (C), and the combination of (B) and (C) referred to for brevity as hyperactive RyRs (D). The first row shows V_m traces for representative beats in the steady state. The second row shows whole-cell cytosolic calcium concentration [Ca²⁺]_i. The third row shows SR calcium concentration. The fourth row shows whole-cell average NCX current I_NCX. The fifth row shows whole-cell long type Ca²⁺ channel current I_Ca,L. The sixth row shows a confocal line scan of cytosolic calcium concentration. (A) Stabilized RyRs (c^∗ = 7 μM and $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U = 0.01) with normal Ca²⁺ transient amplitude and AP are shown. (B) Increased Ca²⁺ sensitivity (c^∗ = 3 μM and $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U = 0.01) significantly decreases Ca²⁺ transient amplitude but does not produce EADs. (C) Reduced RyR refractoriness (c^∗ = 7 μM and $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U = 0.6) slightly decreases Ca²⁺ transient amplitude and produces a single EAD. (D) Both increased Ca²⁺ sensitivity and reduced refractoriness (hyperactive RyRs with c^∗ = 3 μM and $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U = 0.6) significantly decrease Ca²⁺ transient amplitude and produce multiple EADs. In all the simulations, $\overline{\text{k}}$_p,U is fixed at 4 ms⁻¹. The original code to produce the red and blue lines is available at https://github.com/MingwangZhong/NCX-mediated-EADs-in-LQT2. The red traces in (B)–(D) correspond to the control condition of (A). Scale bar, 30 μm. To see this figure in color, go online.

Fig. 3 B shows the effect of increased Ca²⁺ sensitivity by reducing c^∗ from 7 to 3 μM. AP traces in the top panel show that the increased sensitivity causes only a minor deflection in the AP waveform and is insufficient to evoke EADs. The increased RyR open probability results in a reduction in the diastolic SR Ca²⁺ load (middle panel). Because there is no difference in the luminal dependence of RyR gating, CSQN will bind to the channel and prevent SR Ca²⁺ release below 550 μM. As a result, the nadir of the SR depletion during systole remains unchanged. This results in a reduced Ca²⁺ transient amplitude (second panel). Confocal line-scan equivalents show that the number of late Ca²⁺ sparks during repolarization does not significantly increase when Ca²⁺ sensitivity is increased in this way (Fig. 3 A versus Fig. 3 B, bottom panels). Consequently, the NCX current is largely unchanged during the repolarization phase (Fig. 3 B, fourth panel).

We then compare the LQT2 model with stabilized RyRs to a model in which RyR refractoriness is hindered by increasing the RyR open rate in the bound state from $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U = 0.01 to $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U = 0.6. The top panel of Fig. 3 C shows that without RyR refractoriness, AP repolarization is interrupted with a large EAD, consistent with the results of Terentyev et al. (10). Without CSQN-mediated inactivation of RyRs at low SR load, both the diastolic and systolic SR loads are reduced dramatically (middle panel). Ca²⁺ transient amplitudes are slightly smaller when refractoriness is reduced, whereas the rate of decay of the Ca²⁺ transient is noticeably slower (second panel). This is due to the late aberrant Ca²⁺ sparks that occur during repolarization when refractoriness is reduced, which can be seen in the confocal line scan (bottom panel). When this late Ca²⁺ release activity occurs, the NCX current shifts toward forward-mode (fourth panel), which slows repolarization and allows I_Ca,L to recover from inactivation.

When we model both increased Ca²⁺ sensitivity and reduced RyR refractoriness, the V_m traces show a significantly elongated AP with many EADs (top panel in Fig. 3 D). As before, this model has a reduced SR Ca²⁺ load (middle panel) but with a much greater reduction in Ca²⁺ transient amplitude (second panel) and the slower rate of Ca²⁺ transient decay. Because of the increased Ca²⁺ sensitivity (Fig. 2 D), CICR during the repolarization phase (−20 to 0 mV) is much more sensitive to I_Ca,L current, increasing the rate of late aberrant Ca²⁺ releases during this period (bottom panel of Fig. 3 D; also see Video S1). There is therefore an even greater increase in the forward-mode NCX current that slows repolarization and allows reactivation of I_Ca,L (Fig. 3 D). This results in the repolarization being interrupted multiple times, leading to multiple EADs.

Video S1. EAD Initiation in LQT2 Myocytes

The movie shows the spatially distributed cytosolic calcium concentration versus time in a 3-dimensional virtual myocyte during an action potential. Also shown on top are corresponding time traces of the whole-cell membrane voltage and cytosolic calcium concentration. Late aberrant Ca2+ releases, which increase forward mode NCX1 current and promote EADs, are highlighted during the time window 100–320 ms.

The interruption to repolarization occurs in a vulnerable V_m window in which LTCCs begin to recover from inactivation but have not yet fully deactivated (15, 33). For time t > 300 ms after initial depolarization, corresponding to late phase 2 of the AP, V_m enters the critical window in which I_Ca,L begins to recover from inactivation but is still sufficiently activated to allow the current to increase. It is inside this window that V_m in the hyperactive RyR model begins to diverge from the stabilized model toward the first EAD (top panel of Fig. 3 D). The whole-cell NCX current during this time window is larger in the hyperactive RyR model by 110% (−0.55 pA/pF vs. −0.26 pA/pF at t ∼350 ms, Table 1). Although the forward-mode NCX current increase clearly follows the increase in SR Ca²⁺ release, it is not accompanied by an increase in whole-cell [Ca²⁺]_i, which is traditionally assumed to determine NCX magnitude. Table 1 shows that [Ca²⁺]_i has comparable magnitudes in the hyperactive and stabilized models at t ∼ 350 ms (Table 1) and that the average submembrane calcium concentration [Ca²⁺]_s is only 30% larger in the hyperactive model compared to the stabilized one.

Table 1.

Instantaneous Values at the Whole-Cell Level

	RyR Gating Model	[Ca2+]I (μM)	[Ca2+]s (μM)	Jrel (μMcyt/ms)	Spark Rate (sparks/ms)	INCX (pA/pF)
t = 20 ms	stabilized	0.69	2.41	2.31	8951	−0.44
	hyperactive	0.25	0.98	1.29	7671	−0.13
t = 322 ms	stabilized	0.09	0.15	0.04	107	−0.26
t = 350 ms	hyperactive	0.1	0.2	0.11	609	−0.55

Fig. 4 A maps the effects of varying independently and jointly the two RyR gating parameters 1/c^∗ and $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U ($\overline{\text{k}}$_p,U fixed) that control the sensitivity of RyRs to cleft Ca²⁺ and refractoriness, respectively. The number of EADs increases when both $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U and 1/c^∗ are increased. When we examine the diastolic SR Ca²⁺ load over the same range of $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U and 1/c^∗ (Fig. 4 B), the load tends to be depleted when these parameters are increased. Fig. 4 C shows that reducing c^∗ reduces the Ca²⁺ transient magnitude, which is consistent with the experimental observations of Terentyev et al. (10) in slowly paced rabbit ventricular myocytes with hyperactive RyRs and addition of ISO. This is because the increased RyR open rate will deplete the diastolic load without allowing the SR nadir during systole to deplete. When $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U is increased, the effect on Ca²⁺ transient amplitude is similarly as pronounced because it also increases RyR open probability in the bound state.

Figure 4.

Effect of altering RyR gating on EAD formation and SR release characteristics. (A) The number of EADs as a function of RyR Ca²⁺ sensitivity, which is increased by decreasing c^∗ (increasing 1/c^∗), and refractoriness, which is reduced by increasing the ratio $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U is shown. Both reducing refractoriness and increasing Ca²⁺ sensitivity produce unstable phenotypes with many EADs. Red diamond, blue triangle, blue circle, and blue diamond denote parameters used in Figs. 3, A–D, respectively. $\overline{\text{k}}$_p,U is fixed at 4 ms⁻¹. (B) SR load as a function of 1/c^∗ and $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U is plotted. (C) Ca²⁺ transient amplitude as a function of 1/c^∗ and $\overline{\text{k}}$_p,B/$\overline{\text{k}}$_p,U is plotted. To see this figure in color, go online.

Fig. 3 only shows results in steady state. As shown in Fig. S8, when RyR sensitivity is suddenly increased by lowering c^∗ starting from a diastolic control SR load, EADs form transiently at the first beat even without shortened RyR refractoriness. However, EADs are not sustained because the SR load adjusts to a lower level during subsequent beats because of increased SR leak. A similar transient behavior has been observed in previous studies of Trafford et al. (34) and Venetucci et al. (35). One difference, however, is that those studies were conducted in rat ventricular myocytes with voltage clamped at 0.5 Hz under Ca²⁺ overload conditions. Under those conditions, spontaneous Ca²⁺ release is typically manifested in the form of Ca²⁺ waves causing delayed afterdepolarizations under the combination of ISO and caffeine. Our experiments and those of Terentyev et al. (10) used rabbit ventricular myocytes (either LQT2 rabbit myocytes with leaky RyR + ISO or control rabbit myocytes with caffeine + ISO). In those experiments, Ca²⁺ cycling instability is manifested in the form of late SR Ca²⁺ releases triggered by Ca²⁺ entry through L-type Ca²⁺ channels at low SR load. Those late releases then drive NCX to slow down repolarization during the AP plateau and cause reactivation of LCCs and EADs.

Mechanism of increased whole-cell forward-mode NCX current without increasing whole-cell cytosolic calcium concentration

As noted earlier, the forward-mode NCX current in the hyperactive RyR model has an ∼110% larger magnitude than in the stabilized RyR model at the time of EAD onset. This increase in NCX current is present even though [Ca²⁺]_i is only slightly increased in the hyperactive model (second panel of Fig. 3 D at t ∼ 350 ms and Table 1). Because RyRs are located in dyads along the T-tubules in the submembrane space, the Ca²⁺ flux generated by late aberrant releases will preferentially increase [Ca²⁺]_s compared to [Ca²⁺_i (Fig. 5 A). The inset of Fig. 5 A shows that at t ∼ 350 ms, the hyperactive RyR model has a larger total SR Ca²⁺ release current than the stabilized RyR model by a factor of 3 (0.11 μM_cyt/ms vs. 0.04 μM_cyt/ms). This larger release current causes the whole-cell averaged [Ca²⁺]_s to be ∼33% larger in the hyperactive RyR model compared to the stabilized RyR model at t ∼ 350 ms shown in Table 1 (the increase in [Ca²⁺]_s is smaller than the increase in SR release current because [Ca²⁺]_s has a finite background value). Importantly, this ∼33% increase in [Ca²⁺]_s cannot account for the ∼110% increase in forward-mode NCX current in a simplistic common-pool model in which whole-cell [Ca²⁺]_s is assumed to drive the whole-cell NCX current. In the more realistic spatially distributed model of Ca²⁺ release used in this study, the local [Ca²⁺]_s that determines the local NCX current is different in each compartment, varying spatially based on stochastic LTCC openings and SR Ca²⁺ sparks.

Figure 5.

(A) Calcium concentration in the submembrane space ([Ca²⁺]_s) is shown as a function of time for the stabilized RyR model (red) and the hyperactive RyR model (blue). Arrows indicate the peak calcium transient at t = 20 ms and the EAD onset point at t ∼ 350 ms. The inset is the calcium release current as a function of time. (B) The Ca²⁺ spark frequency as a function of time is shown, computed by summing all the events satisfying N_o ≥ 3, where N_o is the number of open RyRs in a CRU. (C) The local NCX current is shown as a function of local Ca²⁺ for V_m = −20, 0, and 20 mV, with [Na⁺]_i = 6 mM and allosteric Ca²⁺ activation A_NCX = 0.5. The current saturates at [Ca²⁺]_s ∼ 4 μM. (D) The distribution of local submembrane calcium concentration in each CRU at t = 20 ms is shown. (E) The distribution of local NCX currents in each CRU at t = 20 ms is shown. (F) The relation of the local NCX current to local [Ca²⁺]_s for the stabilized RyR model (red squares) and the hyperactive RyR model (blue circles) at 20 ms, with bin width 0.1 μM, is shown. (G–I) The similar results at t ∼ 350 ms, with V_m at −15.5 mV, are shown. The vertical arrow in (G) indicates the Ca²⁺ threshold of allosteric activation (0.3 μM), and the vertical arrow in (H) indicates the corresponding NCX current (1.2 μM/ms). To see this figure in color, go online.

To understand the relationship between the increased SR Ca²⁺ release and the increased NCX current, we examine the spatially distributed nature of Ca²⁺ release underlying NCX-mediated Ca²⁺ to V_m voltage signal transduction. For this purpose, we first compare the total spark-firing rates in the hyperactive and stabilized RyR models (Fig. 5 B) and also give their values at the times t = 20 and 350 ms in Table 1, corresponding to the peak of calcium transient and EAD onset, respectively. The whole-cell spark rate at t ∼ 350 ms is around sixfold larger in the hyperactive RyR model (609 sparks/ms) than the stabilized RyR model (107 sparks/ms), even though the whole-cell SR Ca²⁺ release current is only ∼3-fold larger. This implies that there are a smaller number of large sparks in the stabilized RyR model compared to a greater number of small sparks in the hyperactive RyR model. A smaller number of larger sparks occur in the stabilized model because the larger SR Ca²⁺ load causes a larger Ca²⁺ flux during each spark, and sparks are less abundant because RyR channels are less active.

To understand why a larger number of smaller sparks contribute to a larger NCX current in the hyperactive model, we note that the local NCX current is a nonlinear function of the local [Ca²⁺]_s. This nonlinearity stems from the ubiquitous physical limitation on ion transport rate through ion channels, which here causes the NCX current to saturate above [Ca²⁺]_s ∼ 4 μM to a current of −11 μM/ms at V_m = −20 mV and A_NCX = 0.5 (Fig. 5 C). As a direct result of this nonlinearity, the whole-cell NCX current cannot be determined by the spatial average of [Ca²⁺]_s compartments as it would be in a “common-pool” model. Furthermore, because NCX saturates at larger [Ca²⁺]_s, a smaller number of large sparks could potentially contribute less to the total NCX current than a greater number of small sparks, even though both sets of sparks contribute to the same whole-cell [Ca²⁺]_s. For this to be true, at least a subset of the larger sparks needs to fall in the range of [Ca²⁺]_s in which NCX saturates (Fig. 5 C).

Therefore, we constructed histograms of local [Ca²⁺]_s and I_NCX current at t = 20 ms, corresponding to the peak of the calcium transient (Figs. 4 E and 5 D, respectively), and t ∼ 350 ms, corresponding to the critical time of EAD onset (Figs. 4 H and 5 G, respectively). At t = 20 ms, SR Ca²⁺ releases are highly synchronized, and a large fraction of the CRUs have elevated [Ca²⁺]_s. In the stabilized RyR model, the CRUs have [Ca²⁺]_s as high as 7 μM (the tail of the red distribution in Fig. 5 D), whereas in the hyperactive RyR model, the peak [Ca²⁺]_s is 3 μM (the tail of the blue distribution in Fig. 5 D). At t = 20 ms, the stabilized RyR model has more CRUs with larger peak local NCX current than the hyperactive RyR model (Fig. 5 E), resulting in a larger whole-cell NCX current. The direct relation of the local NCX current to the local [Ca²⁺]_s is shown in Fig. 5 F, which shows the saturation effect for [Ca²⁺]_s larger than 4 μM.

At t ∼ 350 ms, during the critical period in which V_m enters the I_Ca,L window, the heightened [Ca²⁺]_s in the hyperactive RyR model is being driven by a threefold-larger release current from JSR, which results from a sixfold-larger spark rate (Table 1). This implies that in the stabilized RyR model, the SR Ca²⁺ flux elevating [Ca²⁺]_s is highly localized to the CRUs undergoing large sparks, whereas in the hyperactive RyR model, there are more sparks with smaller SR Ca²⁺ flux. With a greater number of CRUs with [Ca²⁺]_s in the range 0.3–1.5 μM (Fig. 5 G), more CRUs have NCX current in the range from −1.2 to −6 μM/ms (blue bars in Fig. 5 H), which results in larger whole-cell average NCX current. In contrast, the stabilized RyR model has a greater number of CRUs with high values of [Ca²⁺]_s that extend into the range in which the nonlinearity of the NCX versus [Ca²⁺]_s relation becomes significant (red squares versus blue squares in Fig. 5 I). We note that the small difference between the red and blue squares in Fig. 5 I, which is due to different amounts of time-dependent allosteric Ca²⁺ activation of NCX (A_NCX), implies that this nonlinearity is predominantly responsible for the 110% larger whole-cell average NCX current for hyperactive compared to stabilized RyRs.

Suppression of EAD formation via reduction of NCX current

To investigate the effect of reducing NCX conductance on EAD formation, we modify the hyperactive RyR model such that the strength of the NCX current (g_NCX) is 20% of the normal value (10.5 vs. 52.5 μM/ms). Fig. 6 A shows that in this reduced NCX model, EADs are consistently suppressed. Suppression occurs despite the fact that late aberrant Ca²⁺ release events during repolarization are still present when NCX conductance is reduced (Fig. 6 D). Fig. 6 B shows that cytosolic Ca²⁺ content in the reduced NCX model is elevated through all stages of the AP until it repolarizes. This is to be expected, as reduced NCX conductance will slow the rate of Ca²⁺ extrusion from the myocyte and increase the SR Ca²⁺ load (Fig. 6 C). Although we find no evidence to suggest that the suppression of EAD onset is due to differences in other Ca²⁺-dependent sarcolemmal currents including I_Ca,L (Fig. 6 G) and I_Ks (Fig. 6 I), we see only a modest decrease in forward-mode depolarizing NCX current in the reduced NCX-conductance model during the critical time window of EAD onset (Fig. 6 H).

Figure 6.

Effect of reducing NCX conductance to 20% of its normal value in the computational model of LQT2 under β-adrenergic stimulation. NCX reduction suppresses EADs despite hyperactive RyRs causing late aberrant Ca²⁺ releases. (A) V_m traces for four consecutive beats in steady state with reduced (red) and normal (blue) NCX conductance are shown. (B–I) Detailed comparisons for the first beat in (A) of V_m traces (B), the SR calcium concentration (C), confocal line scans for reduced NCX (D) and normal NCX (E), the cytosolic calcium concentration (F), and three key sarcolemmal currents including I_Ca,L (G), I_NCX (H), and I_Ks (I) are shown. The origin of time in (B)–(I) corresponds to the start of the first beat in (A). Scale bar, 30 μm. To see this figure in color, go online.

When EADs are suppressed by stabilizing RyR activity, V_m follows a very similar time course to the hyperactive RyR model, slowly deviating only during the critical window after t $>$ ∼300 ms (Fig. 3 D). In contrast, when EADs are suppressed via reducing NCX conductance, the time course of V_m begins to deviate from the full NCX model very early in the AP. As a result, comparing the magnitude of the NCX current at the same point in time is misleading. When comparing NCX currents by comparing the magnitude of the current at a given time, it is difficult to quantitatively distinguish the effects of V_m and submembrane Ca²⁺ on the NCX current. Additionally, as the time course of AP differs, the time differs at which the V_m is within the critical window for I_Ca,L reactivation. We therefore compare the NCX currents as a function of V_m during pacing (Fig. 7 A). Using this dynamic current versus voltage (I-V) plot to represent the NCX current, we find that within the critical window of V_m (around −20 mV), the reduced conductance NCX model has ∼70% of the magnitude of the normal conductance NCX model. When the NCX current is reduced, the forward mode of this current responsible for Ca²⁺ extrusion is unable to keep up with Ca²⁺ influx through I_Ca,L. As a result, the SR load increases (Fig. 6 C). When NCX conductance is reduced, the higher SR load increases [Ca²⁺]_s during systole and hence both NCX driving force (Fig. 7 B) and Ca²⁺-dependent allosteric activation of NCX (Fig. 7 C). This model predicts that reduction in NCX conductance is an effective approach to suppress EAD onset for a wide range of I_Ca,L conductances (Fig. S4). When NCX conductance is reduced in the model, I_Ca,L conductance must be increased further (from 182 to 240 mmol/cm/C) to reach the threshold for EAD onset.

Figure 7.

Phase plane plots dissecting the V_m and Ca²⁺ contributions to NCX for the models with reduced (red) and normal (blue) NCX conductance at the same beat corresponding to Fig. 6, B–I. Those plots are intended to show that partial blockade of NCX leads to smaller I_NCX magnitude together with higher [Ca²⁺]_s and higher allosteric activation of I_NCX for V_m in the I_Ca,L window range (V_m ∼ −20 mV). Regions of the plots outside this V_m range are included to represent a complete cycle length but are not directly relevant to the mechanism of EAD suppression by NCX blockade. (A) The dynamic I-V plot of NCX is shown. The hyperactive model with reduced NCX conductance (red) simply repolarizes, whereas the one without reduced NCX conductance (blue) loops back on itself once it reaches −30 mV. The NCX current at the point of EAD onset is larger in the model with normal NCX conductance. (B) The whole-cell average submembrane calcium concentration as a function of V_m is shown. The hyperactive model with reduced NCX conductance has a steep peak because of impaired Ca²⁺ extrusion leading to increased SR Ca²⁺ load. (C) Allosteric activation of NCX channels as a function of V_m is shown. Because of the Ca²⁺ buildup in the reduced conductance NCX model, Ca²⁺ will activate the channel more rapidly and compensate for the reduced conductance. To see this figure in color, go online.

To validate the predictions of computer modeling, we recorded Ca²⁺ transients in LQT2 myocytes exposed to 50 nM of ISO, a β-adrenergic agonist, for 10–15 min before and after application of 350 nM 2-[4-[(2,5-difluo- rophenyl)methoxy]phenoxy]-5-ethoxyaniline (SEA0400) to partially block NCX (Fig. 8). Without the blocker, myocytes paced at 0.25 Hz experienced significant prolongation of AP and EADs and a protracted tail component of Ca²⁺ transients (10). Under SEA0400, the peak Ca²⁺ transient amplitude tends to increase (F/F₀ = 4.04 ± 0.44 after vs 3.37 ± 0.69 before SEA0400, n = 3), with confocal line scans continuing to show late intracellular Ca²⁺ cycling activity. However, AP prolongation was suppressed (from 1404 ± 335 to 158 ± 43 ms) and EADs were fully abolished, in agreement with our computational modeling results with reduced NCX conductance (Fig. 6). AP traces of all LQT2 myocytes treated with SEA0400 are shown in Fig. S5. We note that the spatial heterogeneity of Ca²⁺ release seen in confocal line scans of LQT2 myocytes (Fig. 8 and previous experiments (10)) is also observed in control rabbit myocytes (10, 36) and is not due to cell damage. In addition, the long plateau of the calcium transient in the experiment (Fig. 8) or the computational model (Fig. 3 D) originates from the fact that, during an EAD, the V_m remains in the window range of the L-type calcium current, as seen by the finite amplitude of I_Ca,L (blue trace of (D) of Fig. 3 corresponding to I_Ca,L). The I_Ca,L current sustains a constant influx of Ca²⁺ into the cytosol that in turn sustains late SR Ca²⁺ releases via CICR, as seen in the computed ((D) of Fig. 3) and experimentally measured (Fig. 8; (10)) confocal line scans. In the computational model, I_Ca,L and SR release contribute ∼10 and 90% to the influx of Ca²⁺ into the cytosol during the long plateau of the calcium transient, respectively.

Figure 8.

Experimental validation that NCX suppression using NCX blocker SEA0400 eliminates EADs in LQT2 myocytes exposed to 50 nM ISO. V_m traces (black) and corresponding averaged time-dependent profiles (red) and confocal line scan images of Ca²⁺ transients recorded in current clamped LQT2 myocytes with (A) and without (B) SEA0400 are shown. Despite shortened AP and absence of EADs in myocytes with SEA0400, abnormal Ca²⁺ activity is evident during repolarization and diastole. To see this figure in color, go online.

EAD mechanism in littermate control myocytes

The important role of RyR activity in EAD initiation can also be shown in littermate control myocytes. Similar to Fig. 3, Fig. S6 shows the simulation results under β-adrenergic stimulation for stabilized RyRs, increased Ca²⁺ sensitivity, reduced RyR refractoriness, and hyperactive RyRs. Increased RyR activity resulting from the addition of caffeine induces aberrant late Ca²⁺ releases, which drives the depolarizing forward-mode NCX current, prolongs the action potential duration, and reactivates the I_Ca,L channels. Moreover, caffeine reduced RyR refractoriness, which allows RyR to reopen after the I_Ca,L channels are reactivated, generating an EAD.

The effect of pacing frequency

Even though I_Ks in the hyperactive RyR model tends to eliminate EADs instead of initiating them (Fig. S7 C), it plays an important role in rate-dependent EAD elimination (Fig. S7, A and B). The activation timescale I_Ks is 0.5 s. Therefore, this current starts to accumulate for stimulation frequency faster than 0.5 Hz. At 1 Hz, EADs are only intermittent. At 2 Hz, the diastolic interval is ∼0.1 s, and the large I_Ks accumulation suffices to eliminate all EADs.

Discussion

Previous computational modeling studies have revealed many important ionic mechanisms of EAD formation. However, those studies have focused primarily on alterations of sarcolemmal membrane currents. Furthermore, they used common-pool models (37, 38), in which both the Ca²⁺ flux through LTCCs and the release flux through RyRs feed into the same (whole-cell) compartment and Ca²⁺ cycling is described by a deterministic set of equations. Our work uses a multiscale ventricular myocyte model to directly probe how alterations of stochastic RyR activity at the single-channel level affect the Ca²⁺ and voltage dynamics at the whole-cell level. Smaller Ca²⁺ transient amplitudes have traditionally been associated with a smaller forward-mode NCX current, which would shorten the AP and contribute to suppressing EADs, as predicted in a computer-modeling study of EAD formation in pharmacological LQT2 (18). In contrast, our detailed computational model was able to reproduce the experimental observation that RyR hyperactivity promotes EAD formation while reducing the Ca²⁺ transient amplitude but promotes late aberrant Ca²⁺ releases during repolarization (10). Here, we show that those late sparks are a product of modified RyR gating at the single-channel level, which is currently not reproducible in any single-pool model. This modified gating requires both increasing RyR sensitivity to cleft Ca²⁺ and reducing RyR refractoriness. Although depletion of SR Ca²⁺ load has been shown to be sufficient for spark termination (39, 40, 41, 42), it remains unclear whether refilling after local SR depletion is the main mechanism of spark refractoriness (20, 43) or whether additional mechanisms (such as CSQN binding to RyR/T/J (24) used in this model) contribute to a delay between refilling and full RyR recovery.

Our modeling results show that NCX current is less depolarizing with hyperactive than with stable RyRs in early phase 2 when [Ca²⁺]_i peaks (Fig. 3 D). However, the NCX current becomes more depolarizing in the hyperactive case within a critical interval of time during late phase 2 to early phase 3, during which the voltage traverses the window for voltage-dependent reactivation of LTCCs. We have previously demonstrated that the higher rate of SR Ca²⁺ release throughout the vulnerable time window increases Ca²⁺ flux through the submembrane region, which drives forward-mode NCX current (10). Here, we have shown that increased NCX current may not be predictable using only whole-cell measurements of cytosolic Ca²⁺ content, as whole-cell average [Ca²⁺]_i in Fig. 3 D insufficiently differs between the hyperactive and stabilized models.

Even in a case of equal total SR Ca²⁺ release flux, we expect NCX current to be driven more in a hyperactive RyR model with increased RyR activity and depleted SR load than in the stabilized RyR model with higher SR load. In a hyperactive model in which the SR Ca²⁺ content is depleted, a greater number of smaller individual Ca²⁺ release events drive a greater NCX current compared to a case with fewer, larger individual sparks, in which NCX current is limited by local current saturation because of limited ion-transport rates (44). This NCX-mediated Ca²⁺-to-voltage signal transduction mechanism explains how altered Ca²⁺ handling can promote EAD formation in the setting of reduced SR load with NCX driven primarily by late aberrant Ca²⁺ releases induced by LTCCs, as opposed to spontaneous Ca²⁺ waves in the setting of Ca²⁺ overload in which both early and delayed afterdepolarizations can coexist (45, 46, 47).

The LQT2 model predicts that reducing NCX conductance will result in complete suppression of EADs despite late aberrant Ca²⁺ releases occurring throughout the repolarization phase. We found that a factor of five reduction in conductance causes only a 20% decrease in the resulting current (Fig. 6). This self-tuning compensatory effect is due to the build-up of cytosolic Ca²⁺ content, which both increases the driving force of forward-mode NCX and also increases the Ca²⁺-dependent allosteric activation of the channel.

Identifying changes in currents that are both voltage and time dependent is difficult when investigating the root cause of altered electrophysiological behavior in the setting of a ventricular myocyte with nonlinearly coupled voltage and Ca²⁺ dynamics. Comparing NCX current at any given instant during repolarization in Fig. 6 H appears to suggest no significant difference between NCX currents in the reduced NCX and full NCX models. By examining NCX behavior as a dynamic I-V plot as in Fig. 7, we exploited the ability to compare the NCX current in each model at equal V_m, revealing a difference in the degree of Ca²⁺-dependent potentiation of the current. This is critical, as the vulnerable window for EAD formation is the voltage range in which I_Ca,L under β-adrenergic stimulation has the propensity to spontaneously recover from inactivation and reactivate.

Experiments using SEA0400 to reduce NCX current in LQT2 rabbit myocytes are consistent with computer modeling and validate the role of NCX in EAD onset. This provides a potential pharmacological intervention to treat arrhythmia caused by reduced repolarization reserve exacerbated by irregular SR Ca²⁺ release. Although we have shown that this arrhythmia may be common in hereditary LQT2, it may also play a role in other human cardiac diseases exhibiting RyR hyperphosphorylation such as heart failure (48). NCX antagonists may therefore be viable as a general intervention for suppressing premature ventricular depolarizations in a variety of human cardiac pathologies.

The mechanism of increased Ca²⁺ sensitivity of RyRs in LQT2 myocytes was studied in Terentyev et al. (10). Coimmunoprecipitation experiments demonstrated that increased phosphorylation of RyRs in LQT2 myocytes versus controls is due to loss of protein phosphatases type 1 and type 2 from the RyR complex. However, the biological mechanism by which loss of function of I_Kr causes this loss of phosphatases from the RyR complex is not precisely known. We can only speculate that it is linked to remodeling of Ca²⁺ homeostasis caused by sustained AP prolongation or changes in energetics (49) that shift the phosphatase to other subcellular components.

Limitations

We used a model of CSQN-dependent RyR refractoriness (21, 22), which is supported by experiments showing reduced RyR refractoriness in transgenic mice under-expressing CSQN (50). However, the biological origin of RyR refractoriness is still not fully understood (20, 43). Additionally, we assumed that each CRU in the network has the same number of LTCC and RyRs, thereby neglecting heterogeneities in CRU properties that may be present (40, 51) and could potentially affect the distributions of local Ca²⁺ spark amplitudes and local NCX currents. Moreover, we have only considered one specific NCX model, and whether similar effects occur with other available NCX models remains to be investigated (52). Finally, we have neglected the spatial variation of Ca²⁺ within the submicron dyadic space. Although the impact of this variation can in principle be investigated using higher-resolution models (41, 53, 54), we do not expect that its incorporation will fundamentally change the basic mechanism of NCX-mediated subcellular Ca²⁺ to voltage signal transduction elucidated in our study.

Conclusions

We have investigated the effect of increased RyR channel activity in the form of reduced refractoriness and increased open probability on the genesis of cellular EADs in the setting of LQT2. Our study was motivated by a recent experimental and computational study that linked EAD formation in LQT2 myocytes to RyR hyperactivity (10). However, this study did not explain why forward-mode NCX current can be larger in LQT2 myocytes with hyperactive RyRs than in LQT2 myocytes with stabilized RyRs even though the cytosolic Ca²⁺ concentration is comparable in the two cases during the vulnerable time period when the V_m traverses the window range for I_Ca,L reactivation. Our study explains this phenomenon and provides novel mechanistic insights, to our knowledge, into the complex relationship between the spatiotemporal dynamics of intracellular Ca²⁺ and whole-cell NCX current. Modeling results reveal that, because of the saturation of NCX current as a function of the local submembrane calcium concentration, transduction of elevated Ca²⁺ to a depolarizing current via forward-mode NCX can be more potent when RyR channels are hyperactive. This is because a larger number of smaller-amplitude discrete Ca²⁺ release events can produce a large increase in whole-cell forward-mode NCX current, despite reduced SR load, without significantly increasing the whole-cell cytosolic calcium concentration, [Ca²⁺]_i. As a result, [Ca²⁺]_i is not the sole determinant of whole-cell NCX current magnitude as assumed in traditional common-pool models of Ca²⁺ cycling. This highlights the importance of detailed multiscale modeling in correctly reproducing the behavior of cardiac Ca²⁺ cycling and excitation-contraction coupling. In addition, we have validated the role of NCX in EAD formation in LQT2 by single-cell electrophysiological experiments. The results confirm the modeling predictions that reduced NCX conductance abolishes EADs and suggests that pharmacological alteration of NCX may be a potential therapeutic intervention to treat pVT in diseases accompanied by RyR hyperactivity and reduced repolarization reserve, including LQT2. Future studies that image Ca²⁺ activity in myocytes in intact heart remain needed to investigate the relevance of our findings to arrhythmias at the organ scale.

Author Contributions

Conceptualization, C.M.R. and A.K.; Methodology, C.M.R. and D.T.; Software, M.Z. and C.M.R.; Formal Analysis, M.Z. and C.M.R.; Investigation, M.Z., C.M.R., and D.T.; Writing—Original Draft, C.M.R.; Writing, Review and Editing, M.Z., C.M.R., D.T., G.K., and A.K.; Supervision, A.K. and G.K.; Funding Acquisition, G.K. and D.T.

Editor: James Keener.

Supporting Information

References (55, 56, 57) appear in the Supporting Material.