Ca²⁺/calmodulin-dependent kinase II-dependent regulation of atrial myocyte late Na⁺ current, Ca²⁺ cycling, and excitability: a mathematical modeling study

Here, we present a novel computational model to study the effects of late Na⁺ current (I_Na,L) in human atrial myocytes. Simulations predict that I_Na,L promotes intracellular accumulation of Ca²⁺, with subsequent dysregulation of Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) signaling and ryanodine receptor 2-mediated Ca²⁺ release. Although I_Na,L plays a small role in regulating atrial myocyte excitability at baseline, CaMKII-dependent enhancement of the current promoted arrhythmogenic dynamics.

Abstract

Atrial fibrillation (AF) affects more than three million people per year in the United States and is associated with high morbidity and mortality. Both electrical and structural remodeling contribute to AF, but the molecular pathways underlying AF pathogenesis are not well understood. Recently, a role for Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) in the regulation of persistent “late” Na⁺ current (I_Na,L) has been identified. Although I_Na,L inhibition is emerging as a potential antiarrhythmic strategy in patients with AF, little is known about the mechanism linking I_Na,L to atrial arrhythmogenesis. A computational approach was used to test the hypothesis that increased CaMKII-activated I_Na,L in atrial myocytes disrupts Ca²⁺ homeostasis, promoting arrhythmogenic afterdepolarizations. Dynamic CaMKII activity and regulation of multiple downstream targets [I_Na,L, L-type Ca²⁺ current, phospholamban, and the ryanodine receptor sarcoplasmic reticulum Ca²⁺-release channel (RyR2)] were incorporated into an existing well-validated computational model of the human atrial action potential. Model simulations showed that constitutive CaMKII-dependent phosphorylation of Na_v1.5 and the subsequent increase in I_Na,L effectively disrupt intracellular atrial myocyte ion homeostasis and CaMKII signaling. Specifically, increased I_Na,L promotes intracellular Ca²⁺ overload via forward-mode Na⁺/Ca²⁺ exchange activity, which greatly increases RyR2 open probability beyond that observed for CaMKII-dependent phosphorylation of RyR2 alone. Increased I_Na,L promotes atrial myocyte repolarization defects (afterdepolarizations and alternans) in the setting of acute β-adrenergic stimulation. We anticipate that our modeling efforts will help identify new mechanisms for atrial Na_V1.5 regulation with direct relevance for human AF.

NEW & NOTEWORTHY Here, we present a novel computational model to study the effects of late Na⁺ current (I_Na,L) in human atrial myocytes. Simulations predict that I_Na,L promotes intracellular accumulation of Ca²⁺, with subsequent dysregulation of Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) signaling and ryanodine receptor 2-mediated Ca²⁺ release. Although I_Na,L plays a small role in regulating atrial myocyte excitability at baseline, CaMKII-dependent enhancement of the current promoted arrhythmogenic dynamics.

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INTRODUCTION

The number of patients with atrial fibrillation (AF) is expected to exceed 15.9 million in the United States by the year 2050 (31). Patients with AF face high morbidity and mortality as well as increased risk of stroke and heart failure (3). The present AF therapies include a combination of anticoagulants with catheter ablation and surgical- or drug-based therapies to maintain sinus rhythm or ventricular rate (19, 37) but face important limitations related to low efficacy attributable to off-target ion channel effects or proarrhythmic impact on ventricular tissue (10, 44, 55).

Recently, there has been growing interest in antiarrhythmic drug therapies targeting “late” Na⁺ current (I_Na,L), a low-amplitude current that persists throughout the duration of the action potential (AP) attributable to failed/incomplete voltage-dependent inactivation (12, 46). Enhancement of I_Na,L is well documented in ventricular myocytes of animal models and human patients with congenital or acquired cardiac arrhythmia (20, 28, 32, 43, 52). More recently, there have been reports supporting a potential role for increased I_Na,L in human AF (27, 38) with I_Na,L blockers such as ranolazine or GS-458967 showing promise for suppressing atrial arrhythmias in preclinical models (4, 13, 17, 39–41, 63, 64). Previous work from our group has shown that Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) is an upstream regulator of I_Na,L in cardiac myocytes through phosphorylation of Ser⁵⁷¹ in the DI-DII linker of Na_v1.5 (Fig. 1A) (16, 24). Furthermore, the effects of I_Na,L on arrhythmogenic activity are attenuated by CaMKII inhibition (26). Although I_Na,L is thought to promote triggered Ca²⁺ activity, the mechanistic link between increased I_Na,L and dysregulation of Ca²⁺ handling proteins [e.g., the ryanodine receptor sarcoplasmic reticulum (SR) Ca²⁺-release channel (RyR2)] remains to be defined. Furthermore, the specific role of I_Na,L in atrial arrhythmogenesis, attributable in part to lack of mathematical models of the atrial AP that incorporate CaMKII-dependent signaling, is underexplored.

Fig. 1.

Mathematical model of Ca²⁺/calmodulin-dependent protein kinase (CaMKII) signaling in human atrial myocyte. A: the structure of voltage-gated Na⁺ channel α-subunit Na_v1.5. Ser⁵⁷¹ in the DI-DII loop is critically important for CaMKII-dependent regulation of late Na⁺ current (I_Na,L) (16). B: schematic of key plasma membrane ion currents and sarcoplasmic reticulum (SR) protein channels in the Grandi atrial cell model (18). I_Ca,L, L-type Ca²⁺ current; I_Na, fast Na⁺ current; I_Kur, ultrarapid delayed rectifier K⁺ current; I_Ks, slow delayed rectifier K⁺ current; I_Kr, rapid delayed rectifier K⁺ current; I_K1, inward rectifier K⁺ current; I_to, 4-aminopyridine-sensitive transient outward K⁺ current; J_SR,up, Ca²⁺ uptake into the SR; I_NCX, Na⁺/Ca²⁺ exchanger current; I_NaK, Na⁺-K⁺ pump ATPase; I_Cl,b, background Cl⁻ current; I_Na,b, background Na⁺ current; I_Ca,b, background Ca²⁺ current; I_CaCl, Ca²⁺-activated Cl⁻ current; I_pCa, sarcolemmal Ca²⁺ pump. CaMKII activation by Ca²⁺/calmodulin and downstream targeting of RyR2, I_up, I_Ca,L, and I_Na,L is included in this updated model.

In this study, we used a computational approach to test the hypothesis that disruption of Na_v1.5 phosphorylation and a CaMKII-facilitated increase in I_Na,L contribute to intracellular Ca²⁺ accumulation and irregular atrial cell membrane excitability. We incorporated formulations for CaMKII-dependent regulation of I_Na,L and other targets important for intracellular Ca²⁺ cycling [L-type Ca²⁺ current (I_Ca,L), phospholamban (PLB), and RyR2] into an established mathematical model of the human atrial cell (Fig. 1B). We then explored the downstream effects of CaMKII-dependent phosphorylation of I_Na,L on intracellular ion homeostasis and other downstream CaMKII targets in atrial myocytes. Finally, we defined the contribution of CaMKII-facilitated I_Na,L to atrial proarrhythmia associated with acute β-adrenergic receptor (β-AR) stimulation.

METHODS

Ion channel kinetics were simulated using an existing well-validated model of the human atrial cell (18). Modifications to the original equations are provided in appendix a. Briefly, the original atrial AP model was modified to include a previously defined formulation for I_Na,L (9). CaMKII activation kinetics were also incorporated based on a mathematical description previously developed by our group that accounts for CaMKII activation by dynamic changes in Ca²⁺/calmodulin as well as modulation by autophosphorylation and/or oxidation (9). CaMKII was assumed to catalyze a transition from nonphosphorylated to phosphorylated Na_v1.5 populations, based on previously described population-based modeling techniques (48), where the maximal conductance of I_Na,L was fit to experimental data from two different Scn5a knockin mouse models: 1) mice expressing Na_v1.5 with the CaMKII phosphorylation site replaced by alanine (Na_v1.5-S571A) to model 100% nonphosphorylated channels (phospho-resistant) and 2) mice expressing Na_v1.5 with the CaMKII phosphorylation site replaced by glutamic acid (Na_v1.5-S571E) to model 100% phosphorylated channels (phospho-mimetic) (16) (Fig. 2A). The wild-type (WT) Na_v1.5 model transitions between phosphorylated and nonphosphorylated fractions based on the dynamic activity of CaMKII. A similar approach was taken to model CaMKII targeting of RyR2 using experimental data from RyR2-S2814D (phospho-mimetic) and RyR2-S2814A (phospho-resistant) mouse models (Fig. 2B) (45, 53, 57). CaMKII effects on PLB and I_Ca,L were also incorporated into the model based on their importance for normal Ca²⁺ cycling. I_Ca,L conductance was made dependent on CaMKII to produce a maximal change of 16% facilitation when pacing frequency increased from 1 to 2 Hz, within the range of experimentally measured values (1, 29). CaMKII effects on PLB were incorporated by introducing CaMKII dependence to the half-maximal saturation constant for Ca²⁺ binding to SERCA2a [altering Ca²⁺ uptake into the SR (J_SR,up)], consistent with previous experimental and modeling studies (22). Although other CaMKII targets likely regulate atrial excitability in response to stress (47), as a first approximation we focused on Na_v1.5, I_Ca,L, PLB, and RyR2 to address the specific role of dysregulation of Ca²⁺ cycling.

Fig. 2.

Simulated Ca²⁺/calmodulin-dependent protein kinase (CaMKII)-dependent regulation of late Na⁺ current (I_Na,L) and ryanodine receptor sarcoplasmic reticulum (SR) Ca²⁺-release channel (RyR2) compared with experimental data. A: experimentally measured (16) and simulated I_Na,L (expressed as ratio of levels in Na_v1.5-S571E to Na_v1.5-S571A). B: experimentally measured (53, 57) and simulated intracellular Ca²⁺ concentration ([Ca²⁺]_i) amplitude [ratio relative to the wild-type (WT) model] in RyR2-S2814D and RyR2-S2814A models. Simulations used Grandi human atrial model (18) with modifications as described in methods.

AP duration (APD) after 490 s of pacing (to allow for the model to reach steady-state condition) was compared with experimental data recorded at body temperature from human atrial myocytes in a sinus rhythm over a range of pacing frequencies to verify that modifications did not disturb agreement of simulated and experimental APD (Fig. 3) (15, 36). The maximal conductance value for I_Na,L in the WT model was selected to yield APD at 90% repolarization (APD₉₀) in the physiological range at baseline. In a subset of simulations, the effects of β-AR stimulation were simulated according to a previously published approach with changes to slow delayed rectifier K⁺ current (I_Ks), ultrarapid delayed rectifier K⁺ current (I_Kur), troponin I, J_SR,up, I_Ca,L, and RyR2 (18, 42). Model parameter sensitivity analysis was performed using random model parameter perturbation and regression, as previously described (51). Briefly, random scale factors for I_Ca,L, inward rectifier K⁺ current (I_K1), rapid delayed rectifier K⁺ current (I_Kr), I_Ks, I_Kur, fast Na⁺ current (I_Na), Na⁺/Ca²⁺ exchanger current (I_NCX), Na⁺-K⁺-ATPase current (I_NaK), I_Na,L, transient outward K⁺ current (I_to), SR Ca²⁺ release, and J_SR,up were selected randomly for 600 independent simulations under basal conditions and in the presence of β-AR stimulation. The following steady-state model outputs were saved for each simulation and used for regression analysis: maximal diastolic intracellular Na⁺ concentration ([Na⁺]_i), maximal intracellular Ca²⁺ concentration ([Ca²⁺]_i), maximal Ca²⁺ concentration in the SR ([Ca²⁺]_SR), and maximal CaMKII activity. To avoid artifacts induced by perturbation procedure, the final analysis included only simulations that produced an AP with a resting membrane potential more negative than −70 mV, an APD₉₀ of <1,000 ms, and no alternans (criteria were met by 479 simulations under basal conditions and 379 simulations in the presence of β-AR stimulation).

Fig. 3.

Simulated action potential duration (APD) compared with experimental data from human atrial myocytes. Simulated (black circle) and experimentally measured (15, 36) wild-type APDs at 90% repolarization (APD₉₀) over a range of pacing frequencies are shown.

Computer code was written in C++ 11 and compiled using GNU compiler collection (gcc) for Linux. Model equations were solved numerically using the forward Euler method and a time step of 5 µs. The full model is available for download and use on a cross-platform, threaded application with graphic user interface called “LongQt” (https://hundlab.engineering.osu.edu/research/LongQt, version 0.2) (35). All other computer simulations were performed on a Dell PowerEdge R515 server (Dual 6 core, 32 GB RAM running CentOS-6.2). A single simulation to steady state required 9 min of computational time using these resources. Analysis was performed using MATLAB R2016b on a MacBook Pro with a 2.5-GHz Intel Core i7 processor.

RESULTS

Effect of CaMKII-dependent I_Na,L on atrial myocyte intracellular ion homeostasis.

CaMKII regulates the rate dependence of cardiac Ca²⁺ handling with implications for human disease (22). Previous studies have shown that CaMKII phosphorylation of Ser⁵⁷¹ in the Na_v1.5 DI-DII linker increases I_Na,L (21, 24). Therefore, we hypothesized that constitutive CaMKII-dependent phosphorylation of Na_v1.5 would delay atrial AP repolarization and promote Ca²⁺ dysregulation. Consistent with our hypothesis, APD was prolonged in the simulated Na_v1.5-S571E atrial myocyte compared with Na_v1.5-S571A or WT atrial myocytes (Fig. 4A). At the same time, simulations predicted an increase in intracellular Ca²⁺ (cytoplasmic and SR) and CaMKII activity in Na_v1.5-S571E compared with WT atrial myocytes (Fig. 4, B–D). On the basis of previous work showing an important role for CaMKII-dependent RyR2 phosphorylation in AF susceptibility (6, 25, 57), we also evaluated the effects of constitutive (RyR2-S2814D) or ablated (RyR2-S2814A) RyR2 phosphorylation at Ser²⁸¹⁴ (CaMKII site) on atrial membrane excitability and Ca²⁺ handling. Consistent with experiments (53), our simulations predicted a decrease in steady-state [Ca²⁺]_SR in RyR2-S2814D myocytes compared with WT or RyR2-S2814A myocytes, without any detectable difference in the AP, Ca²⁺ transient amplitude (slight, offsetting decrease in both peak and maximum diastolic [Ca²⁺]_i), or CaMKII activity (slight decrease in peak) (Fig. 4, E–H).

Fig. 4.

Effects of Ca²⁺/calmodulin-dependent protein kinase (CaMKII)-dependent phosphorylation of Na_v1.5 and ryanodine receptor sarcoplasmic reticulum (SR) Ca²⁺-release channel (RyR2) on atrial myocyte membrane excitability and Ca²⁺ cycling. A−D: steady-state action potentials, intracellular Ca²⁺ concentration ([Ca²⁺]_i), fraction of active CaMKII subunits, and Ca²⁺ concentration in the SR ([Ca²⁺]_SR) transients at 1-Hz pacing frequency for simulated wild-type (WT), phospho-resistant Na_v1.5-S571A, and phospho-mimetic Na_v1.5-S571E atrial myocytes. E−H: steady-state action potentials, [Ca²⁺]_i, fraction of active CaMKII subunits, and [Ca²⁺]_SR transients at 1-Hz pacing frequency for simulated WT, phospho-resistant RyR2-S2814A, and phospho-mimetic RyR2-S2814D atrial myocytes. V_m, membrane potential.

To determine the role of CaMKII-dependent I_Na,L in the regulation of intracellular ion homeostasis in atrial myocytes, we compared [Ca²⁺]_i, [Na⁺]_i, and CaMKII activity in phospho-mimetic Na_v1.5-S571E, phospho-resistant Na_v1.5-S571A, and WT models over a range of pacing frequencies. Interestingly, the Na_v1.5-S571E model showed a small (<10%) increase in [Na⁺]_i compared with Na_v1.5-S571A and WT models, which resulted in a substantial increase in [Ca²⁺]_i and CaMKII activity, especially at pacing frequencies of <1 Hz (Fig. 5). For comparison, the phospho-mimetic RyR2-S2814D model yielded a decrease in [Ca²⁺]_i and CaMKII activity compared with the simulated WT model (Fig. 5). These simulation results indicate that small changes in [Na⁺]_i induced by CaMKII-dependent hyperphosphorylation of Na_v1.5 and increased I_Na,L have strong effects on Ca²⁺ handling and CaMKII activity in atrial myocytes. Furthermore, the model predicts that constitutive phosphorylation of Na_v1.5 alone has a greater impact on [Ca²⁺]_i and CaMKII than constitutive phosphorylation of RyR2 alone. Together, these data indicate that a CaMKII-dependent increase in I_Na,L is sufficient to produce defects in atrial AP repolarization and Ca²⁺ handling and likely resides upstream of RyR2 in promoting atrial arrhythmogenesis. Furthermore, our simulations predict that atrial I_Na,L and CaMKII reside in a feedback loop linked to Ca²⁺ homeostasis (33).

Fig. 5.

Effects of Ca²⁺/calmodulin-dependent protein kinase (CaMKII)-dependent phosphorylation of Na_v1.5 and ryanodine receptor sarcoplasmic reticulum (SR) Ca²⁺-release channel (RyR2) on atrial myocyte ion concentration and CaMKII rate dependence. A–C: steady-state peak intracellular Ca²⁺ concentration ([Ca²⁺]_i), diastolic intracellular Na⁺ concentration ([Na⁺]_i), and maximal CaMKII activity values over a range of pacing frequencies in simulated wild-type (WT), Na_v1.5-S571A, and Na_v1.5-S571E myocytes. D−F: steady-state peak [Ca²⁺]_i, diastolic [Na⁺]_i, and maximal CaMKII activity values over a range of pacing frequencies in simulated WT, RyR2-S2814A, and RyR2-S2814D myocytes.

Effect of CaMKII-dependent I_Na,L on RyR2 function and Ca²⁺ cycling.

On the basis of our results showing altered Ca²⁺ homeostasis attributable to hyperphosphorylated Na_v1.5, we sought to more fully characterize CaMKII effects on RyR2 function and SR Ca²⁺ release. The phospho-mimetic Na_v1.5-S571E model produced only a small increase in phosphorylated RyR2 compared with the WT or RyR2-S2814D model (Fig. 6A). However, despite the small effect on phosphorylated RyR2, the Na_v1.5-S571E model showed a dramatic increase in RyR2 open probability compared with the WT model, especially at pacing frequencies of <1 Hz. Surprisingly, Na_v1.5 phosphorylation increased RyR2 open probability even beyond that observed in the RyR2-S2814D model, despite the negligible effect on phosphorylated RyR2, reflecting the greater SR Ca²⁺ load in the Na_v1.5-S571E model compared with the RyR2-S2814D model (Fig. 6C). These data indicate that increasing Ca²⁺ load (downstream of increased [Na⁺]_i) has a greater overall effect on RyR2 open probability than RyR2 phosphorylation alone.

Fig. 6.

Late Na⁺ current (I_Na,L) increases Ca²⁺/calmodulin-dependent protein kinase (CaMKII)-dependent ryanodine receptor sarcoplasmic reticulum (SR) Ca²⁺-release channel (RyR2) phosphorylation and open probability. A: maximum phosphorylation of RyR2. B: maximum RyR2 open probability. C: maximum Ca²⁺ concentration in the SR ([Ca²⁺]_SR) over a range of frequencies for wild-type (WT), Na_v1.5-S571E, and RyR2-S2814D simulated mouse models.

At steady state, our simulations predicted a net decrease in [Ca²⁺]_i with constitutive RyR2 phosphorylation but an increase with Na_v1.5 phosphorylation (Fig. 4). In an effort to understand the differential response of steady-state Ca²⁺ to constitutive RyR2 or Na_v1.5 phosphorylation, we compared the behavior of I_NCX in the two models both at steady state and transiently during the onset of pacing (Fig. 7). The phospho-mimetic RyR2-S2814D model showed a slight decrease in forward-mode I_NCX at steady state compared with the Na_v1.5-S571E or WT models (Fig. 7, A and B), consistent with the reduced steady-state Ca²⁺ load and SR Ca²⁺ release. However, our simulations predicted that initially peak [Ca²⁺]_i and forward-mode I_NCX are potentiated in the RyR2-S2814D model compared with the other models (Fig. 7, C and D), which leads to intracellular Ca²⁺ depletion within 10–20 beats. In contrast, constitutive Na_v1.5 phosphorylation produces a gradual increase in [Ca²⁺]_i due to accumulation of [Na⁺]_i and change in the driving force for I_NCX (reflected as small initial decrease in reverse-mode I_NCX during the first 3–5 pacing beats). These results demonstrate that RyR2 phosphorylation increases Ca²⁺ release transiently, but ultimately forward-mode I_NCX produces a steady-state condition where intracellular Ca²⁺ (cytosolic and SR) is depleted.

Fig. 7.

Role of the Na⁺/Ca²⁺ exchanger in altered Ca²⁺ homeostasis induced by phosphorylation of Na_v1.5 and ryanodine receptor sarcoplasmic reticulum (SR) Ca²⁺-release channel (RyR2). A: Na⁺/Ca²⁺ exchanger current (I_NCX) values over time at steady-state 1-Hz pacing frequency for simulated wild-type (WT), Na_v1.5-S571A (superimposed on WT), and Na_v1.5-S571E models. B: I_NCX values over time at steady-state 1-Hz pacing frequency for simulated WT, RyR2-S2814A (superimposed on WT), and RyR2-S2814D models. C and D: peak forward-mode I_NCX (C) and maximum intracellular Ca²⁺ concentration ([Ca²⁺]_i; D) during action potential from initiation of simulation for WT, Na_v1.5-S571E, and RyR2-S2814D models.

Effect of CaMKII-dependent I_Na,L on atrial myocyte excitability.

Under baseline conditions, proarrhythmic cellular afterdepolarizations were not observed in phospho-mimetic Na_v1.5-S571E, phospho-resistant Na_v1.5-S571A, or WT models over a range of pacing frequencies (up to 3.3 Hz; data not shown). However, proarrhythmic repolarization defects (early afterdepolarizations with or without alternans) emerged at slower pacing (below 1.3 Hz) in WT and mutant models in the presence of simulated acute β-AR stimulation (Fig. 8). Notably, the phospho-mimetic Na_v1.5-S571E model produced repolarization defects over a wider range of pacing frequencies compared with the WT or phospho-resistant Na_v1.5-S571A models. To determine whether proarrhythmia associated with constitutive Na_v1.5 phosphorylation acted through positive feedback on CaMKII and subsequent phosphorylation of RyR2, excitability was assessed in models with phospho-mimetic or phospho-resistant changes to both Na_v1.5 and RyR2 (Na_v1.5-S571E × RyR2-S2814D, Na_v1.5-S571E × RyR2-S2814A, Na_v1.5-S571A × RyR2-S2814D, and Na_v1.5-S571A × RyR2-S2814A). Constitutive phosphorylation or ablation of the RyR2-S2814 model altered the repolarization morphology but failed to normalize the increase in range over which repolarization defects were observed in the Na_v1.5-S571E model (compare Na_v1.5-S571E × RyR2-S2814D and Na_v1.5-S571E × RyR2-S2814A with Na_v1.5-S571E and WT in Fig. 8). Similarly, altering phosphorylation status of RyR2 had little impact on behavior in the Na_v1.5-S571A model. These results indicate that CaMKII-dependent phosphorylation of Na_v1.5 promotes atrial myocyte proarrhythmia in response to acute β-AR stimulation. Furthermore, our simulations indicate that constitutive Na_v1.5 phosphorylation promotes atrial repolarization defects primarily by increasing SR Ca²⁺ load (and therefore RyR2 open probability) as opposed to enhancing RyR2 phosphorylation status.

Fig. 8.

Afterdepolarization activity under conditions of acute β-adrenergic stimulation. Simulated steady-state wild-type (WT) action potentials (APs) for three different pacing frequencies in the presence of β-adrenergic stimulation showed the following behavior: normal repolarization (no proarrhythmia events' A), AP with early afterdepolarizations (EADs' B), and AP alternans and EADs (C). D: summary of steady-state AP behavior observed over a range of pacing frequencies (0.51–1.43 Hz) for the following models: 1) normal Na_v1.5 and ryanodine receptor sarcoplasmic reticulum (SR) Ca²⁺-release channel (RyR2) (WT × WT); 2) phospho-mimetic or phospho-resistant Na_v1.5 on the background of normal RyR2 (S571E × WT and S571A × WT, respectively); and 3) phospho-mimetic or phospho-resistant Na_v1.5 on the background of phospho-mimetic or phospho-resistant RyR2 (S571E × S2814D, S571E × S2814A, S571A × S2814D, and S571A × S2814A, respectively). V_m, membrane potential.

Relative contribution of I_Na,L to the regulation of atrial ion homeostasis and CaMKII activity.

To provide insight into the importance of I_Na,L in regulating atrial myocyte physiology relative to other major atrial ion currents, a parameter sensitivity analysis was conducted on the model under baseline conditions and in the presence of β-AR stimulation (Fig. 9). Although perturbation of I_Na,L had only a limited effect on intracellular ion concentrations or CaMKII activity at baseline, its impact was greatly enhanced in the setting of β-AR stimulation. In fact, I_Na,L was associated with positive regression coefficients for intracellular Na⁺, Ca²⁺, and CaMKII activity, meaning an increase in I_Na,L (as in response to CaMKII activation) is expected to increase all of these properties. In contrast, RyR2 flux rate (J_SRrel) showed negative regression coefficients for the same properties, whereas SR Ca²⁺ uptake (J_SRup) showed a combination of positive and negative values. Finally, I_Ca,L showed positive but relatively small regression coefficients. In summary, of all CaMKII targets included in the model (I_Na,L, J_SRrel, J_SRup, and I_Ca,L), our analysis predicts that an increase in I_Na,L is a relatively efficient way of promoting intracellular ion accumulation and positive feedback on CaMKII.

Fig. 9.

Relative contribution of late Na⁺ current to changes in atrial myocyte ion homeostasis and Ca²⁺/calmodulin-dependent protein kinase (CaMKII) signaling. Regression coefficients showed how changes in the model parameters affected ion homeostasis and CaMKII activity in baseline wild-type (WT) simulated cells (A–D) and in the presence of the β-adrenergic agonist isoproterenol (E–H). Shown are parameter sensitivities of ion channel conductance parameters affecting maximum diastolic intracellular Na⁺ concentration ([Na⁺]_i; A and E), maximum intracellular Ca²⁺ concentration ([Ca²⁺]_i; B and F), maximum Ca²⁺ concentration in the sarcoplasmic reticulum ([Ca²⁺]_SR; C and G), and maximum fraction of activated CaMKII subunits (D and H). Abbreviations are as follows: gTo, maximal conductance (gMax) of the transient outward K⁺ current; gK1, gMax of the inward rectifier K⁺ current; gKr, gMax of the rapid delayed rectifier K⁺ current; gKs, gMax of the slow delayed rectifier K⁺ current; gKur, gMax of the ultrarapid K⁺ current; gNa, gMax of the rapid Na⁺ current; gNaca, maximal transport rate of the Na⁺/Ca²⁺ exchanger; gNaL, gMax of the late Na⁺ current; JSRrel, maximal Ca²⁺ release flux from the junctional sarcoplasmic reticulum; JSRup, maximal Ca²⁺ uptake rate into the sarcoplasmic reticulum; gCaL, gMax of the L-type Ca²⁺ channel.

DISCUSSION

In this study, we used mathematical modeling to explore the role of CaMKII-dependent I_Na,L in the regulation of atrial myocyte ion homeostasis and membrane excitability. Our simulations led to a number of important findings, including 1) a CaMKII-dependent increase in I_Na,L promotes significant accumulation of intracellular Ca²⁺ (cytosolic and SR) in atrial myocytes; 2) I_Na,L-induced Ca²⁺ accumulation, in turn, enhances atrial CaMKII activity and phosphorylation of downstream targets (e.g., RyR2); 3) CaMKII phosphorylation of atrial Na_v1.5 (and the subsequent increase in I_Na,L) alone produces greater intracellular Ca²⁺ accumulation, CaMKII activation, and increase in RyR2 open probability compared with RyR2 phosphorylation alone; and 4) increased I_Na,L promotes proarrhythmic behavior under conditions of acute β-AR stimulation in atrial myocytes primarily by increasing intracellular Ca²⁺ stores. Although previous studies have examined the role of CaMKII as a molecular driver for Ca²⁺ homeostasis and cardiac dysfunction (47), our effort represents a novel approach to dissect the complex effects of CaMKII on downstream targets in atrial cells.

Atrial myocytes from human patients with AF show increased CaMKII activity and altered I_Na,L compared with sinus rhythm, although the pathophysiological relevance remains unclear (6, 13, 16). In parallel, enhanced I_NCX activity has been measured in human AF myocytes, which has been attributed to higher [Na⁺]_i (8). Furthermore, increased I_Na,L in Na_v1.5-S571E or through application of the I_Na,L enhancer ATX-II promotes abnormal [Ca²⁺]_i handling and SR Ca²⁺ leak (13, 16). These findings are consistent with predictions of our model that a CaMKII-dependent increase in I_Na,L promotes accumulation of intracellular Na⁺ and Ca²⁺ together with enhanced I_NCX activity in atrial myocytes. Furthermore, these data support the notion that I_NCX is a critical node linking CaMKII-dependent I_Na,L to dysregulation of intracellular Ca²⁺ homeostasis, promoting arrhythmogenesis in AF.

It is important to note that studies in preclinical models and human myocytes indicate that dysregulation of multiple CaMKII targets (not just Na_v1.5) occurs in AF and likely contributes to arrhythmogenesis (54, 56, 60). For example, impaired CaMKII-dependent regulation of RyR2 has been demonstrated to alter Ca²⁺ cycling and increase atrial ectopy and AF susceptibility in the mouse (7, 30, 50, 53). Specifically, increased diastolic SR Ca²⁺ leak through phosphorylated RyR2 has been proposed as an important causal factor in AF (57). In our simulations, constitutive CaMKII-dependent RyR2 phosphorylation produced a transient elevation in SR Ca²⁺ release (due to higher RyR2 open probability), which ultimately produced a decrease in intracellular Ca²⁺ (cytosolic and SR) via activation of forward-mode I_NCX. In contrast, constitutive phosphorylation of Na_v1.5 (and the subsequent increase in I_Na,L) produced a gradual but sustained increase in intracellular Na⁺ and Ca²⁺ in the model. Together, these results highlight distinct but potentially synergistic pathways for altering intracellular Ca²⁺ cycling. Future studies with available mouse models (e.g., Na_v1.5-S571E/A or RyR2-S2814D/A) will be necessary to test these model predictions and further dissect the relative roles of Na_v1.5 and other CaMKII targets in atrial arrhythmogenesis.

It is interesting to note that our simulations predicted a complex relationship between CaMKII-dependent I_Na,L and atrial excitability with both pro- and antiarrhythmic effects. Namely, CaMKII-induced I_Na,L prolongs atrial APD, which promotes formation of early afterdepolarizations at slow rates and in the presence of isoproterenol but also would be expected to decrease the likelihood for sustained reentrant arrhythmia. In fact, atrial APD shortening attributable to ion channel remodeling is commonly thought to favor sustained AF in human patients and animal models. It is possible that enhanced I_Na,L increases susceptibility to atrial arrhythmia triggers but that other factors are required to create a substrate for arrhythmia maintenance (e.g., APD shortening, fibrosis, or cell-to-cell uncoupling). It is also important to note that, although our simulations indicate a role for CaMKII-enhanced I_Na,L in proarrhythmic afterdepolarizations and alternans in response to a β-AR agonist, the relationship between β-AR stimulation and alternans has been found in separate studies to be both positive (β-AR-dependent exacerbation) (34) or negative (β-AR-dependent suppression) (14). At the same time, it is interesting to note that, although our simulations predict repolarization defects with β-AR stimulation, these occur only at slower rates (<1.33 Hz). However, β-AR blockers (expected to slow rate) remain a widely used rate control therapy in the treatment of AF (19, 23). Together, these data point to the complex web of factors underlying an arrhythmia phenotype and highlight the need for computational modeling to help tackle these high-dimensional problems.

Recent advances in the development of personalized, whole heart computer models represent an exciting direction for the field (2, 49, 61, 62). These advanced models have been used to study the effects of a wide range of disease factors on cardiac AP propagation, including heterogeneous changes in cell electrophysiology, coupling, and tissue structure. It will be interesting going forward to incorporate dynamic cell signaling pathways (such as the CaMKII pathway studied here) with these higher-dimensional models to consider how acute signaling interacts with more chronic changes in cell excitability or tissue structure. With this goal in mind, it is important to note that the updated formulations incorporated into this model for CaMKII targeting of I_Na,L, PLB, I_Ca,L, and RyR2 are compatible with other atrial cell models used in organ-level simulations (5, 11) and can help elucidate the impact of CaMKII on organ-level AF properties (e.g., rotor stabilization and conduction block). This effort is particularly exciting and poised to inform organ-level simulations as well as other research directions because of the availability of transgenic mouse models (e.g., RyR2-S2814D/A and Na_v1.5-S571E/A mice) to test model predictions.

Limitations.

Although the model used in our study incorporated components important for the CaMKII-dependent behavior under investigation, it is nonetheless a simplification of the physiological system. Namely, CaMKII targets a number of membrane ion channels not included in this analysis, including I_to and I_K1 (47). Furthermore, CaMKII has been demonstrated to regulate not just I_Na,L but also I_Na by reducing channel availability (58). Although inclusion of these and other CaMKII targets could potentially yield further insights into atrial arrhythmia mechanisms, our sensitivity analysis indicates that these targets are unlikely to contribute to the ion homeostasis defects observed in AF (Fig. 9). In the instance of I_to, for example, the model predicted a negative relationship between channel conductance and intracellular Na⁺, Ca²⁺, and CaMKII, meaning that these values would be expected to decrease in response to an increase in I_to (as observed with CaMKII activation). For I_K1 and I_Na, the regression coefficients were relatively small and, in the case of I_Na, work against ion accumulation with CaMKII activation (CaMKII decreases I_Na). At the same time, regression analysis of the model highlights the fact that precise values of certain model parameters may influence absolute values for ion concentrations and CaMKII activity in the model. For example, we were surprised to find that intracellular Na⁺, Ca²⁺, and CaMKII were relatively sensitive to I_Kur as well as I_NaK (less surprising), indicating that small discrepancies in values of conductances/flux rates for these elements would be expected to have a relatively large impact on model predictions. It is also important to note that electrical and structural remodeling changes characteristic of persistent AF (59) are not incorporated into this model. Undoubtedly, it will be interesting to study the interaction between acute effects studied here and changes in tissue structure. Finally, atrial myocyte cell excitability is part of a complex network of signaling mechanisms, and incorporation of CaMKII signaling with PKA (to address cross talk and individual effects) would strengthen the prediction of CaMKII effects in this study.

GRANTS

This work was supported by National Heart, Lung, and Blood Institute Grants HL-114893 (to T. Hund), HL-134824 (to T. Hund), HL-135096 (to T. Hund), and HL-129766 (to B. Onal), by the James S. McDonnell Foundation (to T. Hund), by the Saving Tiny Hearts Society (to T. Hund), and by a TriFit Challenge grant from the Ross Heart Hospital and Davis Heart and Lung Research Institute.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

B.O., D.G., and T.J.H. conceived and designed research; B.O. and D.G. performed experiments; B.O., D.G., and T.J.H. analyzed data; B.O., D.G., and T.J.H. interpreted results of experiments; B.O. prepared figures; B.O. drafted manuscript; B.O., D.G., and T.J.H. edited and revised manuscript; B.O., D.G., and T.J.H. approved final version of manuscript.

APPENDIX: MODEL EQUATIONS

This appendix contains the model equations added to simulate CaMKII phosphorylation of I_Na,L and RyR2. See the original publications for complete model equations and variable/parameter definitions (9, 22, 45, 48).

CaMKII module.

$$P=0.0003;$$

$${\text{calm}}_{\text{total}}=0.00006;$$

$$\text{ros}=0;$$

$$k_{\text{ib}}=246;$$

$$k_{\text{bi}}=0.0022;$$

$$k_{\text{ox}}=0.0002909;$$

$$k_{\text{red}}=0.0000228;$$

$$k_{\text{bp}}=0.0022;$$

$$\text{kn93}=0;$$

$$k_{\text{bli}}=0.0022;$$

$$k_{\text{ibl}}=0.0008536;$$

$$\text{Calm}={\text{calm}}_{\text{total}}\times \left(\frac{{\text{Ca}}_{\text{sl}}^{\text{4}}}{{\text{Ca}}_{\text{sl}}^{\text{4}}+\text{0}{\text{.005}}^{\text{4}}}\right)$$

$$t_{\text{camk}}=f_{\text{Bound}}+f_{\text{Phos}}+f_{\text{Ox}}+f_{\text{OxP}}$$

$$k_{\text{t}}=\frac{k_{\text{bi}}}{k_{\text{ib}}}/\left(\frac{1}{t_{\text{camk}}}-1\right)$$

$$k_{\text{a}}=\frac{k_{\text{bi}}\times k_{\text{t}}}{k_{\text{t}}+0.01851}$$

$$v_{\text{a}}=k_{\text{a}}\times f_{\text{Bound}}$$

$$v_{\text{a2}}=k_{\text{a}}\times f_{\text{Ox}}$$

$$\frac{\text{d}{f}_{\text{Bound}}}{\text{d}t}=\left[k_{\text{ib}}\times \text{Calm}\times f_{\text{I}}+P\times f_{\text{Phos}}+k_{\text{red}}\times f_{\text{Ox}}-\left(k_{\text{bi}}+k_{\text{ox}}\times \text{ros}\right)\times f_{\text{Bound}}-v_{\text{a}}\right]+f_{\text{Bound}}$$

$$\frac{\text{d}{f}_{\text{Phos}}}{\text{d}t}=\left[v_{\text{a}}+k_{\text{red}}\times f_{\text{OxP}}-\left(k_{\text{ox}}\times \text{ros}+P\right)\times f_{\text{Phos}}\right]+f_{\text{Phos}}$$

$$\frac{\text{d}{f}_{\text{Ox}}}{\text{d}t}=\left(k_{\text{ox}}\times \text{ros}\times f_{\text{Bound}}+P\times f_{\text{OxP}}-k_{\text{red}}\times f_{\text{Ox}}-v_{\text{a2}}\right)+f_{\text{Ox}}$$

$$\frac{\text{d}{f}_{\text{OxP}}}{\text{d}t}=\left(v_{\text{a2}}-P\times f_{\text{OxP}}+k_{\text{Ox}}\times \text{ros}\times f_{\text{Phos}}-k_{\text{red}}\times f_{\text{OxP}}\right)+f_{\text{OxP}}$$

$$\frac{\text{d}{f}_{\text{Block}}}{\text{d}t}=\left(k_{\text{ibl}}\times \text{kn93}\times f_{\text{I}}-k_{\text{bli}}\times f_{\text{Block}}\right)+f_{\text{Block}}$$

$$f_{\text{I}}=1-f_{\text{Bound}}-f_{\text{Phos}}-f_{\text{Ox}}-f_{\text{OxP}}-f_{\text{Block}}$$

$$\text{CaMKII}=0.75\times f_{\text{Bound}}+f_{\text{PHos}}+f_{\text{OxP}}+0.5\times f_{\text{Ox}}$$

Persistent Na⁺ current.

$$E_{\text{Na}}=\frac{R\text{T}}{F}\times \log \frac{{\text{Na}}_{\text{o}}}{{\text{Na}}_{\text{i}}}$$

$${\alpha }_{\text{ml}}=\frac{0.32\times \left(V+47.13\right)}{1-\exp \left[-0.1\times \left(V+47.13\right)\right]}$$

$${\beta }_{\text{ml}}=0.08\times \exp \left(\frac{-V}{11}\right)$$

$${\text{hl}}_{\text{inf}}=\frac{1}{1+\exp \left(\frac{V+91}{6.1}\right)}$$

$$\text{ms}=\frac{{\alpha }_{\text{ml}}}{{\alpha }_{\text{ml}}+{\beta }_{\text{ml}}}$$

$${\text{τ}}_{\text{ml}}=\frac{\text{1}}{{\alpha }_{\text{ml}}{\text{+β}}_{\text{ml}}}$$

$${\text{Gate}}_{\text{ml}}=\text{ms}-\left(\text{ms}-{\text{Gate}}_{\text{ml}}\right)\times \text{exp}\left(\frac{-\text{d}t}{{\text{τ}}_{\text{ml}}}\right)$$

$$t_{\text{hl}}=600$$

$${\text{Gate}}_{\text{hl}}={\text{hl}}_{\text{inf}}-\left({\text{hl}}_{\text{inf}}-{\text{Gate}}_{\text{hl}}\right)\times \text{exp}\left(\frac{-\text{d}t}{{\text{τ}}_{\text{hl}}}\right)$$

For WT:

$$I_{\text{Na,L,NP}}=0.0325\times {\text{Gate}}_{\text{ml}}^{\text{3}}\times {\text{Gate}}_{\text{hl}}\times \left(V-E_{\text{Na}}\right)$$

$$I_{\text{Na,L,P}}=3.2\times I_{\text{Na,L,NP}}$$

$$\frac{\text{d}{f}_{I_{\text{Na,L,P}}}}{\text{d}t}=\frac{\text{CaMKII/}\left(\text{CaMKII}+0.15\right)-f_{I_{\text{Na,L,P}}}}{100}$$

$$I_{\text{Na,L}}=f_{I_{\text{Na,L,P}}}\times I_{\text{Na,L,P}}+f_{I_{\text{Na,L,NP}}}\times I_{\text{Na,L,NP}}$$

RyR Ca²⁺ release and SERCA2a flux targeting by CaMKII.

$${\text{RyR}}_{\text{tot}}=0.3826;$$

$${\text{RyR}}_{\text{ratio}}={\text{RyR}}_{\text{P}}/{\text{RyR}}_{\text{tot}};$$

$$k_{\text{b,2815}}=0.00035;$$

$$k_{\text{ck,ryr}}=0.0004;$$

$$k_{\text{m,ckryr}}=0.012;$$

$$\text{PP1}=0.0956;$$

$$\text{PP2A}=0.0956;$$

$$k_{\text{pp1,ryr}}=0.00107;$$

$$k_{\text{m,pp1ryr}}=0.009;$$

$$k_{\text{m,pp2ryr}}=0.047;$$

$$k_{\text{pp2,ryr}}=0.000481;$$

$$k_{\text{ioa,pp1}}=0.00078;$$

$$k_{\text{ioa,pp2}}=0.000037;$$

$$\text{OA}=0;$$

$${\text{OA}}_{\text{pp1}}=\frac{1}{1+\frac{{\left(\text{OA}\right)}^3}{k_{\text{ioa,pp1}}}}$$

$${\text{OA}}_{\text{pp2}}=\frac{1}{1+\frac{{\left(\text{OA}\right)}^3}{k_{\text{ioa,pp2}}}}$$

$$\text{Ry}{\text{R}}_{\text{N}}=\text{Ry}{\text{R}}_{\text{tot}}-\text{Ry}{\text{R}}_{\text{P}}$$

$${\text{Rxn}}_{\text{basal}}=k_{\text{b,2815}}\times {\mathrm{RyR}}_{\text{N}}$$

$${\text{Rxn}}_{\text{ckryr}}=\frac{2.4\times k_{\text{ckryr}}\times \text{CaMKII}\times {\text{RyR}}_{\text{N}}}{k_{\text{m,ckryr}}+{\text{RyR}}_{\text{N}}}$$

$${\text{Rxn}}_{\text{pp1ryr}}=\frac{k_{\text{pp1ryr}}\times \text{PP1}\times {\text{RyR}}_{\text{P}}\times \text{OApp1}}{k_{\text{m,pp1ryr}}+{\text{RyR}}_{\text{P}}}$$

$${\text{Rxn}}_{\text{pp2ryr}}=\frac{k_{\text{pp2ryr}}\times \text{PP2A}\times {\text{RyR}}_{\text{P}}\times \text{OApp2}}{k_{\text{m,pp2ryr}}+{\text{RyR}}_{\text{P}}}$$

$$k_{\text{leak}}=\frac{1}{3}+\frac{10}{3}{\text{RyR}}_{\text{ratio}}$$

$$k_{\text{o,RyRCKII}}=\frac{20}{3}\times {\text{RyR}}_{\text{ratio}}-\frac{1}{3}$$

$${\text{PKA}}_{\text{ratio}}=0.5$$

$$k_{\text{o,RyRPKA}}=1.025\times {\text{PKA}}_{\text{ratio}}+0.975$$

$$k_{\text{o,RyR}}=k_{\text{o,RyRCKII}}+k_{\text{o,RyRPKA}}-1$$

$$k_{\text{o,SRca}}=\frac{k_{\text{o,RyR}}\times k_{\text{o,Ca}}}{k_{\text{Casr}}}$$

$$\frac{{\text{dRyR}}_{\text{P}}}{\text{d}t}={\text{Rxn}}_{\text{basal}}+{\text{Rxn}}_{\text{ckryr}}-{\text{Rxn}}_{\text{pp1ryr}}-{\text{Rxn}}_{\text{pp2ryr}}$$

$$K_{\text{M,CAM}}=0.2;$$

$$\text{camfact}=\frac{1}{1+\frac{{\left(K_{\text{M,CAM}}\right)}^5}{\text{CaMKII}}}$$

$$\text{pbl}=0.00011\times \text{camfact}$$

$$\alpha =\frac{{\text{Ca}}_{\text{i}}^{\text{Hill}}}{k_{\text{m,f}}-\text{plb}}-\frac{{\text{Ca}}_{\text{SR}}^{\text{Hill}}}{k_{\text{m,r}}}$$

$$\beta =1+\frac{{\text{Ca}}_{\text{i}}^{\text{Hill}}}{k_{\text{m,f}}-\text{plb}}+\frac{{\text{Ca}}_{\text{SR}}^{\text{Hill}}}{k_{\text{m,r}}}$$

$$J_{\text{serca}}=V_{\text{max,SR}}\times \frac{\alpha }{\beta }$$

L-type Ca²⁺ channel.

$${\text{camfact}}_{I_{\text{Ca,L}}}=\frac{1.2\times \text{CaMKII}}{0.15\times {\text{CaMKII}}^4}$$

$$I_{\text{Ca,L}}=\left(1+{\text{camfact}}_{I_{\text{Ca,L}}}\right)\times \left(I_{\text{Ca}}+I_{\text{CaK}}+I_{\text{CaNa}}\right)$$