Synergy between CaMKII Substrates and β-Adrenergic Signaling in Regulation of Cardiac Myocyte Ca²⁺ Handling

Abstract

Cardiac excitation-contraction coupling is a highly coordinated process that is controlled by protein kinase signaling pathways, including Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) and protein kinase A (PKA). Increased CaMKII expression and activity (as occurs during heart failure) destabilizes EC coupling and may lead to sudden cardiac death. To better understand mechanisms of cardiac CaMKII function, we integrated dynamic CaMKII-dependent regulation of key Ca²⁺ handling targets with previously validated models of cardiac EC coupling, Ca²⁺/calmodulin-dependent activation of CaMKII, and β-adrenergic activation of PKA. Model predictions are validated against CaMKII-overexpression data from rabbit ventricular myocytes. The model demonstrates how overall changes to Ca²⁺ handling during CaMKII overexpression are explained by interactions between individual CaMKII substrates. CaMKII and PKA activities during β-adrenergic stimulation may synergistically facilitate inotropic responses and contribute to a CaMKII-Ca²⁺-CaMKII feedback loop. CaMKII regulated early frequency-dependent acceleration of relaxation and EC coupling gain (which was highly sarcoplasmic reticulum Ca²⁺ load-dependent). Additionally, the model identifies CaMKII-dependent ryanodine receptor hyperphosphorylation as a proarrhythmogenic trigger. In summary, we developed a detailed computational model of CaMKII and PKA signaling in cardiac myocytes that provides unique insights into their regulation of normal and pathological Ca²⁺ handling.

Introduction

Ca²⁺/Calmodulin-dependent protein kinase II (CaMKII) is a key regulator of cardiac excitation-contraction coupling (ECC) that has emerged as a potential therapeutic target for heart failure and arrhythmia (1). The activation of CaMKII by Ca²⁺-bound calmodulin (CaM) affords it the ability to decode both the frequency and location of Ca²⁺ signals (2,3). CaMKII expression is increased in failing human myocardium (4) and hyperactivity has been linked to the induction of hypertrophy and arrhythmias (5,6). Chronic (7) and acute (8) CaMKII overexpression studies have demonstrated that this kinase regulates myocyte Ca²⁺ handling, though the specific mechanisms by which these changes occur are unclear. Both CaMKII and protein kinase A (PKA) phosphorylate a number of Ca²⁺ handling targets with similar functional consequences (including L-type Ca²⁺ channels (LCCs), ryanodine receptors (RyRs), and phospholamban (PLB)), though how these two pathways communicate with one another remains unresolved.

To examine how the known molecular mechanisms of CaMKII and PKA interact to coordinate ECC and trigger arrhythmia, we developed an integrated computational model of CaMKII and PKA signaling in the rabbit ventricular myocyte. The model includes dynamic phosphorylation of LCCs, RyRs, and PLB by CaMKII and PKA, as well as functional regulation of additional targets distinct to each kinase. These interactions were integrated with previously validated models of Ca²⁺/CaM-dependent activation of CaMKII (3), β-adrenergic activation of PKA (9), and cardiac ECC in the rabbit ventricular myocyte (10). With this framework, we examined a number of unanswered questions in cardiac CaMKII/PKA signaling:

• How do the individual actions of CaMKII substrates work together to modulate overall Ca²⁺ handling?

• Can CaMKII enhance its own activity via a CaMKII-Ca²⁺-CaMKII positive feedback loop?

• Does β-adrenergic stimulation increase dyadic CaMKII activity via enhanced Ca²⁺ fluxes and, if so, does this additional activity contribute to inotropic responses?

• Finally, under what conditions can CaMKII activity lead to the development of cellular arrhythmias?

The model shows how synergy between individual CaMKII activities modulates overall myocyte Ca²⁺ handling, that CaMKII-PKA synergy may contribute to full adrenergic responses, and that CaMKII-dependent modulation of RyR function can trigger arrhythmias.

Methods

Dynamic CaMKII and PKA-dependent phosphorylation were modeled using mass action and Michaelis-Menten kinetics (11). PKA phosphorylation modules are essentially the same as those in our previous model (9). Model parameters were obtained from the biochemical literature or estimated by nonlinear least-squares fitting to cellular data as described in the Supporting Material.

Structurally, the model consists of three main modules:

• 1.Activation of CaMKII and phosphorylation of ECC targets,
• 2.β-adrenergic activation of PKA and phosphorylation, and
• 3.The cardiac ECC model of the rabbit ventricular myocyte from Shannon et al. (10), including detailed cellular electrophysiology, Ca²⁺ diffusion between distinct compartments, and graded Ca²⁺ release from the sarcoplasmic reticulum (SR), in which regulation by modules 1 and 2 was included.

To model the effects of CaMKII and PKA on LCC modal gating (12,13), we adapted an established Markovian formulation for the LCC (14) (see Fig. S1 in the Supporting Material). All simulations were performed in MATLAB (The MathWorks, Natick, MA) using the stiff ODE solver ode15s.

Phosphorylation modules

LCC

CaMKII phosphorylation rapidly facilitates LCC current (I_Ca), seen as a stepwise increase in peak I_Ca with repeated stimulation (Fig. S2) (13,15,16). CaMKII alters LCC gating by increasing the fraction of channels operating in mode 2, characterized by high P_o (13). Facilitation is enhanced during CaMKII overexpression (8) and eliminated during CaMKII knockout. Additional properties of CaMKII-dependent changes to I_Ca are provided in Fig. S3. PKA increases LCC P_o and availability via phosphorylation of α_1C and β_2a sites, respectively (9).

RyR

CaMKII phosphorylation of RyRs (mainly at Ser²⁸¹⁵ in rabbit) has been reported to increase channel Ca²⁺ sensitivity, opening probability, and leak (17–20). Basal phosphorylation and biphasic dephosphorylation by PP1 and PP2A at Ser²⁸¹⁵ were included by fitting to experimental data of increasing phosphatase inhibition by okadaic acid (Fig. S4). PKA also enhances RyR Ca²⁺ sensitivity during adrenergic stimulation.

PLB, I_Na, and I_to

CaMKII phosphorylation of PLB (at Thr¹⁷) may be <5% in normal conditions (21). In our model, cytosolic CaMKII is not sufficient to regulate PLB (3). To achieve appropriate frequency-dependent Thr¹⁷ phosphorylation (22), we modeled this using dyadic cleft CaMKII signals (see the Supporting Material). PLB phosphorylation by both CaMKII and PKA (at Ser¹⁶) relieves SERCA inhibition and roughly doubles the pump's Ca²⁺ sensitivity (22–24). Also, PKA activation of inhibitor-1 blocks PP1 near PLB, thereby increasing Thr¹⁷ phosphorylation during adrenergic stimulation (Fig. S6). Lastly, CaMKII overexpression in rabbit myocytes delays I_Na recovery from inactivation, enhances I_Na,L magnitude (Fig. S7 A), hastens I_to recovery from inactivation (Fig. S8 A), and increases I_to magnitude (Fig. S8 B) (25,26).

Others

PKA-specific regulation of the slow delayed rectifier K⁺ current (I_Ks), troponin I, and the cystic fibrosis transmembrane conductance regulator Cl⁻ current were included. An overall model schematic is provided in Fig. 1, with further details of model equations, parameters, and justification provided in Table S1 in the Supporting Material.

Figure 1.

Model schematic. CaMKII is activated by Ca²⁺/CaM binding in the dyadic cleft, subsarcolemma, and cytosolic compartments. Active CaMKII phosphorylates LCCs, RyRs, and PLB. During overexpression simulations, CaMKII-dependent alterations to I_Na(f,L) and I_to were included. PKA phosphorylates LCCs, RyRs, PLB, Inhibitor-1, troponin I (TnI), I_Ks, and cystic fibrosis transmembrane conductance regulator (CFTR) and phosphatases 1 and 2A oppose phosphorylation by either kinase.

Results

Frequency-dependence of CaMKII-mediated phosphorylation

Phosphorylation of all CaMKII substrates is predicted to exhibit positive frequency dependence, though phosphorylation levels and kinetics are quantitatively quite distinct (Fig. 2). The model predicts highly dynamic CaMKII activity and oscillatory phosphorylation kinetics, which adapt to changes in pacing with distinct kinetics (Fig. 2 A). LCCs exhibit moderate to high phosphorylation during control scenarios (Fig. 2 B). LCC phosphorylation reaches steady state within ∼5 beats when the myocyte is paced from rest, consistent with I_Ca facilitation kinetics in Fig. S2. With CaMKII overexpression (CaMKII-OE, 6× increase), LCC phosphorylation saturates at lower frequencies. In contrast, RyR and PLB phosphorylation exhibit moderate positive frequency-dependence in control conditions. RyR phosphorylation increases from ∼15% at rest to ∼29% at 3 Hz pacing (Fig. 2 C), while PLB phosphorylation is <10% at all frequencies (Fig. 2 D). During CaMKII-OE, however, RyR and PLB phosphorylation is amplified. The predicted increase in RyR phosphorylation with CaMKII-OE at 1 Hz is similar to that seen experimentally (8) (Fig. S5). Together, these predictions indicate that the frequency-dependence of CaMKII substrates may vary considerably even when regulated by the same Ca²⁺ and CaMKII signals.

Figure 2.

Time-course and frequency-dependence of CaMKII phosphorylation. (A) Dyadic CaMKII activity and phosphorylation profiles during a CaMKII-OE simulation at low (0.5 Hz) and higher (2 Hz) frequency pacing. Note the differences between phosphorylation kinetics, which are very fast at the LCC, slower at the RyR, and very slow at PLB. (B–D) Time-averaged steady-state phosphorylation levels at (B) LCC, (C) RyR, and (D) PLB are frequency-dependent and sensitive to the amount of active CaMKII (control versus OE).

CaMKII-dependent changes to Ca²⁺ handling and electrophysiology

At 1 Hz pacing, Ca²⁺ transient magnitude (Δ[Ca²⁺]_i) was 402 nM in control simulations, though CaMKII-OE slightly reduced Δ[Ca²⁺]_i to 366 nM (∼91% of control) (Fig. 3 A). Experimental Ca²⁺ transients showed a similar, though statistically insignificant, decrease in Δ[Ca²⁺]_i with acute CaMKII-OE (72 ± 8% of control) (Fig. 3 C, left columns). With CaMKII-KO, the model predicted a decrease in Δ[Ca²⁺]_i to 281 nM (Fig. 3 A, dashed line). Both CaMKII-OE and CaMKII-KO reduced action potential duration (APD), consistent with the experimentally measured APD for CaMKII-OE but somewhat overestimating the amount of APD shortening due to CaMKII inhibition in rabbit myocytes (26) (Fig. 3 B).

Figure 3.

Effects of CaMKII on myocyte Ca²⁺-handling and electrophysiology. (A) At 1 Hz pacing, both CaMKII-OE and CaMKII-KO depress Δ[Ca²⁺]_i compared to control. Diastolic [Ca²⁺]_i for control, OE, and KO simulations was 92.6, 69.1, and 95.8 nM, respectively. (B) APD is shorter during CaMKII-OE (194 ms) and CaMKII-KO (199 ms) simulations compared to control (213 ms). (C) Comparison of Δ[Ca²⁺]_i and [Ca²⁺]_SRT during CaMKII-OE in model (gray bars) and experimental data (black bars, data from (8), n.s. = not significant). (D) CaMKII overexpression increases fractional release of Ca²⁺ from the SR (data from (8)). (E and F) Frequency-dependence of Δ[Ca²⁺]_i and [Ca²⁺]_SRT. (E) Model predicts slightly smaller Δ[Ca²⁺]_i at larger frequencies (≥1 Hz) with CaMKII-OE and depressed Δ[Ca²⁺]_i at all frequencies during CaMKII-KO. (F) CaMKII-OE dramatically decreases SR Ca²⁺ across all frequencies, while CaMKII-KO allows greater SR filling at higher frequencies.

Total SR Ca²⁺ content ([Ca²⁺]_SRT) was reduced in response to CaMKII-OE in both model predictions (∼23%) and published experiments (∼40 ± 15%) (Fig. 3 C, right). Additionally, fractional SR Ca²⁺ release was enhanced in both model predictions (127% of control) and experimental data (158 ± 23% of control). Absolute fractional release values at 1 Hz pacing are also in agreement with experimental data (Fig. 3 D). The model exhibits the positive frequency dependence of Δ[Ca²⁺]_i (Fig. 3 E) and [Ca²⁺]_SRT (Fig. 3 F) observed in rabbit ventricular myocytes (though SR content changes only slightly beyond 1 Hz) (10). During CaMKII-OE, however, Δ[Ca²⁺]_i and [Ca²⁺]_SRT progressively deviate from control values. At low frequencies (0.25 and 0.5 Hz), Δ[Ca²⁺]_i slightly rises in response to CaMKII-OE, though the relationship flips at frequencies ≥1 Hz. These predictions can be explained by the quantitative differences between phosphorylation levels at low and high frequencies (Fig. 2). Also, CaMKII-KO reduced Δ[Ca²⁺]_i despite a higher SR Ca²⁺ content, suggesting the potential role of CaMKII in the positive frequency dependence of Δ[Ca²⁺]_i in normal myocytes.

As additional validations, postrest decay was enhanced by CaMKII-OE (as seen in similar experiments (8), Fig. S10) and [Na]_i was slightly greater at all tested frequencies during CaMKII-OE (though larger increases have been observed experimentally (25), perhaps due to additional mechanisms; see Fig. S7, B and C). The included effects on I_Na(f,L) and I_to in combination contributed to slightly larger [Ca²⁺]_i transients during pacing (Fig. S9). These results demonstrate that our model is capable of predicting key changes to myocyte Ca²⁺ handling and electrophysiology that have been shown experimentally with CaMKII-OE.

Role of CaMKII in FDAR and ECC gain

CaMKII is believed to participate in frequency-dependent acceleration of relaxation (FDAR), though the mechanisms for such control are unclear and may not involve PLB (21,27,28) or SERCA (29). Between 0.5 and 3 Hz, we found that steady-state FDAR (quantified as the t₅₀ of Δ[Ca²⁺]_i relaxation) was only modestly CaMKII-dependent (CaMKII-OE and KO made the slope of FDAR slightly more and less negative, respectively; see Fig. S11). As an additional test for CaMKII-dependence, we monitored the time course of FDAR development during a rapid switch from 0.25 to 1 Hz pacing (see Fig. 4 A and Fig. S12). As expected, our control model rapidly adapted to faster pacing. However, the early phase of FDAR was blunted in CaMKII-KO simulations, suggesting CaMKII contributes to the early phase of FDAR. Additional simulations were performed with CaMKII-dependent LCC or RyR phosphorylation eliminated (Fig. S12, right panels), showing that LCC phosphorylation is necessary for this early phase. Steady-state FDAR was enhanced by elimination of RyR phosphorylation but reduced by elimination of LCC phosphorylation (Fig. S12 F). Thus, overall FDAR appears to depend on a balance of LCC and RyR phosphorylation by CaMKII.

Figure 4.

CaMKII-dependent enhancement of FDAR via LCC phosphorylation and effects on ECC gain. (A) Time course of Δ[Ca²⁺]_it₅₀ values in response to increased pacing frequency (0.25–1 Hz at 4 s). Control simulations showed rapid FDAR adaptation, though CaMKII-KO slowed early FDAR. (B) ECC gain assessed by voltage-clamp (−80 mV holding potential, 0 mV test for 200 ms, 500 ms basic cycle length) until steady state was reached. ECC gain is reported as peak steady-state J_RyR over peak steady-state J_LCC. ECC gain was reduced by both CaMKII-OE and CaMKII-KO simulations, though SR loads varied considerably between conditions. The last two bars are from simulations with SR content fixed to the control value. In this case, CaMKII-OE dramatically increased ECC gain at 0 mV (from 7.2 to 25), while CaMKII-KO decreased ECC gain (to 1.7) compared to control.

ECC gain, defined by the ratio of peak RyR Ca²⁺ flux to peak trigger LCC Ca²⁺ flux, is a central element of ECC. To determine whether CaMKII modulates ECC gain, we paced the model myocyte under voltage-clamp to steady state (−80 mV holding potential, 0 mV test, 2 Hz) and quantified peak LCC and RyR fluxes (J_LCC and J_RyR, respectively). Surprisingly, the control model exhibited the highest ECC gain, despite increased I_Ca amplitude and RyR P_o in the CaMKII-OE model (Fig. 4 B, left columns). However, [Ca²⁺]_SRT was not equal across the three tested conditions (see labels in Fig. 4 B). To eliminate the influence of SR loading on these results, we ran additional simulations for CaMKII-OE and KO at fixed [Ca²⁺]_SRT (1.74 mM, the control level) and found that, in these conditions, CaMKII-OE dramatically enhanced ECC gain, while gain in the KO condition was depressed substantially (Fig. 4 B, right columns).

Comparative analysis of CaMKII target effects

We used the model to further examine how individual CaMKII substrates produce the combined effects discussed earlier. Individual substrate contributions to the overall CaMKII-OE response at 1 Hz were isolated by overexpressing CaMKII and allowing CaMKII-dependent phosphorylation of a single substrate; the results are summarized in Table 1. CaMKII enhancement of I_Ca in isolation mainly enhanced Ca²⁺ transients (∼31%). On the other hand, RyR effects substantially decreased Δ[Ca²⁺]_i (∼24%) and [Ca²⁺]_SRT (∼23%), while PLB phosphorylation alone modestly affected all parameters, perhaps due to the low quantitative phosphorylation levels at PLB-Thr¹⁷. Net I_to and I_Na effects increased Δ[Ca²⁺]_i (∼7%) and decreased APD (∼12%). Thus, the overall decreased Δ[Ca²⁺]_i and [Ca²⁺]_SRT seen with CaMKII-OE may be primarily explained by increased phosphorylation of RyRs, although LCC phosphorylation largely compensates for the decreased Δ[Ca²⁺]_i and, to a lesser extent, [Ca²⁺]_SRT. Interestingly, all targets positively influenced fractional release to a small extent, but the overall 27% increase is only seen when combining all effects. This indicates that global changes to ECC are dictated by the relative strengths of several CaMKII interactions working in synergy. Results from 1 Hz CaMKII-KO simulations are also shown for comparison.

Table 1.

Comparative analysis of individual CaMKII interactions

	Control	CaMKII overexpression					KO
Parameter	All targets	All targets	LCC effect only	RyR effect only	PLB effect only	Ito/INa effects only	All targets
Δ[Ca]i (nM)	402	365	525	306	414	431	281
[Ca]SRT (mM)	1.87	1.44	1.91	1.44	1.88	1.86	1.93
Fractional release	0.34	0.43	0.39	0.39	0.35	0.35	0.26
APD90 (ms)	213	194	220	213	210	190	199

Effects of overexpressing CaMKII for individual targets (LCC, RyR, PLB, and I_to/I_Na) on overall Δ[Ca²⁺]_i, [Ca²⁺]_SRT, fractional release, and APD during 1 Hz pacing. RyR phosphorylation is the only effect responsible for decreasing Δ[Ca²⁺]_i and [Ca²⁺]_SRT, while no one effect dominates the overall increase in fractional release. The net effect of I_to and I_Na regulation mostly contributes to APD shortening. The effects of global CaMKII inhibition are provided in the last column.

CaMKII-Ca²⁺-CaMKII positive feedback during normal ECC and β-adrenergic stimulation

We hypothesized that positive feedback from CaMKII to Ca²⁺ to CaMKII (via enhanced Ca²⁺ fluxes) may be a prominent feedback loop. To test this in the model, we analyzed dyadic CaMKII activity during control and CaMKII-OE simulations (Fig. 5 A). At 2 Hz pacing, CaMKII-OE increased average CaMKII activity (59.5% vs. 53.8% for control) and t_50% (222 vs. 210 ms). To test whether this increased activity is the result of feedback as opposed to the fact that overall CaMKII availability is enhanced, additional CaMKII-OE simulations were run with phosphorylation levels at each CaMKII substrate fixed to their steady-state diastolic levels (CaMKII-OE + Target KO). In this case, CaMKII average activity and t_50% were 57.5% and 216 ms, respectively, suggesting that overexpression of CaMKII alone enhances activity, though the subsequent CaMKII-dependent enhancement of Ca²⁺ fluxes feeds back to increase activity further.

Figure 5.

CaMKII-Ca²⁺-CaMKII feedback and β-adrenergic response. (A) Single 2 Hz dyadic cleft CaMKII transients from control, CaMKII-OE, and CaMKII-OE + Target KO (i.e., all target phosphorylation levels fixed to control values) simulations. Feedback is evident because t₅₀ and average CaMKII activity increase with overexpression alone, though CaMKII-OE with all functional targets present increases these parameters further. (B and C) Analysis of individual target contributions to enhanced CaMKII activity. ISO also increased t₅₀ and average activity of CaMKII. (D) ISO substantially increases [Ca²⁺]_i transients during 2 Hz pacing, though the full response depends on synergy between CaMKII and PKA substrates.

We next evaluated how much each individual CaMKII substrate contributed to overall CaMKII-Ca²⁺-CaMKII feedback. Interestingly, most CaMKII substrates contributed to the overall feedback (except I_to and I_Na), with RyR phosphorylation producing the strongest individual effect. However, all targets working together produced the strongest response (Fig. 5, B and C, middle columns). Increases in Ca²⁺ fluxes by other kinases may enhance CaMKII activity in a similar manner. To test whether β-adrenergic signaling through PKA enhances CaMKII activity, we ran additional simulations with 1 μM isoproterenol (ISO) (see Fig. S13 for sample outputs from the β-adrenergic model). Through PKA enhancement of Ca²⁺ fluxes, CaMKII activity and t_50% were enhanced, which was further potentiated by CaMKII-OE (Fig. 5, B and C, right columns).

We next tested whether this feedback loop contributes to the increased Ca²⁺ transients during β-adrenergic stimulation. As expected for the control model, ISO significantly enhanced Ca²⁺ transients (∼2.6-fold) (Fig. 5 D). But when CaMKII was eliminated (CaMKII-KO), the ISO response was partially diminished. We found that the change in Ca²⁺ transients from CaMKII-KO to “control + ISO” models (Δ[Ca²⁺]_i of 1181 nM) was larger than the sum of the Ca²⁺ transient increases from CaMKII-KO to control (Δ[Ca²⁺]_i = 239 nM) and “CaMKII-KO + ISO” (Δ[Ca²⁺]_i = 860 nM), indicating synergy between PKA and CaMKII in the overall β-adrenergic response. Thus, this feedback loop appears to be both stimulated by and partially contribute to the response of Ca²⁺ transients to β-adrenergic stimulation.

Arrhythmogenesis

Abnormal CaMKII signaling is suggested to be proarrhythmogenic (5,6,30), so the model was used to test whether the included mechanisms could predict such scenarios. The model was stimulated to steady state with 2 Hz pacing and spontaneous activity was monitored after abrupt stimulus removal. Control simulations with 1 μM ISO show [Ca²⁺]_i (Fig. 6 A) and membrane potential (Fig. 6 B) profiles that return to rest after stimulus removal. With CaMKII-OE, however, peak [Ca²⁺]_i is reduced by ∼36% and delayed after-depolarizations (DADs) are seen after stimulus removal. Typically, DADs occur after repolarization of the membrane has completed and are triggered by aberrant release of Ca²⁺ from the SR (30). In the model, enhanced RyR Ca²⁺ sensitivity together with rising [Ca²⁺]_SR increases RyR leak. Initially, RyR leak slowly increases dyadic [Ca²⁺] and begins to decrease [Ca²⁺]_SR once J_leak > J_SERCA. But once dyadic [Ca²⁺] rises sufficiently, it triggers RyR opening, causing sharp increases in dyadic Ca²⁺ and then subsarcolemmal [Ca²⁺]. Increased subsarcolemmal [Ca²⁺] stimulates inward Na⁺/Ca²⁺ exchange (I_NCX), resulting in membrane depolarization (DADs).

Figure 6.

CaMKII overexpression induces DADs. (A and B) After abrupt removal of a >60 s, 2 Hz stimulus (see arrows labeled stimuli), DADs are observed in CaMKII-OE simulations with ISO. Note that CaMKII-OE also reduces Δ[Ca²⁺]_i in response to ISO (A). SR Ca²⁺ release during each DAD was assessed by integrating total RyR flux during afterdepolarizations. The smaller 65-μM release event produced a subthreshold DAD, while the larger 86-μM release induced a full AP (B). Both values fall on either side of our model's threshold of ∼70 μM for generation of a full AP, which is quantitatively consistent with an experimentally measured value of ∼64 μM (31).

To validate the predicted relationship between SR Ca²⁺ release and DAD generation, we induced graded SR Ca²⁺ release events after 2-Hz pacing during CaMKII-OE + ISO and measured subsequent changes in membrane potential. We found that our model has a full DAD threshold of ∼70 μmol/L cytosol Ca²⁺, which is quantitatively consistent with an experimentally measured threshold of ∼64 μmol/L cytosol (31) (see Fig. S14 for details of this analysis).

Interestingly, CaMKII-OE + ISO produced DADs only at frequencies ≥2 Hz. During CaMKII-OE alone at 2 Hz, diastolic RyR leak (J_leak) increased from ∼5 to 12 μmol/L cytosol/s, though [Ca²⁺]_SRT was insufficient for spontaneous release (Fig. 3 F). However, the addition of ISO during CaMKII-OE increased [Ca²⁺]_SRT. This effect, coupled with CaMKII-induced increases in RyR Ca²⁺ sensitivity and J_leak (∼15 μM/s in this case), induced spontaneous RyR opening that triggered the predicted DADs. At 3 Hz, increased RyR phosphorylation further lowered the threshold for SR release, triggering a subthreshold DAD even in the absence of ISO (data not shown). With ISO alone in the control model, J_leak increased only slightly (from ∼5 to ∼7 μM/s) and no DADs were produced. If CaMKII phosphorylation of RyRs is specifically eliminated during CaMKII-OE + ISO, no DADs are seen (Fig. S15). In contrast, if PKA-mediated phosphorylation of RyRs is eliminated, DADs are still observed.

Discussion

We incorporated CaMKII and PKA-dependent regulation of cardiac myocyte Ca²⁺ handling into a computational model of the rabbit ventricular myocyte. From this study, we were able to obtain new mechanistic insights regarding how these kinases coordinate control of excitation-contraction coupling. We also explored scenarios where CaMKII-induced dysregulation of ECC promoted cellular arrhythmias.

Several groups have developed models of CaMKII-dependent regulation of ECC. Hund and Rudy (32) found that ECC gain increases with frequency due to CaMKII, leading to a positive Ca²⁺ transient-frequency relationship. Grandi et al. (33) showed that static CaMKII-dependent modulations to I_Ca, I_to, and I_Na have distinct functional consequences on APD, though their collective activity promotes AP shortening. Hund et al. (34) showed that CaMKII hyperactivity and effects on I_Na contribute to abnormal Ca²⁺ homeostasis and AP upstroke velocity in infarct border zones. Hashambhoy et al. (35) developed a detailed, stochastic model of CaMKII-LCC interactions, finding that CaMKII-induced redistribution of LCC gating modes explains I_Ca facilitation.

Our model builds on this past work, providing a number of methodological advances that led to new mechanistic insights. Methodological advances include:

• 1.Development of biochemically detailed phosphorylation models of LCCs, RyRs, and PLB regulated by Ca²⁺/CaM-activated CaMKII.
• 2.Integration of these phosphorylation modules with well-validated models of β-adrenergic signaling and ECC.
• 3.
  Successful validation of our model against a number of experimental readouts, including CaMKII effects on

  • i. LCC facilitation and recovery from inactivation;
  • ii. RyR and PLB phosphorylation;
  • iii. SR Ca²⁺ content;
  • iv. fractional release;
  • v. Ca²⁺ transient amplitude;
  • vi. APD;
  • vii. FDAR; and
  • viii. postrest decay.

Using this quantitative framework, model analysis provided a number of new mechanistic insights, showing how:

• 1.CaMKII substrates are differentially phosphorylated in a context-dependent manner.
• 2.Interactions among CaMKII substrates determine overall consequences to myocyte Ca²⁺ handling and APD.
• 3.CaMKII participates in a CaMKII-Ca²⁺-CaMKII positive feedback loop that is potentiated by enhanced Ca²⁺ fluxes through PKA signaling.
• 4.Synergy between PKA and CaMKII, including effects on inhibitor-1, facilitates full responses to β-adrenergic stimulation.
• 5.CaMKII is responsible for early adaptation of FDAR via LCC phosphorylation.
• 6.CaMKII modulates ECC gain, though this influence is highly dependent on SR Ca²⁺.
• 7.CaMKII hyperphosphorylation of RyRs is arrhythmogenic and further potentiated by adrenergic stimulation.

CaMKII substrate phosphorylation and regulation of Ca²⁺ handling

While there is limited kinetic data regarding CaMKII phosphorylation at the modeled targets, our quantitative steady-state levels are generally consistent with available experimental measurements (see the Supporting Material) (20,21). At the LCC, we assumed quick kinetics to mimic rapid CaMKII-dependent I_Ca facilitation (13,15,16). As suggested by a number of experiments (21,29), we predicted slower kinetics at PLB that resulted in quantitatively small phosphorylation levels. While we predicted somewhat slow RyR kinetics, some data suggests that CaMKII-dependent RyR phosphorylation occurs on the order of ∼3 min (21). Such slow kinetics are difficult to reconcile with the much faster functional consequences of I_Ca facilitation (13,15,16), given that RyRs are concentrated near LCCs in dyads. Further experimental work is needed to clarify these issues. Also, data regarding CaMKII-dependent RyR regulation is somewhat conflicting (36,37), though our results indicate that positive regulation is critical for predictions of reduced SR Ca²⁺ content and enhanced leak during CaMKII-OE (as in experiments (11)).

Our model reproduced a range of data from rabbit myocytes acutely overexpressing CaMKII, including Ca²⁺ transient amplitudes, [Ca²⁺]_SRT, fractional release, APD, changes in [Na]_i, postrest decay, and FDAR (8,25,26). In transgenic mouse models, similar results are observed (in terms of Ca²⁺ sparks and [Ca²⁺]_SRT) though these animals show dramatically depressed Ca²⁺ transients and longer APD. In addition to species differences, these myocytes exhibit compensatory changes in protein expression including decreased RyR, PLB, and SERCA with increased Na⁺/Ca²⁺ exchanger, that are not observed in the rabbit experiments. These alterations may partially explain phenotypic differences between these animal models. Koivumäki et al. (38) recently modeled CaMKII-OE and found that inclusion of these secondary expression changes was critical for reproducing the mouse phenotype. Also, our predicted changes in [Na]_i are qualitatively similar but smaller than the levels measured experimentally (25), suggesting that CaMKII may regulate [Na]_i through additional mechanisms.

We predicted that CaMKII-KO decreases steady-state Δ[Ca²⁺]_i and APD compared with control conditions. But in CaMKII-KO or CaMKII inhibited mice, Δ[Ca²⁺]_i is normal (39,40), though secondary compensatory mechanisms play a role in maintaining Ca²⁺ handling (40). In Wagner et al. (26), the CaMKII inhibitor AIP somewhat reduced APD in normal myocytes but reversed the AP shortening effect of CaMKII-OE. The subtle model-experiment differences here may be due to partial CaMKII inhibition by AIP but complete CaMKII elimination in our model.

We provided additional evidence for the role of CaMKII in early FDAR and ECC gain. Several experiments have indicated that FDAR adaptation and PLB-Thr¹⁷ phosphorylation are temporally dissimilar (21,29). Our model agrees with these findings, where FDAR is rapid and PLB phosphorylation is slow and quantitatively small in control scenarios. However, we found that CaMKII-KO slowed FDAR and that LCC phosphorylation appeared to facilitate this quick adaptation. In addition, CaMKII-OE made the slope of steady-state FDAR more negative (consistent with experiments (7)), while the converse was true for CaMKII-KO. CaMKII inhibition either strongly inhibits (27), partially inhibits (8), or fails to affect (29) steady-state FDAR in experiments; our included mechanisms support findings of only slight CaMKII-dependence on steady-state FDAR. We also showed that the presence of CaMKII enhances ECC gain, though gain was smaller during CaMKII-OE. However, gain is highly SR-load-dependent (10), so we tested our model in scenarios of matched SR load. We found that CaMKII-OE dramatically enhanced gain, while CaMKII-KO produced the opposite effect. Thus, CaMKII can enhance gain, though this effect may be masked in conditions of low SR Ca²⁺.

Role of CaMKII-Ca²⁺-CaMKII feedback

The model predicted that the three dynamic CaMKII substrates contribute to CaMKII-Ca²⁺-CaMKII feedback, though RyR phosphorylation was most prominent. CaMKII activity was also enhanced in simulations with the β-adrenergic agonist ISO due to enhanced Ca²⁺ fluxes via PKA phosphorylation. We found that CaMKII helped facilitate overall β-adrenergic enhancement of Ca²⁺ transients via synergy between PKA and CaMKII-dependent phosphorylation. Specifically, it appeared that PKA-dependent increases in LCC and SERCA flux, combined with CaMKII-dependent RyR fluxes, were a major source of crosstalk. PKA activation of inhibitor-1, another route of crosstalk between these pathways, substantially increased Thr¹⁷ PLB phosphorylation independent of enhanced Ca²⁺ signals.

Interestingly, Curran et al. (19) found that the CaMKII inhibitor KN-93 eliminated ISO-induced enhancement of peak [Ca²⁺]_i in rabbit myocytes, in accordance with our results. However, KN-93 can inhibit I_Ca in a CaMKII-independent manner which complicates these findings (41). In another study, transgenic mice expressing a CaMKII inhibitor (AC3-I) produced full adrenergic responses, though these results are complicated by secondary PKA-dependent increases in I_Ca (40). Our results thus suggest that, excluding secondary compensatory mechanisms, CaMKII can play a role in facilitating inotropic responses to acute adrenergic stimulation.

Arrhythmogenesis

Hyperactive CaMKII is suspected to be proarrhythmogenic, due mainly to its ability to enhance LCC gating and RyR sensitivity (5,30). We found that CaMKII-OE + ISO with ≥2 Hz pacing or CaMKII-OE alone with ≥3 Hz pacing produced DADs after abrupt stimulus removal. Use of a well-validated model of the RyR (in terms of open probability, leak, fractional release, and response to agonists (e.g., caffeine)) and a Na⁺/Ca²⁺ exchanger model that responds to subsarcolemmal Ca²⁺ signals was critical for our analysis (10). Our model demonstrates that CaMKII-dependent increases in RyR Ca²⁺ sensitivity and leak can lower the threshold for spontaneous SR Ca²⁺ release, while ISO-induced enhancement of [Ca²⁺]_SRT can potentiate these effects. We also showed that the threshold amount of Ca²⁺ release required to trigger a full DAD is consistent with experimental measurements (31). In our simulations, elimination of CaMKII's ability to hyperphosphorylate the RyR (i.e., fixing phosphorylation to control levels) eliminated DADs, with less influence from PKA-dependent RyR phosphorylation. Sag et al. (42) demonstrated that β-adrenergic stimulation of CaMKII-OE mouse myocytes increased the number of DADs, consistent with our model predictions. While DADs involve the complex interplay of several mechanisms, the model illustrates a quantitatively significant contribution from CaMKII-dependent hyperphosphorylation of RyRs.

While early after-depolarizations (EADs) have been linked to abnormal CaMKII signaling (5,6,42), EADs were not observed in our model, even during adrenergic stimulation. CaMKII is believed to induce EADs through its interactions with LCCs (5). Though LCC-mediated EADs can be generated using deterministic computational models (43), the CaMKII-dependent LCC alterations included here, with and without adrenergic stimulation, were insufficient. Stochastic models of LCC modal gating can trigger EADs (44), which may suggest that EAD formation via CaMKII is sensitive to stochasticity. CaMKII-RyR interactions may also be sensitive to stochasticity. Also, the mechanism of DAD formation could be sensitive to model formulation (e.g., a single dyad versus multiple, independent dyads). Given that our CaMKII-RyR model is sufficient to predict global changes in [Ca²⁺]_SRT and SR leak seen experimentally and the much larger computational burden for stochastic simulations, our deterministic model appears to be an appropriate first step for analyzing changes in Ca²⁺ handling that may lead to arrhythmia.

Limitations

While we were careful to focus on well-validated interactions constrained by quantitative measurements, uncertainties in the exact mechanisms underlying the functional consequences of these interactions are unavoidable. In our CaMKII model, basal kinase activity is low (<1%) due to limited Ca²⁺/CaM binding at diastolic Ca²⁺ levels and high [PP1] in the dyadic cleft. However, increased Ca²⁺ spark frequency during CaMKII-OE indirectly suggests that CaMKII is partially active during rest (7,8,45). This discrepancy could be due to a change in the balance of kinase and phosphatase activities (3), but additional experimental data and analysis are needed.

While we included several CaMKII activation mechanisms (e.g., Ca²⁺/CaM-dependent, autonomous, ECC feedback, and ISO), there are still other Ca²⁺-independent mechanisms that control CaMKII activity. Erickson et al. (46) demonstrated that CaMKII can be oxidized at methionine residues (281/282), conferring additional memory to CaMKII. Christensen et al. (47) modeled CaMKII oxidation, showing increased activity in infarct border zones that was predicted to reduce conduction velocity and increase susceptibility to conduction block. CaMKII can also autophosphorylate at Thr³⁰⁶ after Thr²⁸⁷ phosphorylation, but Thr²⁸⁷ autophosphorylation is not prominent in our simulations. In addition, CaMKII can be activated during β₁-specific adrenergic stimulation via formation of a β-arrestin-CaMKII-Epac1 complex, which may confer additional signaling potential to CaMKII during adrenergic stimulation (48). These additional activation mechanisms may be examined in subsequent studies.