Rate Dependence and Regulation of Action Potential and Calcium Transient in a Canine Cardiac Ventricular Cell Model
Background— Computational biology is a powerful tool for elucidating arrhythmogenic mechanisms at the cellular level, where complex interactions between ionic processes determine behavior. A novel theoretical model of the canine ventricular epicardial action potential and calcium cycling was developed and used to investigate ionic mechanisms underlying Ca2+ transient (CaT) and action potential duration (APD) rate dependence.
Methods and Results— The Ca2+/calmodulin-dependent protein kinase (CaMKII) regulatory pathway was integrated into the model, which included a novel Ca2+-release formulation, Ca2+ subspace, dynamic chloride handling, and formulations for major ion currents based on canine ventricular data. Decreasing pacing cycle length from 8000 to 300 ms shortened APD primarily because of ICa(L) reduction, with additional contributions from Ito1, INaK, and late INa. CaT amplitude increased as cycle length decreased from 8000 to 500 ms. This positive rate–dependent property depended on CaMKII activity.
Conclusions— CaMKII is an important determinant of the rate dependence of CaT but not of APD, which depends on ion-channel kinetics. The model of CaMKII regulation may serve as a paradigm for modeling effects of other regulatory pathways on cell function.
Received January 29, 2004; de novo received April 19, 2004; accepted June 7, 2004.
The dependence of action potential duration (APD) and the Ca2+ transient (CaT) on pacing rate is a fundamental property of cardiac myocytes that, when altered, may promote life-threatening cardiac arrhythmias. We have developed a detailed and physiologically based mathematical canine ventricular cell model (Hund-Rudy dynamic [HRd] cell model) that simulates rate-dependent phenomena associated with ion-channel kinetics, AP properties, and Ca handling. The dog is commonly used to investigate cardiac electrophysiology, making it a logical choice for modeling. An epicardial myocyte was chosen rather than endocardial or midmyocardial myocytes because epicardial cells contain the highest density of Ito1 (transient outward K+ current), producing a unique and complex AP morphology.
Ca2+/calmodulin-dependent protein kinase1 (CaMKII) mediates an important regulatory pathway in myocytes.2 On activation by Ca2+/calmodulin, CaMKII phosphorylates neighboring subunits (autophosphorylation), which enables detection of Ca2+ spike frequency.3 In cardiomyocytes, CaMKII substrates include L-type Ca2+ channels (LTCCs), ryanodine receptor Ca2+-release channels (RyRs), sarcoplasmic reticulum Ca2+-ATPase (SR Ca2+-uptake pump), and phospholamban (PLB).4–10 This suggests an important role for CaMKII in cardiac Ca2+-handling rate dependence and electrophysiology. We used the HRd model to gain new insights into ionic processes underlying AP and CaT rate dependence and how CaMKII regulates these processes.
Complete HRd equations, definitions, and detailed comments appear in the online-only Data Supplement. Important model properties (schematic in Figure 1A) are summarized here.
Ca2+/Calmodulin-Dependent Protein Kinase II
The CaMKII formulation was adapted from Hanson et al3 and responds dynamically to [Ca2+]ss (subspace Ca2+ concentration) elevation during the CaT. Kinase subunits can be inactive, in a Ca2+/calmodulin-bound active state (CaMKbound), or in a “trapped” state (CaMKtrap), wherein the subunit remains active for some time after [Ca2+]ss returns to diastolic values. Autophosphorylation of 1 subunit by another promotes transition from CaMKbound to CaMKtrap. Trapped subunits are dephosphorylated at a constant rate, βCaMK, of 0.00068 ms−1, a moderate value compared with the cycle-length (CL) range investigated here.
The junctional SR membrane abuts the sarcolemma along t-tubules, where LTCC and RyR clusters are localized,11 creating a subspace in which the Ca2+ concentration ([Ca2+]ss) rises faster and reaches larger values compared with that of the bulk myoplasm. We modeled the subspace as a compartment into which LTCCs and RyRs open, generating a local Ca2+ concentration, [Ca2+]ss. Anionic sarcolemmal and SR membrane binding sites act as calcium buffers.12 The Ca2+-dependent transient outward current (Ito2) is a ligand-gated Cl−-selective channel. Its low Ca2+ sensitivity (K0.5=0.1502 mmol/L)13 supports its incorporation into the Ca2+ subspace. CaMKII forms a complex with RyR14 and is also assumed to be in the subspace.
RyR Ca2+-Release Channel Irel
The Irel formulation includes activation by the L-type Ca2+ current, Ca2+-dependent inactivation,15,16 and open-probability modulation by junctional SR [Ca2+] and [Ca2+]ss17. Although it is generally accepted that the RyR is regulated by SR Ca2+ content17 and inactivated by cytosolic Ca,15,16 the relative contribution of each process to SR Ca2+-release termination is unknown. Irel in our formulation terminates via both inactivation and SR regulation of the activation gate.18 Graded release is achieved by making steady-state activation a continuous function of ICa(L). Voltage-dependent SR release gain19 (variable gain, Figure 1B) is introduced through a multiplicative factor dependent on the ICa(L) driving force.
Though controversial (online-only Data Supplement section J), CaMKII phosphorylation is thought to promote RyR channel opening.5,14,20 Accordingly, the Irel inactivation time constant (τri) depends on CaMKII activity. A 10-ms maximal CaMKII-dependent increase in τri yields a steady-state CaT amplitude (CaTamp) 95%20 greater for control than with CaMKII suppressed at rapid pacing (CL=300 ms).
SR Ca2+-ATPase and PLB
CaMKII phosphorylates the SR,6 targeting SERCA2a (SR Ca2+-ATPase)7 and PLB,8,10 which associates with SERCA2a to inhibit uptake. PLB phosphorylation shifts the Ca2+-binding K0.5 and relieves inhibition,9 whereas direct SERCA2a phosphorylation increases the maximum uptake rate,7 although this is controversial9 (online-only Data Supplement section K). and K0.5 depend on CaMKII activity to represent this behavior. The maximal CaMKII-dependent increase is 75%,7 whereas the maximal K0.5 decrease is 0.17 μmol/L9.
L-Type Ca2+ Channel
ICa(L) steady-state activation and current density yield a current-voltage (I-V) relation consistent with canine ventricular data21 (Figure 1C). The activation variable, d, is raised to a time-dependent and voltage-dependent power (see the online-only Data Supplement). We assume 2 voltage-dependent inactivation gates with steady-state values (Figure 1D) and time constants fitted to canine ventricular data21,21a (online-only Data Supplement Figure I). Ca2+-dependent inactivation has a fast process22 dependent on [Ca2+]ss and LTCC Ca2+ entry (approximated as ICa(L)23) and a slow process dependent on ICa(L).22
Ca2+-dependent facilitation occurs via CaMKII phosphorylation.4 The rapid Ca2+-dependent inactivation time constant (τfca) is CaMKII dependent, producing a maximal 40%20 increase in peak ICa(L) relative to the model, with CaMKII suppressed at rapid pacing (CL=500 ms).
Two Components of the Delayed Rectifier K+ Current
The canine delayed rectifier K+ current has a rapidly activating component (IKr) and a slowly activating component (IKs).24 The model IKs has fast (xs1, with time constant τxs1) and slow (xs2) activation gates. Voltage dependence of τxs1 fits canine data.24 The slow activation gate is 10 times slower than xs124. IKr has 1 activation gate, xr, based on experimental data.24 IKs and IKr conductances were chosen to agree with experimental data24 (Figure 1E).
Transient Outward K+ Current
The 4AP-sensitive transient outward K+ current, Ito1, incorporates the activation and inactivation kinetics of Dumaine et al.25 We add a second inactivation gate with a slower time constant26 than in Dumaine’s formulation. The model Ito1 I-V curve agrees with experimental data27 (Figure 1F).
The Na+-Ca2+ exchanger (INaCa), from Weber et al,30 includes an allosteric interaction between intracellular Ca2+ and the exchanger.
The model was paced with a conservative current stimulus34 (carried by KCl) for 2000 seconds from rest (initial conditions in online-only Data Supplement Table II) at a constant CL. Steady-state APD (at 90% repolarization) and CaTamp (peak systolic [Ca2+]i−minimal diastolic [Ca2+]i) were used to create the APD adaptation curves and the CaTamp-frequency curves, respectively.
APD Rate Dependence (Adaptation)
The model AP morphology (Figure 2A) and APD (Figure 2B) agree with canine epicardial recordings26 over a CL range from 8000 to 300 ms. Most important for canine APD rate adaptation is ICa(L), supported by the fact that eliminating ICa(L) from the model reduced adaptation (CL range of 8000 to 300 ms) from 99 to 30 ms (71% decrease, Figure 2B). Ito1 also plays a role: its elimination reduced adaptation by 38% (Figure 2B). Of secondary importance are INaK (clamping [Na+]i during pacing reduces adaptation by 15%) and INa,L (eliminating IN,aL reduces adaptation by only 9%). CaMKII inhibition had very little effect on APD adaptation (Figure 2B).
Interestingly, a decrease in the repolarizing current Ito1 facilitates APD shortening at a fast rate. Comparing steady-state AP with (=0.19 mS/μF) and without (=0 mS/μF) Ito1 reveals the effect of Ito1 on APD (Figure 3). At a slow rate, a large Ito1 produced a rapid phase 1 repolarization (Figure 3A, arrow) which increased the ICa(L) driving force and enhanced its voltage-dependent activation during the AP plateau (Figure 3B, arrow). Phase 1 repolarization also increased IKr activation and decreased the driving force for reverse-mode INaCa, thus reducing these repolarizing currents (Figure 3C and 3D, respectively). By increasing ICa(L) and decreasing IKr and INaCa, Ito1 indirectly prolonged APD. During rapid pacing, Ito1 decreased owing to slow recovery from inactivation, and phase 1 repolarization slowed (Figure 2A). Consequently, indirect APD prolongation by Ito1 was suppressed at fast pacing rates.
Figure 4 compares rate-dependent changes in AP (Figure 4A) and major ionic currents between the HRd canine model and the LRd guinea pig model.32 Reduction in ICa(L) at fast rates was observed in the dog but not in the guinea pig (Figure 4B). Guinea pig adaptation instead is primarily caused by an accumulation of slow deactivating IKs at fast rates (Figure 4C, arrow).35 Canine IKs is small and does not accumulate between beats because of its faster deactivation (Figure 4C). Whereas guinea pig IKs during the AP was larger than IKr, canine IKr is much larger than IKs (Figure 4C and 4D).
Steady-state CaTamp and morphology (Figure 5A), measured36 and simulated, agreed over a wide pacing range. Consistent with experiment,36 the model diastolic [Ca2+]i and CaTamp increased as pacing frequency increased from 0.25 to 2.0 Hz (positive CaTamp-frequency relation, Figure 5B), associated with an increase in simulated CaMKII activity, excitation-contraction coupling (ECC) gain (Figure 5C), and PLB phosphorylation by CaMKII (Figure 5D). CaMKII inhibition produced a negative CaTamp-frequency relation for frequencies >1 Hz (Figure 5B) and flattened the gain-frequency relation (Figure 5C). CaMKII inhibition during pacing (2.0 Hz) (Figure 6) reduced CaTamp (Figure 6B) by decreasing Iup (Figure 6C), which reduced SR Ca2+ load (Figure 6D) by decreasing peak ICa(L) (Figure 6E), which reduced the trigger for SR release, and by reducing Irel directly (Figure 6F).
We present a dynamic model of the canine ventricular epicardial cell that reproduces experimentally measured AP and CaT over a wide pacing frequency range. Given the broad frequency range during cardiac arrhythmias and the interplay between Ca cycling and cellular electrophysiology in arrhythmogenesis, this model serves as a valuable research tool.
Summary of Important Mechanistic Findings
The major findings of this study are that (1) canine APD adaptation is determined primarily by ICa(L) reduction at fast rates; (2) Ito1 contributes to APD adaptation indirectly by augmenting the phase 1 notch at slow rate; (3) ECC gain increases with frequency owing to increased CaMKII activity, producing a positive CaTamp-frequency relation; and (4) CaMKII is important for rate-dependent changes in CaT but does not significantly effect APD adaptation.
Comparison With Existing Models
Canine ventricular AP models have been previously developed to study electrophysiologic remodeling after heart failure37 and myocardial infarction38 and APD alternans during rapid pacing.39 The model presented here distinguishes itself by incorporating (1) dynamic CaMKII activity and regulation of intracellular Ca2+ handling; (2) the late Na+ current, INa,L, and the Ca2+-dependent transient outward current, Ito2; (3) dynamic intracellular Cl− concentration changes; and (4) a novel Irel formulation. Our model represents an important advance in the physiologic representation of rate-dependent cell processes through its inclusion of the CaMKII regulatory pathway, shown experimentally to play a role in the force-frequency relation and rate-dependent CaT abbreviation.14,20,40
“Local-control”41 Ca2+ release has been integrated into a canine AP model,42 wherein SR Ca2+ release involves statistical recruitment of individual Ca2+ release units. Although this model reproduces macroscopic release based on individual diadic events, computational demands discourage its use in modeling cardiac arrhythmias. Therefore, we reproduced local-control features (variable gain and graded release) by using a macroscopic approach with reduced computational demand.
Effect of CaMKII on Ca2+ Handling
We have shown that increased CaMKII activity during rapid pacing augments SR Ca2+ release and promotes a positive CaTamp-frequency relation. Our findings are supported by recent experiments measuring increased CaMKII activity and CaMKII-dependent SR Ca2+ release after pacing.14 It is important to note that additional factors determine the CaTamp-frequency relation. Even in the presence of CaMKII inhibition, a positive relation exists over a limited frequency range from 0.125 to 1 Hz (see Figure 5B). Intracellular Na+ and Ca2+ accumulation during rapid pacing produces CaMKII-independent SR loading. Intracellular Ca2+ buffer saturation at fast rates also may contribute to a positive force-frequency relation.43
In the guinea pig, IKs activates and deactivates more slowly than does IKr44. In the dog, IKr and IKs deactivation kinetics are reversed, with IKs deactivating faster than IKr.24 Our simulations suggest that IKs does not contribute significantly to canine APD adaptation owing to its small amplitude and fast deactivation, consistent with recent canine experiments.45,46 However, β-adrenergic stimulation enhances IKs,47 possibly increasing its importance in AP repolarization and adaptation in vivo.
Our results also suggest a role for Ito1 in determining APD and APD adaptation. Consistent with previous theoretical48 and experimental49 studies, we found that Ito1 creates a phase 1 notch that increases the driving force for ICa(L) and facilitates activation of a sustained component. In addition, the phase 1 notch decreases the repolarizing currents IKr and reverse-mode INaCa. Together, these processes prolong APD. New insight is obtained into the role of Ito1 in APD adaptation: slow recovery promotes Ito1 reduction, notch suppression, and less associated APD prolongation at fast rates. Our findings are consistent with greater adaptation in epicardial than in endocardial cells (85 and 65 ms, respectively26), which have a greatly diminished Ito1 density. We also found (not shown) that the notch accelerates the time to peak CaT (62 ms in control vs 83 ms without Ito1), consistent with experimental observations.50
The model formulation was based, wherever possible, on recent experimental data and current understanding of cardiac electrophysiology and Ca2+ handling. However, there are controversies regarding CaMKII and its regulatory effects. Disparate findings exist on whether or not CaMKII phosphorylates SERCA2a directly.7,9 Similarly, conflicting reports exist on CaMKII regulation of RyR activity.5,20,51,52 These issues remain unresolved (see online-only Data Supplement, sections J and K). We hope that this study will motivate detailed experimental characterization of CaMKII effects on cellular function.
This work was funded by grants R01-HL49054 and R37-HL33343 (to Y.R.) from the National Institutes of Health—National Heart, Lung, and Blood Institute, and a Whitaker Foundation Development Award. We thank Greg Faber, Jonathan Silva, and Keith Decker for helpful discussions and Marlene Siegal for administrative assistance.
An online-only Data Supplement is available at http://www.circulationaha.org
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