Regulation of Ca²⁺ and electrical alternans in cardiac myocytes: Role of CaMKII and repolarizing currents

Abstract

Alternans of cardiac repolarization is associated with arrhythmias and sudden death. At the cellular level, alternans involves beat-to-beat oscillation of the action potential (AP) and possibly Ca²⁺ transient (CaT). Because of experimental difficulty in independently controlling the Ca²⁺ and electrical subsystems, mathematical modelling provides additional insights into mechanisms and causality. Pacing protocols were conducted in a canine ventricular myocyte model with the following results: 1. (I) CaT alternans results from refractoriness of the SR Ca²⁺ release system; alternation of the L-type calcium current (I_Ca(L)) has a negligible effect; (II) CaT-AP coupling during late AP occurs through the sodium-calcium exchanger (I_NaCa) and underlies APD alternans; (III) Increased Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) activity extends the range of CaT and APD alternans to slower frequencies and increases alternans magnitude; its decrease suppresses CaT and APD alternans, exerting an antiarrhythmic effect; (IV). Increase of the rapid delayed rectifier current (I_Kr) also suppresses APD alternans, but without suppressing CaT alternans. Thus, CaMKII inhibition eliminates APD alternans by eliminating its cause (CaT alternans), while I_Kr enhancement does so by weakening CaT-APD coupling. The simulations identify combined CaMKII inhibition and I_Kr enhancement as a possible antiar-rhythmic intervention.

INTRODUCTION

T-wave alternans is closely associated with dispersion of repolarization, ventricular arrhythmias and sudden death [47, 53]. One hypothesis states that T-wave alternans originates from alternation of cardiac repolarization at the cellular level, particularly beat-to-beat variation of the action potential (AP) duration (APD) [35, 49]. APD alternans can be electrical in nature, caused by ionic currents restitution[35]. Alternatively, alternation of the intracellular Ca²⁺ transient (CaT alternans) can modulate electrical activation and induce APD alternans [38, 48]. The mechanism of Ca²⁺ alternans and its coupling to electrical activation is not completely understood [15, 55] Several mechanisms of Ca²⁺ alternans have been proposed: a) restitution of L-type Ca²⁺ current (I_Ca(L)) [20]; b) refractoriness of sarcoplasmic reticulum (SR) Ca²⁺ release channels (RyR) [50]; c) dependence of Ca²⁺ uptake by the SR Ca²⁺-ATPase/phosholamban complex (SERCA/PLB) on [Ca²⁺]_i [31]; d) SR Ca²⁺ overloading and Ca²⁺ wave propagation [13]; e) steep dependence of SR Ca²⁺ release on SR Ca²⁺ concentration [1, 14]. Interactions among these processes and with metabolic and/or Ca²⁺- dependent regulatory pathways can promote alternans [6, 30, 48].

Due to tight coupling between the Ca²⁺ and electrical cellular subsystems, it is difficult to determine cause and effect experimentally because the ability to independently control each subsystem is limited [23]. Even more challenging is the study of interactions between specific SR processes and sarcolemmal currents [50]. Several studies have shown that CaT alternans persists when the cell is voltage clamped either with constant voltage [13, 48, 50] or constant duration action potentials [9], suggesting that Ca²⁺ oscillation plays the primary role in alternans generation at moderately-fast rate of pacing.

Theoretical modeling can realize precise independent control of individual components and is therefore very useful for studying the highly interactive mechanism of alternans. While important insights have been obtained from simplified models [1, 2, 20, 55, 59], processes relevant to alternans formation such as dynamic ion accumulation and regulation by Ca²⁺ – dependent regulatory pathways have not been considered. Moreover, properties of CaT-AP coupling are species dependent [4, 15, 23, 50], each with remarkably different CaT and AP morphologies and durations. In addition, there is the well-documented transmural heterogeneities in AP and CaT cycling properties in the same species, which have been documented to affect the onset and amplitude of alternans [51, 68].

It has been observed that the large CaT during beat-to-beat (large-small) CaT alternans is accompanied by a short APD in some species (or certain experimental conditions) [33, 46], while in other species by a prolonged APD [48, 50]. It was suggested that the Na⁺/Ca²⁺ exchanger, I_NaCa, is responsible for prolongation of APD during large CaT, while Ca²⁺ –dependent inactivation of I_Ca(L) is the mechanism of APD shortening [48, 59]. However , the specific mechanism of CaT-APD coupling during alternans and its modulation by the whole-cell environment require further exploration. A delicate balance between repolarizing and depolarizing currents provides for precise control of the AP time course [54]. Because this balance is modulated by [Ca²⁺]_i, it is important to use physiologically detailed models of the cardiac myocyte for studying the interaction between the Ca²⁺ and electrical subsystems in the study of alternans.

Here, we investigate the cellular mechanism of alternans that involves both CaT and APD alternation. Specifically, we examine the following hypotheses: 1. Calcium alternans drives APD alternans via coupling of the Ca²⁺ and electrical subsystems through I_NaCa. 2. Calcium alternans is caused by refractory properties of the SR Ca²⁺ release process and steep dependence of Ca²⁺ release on SR Ca²⁺ load. 3. Repolarizing currents have a modulatory effect on alternans by influencing APD in a Ca²⁺-independent manner. 4. By modulating SR Ca²⁺ cycling, CaMKII is a major determinant of alternans and its rate dependence. Ca²⁺/calmodulin-dependent protein kinase II (CaMKII), is a regulatory pathway that modulates its activity in response to frequency, amplitude and duration of Ca²⁺ pulses [10, 26]. It plays an essential role in frequency-dependent augmentation of normal cardiac contractility [69] and acceleration of relaxation [12], particularly during stress or exercise. CaMKII hyperactivity can lead to structural heart disease and arrhythmias [3, 32, 75]. For the purpose of this study, an updated mathematical formulation of SR Ca²⁺ release (I_Rel) was developed. It includes activation of RyR by I_Ca(L) and its regulation by junctional SR Ca²⁺ concentration ([Ca²⁺]_JSR) and CaMKII. This formulation was incorporated into theoretical models of ventricular epicardial myocytes of two species, guinea-pig [16, 43] and canine [28].

The article outline is as follows: First, reformulated I_Rel is validated by reproducing experimental protocols that reveal properties of the Ca²⁺ induced Ca²⁺ release (CICR) process. Second, the dependence of CaMKII on CaT and APD and its inotropic effect are simulated and compared to experiment. Third, the roles of I_Ca(L), SR Ca²⁺ fluxes and CaMKII in alternans onset and termination at moderately fast rate are studied. Fourth, the nature of bidirectional CaT-APD coupling during alternans is investigated, particularly the role of I_Ca(L), I_NaCa and I_Kr. Aspects of this work have been presented in abstract form [41].

METHODS

Myocyte Models

Table I in the Appendix contains parameter definitions. The theoretical LRd [16, 43] and HRd [28] models of mammalian ventricular AP provide the basis for the simulations. The LRd model is based on guinea pig data; it includes membrane ion-channel currents, pumps and exchangers, and accounts for dynamic concentration changes of Na⁺, K⁺, and Ca²⁺. The HRd model ( Figure 1A) is based on epicardial canine data [28] and adds to LRd processes of chloride (Cl⁻) homeostasis and the CaMKII regulatory pathway. The model includes the following phosphorylation targets of CaMKII: I_up, I_Ca(L) and I_Rel. I_up includes effects of CaMKII on both the SERCA pump maximal turnover rate and its affinity to Ca²⁺. I_Ca(L) and I_Rel interact in a subsarcolemmal restricted subspace for Ca²⁺ distribution. Models equations and codes can be found in the research section of http://rudylab.wustl.edu.

TABLE I.

Abbreviations and Definitions

Abbreviation	Definition	Units
SR	Sarcoplasmic reticulum
CaMKII	Ca2+/calmodulin-dependent protein kinase II
RyR	ryanodine receptor
LCC	L-type calcium channel
SERCA	SR Ca2+-ATPase pump
PLB	phospholamban
SERCA/PLB	the SERCA/PLB complex
CSQN	calsequestrin
CICR	Ca2+ induced Ca2+ release process
JSR	junctional SR
NSR	network SR
AP	action potential	mV
APD	AP duration at 90% repolarization	ms
CL	cycle length	ms
FDAR	frequency-dependent acceleration of relaxation
PFFR	positive force-frequency relation
CaMKactive	Fraction of active CaMKII binding sites
CaMK0	Fraction of low affinity calmodulin CaMKII binding sites
IRel	flux through RyR	mmol/L/ms
Itr	Ca2+ translocation flux from NSR to JSR	mmol/L/ms
CTNaCl	Na+ − Cl− cotransporter	mmol/L/ms
CTKCl	K+ − Cl− cotransporter	mmol/L/ms
Idiffusion	Ca2+ translocation flux from subspace to myoplasm	mmol/L/ms
Iup	Ca2+ uptake flux by SERCA pump	mmol/L/ms
Ileak	Ca2+ leak from SR	mmol/L/ms
[Ca2+]JSR	free Ca2+ concentration in JSR	mmol/L
[Ca2+]JSR,t	total Ca2+ concentration in JSR	mmol/L
[Ca2+]NSR	Ca2+ concentration in NSR	mmol/L
$C{a}_{SR}^{2+}$	total Ca2+ content in SR	mmol
INa	fast sodium current	μA/μF
INa,L	Slowly inactivating late Na+ current	μA/μF
ICa(L)	current through LCC	μA/μF
IKr	Rapid delayed rectifier K+ current	μA/μF
IKs	Slow delayed rectifier K+ current,	μA/μF
IK1	Inward rectifier K+ current,	μA/μF
INaCa	current through Na+/Ca2+ exchanger	μA/μF
INaK	current through Na+/K+ pump	μA/μF
Ito1	transient outward K+ current	μA/μF
IK,ATP	ATP dependent K+ current	μA/μF
Ito2	Ca2+ depended transient outward (Cl−) current	μA/μF
ΔCa2+	max(CaT)- min(CaT)	μmol/L
CaT ,[Ca2+]i	free Ca2+ concentration in myoplasm	μmol/L
[Ca2+]ss	free Ca2+ concentration in subspace	μmol/L
$\overline{\mathit{CaT}}$	ratio of max(CaT)/min(CaT)

FIG. 1.

(A) Ventricular myocyte model. Symbols are defined in Appendix Table I. Model equations are provided (including code) in research section of http://rudylab.wustl.edu. (B) SR Ca²⁺ release model. (C) Variable gain. Measured (grey) ([63], reproduced with permission) and simulated (black) excitation-contraction coupling (ECC) gain as function of membrane voltage. (D) Graded release. Ca²⁺ released by RyR (∫_CL I_Reldt, CL=1000 ms) as function of peak I_Ca(L). (E) Fractional SR Ca²⁺ release. Ca²⁺ released by RyR (∫_CL=1000 I_Reldt) as function of JSR end-diastolic loading ([Ca²⁺]_JSR,t) in percentage of [Ca²⁺]_JSR,t.

Calcium Induced Calcium Release Process (I_Rel)

We formulated a two-state (closed-open) model of SR Ca²⁺ release kinetics (Figure 1B) and incorporated it in LRd and HRd. We assumed that in nonfailing myocytes CICR is a spatially uniform process [50]. Based on this assumption and the assumptions that RyRs are independent and identical, the two-state model can describe the kinetics of the SR Ca²⁺ release process [61, 62, 64]. Transition kinetics between release (open) and no-release (closed) states depend on I_Ca(L) [42, 59], Ca²⁺ concentration in junctional SR ([Ca²⁺]_JSR) [19, 67] and CaMKII activity. This is consistent with experiments [7, 18, 34] and early modeling work [16, 43, 58] where efficiency of release was linked to the rate of Ca²⁺ elevation in myoplasm and not to the level of myoplasmic Ca²⁺ per se. The differential equations for the model are presented in the Appendix.

Simulation Protocols

The 0.5 ms or 1 ms -80 μA/μF current stimuli were used to pace LRd or HRd, respectively. The stimulus current was assigned Cl⁻ and/or K⁺ ions as charge carrier to insure charge conservation and model stability [29]. Numerical integration was performed using Matlab (Mathworks, Natick,MA) [56], with error tolerance 10⁻⁶. Steady-state was defined when all state variables showed less than 0.1% variability over 100 beats (1 min). The models were tested for convergence and long-term stability over the entire frequency range and parameter values considered. Steady-state APD (90% repolarization) and peak CaT (or Δ[Ca²⁺]= max(CaT)-min(CaT)) were used to create rate-adaptation curves. Results are shown for HRd simulations except for Figure 4, where alternans are also shown for LRd to demonstrate model (species) independence of the alternans phenomenon.

FIG. 4.

APD and CaT rate-adaptation curves. Insets show bifurcation portions on enlarged scale. (A) and (B) Guinea pig (C) and (D) Canine. Inset in (C) shows experimental data ([23], reproduced with permission).

RESULTS

MODEL PROPERTIES VALIDATION

Because we hypothesize that SR Ca²⁺ cycling plays a key role in CaT alternans, it is essential to verify that the models of SR Ca²⁺ release and CaMKII activity reproduce the experimentally observed behaviors that are relevant to alternans generation. The following sections and Figures 1, 2, and 3 provide such validation. Table VI and Table V in the Appendix contain documentation of the electrophysiological data used for the canine model validation and CaMKII data, respectively.

FIG. 2.

(A) Simulated and (B) experimental ([10], reproduced with permission) time course of CaMKII activity at stimulation rates of 1 Hz, 2.5 Hz and 4 Hz; CaT duration and amplitude are held constant at 200 ms and 20 μmol/L. Different time scales reflect different isoforms in model and experiment (see text). (C) Simulated and (D) measured [10] frequency dependence of CaMKII activity for indicated CaT durations (CaTd). (E) Time course of AP, CaT, CaMKII ctivity and [Ca²⁺]_JSR at 1 Hz stimulation rate. Black: control; grey: AP-clamp pacing with wice APD. (F) CaMKII activity as function of pacing rate for different AP-clamp APDs; control (black), 1.5xAPD (dashed-dotted grey), 2xAPD (dashed grey).

FIG. 3.

Simulated (top) and measured (bottom)([60], reproduced with permission) CaT during pacing at 0.25-,0.5-,1-, and 2-Hz. Descending limb of CaT is fit by a single exponential with time constant τ. (B) Simulated and (C) measured (mouse, force)([12], reproduced with permission) effect of CaMKII inhibition (by KN-93) on rate of CaT decline and mechanical relaxation. (D) Simulated effect of CaMKII inhibition on force-frequency (CaT-frequency) relation. (E) Corresponding experimental data ([69], reproduced with permission) (rabbit, time-derivative of ventricular pressure, dP/dt).

TABLE V.

CaMKII data

Figure	Source	Experimental conditions
3C	DeSantiago et al.[12] Fig.1B (Adapted)	35°C, mouse, isolated myocyte.
3E	Wehrens et al.[69] Fig. 3A (Adapted)	37°, Rabbit, whole heart.
2B and 2D	De Koninck and Schulman [10] Fig. 3B and Fig. 4A (Adapted)	Room temperature, in vitro CaMKII phosphorylation.
7A	Diaz et al.[13]Fig.2 (Adapted).	Room temperature, perforated patch clamp, isolated rat myocyte.

Relationship Between CaT, I_Ca(L), and SR Ca²⁺ Loading

The SR Ca²⁺ release model is validated by reproducing a number of key properties of excitation-contraction coupling (ECC) that determine CaT: A. Variable Gain: Ca²⁺ influx via I_Ca(L) is an order of magnitude smaller than the Ca²⁺ flux via RyR. The ratio I_Rel/I_Ca(L) (or CaT/I_Ca(L)) [63] is ECC gain; it depends on membrane voltage (variable gain). B. Graded Release. SR Ca²⁺ release and consequently CaT are under tight control of I_Ca(L), i.e., the magnitude of I_Rel is graded with the amplitude of I_Ca(L). C. Fractional SR Ca²⁺ Release. Percent of total available SR Ca²⁺([Ca²⁺]_JSR,t) released via RyR. Experiments show that fractional release is a steep non-linear function of [Ca²⁺]_JSR,t [57]. The above properties of ECC are often evaluated experimentally when exploring the mechanisms underlying alternans and arrhythmias [13, 50].

Figure 1C shows ECC gain (ratio of $\overline{\mathit{CaT}}$ to peak I_Ca(L)) at different membrane voltages. $\overline{\mathit{CaT}}$ is ratio of max(CaT) to min(CaT), a definition consistent with experimental measurements of CaT as peak to minimum fluorescence ratio [63]. The cell was clamped to −40 mV for 50 ms, followed by 50 ms pulse to varying voltages. Both experimental [63] and simulated data show ECC gain to be monotonically decreasing function of voltage.

Figure 1D shows total Ca²⁺ released during one cycle [cycle length (CL)=1000 ms] as function of peak I_Ca(L). [Ca²⁺]_JSR,t was the same (7.8 mmol/L) at the beginning of the pacing cycle for each value of I_Ca(L). The simulation shows an almost linear dependence of Ca²⁺ released on trigger Ca²⁺ entry.

Figure 1E shows fractional SR Ca²⁺ release. Note the steep dependence on [Ca²⁺]_JSR,t at high SR loading. This strong nonlinear dependence has two consequences. At low SR Ca²⁺ load it helps terminate SR Ca²⁺ release, preventing further depletion of SR Ca²⁺. However, at high SR Ca²⁺ load its can cause Ca²⁺ cycling instability [13, 50, 57].

Sensitivity of CaMKII to CaT and APD

In the model-experiment comparison we use in vitro experimental results from neuronal CaMKII isoform due to lack of direct data regarding rate of CaMKII phosphorylation in cardiac myocytes. However, as shown by Gaertner et al. [22] all CaMKII isoforms have very similar catalytic and regulatory properties [5]. It should be noted that CaMKII isoforms with very similar biochemical characteristics can demonstrate remarkably different targeting properties (e.g., anchoring to target proteins) [25, 72]. Simulated CaMKII activity and steepness of frequency dependence increases at fast rate. The CaMKII model reproduces qualitatively the experimentally (in vitro) observed dependence of CaMKII activity (CaMK_active) on CaT frequency, amplitude and duration [10].

Figure 2 shows simulated (A) and measured [10] (B) time course of CaMK_active (% of maximum) at rates of 1 Hz, 2.5 Hz and 4 Hz (CaT duration and amplitude held constant at 200 ms and 20 μmol/L). Both experiment [10] and simulation show increased CaMK_active and steepness at fast rate (slope at 4 Hz is twice steeper than at 2.5 Hz). This rate dependence is due to the autocatalytic nature of the autophosphorylation reaction [27]. The different time course in model and experiment is due to faster kinetic parameters used in the simulations [28], reflecting higher activity of cardiac isoform δ compared to isoforms α and β in the experiments [22]. Figure 2 also shows simulated (C) and measured [10] (D) frequency dependence of CaMKII activity for different CaT durations, (CaTd): 500 ms, 200 ms, 80 ms, 40 ms (40 ms data are not available in experiment but included in simulation because it is comparable to CaTd in the restricted subspace). As CaTd increases the curve shifts to lower frequencies. Note that the same CaMKII activity can be reached at slower rates for longer CaT durations. For example, CaMKII activity of 20% (horizontal line) is achieved at 0.4 Hz, 1 Hz, 3 Hz, and 6 Hz for CaTd 500 ms, 200 ms, 80 ms and 40 ms, respectively (arrows). Both experiment [10] and model show a threshold phenomenon, i.e., no CaMKII activity occurs for specific CaT duration until minimal frequency is reached. Ability of CaMKII to respond to CaT frequency and morphology is important because CaMKII senses different CaT transients when tethered [26] to different targets; for example, RyR and L-type Ca²⁺ channel in the restricted tubular subspace experience a different CaT and consequently CaMKII activity than SERCA/PLB in the bulk myoplasm (Figure 1A). Both experiment [10] and model show a threshold phenomenon, i.e., no CaMKII activity occurs for specific CaT duration until minimal frequency is reached. In addition, model simulations show time-dependent saturation of CaMK_active (Figure 2A).

Figures 2E and 2F show modulation of CaMKII activity by APD. Panel (E) shows (clockwise) time course of AP, CaT, [Ca²⁺]_JSR and CaMK_active at 1 Hz stimulation rate. Control AP waveform (black) is prolonged to double APD at CL=1000 ms from 215 to 430 ms (grey). The prolonged AP is used as command waveform to pace the cell to steady-state (grey lines). APD prolongation leads to dramatic increase of CaT and [Ca²⁺]_JSR, >200% of initial values, consequently CaMK_active is increased by 75%. These simulations show that APD can modulate CaMKII activity by increasing intracellular Ca²⁺ loading and CaT. Panel (F) shows CaMK_active at rates from 0.5 to 3 Hz for control APD and APD increased by 50% or 100%. The same level of CaMKII activity is achieved at lower frequency for longer APD. For example, CaMKII activity of 20 % (horizontal line) is achieved at 1.8 Hz, 2.4 Hz and 2.8 Hz for 2.0, 1.5, and 1.0 control APD, respectively (arrows). The sensitivity of CaMKII activity level to APD is important when considering that CaMKII serves as a frequency sensor in different species (mouse, guinea-pig, dog, human), which have remarkably different AP morphologies and durations [4, 21, 40].

CaMKII underlies FDAR and PFFR

When the heart rate increases, greater force (implying greater CaT) [6] is generated. The increase of force (or CaT) with frequency is termed positive force-frequency relation (PFFR). At fast rate, less time is available for cardiac relaxation, or pumping Ca²⁺ back into the SR. In this subsection we study the effects of CaMKII on the frequency dependence of CaT amplitude and decay. These properties affect CaT in a rate-dependent manner and are therefore relevant to formation of alternans. Experimental data on CaMKII regulation in ventricular myocytes are limited. For experiment-model comparison we use the measured time-derivative of left ventricular pressure (dP/dt) [69] or twitch relaxation [12] as surrogates of CaT when data for myocyte CaT are not available.

Figure 3A shows experimental (bottom) [60] and simulated (top) CaT at different rates. Both experiment and simulation show that CaT amplitude and rate of decay increase at fast rate. Note that simulated and measured [60] peak CaT increase monotonically with pacing frequency (PFFR). The descending limb of CaT is fit by single exponential, with time constant of relaxation τ. Both experiments and simulations show that with increasing frequency, τ decreases monotonically. 10-fold increase in frequency from 0.25 Hz to 2 Hz, results in about two-fold increase of relaxation rate, with τ decreasing from 450 ms to 200 ms. This phenomenon is called Frequency-Dependent Acceleration of Relaxation (FDAR) and is essential for normal diastolic function. Complete suppression of CaMKII effect on all targets in the model (panel B, grey) slows FDAR and blunts its frequency dependence compared to control (panel B, black). Similar behavior is seen experimentally (panel C) [12].

Figures 3D and 3E show the effect of CaMKII inhibition on force-frequency relation. For control with CaMKII active (black curves), experiment (E) [69] and simulation (D) show similar 40% increase of contractility or CaT, respectively, as rate increases over the range shown. Total CaMKII inhibition greatly suppresses this rate dependence. Simulation for Figures 3 was generated by setting CaMKII activity to zero for all its targets (i.e., I_up, I_Ca(L) and I_Rel), which mimics the effect of KN-93 application to the whole cell. The agreement between model and experiment is qualitative. The onset of increased contractility (or CaT) is shifted to lower frequencies in simulations relative to experiments, reflecting the slower heart rate of canine (simulation) compared to rabbit (experiment [69]).

CaT AND APD ALTERNANS

Frequency Dependence of Alternans

Figure 4A and 4B show steady-state APD and ΔCa²⁺ rate dependence (adaptation curves) generated by the guinea-pig (LRd) model. Figure 4 C and 4D show similar curves for canine (HRd). As pacing rate is increased APD shortens, until it reaches a point of bifurcation at which for the same pacing rate APD oscillates between long and short values. Panels B and D show corresponding CaT adaptation curves; CaT amplitude increases at fast rate until exactly at the same frequency as APD, bifurcation occurs. The bifurcation portions of APD and CaT curves are shown in insets on expanded scales. The guinea-pig model alternates at CL from 150–250 ms, consistent with experimental data [49]. Maximal APD and CaT differences between two consecutive beats occur at CL=200 ms with magnitudes of 12 ms and 0.75 μmol/L, respectively.

The canine model alternates at CL 155–275 ms, also consistent with experimental data [23]. Maximal APD and CaT differences between two consecutive beats occur at CL= 250 ms with magnitudes of 35 ms and 0.5 μmol/L, respectively. APD and CaT curves bifurcate also when plotted against the preceding diastolic interval (not shown), as frequently presented [23, 35]. Note that the bifurcation portions of APD adaptation curves are smooth functions of CL; as CL decreases alternans amplitude increases to a maximum and then decreases [23] (Panel 4C, inset). Both canine and guinea-pig models simulations are shown in Figure 4, demonstrating model (species) independence of the alternans phenomenon. The simulated frequency ranges and amplitudes of alternans are consistent with corresponding experimental data [24, 68].

CaT-AP Coupling During Alternans and its Mechanism

To elucidate the link between APD (electrical) and CaT (mechanical) alternans we pace the cell under conditions of AP clamp or CaT clamp (Figure 5). Figure 5A shows AP (top) and CaT (bottom) during alternans at 4 Hz; note that large CaT is accompanied by long APD. In Figure 5B, steady-state behavior is shown during pacing at CL=250 ms with AP (top) clamped to either its short APD=133 ms (grey) or long APD=165 ms (black). Despite elimination of AP alternans by the clamp protocol, CaT alternans persists (Figure 5B, bottom). In Figure 5C CaT (bottom) is clamped to either its small (grey) or large (black) morphology. In either case, AP alternans is eliminated (Figure 5C, top). The SR Ca²⁺ subsystem continues to oscillate during clamping with large CaT morphology and the SR Ca²⁺ release rate is higher during large depletion than during small depletion (not shown). The results reveal that at this pacing rate, CaT alternans is causing AP alternans; in other words, oscillation of the Ca²⁺ subsystem is driving the APD oscillations. Simulations over the entire bifurcation range (170 < CL < 270) show the same Ca²⁺-driven mechanism of AP alternans.

FIG. 5.

AP and CaT clamp protocols. (A) AP (top), CaT (middle) and I_Ca(L)(bottom), during alternans at 4Hz. (B) AP clamp with short (grey) or long (black) AP. In spite of AP clamping (top), calcium subsystem oscillates (bottom). (C) Clamping CaT (bottom) to its small (grey) or large (black) waveform eliminates AP alternans (top). (D) Clamping I_Ca(L) (bottom) to its small (grey) or large (black) waveform does not eliminate AP (top) or CaT (middle) alternans.

To explore the role of I_Ca(L) in CaT alternans we conducted the simulations in Figure 5D. Bottom panel shows that clamping I_Ca(L) to either its small (grey) or large (black) morphology does not eliminate either APD or CaT alternans (top panels) indicating that alternation of SR Ca²⁺ release is not due to alternation of its I_Ca(L) trigger. However, clamping I_Ca(L) to either its small (grey) or large (black) morphology reduces the APD alternans amplitude from 32 ms to 21 ms or 14 ms, respectively, indicating a role of I_Ca(L) in CaT-AP coupling. APD alternans amplitude is defined as the difference between long and short APD.

Figure 6A shows ss(clockwise) superimposed AP, I_Kr, CaT, and I_NaCa during alternans for two consecutive beats, with long (black) and short (grey) APD. The higher early plateau of the short AP (70 ms, arrow) is mainly due to enhanced I_Ca(L) caused by less Ca²⁺-dependent inactivation (Figure 5A, bottom) during the small CaT (grey). Early-plateau I_to2 is also Ca²⁺ –dependent, but is a small current and its effect on AP morphology changes during alternans is small. During the large CaT (black) I_NaCa is more inward than during the small CaT (grey), slowing AP repolarization to cause crossover of the APs and prolongation of APD. The higher plateau of the short AP and the APs crossover are in agreement with experimental data [23] (Figure 6B) from canine ventricular myocytes. The simulations identify I_NaCa as the major coupling link between CaT alternans and APD alternans, due to its major role late in the AP, when repolarization and APD depend on a delicate balance of currents and are easily modulated.

FIG. 6.

(A) Superimposed AP, CaT, I_NaCa and I_Kr of consecutive beats during alternans at CL=250 ms. (B) Measured (canine) ([24], reproduced with permission) AP and I_Kr during alternans.

SR Ca²⁺ Content and CaT Alternans

To explore the role of SR Ca²⁺ fluxes in onset and offset of CaT alternans we conducted the simulations in Figure 7. Figure 7A shows SR releasable Ca²⁺ content changes during alternans at 5Hz. ΔCa²⁺ is shown for two different levels of SR Ca²⁺ loading during alternans. In the simulation (top), increase of [Ca²⁺]_JSR by 40% leads to a four-fold increase in ΔCa²⁺, demonstrating that small changes in [Ca²⁺]_JSR lead to large changes in ΔCa²⁺. Such steep dependence is consistent with experimental findings (bottom) [13]. Total SR Ca²⁺ content [JSR + network SR (NSR)] increases as function of pacing rate (Figure 7B)[45]. In addition, during alternans, change of total SR content is very small, in accordance with experiment [13, 50]. However, [Ca²⁺]_JSR and consequently the releasable pool of Ca²⁺ is slightly decreased with rate after reaching a maximum at 1.5 Hz (15% decrease at 4 Hz, Figure 7C). This property of the model is consistent with experimental observations that refractoriness of the global CICR process has a time constant in the range of 0.3–1 sec [8, 50, 65].

FIG. 7.

Steady state SR Ca²⁺ flux balance during alternans. (A) Dependence of ΔCa²⁺=max(CaT)-min (CaT) on JSR Ca²⁺ content during alternans at 5 Hz. Simulation (top) is compared to experiment (rat)([13], reproduced with permission) (bottom). Only 40% change in [Ca²⁺]_JSR leads to 4-fold change in ΔCa²⁺. [Ca²⁺]_JSR,t= free and buffered Ca²⁺ concentration in JSR before release; black (grey) bars correspond to larger (smaller) [Ca²⁺]_JSR,t, respectively. Data are normalized to small [Ca²⁺]_JSR,t. (B) Total end-diastolic SR Ca²⁺ content ([Ca²⁺]_JSR,t and [Ca²⁺]_NSR) as function of rate. (C) Free Ca²⁺ in JSR ([Ca²⁺]_JSR) as function of frequency. (D) Total Ca²⁺ released by RyR (∫_CL I_Reldt, black thick line), reloaded into NSR [∫_CL(I_up − I_leak)dt, grey] and translocated from NSR to JSR (∫_CL I_trdt, black thin line) over one cycle, as function of frequency.

At slow rates in the absence of alternans, SR fluxes are in balance, i.e. the amount of Ca²⁺ transported from NSR to JSR (∫_CL I_trdt, black thin line) during one beat at steady state equals the amount of Ca²⁺ released (∫_CL I_Reldt, black thick line) and the net flux into the SR (∫_CL(I_up−I_leak)dt, grey, Figure 7D). In addition free diastolic Ca²⁺ is in equilibrium over the entire SR (not shown). However, at moderately-fast rate during alternans following a large CaT (defined as even beat), NSR reloading and Ca²⁺ transfer to JSR is less than the amount released (Figure 7D, even beat). Consequently, less Ca²⁺ is available for release during the next beat (Figure 7C, odd beat) and due to the steep dependence of fractional Ca²⁺ release on [Ca²⁺]_JSR,t (Figure 1E) less Ca²⁺ is released during this beat (Figure 7D, odd beat). Following a small CaT (odd beat), there is accumulation of releasable Ca²⁺ (Figure 7C, even beat) because of imbalance between SR reloading and release, resulting in a large CaT. This alternating behavior repeats to cause sustained alternans. When pacing rate is further increased (>6 Hz), time for Ca²⁺ accumulation after a small release is decreased and the alternans gradually disappear.

Effect of CaMKII

Figure 8A shows APD (top) and ΔCa²⁺ (bottom) adaptation curves for three different levels of CaMKII activity (modulated by changing the fraction of low-affinity calmodulin binding sites CaMKII₀ [27], which mimics the effect of KN-93 [12]. Setting CaMKII₀ to zero completely inhibits CaMKII activity. Increase of CaMKII activity by 25% shifts onset of ΔCa²⁺ and APD alternans to slower frequencies, from 3.3 Hz to 2 Hz, while the frequency of maximal alternans is unchanged (3.6 Hz). However, the amplitudes of ΔCa²⁺ and APD oscillations increase by 10 ms and 0.4 μmol/L, respectively. Increase of CaMKII activity has no effect on offset of CaT and APD alternans, while CaMKII inhibition suppresses alternans (dashed curves) thereby exerting an antiarrhythmic effect. Unfortunately, decrease of CaMKII activity blunts the PFFR ( Figure 3E, 3F) and FDAR ( Figure 3C, 3D) thereby compromising cardiac mechanical function.

FIG. 8.

(A) APD (top) and ΔCa²⁺ (bottom) adaptation curves for three different levels of CaMKII activity: control (100 %), 25 % elevation (125 %) or complete block (0 %). (B) Effect of I_Kr on APD and CaT alternans. APD (top) and CaT (bottom) adaptation curves for three different levels of I_Kr conductance: control (100%), 300% elevation and 50 % reduction. Inset: superimposed consecutive APs at 5 Hz for I_Kr increase of 300%.

Effect of I_Kr

In general, peak I_Kr amplitude is smaller at faster rates [28]. However, our simulations and experiments [23] show that during APD alternans I_Kr is larger during the shorter than longer AP. The simulations indicate that this behavior (large I_Kr at short APD) is due to combined effect of residual activation due to shorter diastolic interval (DI) after the long APD and greater activation due to high early plateau potential of the short AP.

Figure 8B shows APD (top) and CaT (bottom) adaptation curves for three different levels of I_Kr conductance. 50% decrease of conductance increases APD by 15 ms over the entire stimulation range (dashed line). In addition, the magnitude of APD alternans increases by 15 ms. However, CaT and magnitude of CaT alternans are not affected. Note that this modest increase of APD prevents one to one capture at 5Hz because the diastolic interval following the long APD approaches zero. Increase of I_Kr conductance by 200 % (note shown) decreases APD alternans magnitude by 50% (15 ms) with no effect on onset frequency and magnitude of CaT alternans. A large 3-fold increase of I_Kr conductance is necessary to completely eliminate APD alternans, consistent with experiment [23]. Even with such large increase, the onset frequency and magnitude of CaT alternans (not measured in the experiment) are not affected. The 300 % increase of I_Kr decreases APD by 50% and CaT amplitude by 50% (grey line) at slow rate; it extends the frequency range of CaT alternans by shifting its termination to 10 Hz (not shown) from 5.5 Hz. Inset shows overlapped consecutive APs at 5 Hz for 300% I_Kr conductance; while APDs are almost identical, there significant differences in AP morphologies, the AP plateau during small CaT (dotted) is more convex than AP during large CaT.

DISCUSSION

This study shows that at moderately-fast rate (between 3.5 and 5.5 Hz) the SR Ca²⁺ subsystem, strongly modulated by CaMKII, can initiate CaT alternation that induces APD alternans.

CaT Alternans

At moderately-fast rate, the guinea pig (4 – 6.5 Hz) and canine (3.5 – 5.5 Hz) models produce sustained alternans of both APD and CaT. Simulated AP and CaT clamp protocols confirm [38] that oscillation of the Ca²⁺ subsystem is driving the APD alternans in both species. The mechanism underlying CaT alternans is explored by evaluating the roles of the trigger for SR Ca²⁺ release I_Ca(L), SR load, SR Ca²⁺ fluxes and CaMKII activity during alternans. Model simulations show that refractoriness of the SR Ca²⁺ release process is the main mechanism of CaT alternans. Specifically, two rate-limiting processes, I_up and I_tr (Figure 7D) in conjunction with steep dependence of SR Ca²⁺ release on SR Ca²⁺ load (Figure 1E) determine the onset and offset of sustained alternans at moderately-fast rates.

I_tr in the model represents both (local ) RyRs intrinsic recovery from refractoriness and (global) Ca²⁺ diffusion [8] through the SR . While the steep dependence of release and rate of uptake are sufficient to induce alternans in the model (see also reference [70]), I_tr also contributes to alternans formation(Figure 7D). In addition, the model predicts that during Ca²⁺ overload the SR Ca²⁺ cycling subsystem can oscillate even without corresponding beat-to-beat oscillations of CaT (not shown).

In contrast to previous modelling reports [20, 55], we find that alternation of I_Ca(L) is not necessary to evoke steady-state CaT alternans; such alternans are not eliminated under I_Ca(L) clamp, only reduced in amplitude (Figure 5D). This observation is consistent with experimental data [13, 48, 50] showing that contraction or CaT alternans can occur without I_Ca(L) fluctuations.

CaT-AP Coupling

While the magnitude of CaT alternans is comparable in guinea pig and canine (100% relative to minimum CaT, Figure 4B, 4D), that of APD alternans is twice as large in canine (20% canine, 10% guinea- pig, of maximum APD, Figure 4C, 4A), indicating stronger CaT-AP coupling in this species. These values are comparable with experimental data [23, 35, 50] that reflect modest level of CaT-APD coupling during alternans. This is in contrast to recently published simulations[55] where 50% alternation of CaT caused greatly exaggerated (more than 100%) alternation in APD. Such strong dependence of APD on CaT during alternans has never been observed experimentally [24, 30, 35, 49, 50].

While the roles of I_NaCa and I_Ca,(L) in CaT-AP coupling during alternans were discussed previously in general terms [70], precise nature of these interactions in detailed myocyte models was not addressed. The stronger CaT-AP coupling in the canine compared to guinea pig is due to differences in ion channel expression levels and kinetic properties. On the background of smaller I_Kr and I_Ks in the canine [28] in conjunction with a much smaller I_Ca(L) during the late AP plateau [4], CaT-induced changes in I_NaCa have a much greater modulatory effect on AP repolarization and APD. This makes the canine myocyte more susceptible to Ca²⁺-induced AP alternans and suggests that similar sensitivity to arrhythmia is characteristic of the human heart, whose cell electrophysiology and AP morphology resemble those of the canine [21]. The results show that prolongation of APD secondary to a large CaT is mainly due to large inward I_NaCa at the late AP plateau and repolarization phase, identifying I_NaCa as the major CaT-APD coupler during alternans. The other Ca²⁺-dependent currents, I_Ca(L) and I_to2, play a role in shaping the AP during its initial plateau phase, causing crossover between consecutive APs during alternans ( Figure 8A) but have a minimal effect on APD. I_to1 that contributes to APD rate adaptation [28] has little effect on AP morphology during alternans. The situation can be different, with I_Ca(L) playing a role in APD alternans, in species where I_Ca,(L) persists into the late phase of the AP (e.g. the guinea pig). and Ca²⁺-dependent I_Ks has a large conductance [17, 40]. Under such conditions, a large CaT can lead to APD shortening during alternans, due to increased Ca²⁺-dependent inactivation of I_Ca,(L).

Heart failure shifts the onset of APD alternans to slower frequencies and causes a remarkable increase in its amplitude [71]. Upregulation of I_NaCa has been reported in human and animal models of heart failure [6]. This observation supports the role of I_NaCa as the major CaT-APD coupler during alternans. It should be commented that exploration of such mechanistic details requires detailed species-specific and ionic-based cell models. It cannot be accomplished with simplified models [55, 58] where the levels of Ca²⁺ – dependent and voltage-dependent inactivation of I_Ca,(L) are treated as model parameters, not based on experimental data.

Modulation of CaT and APD Alternans by CaMKII and Repolarizing Currents

Elevated CaMKII activity, as occurs in hypertrophy and heart failure [3], extends the range of CaT alternans and consequently APD alternans to slower frequencies and increases alternans magnitude, suggesting its role in arrhythmia and sudden death in these pathologies. Decrease of CaMKII activity suppresses both CaT and APD alternans, thereby exerting an antiarrhythmic effect. Unfortunately, the decrease blunts the PFFR and FDAR (Figure 3E, 3D), thereby compromising cardiac mechanical function.

Modification of I_Kr has been suggested as a possible intervention for reducing APD alternans [20, 23]. Here we describe the first study of the role of Ca²⁺ – independent currents during Ca²⁺ driven APD alternans. The simulations show (Figure 8A, 8B) that only a large three fold increase of I_Kr can completely suppress APD alternans, which limits its potential use as antiarrhythmic intervention. Moreover, increase of I_Kr has no effect on the onset and magnitude of CaT alternans ( Figure 8D). Thus, unlike CaMKII inhibition that suppresses APD alternans by eliminating its cause, CaT alternans, increased I_Kr weakens CaT-AP coupling, thereby suppressing APD alternans by disrupting its link to persistent alternans of CaT. Similar results we obtained by modulating other repolarizing currents, namely the slow delayed rectifier K⁺ current (I_Ks), the inward rectifier K⁺ current (I_K1) and I_K,ATP , the ATP-dependent K⁺ current (not shown). However, results are shown only for I_Kr, because the conductance of I_Ks is Ca²⁺-dependent, increase of I_K1 markedly decreases excitability and conduction velocity [44], and I_K,ATP is activated only during pathological conditions of ischemia (acidosis) [54].

These results suggest two possible antiarrhythmic strategies for alternans suppression : 1. prevention of CaT alternans by partial CaMKII inhibition; or 2. modification of the coupling between the Ca²⁺ and electrical subsystems by modulating repolarizing currents such as I_Kr or I_K,ATP . A combined approach of 1 and 2 above seems reasonable, providing more flexibility for alternans suppression with minimization of deleterious effects on contractility and mechanical performance.

At very fast rate (> 7 Hz) APD alternans is primarily an electrical phenomenon. This electrical alternans (not shown) has been attributed to slow recovery from inactivation of either I_Na [44, 52, 66] or I_Ca(L) [70]. Several studies have shown that cells in the heart can be exposed to such fast and even faster rates (e.g., 11 Hz) [73] during fast ventricular tachycardia and fibrilation. APD alternans at these rates can lead to propagation failure and transition from ventricular tachycardia to fibrilation via wavebreak mechanims [73].

Limitations

A limitation of the study is that ECC spatial heterogeneity is not considered. A phenomenon associated with this heterogeneity is Ca²⁺ waves which are known to be arrhythmogenic [13]. However, Ca²⁺ waves are rarely observed in non-failing myocytes during fast pacing [30, 50], the subject of our investigation. For the same reasons (the models are based on data from non-failing myocytes), only acute up/down regulation of CaMKII was considered. The model does not include the β-adrenergic/PKA regulatory pathway that, while sharing common targets (i.e., I_up, I_Ca(L) and I_Rel) with CaMKII, by itself plays an important role in ECC and cardiac repolarization. Incorporating in the model the β-adrenergic/PKA regulatory pathway together with effects of chronic upregulation of CaMKII as occurs in heart failure [75], will be an important step in future model development and simulation studies. As was recently shown in a transgenic mice model chronic inhibition of CaMKII activity leads to upregulation of repolarizing [39] and I_Ca(L) [75] currents and can compensate for mechanical function impaired due to calcineurin overexpression [32].

The time constant of I_tr in the model represents both (local ) RyRs intrinsic recovery from refractoriness and (global) Ca²⁺ diffusion [8] through the SR. Separation of these time-limiting processes requires additional experimental data that are not yet available and development of a detailed kinetic model of RyR gating. This can be important future work, considering that some studies [50] stress the importance of intrinsic RyR refractoriness in CaT alternans development. The simulations also indicate the need for detailed experimental studies of CaMKII properties in ventricular myocytes and its interactions with RyRs and SERCA/PLB during alternans.

Appendix

Equations and parameters of the of guinea pig (LRd) and canine (HRd) models used in this study are as in previously published papers [16, 28] and in the research section of http://rudylab.wustl.edu. Definitions are provided in Table I of this Appendix. Intracellular calcium buffering was modeled as previously described [74]. Changes made for the purpose of this study are summarized below.

Formulation of I_Rel (see Table II)

TABLE II.

Parameter Values of SR Ca²⁺ Release Model

	Value
Parameter	Dog	Guinea-Pig	Units	Definition
β0	4.75	4.75	ms	minimal value for βτ
Kβ	0.28		mmol/L	Half-saturation constant of Δβτ,CaMK
Δβ0	1		mmol/L	maximal CaMKII-dependent change for βτ
αRel	κβτ	κβτ	mmol/L/ms	amplitude coefficient of IRel,∞
KRel,∞	1	1	mmol/L	Half-saturation constant of IRel,∞
hRel	8	9		Hill coefficient of IRel,∞
hβ	10			Hill coefficient of Δβτ,CaMK
κ	0.1125	0.125	μF/μA	amplitude coefficient ofαRel
KRel,τ	0.0123	0.0123	mmol/L	Half-saturation constant of IRel,τ
τtr	120	120	ms	time constant of Itr
γCai	0.341	1	ms	Ca2+ activity coefficient
Īup,CamK	0.9		mmol/L	maximal CaMKII-dependent change of Iup

The differential equation that describes I_Rel is of the form

$$\frac{d{I}_{\mathit{Rel}}}{dt}=-(I_{\mathit{Rel},\infty }+I_{\mathit{Rel}})/{\tau }_{I_{\mathit{Rel}}}$$ (1)

where

$$I_{\mathit{Rel},\infty }=\frac{{\alpha }_{\mathit{Rel}}{I}_{Ca(L)}}{1+{(K_{\mathit{Rel},\infty }/{[C{a}^{2+}]}_{\mathit{JSR}})}^{h_{\mathit{Rel}}}}$$ (2)

and

$${\tau }_{I_{\mathit{Rel}}}=\frac{{\beta }_{\tau }}{1+K_{\mathit{Rel},\tau }/{[C{a}^{2+}]}_{\mathit{JSR}}}$$ (3)

I_Rel,∞ represents a steady state value of I_Rel and τ_IRel is its time constant, α_Rel is an amplitude coefficient, K_Rel,T is a half-saturation coefficient, β_τ is a maximal value of τ_IRel.

We make τ_IRel in Eq(1) dependent on CaMKII to incorporate CaMKII-dependent facilitation into the model with a maximal change that produces a 100% facilitation of peak Δβ_τ,CamK:

$$\begin{array}{l}{\beta }_{\tau }={\beta }_0(1+\mathrm{\Delta }{\beta }_{\tau ,\mathit{CamK}})\\ \mathrm{\Delta }{\beta }_{\tau ,\mathit{CamK}}=\mathrm{\Delta }{\beta }_0/[1+{(K_{\beta }/\mathit{CaM}{K}_{\mathit{active}})}^{h_{\beta }}].\end{array}$$ (4)

In addition, we make τ_IRel in Eq(3) a function of [Ca²⁺]_JSR to prevent an unphysiological draining of JSR. Sensitivity of the release flux I_rel to luminal [Ca²⁺]_JSR is modelled by Hill equation with a coefficient h_Rel [14, 57] and half-saturation constant K_{Rel, ∞} [37].

Gating variables of I_Ca(L) (see Table III)

TABLE III.

Definitions of I_Ca(L) Model Parameters

Abbreviation	Definition
d∞	steady state fast voltage-dependent activation gate of ICa(L).
fca	fast Ca2+-dependent inactivation gate of ICa(L).
fca∞	steady-state value of fca .
τfca	time constant of fca .

Fast Ca²⁺-dependent inactivation (f_Ca gate) formulation:

$$f_{Ca,\infty }=\frac{0.3}{1-I_{Ca(L)}/0.05}+\frac{0.55}{1+{[C{a}^{2+}]}_{ss}/0.002}+0.15$$ (5)

$${\tau }_{\mathit{fca}}=\frac{\mathrm{\Delta }{\overline{\tau }}_{\mathit{fca},\mathit{CaMK}}}{1+K_{m,\mathit{CaMK}}/\mathit{CaM}{K}_{\mathit{active}}}+0.75+\frac{1.5}{1+{[C{a}^{2+}]}_{ss}/0.002}$$ (6)

where Δτ̄_fca,CaMK is the maximal CaMKII-dependent change of τ_fca (time constant of f_Ca gate) and set to 5 ms, K_m,CamK is a half-saturation coefficient, f_Ca,∞ is steady-state value of f_Ca. In addition, to reflect higher [Ca²⁺] in the subspace ([Ca²⁺]_ss), activity coefficient γ_Cai = 1 was replaced by γ_Cass = 0.341 in the constant field equation for Ī_Ca(L). Steady state formulation of activation d gate was modified as follow

$$d_{\infty }=1/(1+e^{-(V+60)/2})/(1+e^{-(V-4)/6.74}),$$ (7)

where V is the membrane voltage.

SR fluxes

CaMKII dependence of I_up was set to ΔĪ_up,CaMK = 0.9.

Model of SR Ca²⁺ Release and SR fluxes for LRd model

Numerical values for I_{Rel, ∞} and τ_IRel are provided in Table II. I_tr time constant τ_tr was set to 120 ms.

Steady state formulation of activation d gate of I_Ca(L) in LRd model was modified as follow, d_∞ = 1/(1 + e^{− (V +10)/6.24}) / (1 + e^{− (V −60)/0.024}); where V is the membrane voltage.

Table IV provides documentation for the electrophysiological data used for the canine model validation. Table V contains CaMKII data used in simulations.

TABLE IV.

Canine ventricular myocyte electrophysiological data for model validation.

Figure	Source	Experimental conditions
1C	Song et al.[63]. Fig.2E (Adapted).	35°C , whole cell patch-clamp
3A	Sipido et al. [60] Fig.2B	37°C, ruptured patch clamp
4C	Hua and Gilmour. [23],Fig.1B	37°C, perforated patch clamp
6B	Hua et al. [24]. Fig.2A	37°C, perforated patch clamp