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(Circulation Research. 2005;96:459.)
© 2005 American Heart Association, Inc.

Cellular Biology

Action Potential Duration Restitution and Alternans in Rabbit Ventricular Myocytes

The Key Role of Intracellular Calcium Cycling

Joshua I. Goldhaber, Lai-Hua Xie, Tan Duong, Christi Motter, Kien Khuu, James N. Weiss

From the UCLA Cardiovascular Research Laboratory, Departments of Medicine (Cardiology) and Physiology, David Geffen School of Medicine at UCLA, Los Angeles, Calif.

Correspondence to Joshua I. Goldhaber, MD, David Geffen School of Medicine at UCLA, Division of Cardiology, 47-123 CHS, 10833 LeConte Ave, Los Angeles, CA 90095-1679. E-mail jgoldhaber{at}mednet.ucla.edu

	Abstract

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Action potential duration (APD) restitution properties and repolarization alternans are thought to be important arrhythmogenic factors. We investigated the role of intracellular calcium (Ca²⁺_i) cycling in regulating APD restitution slope and repolarization (APD) alternans in patch-clamped rabbit ventricular myocytes at 34 to 36°C, using the perforated or ruptured patch clamp techniques with Fura-2-AM to record Ca²⁺_i. When APD restitution was measured by either the standard extrastimulus (S1S2) method or the dynamic rapid pacing method, the maximum APD restitution slope exceeded 1 by both methods, but was more shallow with the dynamic method. These differences were associated with greater Ca²⁺_i accumulation during dynamic pacing. The onset of APD alternans occurred at diastolic intervals at which the APD restitution slope was significantly <1 and was abolished by suppressing sarcoplasmic reticulum (SR) Ca²⁺_i cycling with thapsigargin and ryanodine, or buffering the global Ca²⁺_i transient with BAPTA-AM or BAPTA. Thapsigargin and ryanodine flattened APD restitution slope to <1 when measured by the dynamic method, but not by the S1S2 method. BAPTA-AM or BAPTA failed to flatten APD restitution slope to <1 by either method. In conclusion, APD alternans requires intact Ca²⁺_i cycling and is not reliably predicted by APD restitution slope when Ca²⁺_i cycling is suppressed. Ca²⁺_i cycling may contribute to differences between APD restitution curves measured by S1S2 versus dynamic pacing protocols by inducing short-term memory effects related to pacing-dependent Ca²⁺_i accumulation.

Key Words: alternans • arrhythmia • Ca²⁺ transients • action potential restitution

	Introduction

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Cardiac repolarization (T wave) alternans has been shown to confer increased mortality in patients with heart disease.¹ One mechanism for generating repolarization alternans is steep action potential duration (APD) restitution. As heart rate increases, the APD shortens to preserve the diastolic filling time and coronary flow. The APD restitution curve quantifies this relationship by plotting APD against the preceding diastolic interval (DI). During pacing and reentrant cardiac arrhythmias, APD restitution slope has been shown to be an important determinant of wave stability.^2–11 In addition to promoting APD alternans, a steep (>1) APD restitution slope can promote breakup of electrical waves into a fibrillation-like state (for review, see Weiss et al¹²). Intracellular Ca²⁺ (Ca²⁺_i) cycling is also a dynamically active process in cardiac muscle. Primary Ca²⁺_i alternans can drive APD to alternate secondarily,^13–15 because APD is shaped by several key membrane currents that are sensitive to Ca²⁺_i, including the L-type calcium current (I_Ca), the sodium-calcium (Na⁺-Ca²⁺) exchange current and calcium-sensitive nonselective and Cl^– currents. Conversely, the Ca²⁺_i transient is shaped by the action potential, so that the action potential and Ca²⁺_i cycling are bidirectionally coupled.

The relationship between APD alternans and APD restitution is complicated by short-term cardiac memory (to be distinguished from long-term cardiac memory, which involves changes in protein regulation and/or gene expression). Short-term cardiac memory reflects the influence of the pacing history in total, not just the previous DI, on APD. In a broad sense, memory includes everything besides the last DI that affects APD, so that its causes, by this definition, are multifactorial. The ionic mechanisms are still only partly understood, but both ionic currents with slow recovery kinetics¹⁶ and Ca²⁺_i cycling have been implicated. An important consequence of short-term memory is that the APD restitution curve depends on the pacing protocol used to measure it.¹⁷

The objective of this study was to analyze experimentally the contribution of Ca²⁺_i cycling to APD alternans and APD restitution in patch-clamped rabbit ventricular myocytes loaded with the Ca²⁺_i indicator Fura-2. Our findings indicate that Ca²⁺_i cycling has major influences on both APD restitution slope and APD alternans. In addition, Ca²⁺_i cycling may also contribute to memory-induced differences in APD restitution curves measured by the S1S2 method versus the dynamic pacing method. These observations support the hypothesis that Ca²⁺_i cycling is an important determinant of dynamic wave instability during ventricular tachyarrhythmias.

	Materials and Methods

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Cell Isolation
We enzymatically isolated ventricular myocytes from the hearts of 2 to 3 kg rabbits as described previously.¹⁸ Briefly, hearts were removed from rabbits anesthetized with intravenous pentobarbital, and perfused retrogradely at 37°C in Langendorff fashion with nominally Ca²⁺-free Tyrode’s buffer containing 1.65 mg/mL collagenase (Sigma Blend H C-8051; Sigma, USA) and 0.8 mg/mL bovine albumin (Sigma A-8806) for 30 to 40 minutes. After washing out the enzyme solution, the hearts were removed from the perfusion apparatus, and swirled in a beaker. The calcium concentration was slowly increased to 1.8 mmol/L, and the cells were stored at room temperature and used within 8 hours. This procedure typically yielded 50% rod-shaped Ca²⁺-tolerant myocytes.

Patch Clamp Methods
Action potentials or ionic currents were measured under current- and voltage-clamp conditions, respectively, using either the whole-cell perforated patch or ruptured patch configurations of the patch clamp technique.¹⁹ For perforated patch experiments, we used the amphotericin method described by Rae et al²⁰ in which the patch pipette (tip diameter 2 to 3 µm, resistance 2 to 3 M) was dipped for 10 seconds into the standard pipette solution containing (in mmol/L) 140 K-Aspartate, 5 NaCl, 10 HEPES, 1 EGTA, 5 MgATP, 5 creatine phosphate, and 0.05 cAMP; pH 7.2 with HCl. The pipette was then back-filled using the same solution containing 240 µg/mL amphotericin-B (Sigma, cat. no. A4888). For ruptured patch experiments, pipettes had a tip diameter of 3 to 5 µm and, after gentle fire-polishing, had to a resistance of 0.5 to 1.5 M when filled with pipette solution above, to which 10 BAPTA was added instead of EGTA (maintaining other ionic concentrations the same, estimated free Ca²⁺_i <0.2 nmol/L). In some experiments, myocytes were loaded with 100 µmol/L BAPTA-AM and 0.02% pluronic (Molecular Probes, Inc) for 20 to 30 minutes. Effective buffering of intracellular Ca²⁺ was confirmed by the absence of Ca²⁺_i transients and contraction. Membrane current and voltage were measured with an Axopatch 200 patch-clamp amplifier controlled by a personal computer using a Digidata 1200 acquisition board driven by pCLAMP 6.0/8.0 software (Axon Instruments).

The standard Tyrode bath solution contained (in mmol/L) 136 NaCl, 5.4 KCl, 0.33 Na₂PO₄, 1.8 CaCl₂, 1 MgCl₂, 10 dextrose, and 10 HEPES-NaOH; pH 7.4. For some experiments, verapamil HCl (10 µmol/L), thapsigargin (200 nmol/L), and ryanodine (10 µmol/L) were added. All patch clamp experiments were performed at 34 to 36°C.

Intracellular Calcium Measurement
Myocytes were loaded with the calcium indicator fura-2 by incubating them for 20 minutes in bath solution containing 5 µmol/L fura-2-AM (Molecular Probes) and 0.016% (wt/wt) pluronic (Molecular Probes), washed, and placed in a heated chamber on an inverted microscope modified for simultaneous patch clamping and fura-2 epifluorescence.¹⁸ Fura-2 fluorescence emitted at 510 nm was measured by a photomultiplier during alternate excitation (1200 Hz) at 335 nm and at 405 nm wavelengths. We used the F₃₃₅/F₄₀₅ ratio as an indirect measure of relative changes in free Ca²⁺_i.²¹ Because the baseline value of the F₃₃₅/F₄₀₅ ratio varied from cell to cell as well as over the course of the study (because of routine replacement of arc lamps and filters in the optical train of the instrument), we rescaled the F₃₃₅/F₄₀₅ ratio (R_335/440) so that during pacing at a cycle length (CL) of 400 ms, diastolic and peak systolic R_335/440 were assigned values of 100 and 1000 arbitrary units, respectively.

APD Restitution Protocols
Three methods were used to measure APD restitution. For the extrastimulus (S1S2) method, the myocyte was paced at a CL of 400 ms for 10 beats (sufficient to achieve steady state APD), and then an extrastimulus (S2) was delivered at progressively shorter S1S2 coupling intervals (in 5 to 10 ms increments) until loss of capture. For the standard dynamic (rapid pacing) method, the myocyte was paced at a cycle length of 400 ms until steady state APD was reached, after which the CL was progressively decreased by 5 to 20 ms either every 6 to 8 seconds or after 12 beats, until 2:1 block occurred. In some experiments, a single beat dynamic method was used: after 12-beat baseline pacing at 400 ms, the CL was decreased by 5 to 20 ms after every beat until 2:1 block occurred. For all three methods, APD was measured at 90% repolarization (APD₉₀), and the DI was calculated as CL minus APD₉₀. APD restitution curves were constructed by plotting APD₉₀ versus DI, and the data points were best fit to a single exponential. The maximum APD restitution slope was calculated from the first derivative of the fitted exponential curve. We also report the range of DIs with slope >1 obtained from the exponential curve, because this parameter is equally important as the maximum APD restitution slope to dynamic wave stability.^10,22

	Results

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APD Restitution Measured by S1S2 Versus Dynamic Protocols
Figure 1 shows representative superimposed action potentials (A) and Ca²⁺_i transients (B) obtained during an S1S2 protocol used to measure APD restitution. The corresponding APD and Ca²⁺_i transient restitution curves are shown to the right, with Ca²⁺_i expressed in arbitrary units as described in Materials and Methods. In 5 cells, the S1S2 protocol was repeated a second time to assess reproducibility. We excluded myocytes in which the control value of APD shortened by more than 10% after the first trial. Using this criterion, Figure 1C demonstrates that both the maximum APD restitution slope (left) and the range of DIs with slope >1 (right) were reproducible. These findings demonstrate the reproducibility of successive APD restitution curves at near physiological temperature, using the perforated patch configuration so as to minimally disturb the intracellular milieu. After more than 2 protocols, however, APD failed to recover to its baseline value. Therefore, separate myocytes were used to test the effects of interventions on S1S2 and dynamic pacing protocols.

View larger version (30K): [in this window] [in a new window]   Figure 1. APD and Ca2+i restitution measured by the S1S2 pacing protocol. A, left, Superimposed action potentials, from the last S1 beat at a pacing cycle length of 400 ms and the S2 beats as the DI was progressively shortened. Right graph, APD restitution curve obtained by plotting APD90 against DIs for the S2 beats (solid points). Line shows the best monoexponential fit to the data points. B, left, Superimposed Ca2+i transients for the same myocyte in A. Right graph, Peak systolic Ca2+i (of the S2 beat, solid circles) and the diastolic Ca2+i (immediately preceding the S2 beat, open circles) plotted against the DI obtained from the voltage record in A. Ca2+i values are in arbitrary units (a.u.), with 100 and 1000 representing the diastolic and systolic levels, respectively, during steady state pacing at CL 400ms. Because the Ca2+i transient decay is slower than Vm repolarization, the peak systolic Ca2+i initially sums with the tail of the previous Ca2+i transient, and therefore increases as the DI shortens. As the DI becomes very short (<175), however, Ca2+i release itself becomes compromised (because of incomplete sarcoplasmic reticulum recovery). Thus, the peak Ca2+i (tail of previous+new release) declines. Inset, Superimposed AP and Ca2+i transient from the last S1 and an S2 beat. C, Reproducibility of successive APD restitution curves measured by the S1S2 method in 5 myocytes. Bars represent the mean±SE of the maximum slope of APD restitution and range of DI with slope >1 obtained from monoexponential fits to the APD restitution curves from the first and second trials. Myocytes were current-clamped in the perforated patch configuration at 35°C.

Figure 2 compares APD restitution curves measured using the S1S2 method versus the dynamic pacing method in representative myocytes. APD restitution slope was steeper with the S1S2 method, although both methods yielded a maximum slope >1 over a large range of DIs. Figure 2C shows that APD alternans developed during dynamic pacing at a CL near 280 ms. Figure 3A summarizes the data. The maximum APD restitution slope averaged 4.6±0.6 using the standard S1S2 method and 1.2±0.1 using dynamic pacing (P<0.001 by unpaired t test). The ranges of DIs with slope >1 were 31±2 and 19±4 ms, respectively (P=0.02 by unpaired t test).

View larger version (18K): [in this window] [in a new window]   Figure 2. Comparison of APD restitution and APD restitution slope during S1S2 pacing (A and D), and dynamic pacing (B and E), in two representative myocytes. C illustrates the onset of APD alternans at a pacing CL of 280 ms during dynamic pacing for the same myocyte whose restitution curve is shown in B (same data plotted differently).

View larger version (18K): [in this window] [in a new window]   Figure 3. A, Maximum slope of APD restitution and range of DIs with slope >1 for the S1S2 and dynamic pacing protocols, respectively. Values are mean±SE for 12 myocytes for S1S2 and 14 myocytes for dynamic pacing protocols. B, Comparison of systolic and diastolic Ca2+i (in arbitrary units as described in Figure 1) during the S1S2 and dynamic pacing protocols. Values are mean±SE for 5 myocytes for S1S2 protocol and 3 myocytes for the dynamic protocol. Myocytes were current-clamped in the perforated patch configuration at 35°C. Error bars are only shown where larger than symbols. Number of cells in each group is shown within parentheses.

To investigate whether Ca²⁺_i cycling might potentially explain the differences between the S1S2 and dynamic APD restitution curves, we compared the levels of systolic and diastolic Ca²⁺_i during the two protocols. Figure 3B shows that as DIs become shorter, systolic and diastolic Ca²⁺_i rose to relatively higher levels during dynamic pacing than during the S1S2 protocol. Thus, for the same DI, dynamic pacing is expected to cause greater modulation of Ca²⁺_i-sensitive ionic currents than the S1S2 method, resulting in a pacing history–dependent short-term memory effect attributable to Ca²⁺_i staircase effect described previously.²³

APD Restitution Slope >1 and the Onset of APD Alternans
There was a poor correlation between the DIs at which APD alternans developed, and the DIs at which the slope of APD restitution became >1. For example, Figure 2C shows that when APD was plotted against the pacing CL, the onset of APD alternans (at the split in the curve) occurred at a cycle length of 280 ms during dynamic pacing. This corresponded to a DI of 120 ms, at which the APD restitution slope (obtained by plotting APD against DIs for the identical data; shown in Figure 2E) was only 0.56. During dynamic pacing, APD alternans occurred in 14/14 myocytes and first developed at an average CL of 260±10 ms, corresponding to an average DI of 130±10 ms. The maximum difference between the long and short APDs during alternans averaged 51±5 ms. On average, the DI at which APD alternans first developed corresponded to an APD restitution slope of 0.40±0.05 during dynamic pacing. The equivalent APD restitution slope at this DI value for S1S2 pacing averaged 0.04±0.02 (although S1S2 pacing protocol does not by design elicit APD alternans). The DI at which APD restitution slope equaled 1 was much shorter than the DI at which APD alternans first occurred, averaging 29±10 ms for dynamic pacing and 41±3 ms for S1S2 pacing. These findings indicate that the onset of APD alternans under these conditions does not require a APD restitution slope >1, and suggests that the interaction with Ca²⁺_i cycling dynamics^13,24 may be critical.

SR Ca²⁺_i Cycling Regulates Both APD Restitution Slope and Alternans
To test the importance of SR Ca²⁺_i cycling on APD restitution and alternans, we treated myocytes with thapsigargin (200 nmol/L) and ryanodine (10 µmol/L) for 10 to 15 minutes before patching to deplete SR calcium stores. As shown in Figure 4, thapsigargin+ryanodine treatment markedly suppressed the Ca²⁺_i transient (Figure 4 B, inset) and prevented APD alternans in all 7 myocytes tested (Figure 4E). In addition, thapsigargin+ryanodine significantly flattened the maximum slope of APD restitution by both the S1S2 and dynamic pacing methods (Figure 5). With the dynamic pacing method, however, APD restitution slope became <1 for all DIs, consistent with the abolition of APD alternans (Figures 4D and 5). For the S1S2 method, the slope was reduced but still remained significantly >1 over a similar range of DIs (Figures 4B and 5).

View larger version (30K): [in this window] [in a new window]   Figure 4. Effect of eliminating SR Ca2+ release on APD restitution and APD restitution slope during S1S2 pacing (A and B) and dynamic pacing (C and D), in two representative myocytes studied in the perforated patch configuration. Solid symbols are before, and open symbols after, treatment with thapsigargin and ryanodine (TG/RY). Inset in B shows that TG/RY markedly suppressed the Ca2+i transient. E illustrates that APD alternans during dynamic pacing was abolished by TG/RY. F shows representative APs at the shortest CL before loss of 1:1 capture for control (top trace) and TG/RY (bottom trace).

View larger version (20K): [in this window] [in a new window]   Figure 5. Effects of TG/RY (open bars) on the maximum slope of APD restitution (left) and range of DIs with slope >1 (right) for the S1S2 and dynamic (Dyn) pacing protocols, respectively. Values are mean±SE for 8 myocytes for S1S2 and 7 myocytes for dynamic pacing protocols. Myocytes were current-clamped in the perforated patch configuration at 35°C.

Ca²⁺_i Cycling Is Required for APD Alternans
We also inhibited the ability of Ca²⁺_i cycling to influence APD by buffering the Ca²⁺_i transient with the high-affinity Ca²⁺ buffer BAPTA-AM. Loading myocytes with 100 µmol/L BAPTA-AM and 5 µmol/L Fura-2-AM for 30 minutes abolished the Ca²⁺_i transient during pacing in the perforated patch configuration. In myocytes loaded with BAPTA-AM, no visible contractions were observed during rapid pacing at any CL, and APD alternans was completely abolished (n=7) (Figure 6). For both protocols, APD restitution slope measured by the S1S2 method remained >1 (Figure 7A), and the range of DIs with slope >1 was modestly prolonged.

View larger version (31K): [in this window] [in a new window]   Figure 6. Effect of buffering Ca2+i with BAPTA-AM on APD restitution and APD restitution slope during S1S2 pacing (A and B) and single beat dynamic pacing (C and D), in representative myocytes studied using the perforated patch configuration. Solid symbols show control and open symbols BAPTA-AM loaded myocytes. APD restitution slopes in B and D were obtained from monoexponential fits to the data points in A and C. In separate experiments, we confirmed that BAPTA-AM eliminated the Ca2+i transient (see text for details). E illustrates that APD alternans during dynamic pacing was abolished by BAPTA-AM. Solid circles indicate control myocytes and open symbols, BAPTA-AM, using the single beat (open circles) or standard dynamic pacing (triangles) methods, respectively. Minimal APD alternans occurred with the single beat, but not the standard dynamic pacing method, indicating that the former was transient behavior. F shows representative APs at the shortest CL with 1:1 capture for control (top trace) and BAPTA-AM (bottom trace) during the standard dynamic pacing protocol.

View larger version (18K): [in this window] [in a new window]   Figure 7. A, Effects of BAPTA-AM (open bars) on the maximum slope of APD restitution (left) and range of DI with slope >1 (right) for the S1S2 and single beat dynamic (Dyn) pacing protocols, respectively. Values are mean±SE, with the number of myocytes indicated above each bar. Myocytes were current-clamped in the perforated patch configuration at 35 to 37°C. B, Same as A, except with 10 mmol/L BAPTA in the patch electrode using the ruptured whole-cell patch configuration.

Attempts to measure APD restitution by the standard dynamic pacing method were complicated by progressive APD shortening at rapid rates, even when the pacing CL was kept fixed. The reason is unclear, but could have been attributable to progressive activation of outward currents by rapid pacing, or by gradual saturation of the BAPTA in the cytoplasm by continued and persistent Ca²⁺ influx during rapid pacing. In support of the latter possibility, we found that when voltage-clamped myocytes were rapidly depolarized from –40 to +10 mV every 400 ms, inactivation of the L-type Ca²⁺ current increased progressively over 20 or more beats, which would be expected to progressively shorten APD if voltage was not clamped. This rate-dependent effect on the Ca²⁺-current was abolished when myocytes with pretreated with caffeine to inhibit SR Ca²⁺_i cycling.

To circumvent this problem, we substituted the single beat dynamic restitution method (see Materials and Methods) for the standard dynamic method. In control myocytes without BAPTA-AM, the single beat dynamic method yielded similar maximum APD restitution slope and DI range with slope >1 as the standard dynamic method (Figure 7). In myocytes loaded with BAPTA-AM (Figure 6), the maximum APD restitution slope remained >1, despite the abolition of APD alternans during dynamic pacing. Thus, suppressing the global Ca²⁺_i transient with BAPTA-AM abolished APD alternans, but did not decrease APD restitution slope to <1 using either the S1S2 or single beat dynamic pacing method. Similar findings were obtained when myocytes were incubated with 0.2 mmol/L instead of 0.1 mmol/L BAPTA-AM for 30 minutes and also when myocytes were dialyzed with 10 mmol/L BAPTA in the patch electrode using the ruptured whole cell patch configuration (Figure 7B).

	Discussion

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Repolarization alternans and steep APD restitution slope are both considered important determinants of dynamic wave instability, with the former used clinically to predict increased risk of ventricular arrhythmias and sudden cardiac death.¹ This study documents that Ca²⁺_i cycling plays an important role in the cellular mechanisms underlying these phenomena.

Ionic Mechanisms Underlying APD Restitution and Alternans
At the level of the single cell, the major factors governing APD restitution are recovery from inactivation of inward currents and deactivation of outward currents. Because Ca²⁺_i-sensitive ionic currents affect repolarization, it is not surprising that Ca²⁺_i cycling affects APD restitution. APD restitution has been analyzed extensively in intact cardiac tissue, using pharmacological tools and ionic substitutions to assess the relative importance of ionic current relaxation properties versus Ca²⁺_i cycling in ventricular muscle and His-Purkinje tissue (eg, see Saitoh et al²⁵). A drawback of studies in intact tissue, however, is the limited ability to analyze membrane currents and Ca²⁺_i in detail, making it difficult to obtain conclusive mechanistic information. Also, these studies did not generally examine restitution properties at rapid heart rates relevant to ventricular tachycardia (VT) and ventricular fibrillation (VF).

In isolated myocytes, on the other hand, the contributions of individual ionic currents and Ca²⁺_i dynamics to APD restitution steepness can be quantitatively assessed. Previous studies have shown that ion accumulation in extracellular clefts or transverse-tubules did not account for APD restitution in isolated myocytes.²⁶ Nanasi et al²⁷ compared APD restitution in human ventricular myocytes isolated from diseased hearts with normal isolated guinea pig and canine ventricular myocytes, but did not address underlying ionic mechanisms. Hiraoka and Kawana²⁸ studied the mechanism of APD prolongation at short DIs after a long pause (10 seconds), whereas Janvier et al²⁹ investigated the roles of K⁺, Ca²⁺, and Na⁺-Ca²⁺ exchange currents at slow heart rates (cycle length 1 second), concluding that all three types of currents were important. Tseng³⁰ showed that restitution of I_Ca, a major determinant of APD, is strongly influenced by SR calcium release, consistent with our findings.

Rubenstein and Lipsius³¹ concluded that Ca²⁺_i dynamics played a key role in APD alternans. We have previously demonstrated that Ca²⁺_i alternans occurred during pacing with an action potential clamp,¹³ indicating that Ca²⁺_i cycling can be a primary cause of APD alternans, as was also demonstrated with voltage clamp protocols.^32,14,15 Our present findings generally agree with these previous studies and extend their observations in several important ways, as described later. A limitation, however, is that we did not attempt to isolate myocytes from separate ventricular layers, so our results represent an average of epicardial, M, and endocardial cell properties.

Ca²⁺_i Cycling, Short-Term Cardiac Memory, and APD Restitution
Similar to our results, Elharrar and Surawicz³³ found that the S1S2 protocol produced a steeper APD restitution slope than dynamic pacing in canine Purkinje fibers, whereas Koller et al¹⁷ reported the opposite in intact canine ventricular muscle and Purkinje fibers. In the latter study, APD restitution >1 measured by dynamic pacing was also associated with APD alternans, and increased propensity for VF. For APD restitution to be independent of the pacing protocol, APD must be a function of the previous DI only. However, this is not generally the case, because the pacing history also influences APD (for theoretical analysis, see Otani and Gilmour³⁴ and Tolkacheva et al³⁵). In addition to time-dependent K⁺ currents,¹⁶ the effects of pacing on diastolic Ca²⁺_i and the state of SR Ca²⁺ loading can contribute to short-term memory effects through their effects on Ca²⁺_i-sensitive currents affecting APD. In our experiments, systolic and diastolic Ca²⁺_i rose to different levels during dynamic and S1S2 pacing (Figure 3A). In the dynamic protocol, sustained rapid pacing enhanced SR Ca²⁺ cycling (the basis for the positive staircase effect in Ca²⁺_i and tension in rabbit ventricle^23,36). The increased Ca²⁺_i fluxes in turn affect Ca²⁺-induced inactivation of I_Ca, the Na⁺-Ca²⁺ exchange current, and other Ca²⁺-sensitive currents, shifting the balance of repolarizing currents and differentially affecting APD during dynamic pacing versus S1S2 pacing. Although there is no doubt that differences in Ca²⁺_i influence APD differentially, based on our results, we cannot determine whether these effects are quantitatively sufficient to explain the differences in dynamic versus S1S2 APD restitution. Other factors, such as K⁺ or other ionic currents with intrinsically long time constants, may have been equally important.

Ca²⁺_i Cycling and APD Alternans
It is known that Ca²⁺_i cycling can exhibit dynamics independently of APD alternans.^13–15 Our findings support a key role of this Ca²⁺_i instability in APD alternans elicited by rapid pacing. APD alternans consistently began at DIs at which the APD restitution slope was <1 measured by either the S1S2 or dynamic pacing methods, which agrees with recent findings in intact guinea pig ventricles.³⁷ In addition, BAPTA-AM, BAPTA, and thapsigargin and ryanodine eliminated APD alternans, despite APD restitution slope remaining >1 by the S1S2 method. This is not necessarily unexpected, because the S1S2 method does not directly elicit APD alternans like the dynamic method, and the two methods give different APD restitution curves. Dynamic APD restitution slope <1 was predictive of abolition of APD alternans by thapsigargin and ryanodine. However, this was not true for BAPTA-AM and BAPTA. APD restitution slope measured by the single beat dynamic method remained >1 over a wide range of DIs, despite the abolition of APD alternans. The finding of APD restitution slope >1 without APD alternans has not been previously described in mammalian cardiac cells to our knowledge, although it was shown in frog ventricle³⁸ and explained by cardiac memory.³⁵

In summary, neither S1S2 nor dynamic APD restitution slopes are universally reliable predictors of APD alternans. The most likely explanation is that Ca²⁺_i cycling dynamics are playing a critical role in the genesis of APD alternans. This does not necessarily mean that APD restitution slope is unimportant, however, because theoretical studies show that instabilities arising from Ca²⁺_i cycling and APD restitution interact synergistically to affect the onset of APD alternans.³⁹

The different effects of thapsigargin and ryanodine, versus BAPTA-AM or BAPTA, on dynamic APD restitution slope, despite both abolishing APD alternans, may be related to their subcellular sites of action. If APD alternans is primarily driven by SR Ca²⁺ cycling dynamics, then either (1) suppressing SR Ca cycling with thapsigargin and ryanodine, or (2) suppressing the ability of SR Ca²⁺ release to modulate Ca²⁺-sensitive currents influencing APD by buffering the global Ca²⁺_i transient with BAPTA-AM or BAPTA would both be expected to abolish APD alternans. However, the effects of these interventions on APD restitution may be different because Ca²⁺-induced inactivation of I_Ca,L is known to be more strongly influenced by SR Ca²⁺ release in the T-tubular/SR junction than by the global Ca²⁺_i transient.⁴⁰ Computer simulations and experiments with Ca²⁺ channel blockers indicate that the L-type Ca²⁺ current is a major determinant of APD restitution slope,^41,42 attributable to the kinetics of recovery from inactivation of I_Ca,L. Suppressing the global Ca²⁺_i transient with BAPTA-AM or BAPTA, without disabling SR Ca²⁺ cycling, would be predicted to have less effect on Ca²⁺-induced inactivation (and hence on recovery from inactivation) of I_Ca,L, and therefore less effect on APD restitution steepness^10,22 than thapsigargin and ryanodine.

Clinical Implications
In most human and animal studies (for survey, see Weiss et al⁴³), the maximal APD restitution slope is near to or >1 in at least one of the APD restitution curves published in each study, although other investigators have argued differently.⁴⁴ Both steep APD restitution slope and Ca²⁺_i cycling are potential causes of repolarization alternans, which is a clinical marker of increased risk of sudden cardiac death.⁴⁵ Repolarization alternans has also been shown to increase dynamic wave instability, enhance wavebreak, increase inducibility of reentry, and promote degeneration of VT to VF.^{10,11,17,41,42,46–49}Our study identifies the cellular mechanisms by which Ca²⁺_i cycling has a key influence on both APD restitution steepness and APD alternans. We find that APD alternans requires normal Ca²⁺_i cycling and is not reliably predicted by APD restitution slope if Ca²⁺_i cycling is suppressed. We conclude that Ca²⁺_i cycling is a critical determinant of APD alternans and hence dynamic wave instability. Therapies directed at preventing VF by increasing dynamic wave stability must take this into account.

	Acknowledgments

 
This work was supported by NIH/NHLBI grant R29 HL51129 and R01 HL70828 (J.I.G.), SCOR in Sudden Cardiac Death P50 HL52319 (J.N.W.), by the Laubisch Fund and the Kawata Endowments. We thank Zhilin Qu, Alain Karma, Alan Garfinkel, Scott Lamp, and Yohannes Shiferaw for helpful discussions.

	Footnotes

 
Original received November 13, 2003; resubmission received August 26, 2004; revised resubmission received January 11, 2005; accepted January 12, 2005.

	References

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