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Copyright © 2006 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 91, Issue 7, 2735-2745, 1 October 2006

doi:10.1529/biophysj.106.083865

Electrophysiology

Action Potential Duration Restitution Portraits of Mammalian Ventricular Myocytes: Role of Calcium Current

Elena G. Tolkacheva^,  , Justus M.B. Anumonwo and José Jalife

Department of Pharmacology, Institute for Cardiovascular Research, State University of New York Upstate Medical University, Syracuse, New York 13210

Address reprint requests to Elena G. Tolkacheva, State University of New York Upstate Medical University, 750 Adams St., Rm. 6301C, Syracuse, NY 13210. Tel.: 315-464-7958.

Electrical restitution plays a vital role in heart function: for a given heart rate, a shorter action potential duration (APD) allows for a longer diastolic interval (DI), thereby giving adequate time for the heart to refill with blood. Although important for life at moderate heart rates, at higher rates restitution may result in life-threatening cardiac rhythms 1,2,3,4,5 such as the beat-to-beat variation of APD, known as alternans. A common technique for studying the initiation and maintenance of alternans and other complex rhythms is to analyze the restitution curve (RC), which expresses the nonlinear functional relation between APD and the preceding DI 6,7. Specifically, it was proposed 6,7 that the slope of the RC might be related to the onset of alternans. However, assessment of the role of restitution in the onset of cardiac arrhythmias has produced mixed results 8, particularly because of the existence of memory in the cardiac response, i.e., the dependence of APD on activating history, not only the preceding DI. Memory gives rise to rate-dependent restitution 9,10, which means that the RC depends on the pacing protocol. Currently, several protocols are used to measure different types of RCs, each of which measures an individual RC, where the dynamic and the S1-S2 RCs are the most common 11. Typically, these RCs have different slopes and none of them predicts the onset of alternans correctly 9,12,13,14,15.

The first attempt to systematically measure the RC was done in Tolkacheva et al. 16 and Kalb et al. 17 where the perturbed downsweep protocol (PDP) was proposed to simultaneously measure a combination of different RCs at each basic cycle length (BCL), instead of individual RCs. The PDP allows one to construct the restitution portrait of periodically paced cardiac tissue, which will enable the visualization of multiple aspects of cardiac dynamics, such as the slopes of different RCs and the APD accommodation effect at various values of BCL.

A variety of ionic currents underlie the action potential (AP) in different species. However, the ionic mechanisms underlying electrical restitution are not clear. A number of experimental and simulation studies investigated AP properties of periodically paced cardiac tissue 18,19,20,21,22. For example, it was proposed that adaptation of APD to cycle length change could be attributed to the recovery kinetics of different ionic currents or to changes in intracellular and extracellular ion concentrations 18. In contrast to the RC, the restitution portrait is a convenient way to investigate the ionic mechanisms underlying multiple aspects of cardiac dynamics 23. It also may be used as a tool to investigate ionic mechanisms of species-dependent differences in cardiac dynamics.

Here we have systematically analyzed restitution portraits of isolated cardiac myocytes obtained from two mammalian species—the rabbit and the guinea pig—that have different underlying ionic mechanisms. We characterized and compared various aspects of the cardiac dynamics, such as slopes of different RCs and the APD accommodation effect, in both species at different pacing rates. We investigated whether restitution portraits of isolated guinea pig and rabbit myocytes are qualitatively and/or quantitatively similar. Also, even though the mechanisms underlying any potential quantitative species-dependent differences in the restitution portraits are very interesting and important of themselves, we decided to start by investigating the species-independent ionic mechanisms underlying multiple aspects of cardiac dynamics in the restitution portrait. In particular, in this study we characterize the role of the calcium current in the restitution portrait obtained from isolated rabbit myocytes.

For myocyte isolation we used the following solutions: Low calcium Tyrode’s solution (in mmol/L): NaCl 148, KCl 5.4, MgCl₂ 1, NaH₂PO₄ 0.4, glucose 5.5, and HEPES 15 (pH 7.2 adjusted with NaOH). Bovine serum albumin (1mg/ml) was added to this solution. The enzyme was the same as the low calcium Tyrode’s solution, except that collagenase type II was added (100units/ml for guinea pig, 200units/ml for rabbit; Worthington Biochemicals, Lakewood, NJ). KB solution (mmol/L): KCl 80, MgSO₄ 5, KH₂PO₄ 30, glucose 20, β-hydroxybutyric acid (sodium salt) 5, creatine 5, ATP 5, taurine 20, EGTA 0.25, pyruvic acid 5.

The standard Tyrode’s solution contained the following (in mmol/L): NaCl 148, CaCl₂ 1.8, KCl 5.4, MgCl₂ 1.0, NaH₂PO₄ 0.4, glucose 5.5, and HEPES 15 (pH 7.4 adjusted with NaOH). This solution was used for cell isolation and as extracellular solution for AP studies. The pipette solution for the ruptured patch contained the following (in mmol/L): K-aspartate 90, KCl 20, KH₂PO₄ 10, EGTA 5, HEPES 5, K₂ATP 1.9. The pipette solution for the perforated patch contained the following (in mmol/L): K-aspartate 140, NaCl 5, MgATP 5, EGTA 1, HEPES 10. After being dipped for ∼10s into the pipette solution, the pipette was then back-filled using the same solution containing 240μg/mL amphotericin-B (Sigma, St. Louis, MO; catN A4888).

To block L-type calcium current (I_Ca-L), nisoldipine (1μmol/L) was added to Tyrode’s solution. To study the effect of extracellular Ca²⁺ cycling, thapsigargin (200nmol/L) and ryanodine (10μmol/L) were added to Tyrode’s solution.

The extracellular solution for calcium current (I_Ca) studies contained the following (in mmol/L) 24: tetraethylammonium-Cl 133, CsCl 5.4, MgCl₂ 1, CaCl 2, NaH₂PO₄ 0.33, Dextrose 10, and HEPES 10 (pH 7.4 adjusted with CsOH). The pipette solution for I_Ca recording contained the following (in mmol/L): CsCl 130, MgCl₂ 5, EGTA 10, GTP 0.1, Mg₂ATP 5, Na₂-phosphocloline 5.

Cardiac myocytes were isolated using the Langendorff retrograde perfusion method as previously described 25,26. Adult animals of either sex (rabbits, 1.5–3kg; guinea pigs, 0.27–0.3kg) were injected with heparin sulfate (300–500units) and anesthetized with sodium pentobarbital (rabbits: 75mg/kg i.v.; guinea pigs: 400mg/kg i.p.). Hearts were quickly removed, immersed in cardioplegic solution and retrogradely perfused with Tyrode’s solution (at 37°C) for ∼8min at 32mL/min (rabbits) or ∼5min at 16mL/min (guinea pigs) to remove any excess blood in the vessels. The hearts were then perfused with Ca²⁺-free Tyrode’s solution for 10–12min, followed by a 10-min (guinea pigs) or a 40-min (rabbits) perfusion with the enzyme solution. Finally, the hearts were perfused with the recovery (KB) solution. Subsequently, strips of tissue were carefully shaved off the left and the right endocardial surfaces of each heart. The tissue strips from each ventricle were separated into tubes containing the KB solution and were mechanically agitated to free the myocytes. After a recovery period of ∼30min, the KB solution was gradually (∼20min) exchanged with normal Tyrode’s solution. All experiments were performed at 37°C±1°C.

APs (Part I) and peak I_Ca were measured under current and voltage-clamp conditions, respectively, using the ruptured patch configuration of the patch-clamp technique (Figure 1 and Figure 2 and Figure 3 and Figure 4 and Figure 7 and Figure 8 and Figure 9). APs (Part II) to study the effects of inhibiting of I_Ca-L and intracellular Ca²⁺ cycling were measured using the whole-cell perforated patch technique 28 (Figure 5 and Figure 6). Borosilicate glass electrodes were pulled with a Brown-Flaming puller (model P-97), yielding a tip resistance of 3–5MΩ when filled with pipette solution. Data were recorded with the use of an Axoclamp-2A amplifier and pClamp8 suite of programs (Axon Instruments, Union City, CA). Stimulus pulses were generated by PCI-6013 Basic Multifunctional I/O board (National Instruments, Austin, TX). A custom-written LabView program (National Instruments) controlled stimulation. APs were elicited by 5-ms stimuli at approximately twice the threshold pulse amplitude. APD was measured at 80% of full repolarization. AP measurements were started ∼2min after patch rupture. Data were sampled at the rate of 20kHz, filtered, and then stored on the hard disk of an IBM computer.

Group data are presented as mean±SE unless otherwise stated. Nonlinear curve fitting was performed using Origin software (Origin 7.0, Northampton, MA). Statistical comparisons among groups were performed by ANOVA. Statistical significance is considered as p<0.05.

The PDP was first proposed theoretically 16 and later implemented experimentally 17. Briefly, the whole PDP consists of segments of external stimuli. The responses (APD and preceding DI pair) to a given stimulus and several segments of the PDP can be recorded by changing BCL in a downsweep (from largest to smallest value) until achieving a stable 1:1 response. Each segment consists of sequences of stimuli combined in a certain order, as presented in Figure 1A. The sequence at each BCL consists of the following steps:

I. N stimuli (or T min of pacing) are applied at BCL B to achieve a steady state.
II. Twenty additional stimuli are applied at the same BCL B to measure the steady-state response.
III. One additional stimulus (long perturbation) is applied at a longer BCL .
IV. 20–40 stimuli are applied at BCL B to reach a steady state after the long perturbation.
V. One additional stimulus (short perturbation) is applied at shorter BCL .
VI. From 20 to 40 stimuli are applied to reach a steady state after the short perturbation.

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Figure 1

Stimulation protocol (A) that was used to record restitution portraits of isolated rabbit (B) and guinea pig (C) myocytes with ruptured patch AP clamp technique. In A, only one segment of PDP for one value of BCL (B) is shown. In B and C, three different responses are present at each value of BCL: APD accommodation (black), dynamic RC (blue), and local S1-S2 RCs (purple). Note that different colors in stimulation protocol A match with recorded responses in B and C. In C, gray traces represent conventional S1-S2 RCs recorded for different values of S1 (S1=900ms and 500ms). Insets demonstrate rabbit and guinea pig AP profiles.

After completion of I–VI at BCL B, BCL is then decreased by Δ ms, and steps I–VI are repeated.

We used four modifications of the PDP: two for rabbit and two for guinea pig myocytes:

The above four modifications were used as a compromise between 1), the number of stimuli that must be applied at a given BCL to reach steady state, and 2), the limited lifetime of the isolated myocyte subjected to periodic pacing (which is ∼20–40min). On the one hand, the more stimuli were applied during step I of the PDP, the more accurately the steady state could be reached. On the other hand, with more stimuli at each BCL, the possibility was greater for cell death before completion of the PDP. Thus, PDP I was more focused on obtaining the whole downsweep without loosing a cell, whereas the PDP II was aimed at reaching the steady state at each BCL during the downsweep. Our results indicate that isolated guinea pig myocytes reach the steady state more quickly than rabbit myocytes, and thus PDP III is similar to PDP I. PDP IV was designed to approach the onset of alternans very accurately by changing BCL in small steps.

The long duration of the PDP might be inconsistent with the lifetime of some cells and also cause unforeseen current rundown effects. To ensure that current rundown does not occur, the initial part of the PDP was repeated at the end of each experiment to reproduce the initial results.

Two different protocols were used in the voltage-clamp mode to measure the peak I_Ca in rabbit ventricular myocytes:

AP clamp (3 rabbits, 12 cells). To measure the peak I_Ca (both L-type and T-type) at steady state, long and short perturbations in the restitution portrait we use AP profiles recorded from steps II–VI of the PDP II for BCL=800, 650, 500, 350, and 200ms (train of 63 AP profiles in each case). During these protocols, both reactivation and inactivation kinetics of I_Ca changed with frequency after frequency-dependent changes in AP profiles.

Voltage steps (3 rabbits, 10 cells): To determine the frequency dependence of I_Ca we used trains of 10 300-ms square pulses from −80 to +10mV, with varying intervals between pulses (from 800 to 200ms). Note that in this conventional voltage-step protocol, the duration of step pulses remains constant. In other words, this protocol is designed to examine frequency-dependent reactivation of I_Ca in the absence of changes in the inactivation kinetics.

Fig. 1 shows representative restitution portraits of isolated rabbit and guinea pig myocytes (B and C, respectively). The respective insets illustrate typical AP profiles for each species. Data in Figure 1B were generated using PDP II, whereas those in Figure 1C were obtained from PDP III. The two restitution portraits are qualitatively similar, and three different aspects of cardiac dynamics are distinguished in both at each BCL: 1), APD accommodation, which is measured during step I of PDP (black dots) and represents the slow change in APD after a step change in BCL. All these responses lie along the BCL line described by the equation APD+DI=BCL (solid black line), and whose slope is equal to −1. 2), Dynamic RC, representing steady-state responses (blue), which are measured during step II of PDP for a wide range of BCLs. At each BCL, the mean values of the APD and DI during step II were calculated and considered as steady-state responses at a given BCL. Steady-state responses at different BCLs form the dynamic RC. 3), Local S1-S2 RCs at each BCL, representing responses after perturbations (purple). These responses are measured during steps II, III, and V of PDP.

For comparison, conventional S1-S2 RCs recorded for different values of S1 (S1=900ms and 500ms) are shown in Figure 1C.

We investigated the influence of pacing history on steady-state response for isolated rabbit myocytes by applying two different modification of PDP: PDP I, where steady state was not attended at each value of BCL, and PDP II, where steady state was achieved at each BCL. Figure 2A presents the mean dynamic RCs for these two cases. The mean dynamic RC for guinea pig isolated cardiac myocytes obtained using PDP III is also plotted for comparison. It is clear from Figure 2A that APDs measured using PDP II are smaller than when measured using PDP I, showing the importance of APD accommodation. Specifically, a change in pacing history may result in up to 50% change in APD, depending on BCL. Note that 150 stimuli applied during PDP I were insufficient to reach steady state in the case of isolated rabbit myocytes.

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Figure 2

(A) Dynamic RCs for rabbit and guinea pig myocytes obtained using ruptured patch AP clamp technique for different stimulation protocols: PDP I (solid squares) and PDP II (open squares) for rabbit and PDP III (open circles) for guinea pig myocytes. (B) Time constant, τ, of APD accommodation as a function of BCL for rabbit (solid squares) and guinea pig (open circles) isolated myocytes.

The APD accommodation, the slow change in APD after step changes in BCLs, was observed in both isolated rabbit and guinea pig cardiac ventricular myocytes. To find the time constant, τ, of APD accommodation, data for the lower BCL were fitted with an exponential function of the form APD=a+b×Exp[−t/τ], where t is the time elapsed since the step change in BCL. Figure 2B shows τ as a function of BCL for both rabbit and guinea pig myocytes. Clearly, τ is a linear function of BCL for both species but is much smaller for guinea pig than for rabbit myocytes at all BCLs (p<0.05). These results demonstrate that the steady state is achieved faster, and thus the influence of pacing history on the dynamics is smaller for guinea pig than for rabbit myocytes.

Two different RCs are present in a given restitution portrait at each value of BCL: the dynamic RC and the local S1-S2 RCs. The following procedure and assumptions enabled the measurements of the slopes of these RCs at each BCL:

Slopes of the dynamic RC (S_dyn): The mean values of the 10 responses measured during step II of the PDP at each BCL were determined as steady-state points that form the dynamic RC (blue curve in Figure 1BC). We fitted the dynamic RC with an appropriate (exponential or polynomial) function and calculated the slopes analytically at steady-state points at each BCL.

Slopes of local S1-S2 RCs (S₁₂): We fitted the steady-state points and responses from steps III and V of the PDP with an appropriate function (linear or polynomial) and calculated slopes of local S1-S2 RCs at steady-state points at each BCL.

In Figure 3A, we present S_dyn (solid symbols) and S₁₂ (open symbols) measured from the restitution portrait of the isolated rabbit ventricular myocyte as functions of BCL. We used two modifications of PDP, PDP I (squares) and PDP II (circles) (see Methods), to investigate the influence of pacing history on the slopes. For both modifications, the slopes S_dyn are linear functions, and S₁₂ are exponential functions of BCL. Hence pacing history dramatically affects both slopes: S_dyn and S₁₂ are smaller for PDP II, where steady state is achieved at each BCL. Figure 3B presents the influence of pacing history on the relationship between S₁₂ and S_dyn (same data as in Figure 3A). There was no significant difference between data obtained using PDP I (solid circles) and PDP II (open circles). Therefore all data were fitted by a single exponential function (), which shows that, unlike the individual values of S₁₂ and S_dyn (Figure 3A), the relationship between these slopes (Figure 3B) does not depend on pacing history. In Figure 3C, we show slopes S_dyn (solid circles) and S₁₂ (open circles) measured in the restitution portrait of a guinea pig myocyte at different values of BCL. Both slopes are exponential functions of BCL. In Figure 3D, the relation between S₁₂ and S_dyn (same data as in Figure 3C) is fitted with an exponential function (). Our results demonstrate quantitative but not qualitative differences in the relationships between S₁₂ and S_dyn for both species (Figure 3BD). Thus, overall, the dynamic behavior of the different slopes in the restitution portrait is clearly species independent.

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Figure 3

Slopes S_dyn (solid symbols) and S₁₂ (open symbols) measured from the restitution portraits of the (A) rabbit and (C) guinea pig myocytes as functions of BCL. In A, two different modifications of PDP were used: PDP I (squares) and PDP II (circles). The relationship between S_dyn and S₁₂ for (B) rabbit and (D) guinea pig myocytes. Note that this relationship does not depend on pacing history: in B, data obtained using different PDPs could be fitted with a single curve.

An important aim of our study was to investigate the ability of the slopes of different RCs measured in the restitution portrait to predict the onset of alternans. We observed two types of steady-state responses during step II of the PDP: stable 1:1 responses and alternans. During stable 1:1 responses, there was a single steady-state value of APD whereas during alternans APD alternated between two different values. It is generally believed that an RC slope equal to one predicts the transition between these two states 6,7. To achieve the onset of alternans very accurately, we designed a specific pacing protocol (PDP IV) to allow the measurement of slopes of different RCs at the onset of alternans. From a total n=30 myocytes from five guinea pigs, we obtained n=6 cases of stable alternans (lasting at least 60s).

In Figure 4A the transition between 1:1 responses (solid circles) and alternans (stars) is demonstrated for the isolated guinea pig myocytes. The inset shows representative traces of APDs for stable alternans, and the local S1-S2 RC (open squares) is presented for the shortest BCL during 1:1 responses. We used two points from Figure 4A to calculate the slopes of different RCs at the onset of alternans: 1), steady-state point (where the dynamic RC intersects with S1-S2 RC); and 2), point of small perturbation for S1-S2 RC, which is also the first point after step change in BCL. We calculated slopes S_dyn and S₁₂ at steady-state points for the shortest BCL, as described above. In addition, we measured the maximal slope of local S1-S2 RC, , for the shortest value of BCL at the point of small perturbation. Note that S₁₂ is different from because local S1-S2 RCs for small BCLs are usually curved rather than linear. Figure 4B presents average values for all three slopes measured at the onset of stable alternans in guinea pig myocytes. The horizontal line at slope=1 shows the standard restitution condition for alternans 6,7. It is clear that predicts the onset of alternans unlike the other two slopes. Our statistical analysis shows that there are significant differences between , S_dyn, and S₁₂ (p<0.05). Overall, our results indicate that slope does predict the onset of alternans.

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Figure 4

(A) Segment of the restitution portrait showing transition between 1:1 responses and alternans: dynamic RC (solid circles), local S1-S2 RC for the shortest BCL (open squares), stable alternans (stars). (Inset) Traces of APs for the stable alternans. (B) Values of different slopes measured at the onset of alternans: S_dyn and S₁₂ were measured at the steady-state point, and was measured at the point of small perturbation (A).

It is well known that the L-type calcium current (I_Ca-L) is an important determinant of the plateau phase of the AP and that it contributes to rate-dependent changes of APs in ventricular myocytes from human 27 and other species. Also, it has been suggested that intracellular Ca²⁺ cycling may contribute to differences between dynamic and S1-S2 RCs 28 in rabbit ventricular myocytes.

To investigate the role of I_Ca-L and intracellular Ca²⁺ cycling on different aspects of cardiac dynamics in the restitution portrait, we used the following procedures 27,28. First, to investigate the particular role of I_Ca-L on the restitution portrait, we blocked this current using nisoldipine (1μmol/L). Second, to test the effects of intracellular Ca²⁺ cycling on different aspects of cardiac dynamics, cells were incubated (10min) in Tyrode’s solution containing thapsigargin (TG) (200nmol/L) and ryanodine (RY) (10μmol/L) (RY/TG conditions) 28, during repetitive pacing at 1Hz. The restitution portraits were recorded using PDP I for normal (5 rabbits, 10 cells), RY/TG (5 rabbits, 8 cells), and nisoldipine (5 rabbits, 8 cells) conditions. For our study, we used perforated patch technique instead of ruptured patch to produce minimal perturbations to the intracellular compartment. Figure 5A illustrates that the different types of techniques do not affect the dynamic RCs. Typical traces of AP (BCL=1000ms) and dynamic RCs recorded using perforated patch technique under control, RY/TG, and nisoldipine conditions are shown in Figure 5BC. Note that blockage of intracellular Ca²⁺ cycling reduces APDs at all values of BCLs (p<0.05), and this effect is more pronounced if I_Ca-L is abolished.

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Figure 5

(A) Dynamic RCs for rabbit myocytes obtained using perforated (open circles) and ruptured (solid circles) patch techniques. Examples of AP profiles (B) (BCL=1000ms) and dynamic RCs (C) for rabbit myocytes obtained using perforated patch technique under control (solid squares), RY/TG (open squares), and nisoldipine (open stars) conditions.

Slopes of different RCs (S_dyn and S₁₂) and τ were measured at different values of BCL as was described above. Fig. 6 depicts the slopes S_dyn (panel A) and S₁₂ (panel B) under control (solid squares), nisoldipine (open stars), and RY/TG (open squares) conditions. Note that S_dyn changed significantly (p<0.05) from the control case for all values of BCL under nisoldipine condition. At the same time, S₁₂ changed significantly (p<0.05) from the control case only at small values of BCLs. Note also in Figure 6AB, that RY/TG superfusion had no significant effect on either slope S_dyn (panel A) or S₁₂ (panel B) at any BCL. These results demonstrate the importance of I_Ca-L, but not intracellular Ca²⁺ cycling, on the frequency-dependent behavior of periodically paced cardiac myocytes.

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Figure 6

(A) Slopes S_dyn, (B) slopes S₁₂, and (D) APD measured from the restitution portraits of the rabbit myocytes (obtained using perforated patch technique) under control (solid squares), nisoldipine (open stars), and RY/TG (open squares) conditions. (C) Time course of APD accommodation under these conditions.

Typical time courses of APD accommodation after abrupt changes of BCL from 350ms to 200ms under control, RY/TG, and nisoldipine conditions are shown in Figure 6C. In Figure 6C, APD accommodation under control and RY/TG conditions and the absence of APD accommodation during superfusion of nisoldipine are similar for all values of BCL. Note that APD accommodation effect could be described as an exponential function of time under control and RY/TG cases. On the contrary, after blocking I_Ca-L the APD upon changing the BCL is no longer an exponential function of time. Thus, to determine the influence of the calcium current on APD accommodation, we introduced a new parameter, ΔAPD, instead of the time constant τ. We define ΔAPD=1−A₂/A₁, where A₁, A₂ are the mean values of the first and last 10 APDs at any given value of BCL. Figure 6D shows the mean values of ΔAPD calculated under control, nisoldipine, and RY/TG conditions at BCL=200ms. These results indicate that in the absence of I_Ca-L the APD accommodation effect disappears (p<0.05). In contrast, the role of intracellular calcium cycling appears insignificant.

We measured peak I_Ca under voltage-clamp conditions using both APs profiles and step pulses recorded at different values of BCLs (see Methods). Representative traces of single step pulse and AP profiles recorded for BCL=800 and 200ms are presented in Figure 7A. The traces of I_Ca under these conditions are shown in Figure 7B. Peak I_Ca was measured as the difference between holding current and peak inward current.

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Figure 7

(A) Representative AP profiles for BCL=800 and 200ms, and step pulse that were used to measure peak I_Ca. (B) Peak I_Ca measurements under these conditions.

An important aspect of cardiac dynamics revealed by the restitution portrait is the difference between the dynamic and the S1-S2 RCs at each value of BCL due to short-term memory effects (see Fig. 1). Using the restitution portrait enables the determination of the role of I_Ca in this aspect through the analysis of I_Ca changes during steady-state stimulation (dynamic RC) and after the long and short perturbations in BCL (local S1-S2 RCs).

Since our initial results indicated that I_Ca-L played a major role in determining the slopes S_dyn and S₁₂, we decided to examine the role of the peak I_Ca in detail. We combined the use of the restitution portrait and AP clamp techniques to measure peak I_Ca during steady-state stimulation (dynamic RC) as well as after long and short perturbations in BCL (local S1-S2 RCs). We measured the peak I_Ca under AP-clamp conditions using segments of restitution portraits for different values of BCL (see Methods). As an example, in Figure 8AB, we have plotted 63 consecutive APDs from the restitution portrait recorded for BCL=350 and 200ms, respectively, using steps II–VI of PDP II. Note that for large values of BCL (≥350ms), APDs for the long and short perturbations are not significantly different from the steady-state values. Thus, both perturbations lead to change in DIs. In contrast, for BCL=200ms, long and short perturbations lead to differences in both APD and DI. The peak I_Ca was measured in each trial for different BCLs (800, 650, 500, 350, and 200ms). In Figure 8CD, we present the mean peak I_Ca normalized to the first value for BCLs 350 and 200ms, respectively. The stars depict the normalized peak I_Ca during long and short perturbations in BCL. Data for BCLs 500, 650, and 800ms are qualitatively similar to those for 350ms (not shown). The data demonstrate that peak I_Ca does not change in response to the perturbations for large values of BCL (≥350ms). However, peak I_Ca is significantly smaller in response to short perturbation for BCL=200ms. These results indicate that the peak I_Ca is responsible for the difference between the dynamic and the S1-S2 RCs only at small values of BCL.

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Figure 8

AP clamp peak I_Ca measurements. APDs from the restitution portrait recorded for BCL=350ms (A) and 200ms (B) using steps II–VI of PDP II. (C) Normalized peak I_Ca at BCL=350ms. (D) Normalized peak I_Ca at BCL=200ms.

Data from the previous section demonstrated that peak I_Ca plays a significant role in the restitution portrait only at small values of BCL. To investigate whether this is due to changes in AP profile at different BCLs, we measured peak I_Ca using conventional voltage-clamp step protocol with different time intervals (corresponding to DI) between steps.

Figure 9A illustrates the difference between conventional voltage-clamp step protocol (open circles) and AP clamp protocol (solid circles) as BCL decreases. Figure 9B shows peak I_Ca recorded using both these techniques. In the step protocol, as BCL decreases the step duration remains the same, and only time intervals between steps decreases, allowing the measurement of frequency-dependent reactivation kinetics of peak I_Ca. The peak I_Ca (Figure 9B) decreases (in absolute value) as DI decreases, indicating a lack of full reactivation of I_Ca at higher frequencies. In the AP clamp, as BCL decreases, both APDs and DIs changed with frequency allowing the measurement of both frequency-dependent reactivation and inactivation kinetics of I_Ca in the restitution portrait. Peak I_Ca measured using AP clamp decreases as DI decreases up to 300ms and then increases again, suggesting interplay between reactivation and inactivation kinetics of I_Ca at high frequencies. An interplay between reactivation and inactivation kinetics at higher frequencies might explain results from the previous section indicating that peak I_Ca plays a significant role in the restitution portrait at small values of BCL (Figure 8C).

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Figure 9

(A) Durations of APs and step pulse as functions of DIs for conventional voltage-clamp step protocol (open circles) and for APs voltage-clamp protocols (solid circles). Broken lines represent equal BCLs for 800 and 500ms. (B) Peak I_Ca recorded during step (open circles) and APs (solid circles) voltage-clamp protocols.

We have utilized the single cell restitution portrait model to begin the characterization of ionic mechanisms underlying the complex phenomena that control heart rate dependence of the APD. Our results show that restitution portraits of isolated guinea pig and rabbit myocytes are qualitatively similar to those seen previously in numerical experiments and in small pieces of bullfrog ventricular muscle 17. In all cases, three different aspects of cardiac dynamics are present at each value of BCL: 1), APD accommodation (i.e., the time necessary for APD to reach a steady state); 2), steady-state responses that form the dynamic RC; and 3), the responses to perturbations that form the local S1-S2 RCs at each BCL. Overall the data suggest that the restitution portrait is a fundamental characteristic of excitation of the myocardial cell, rather than the result of structural complexities of the multi-cellular cardiac tissue. Determining how such complexities affect the restitution portrait will require comparing the single cell data with similar data derived from experiments in the intact mammalian heart.

Another major objective of our study was to determine the time constant, τ, of APD accommodation as one of the important parameters controlling the dynamics of the periodically paced cardiac myocyte. To our knowledge, this is the first set of measurements of τ at a wide range of BCLs. All previous measurements 10,17,29 of τ were made only for one or several values of BCL. Our data demonstrate that τ is a linear function of BCL for both rabbit and guinea pig cardiac ventricular myocytes. The results show also that τ is much smaller for the guinea pig than for the rabbit for all BCLs, which indicates the ability of the guinea pig myocyte to reach steady state in a shorter period of time. The different values of τ for guinea pig and rabbit cardiac myocytes might be due to different ionic currents in these species or different kinetics of the same currents. However, this issue is beyond the scope of our study and will require further investigation.

We investigated the influence of pacing history on the slopes of different types of RC, S_dyn, and S₁₂ in the restitution portraits. In particular, we applied two modifications of the PDP to the isolated rabbit myocyte: one that did and another that did not allow reaching a steady state at each BCL. In both species S_dyn and S₁₂ strongly depend on pacing history; they both increase with decreasing BCL. However, the relationship between these slopes is a generic feature of the species and is independent of pacing history.

We also examined the ability of the slopes of different RCs measured in the restitution portrait to predict the onset of alternans. According to the restitution condition 6,7 the slope of the RC must be equal to 1 at the onset of alternans. Previously it was demonstrated that this condition is not achieved in many situations, in particular, stable 1:1 behavior was observed when the slope of RC was >1 9,12,13 or the transition to alternans occurred in the presence of a shallow RC 14,15. In our experiments, the onset of stable alternans was determined very accurately through a unique pacing protocol, which also allowed measurements of the slopes of different RCs at the shortest possible BCL yielding a 1:1 response. Specifically, we measured S_dyn and S₁₂ at steady-state points and the maximal slope at the point of small perturbation. Previous results 17 demonstrated that predicts the onset of alternans in bullfrog myocardium. However these results needed confirmation in mammalian myocytes. Our results indicate that does predict the onset of alternans in isolated guinea pig myocytes more accurately than can other slopes (r<0.05). Note that slope measured in our experiments is different from the commonly measured S₁₂ slope 11,15,28.

Using nisoldipine in some experiments and ryanodine and thapsigargin in others, we investigated the separate roles of L-type calcium current and intracellular Ca²⁺ cycling in the restitution portrait. Our results indicate that I_Ca-L is important in the mechanisms of different aspects of cardiac dynamics in the restitution portrait. More specifically, I_Ca-L dramatically affects the slopes S_dyn and S₁₂ and also APD accommodation. Note that the I_Ca-L significantly affects S_dyn at different values of BCL, but it affects S₁₂ only at small values of BCL. In contrast, our results indicate that intracellular Ca²⁺ cycling did not affect in any significant way either the slopes S_dyn and S₁₂ or APD accommodation. The latter result seems to be at odds with results from the literature 28 showing a major influence of intracellular Ca²⁺ cycling on the maximal slopes of S_dyn and S₁₂. There are several possible explanations for such a discrepancy. One possibility is that, unlike the investigation by Goldhaber et al. 28 who applied only 10 beats at each BCL, we measured S_dyn while ensuring that steady sate was achieved at each BCL. This process might indeed take several minutes. Moreover, the maximal slope of S_dyn measured by Goldhaber et al. included not only APDs recorded during 1:1 responses (what usually is used to construct the dynamic RC) but also the APDs during alternans (which we did not include in our measurements). Recall that our results indicate that pacing history affects dramatically the slopes of different RCs. This also could be the reason intracellular Ca²⁺ cycling affected S_dyn in Goldhaber et al. but not in our experiments. In addition, the measurement of S₁₂ is also very different in our experiments: we measured local S₁₂ over many values of BCL (S1), whereas S1=400ms in Goldhaber et al.

Although I_Ca-L affects significantly slopes S_dyn and S₁₂ at different values of BCLs, the results of the AP clamp experiments demonstrate that the peak I_Ca does not change in response to the perturbations for the large values of BCL (≥350ms). However, the peak I_Ca is significantly smaller when considering the small perturbation for BCL=200ms. These results indicate that the peak I_Ca plays a significant role in frequency dependence of the slopes S_dyn and S₁₂ only at small values of BCL. Our further investigations indicate that this effect is most probably caused by the size and/or shape of the applied AP profile at high frequencies, when there is an interplay between reactivation and inactivation kinetics.

Thus, the L-type calcium current plays a crucial role in multiple aspects of cardiac dynamics in the restitution portrait. Specifically, in the absence of I_Ca-L there is no APD accommodation or frequency dependence of the slopes. However, our data clearly show that neither intracellular Ca²⁺ cycling nor peak I_Ca is responsible for these phenomena. The exact mechanism of it is still unclear and several possibilities need to be considered. For example, accumulation of calcium ions with time might affect the inactivation of calcium channels, which will lead to APD accommodation and frequency dependence of slopes. In addition, I_Ca-L might affect other currents (through potassium channels, sodium-calcium exchanger, etc.) and cause these effects.

In summary, we systematically analyzed restitution portraits of isolated cardiac myocytes obtained from two different mammalian species—the rabbit and the guinea pig. We characterized various aspects of the cardiac dynamics and the role of calcium current and intracellular calcium cycling in the restitution portrait. We demonstrated that I_Ca-L dramatically affected APD accommodation and the individual slopes of dynamic and S1-S2 RCs measured in the restitution portrait. Furthermore, peak I_Ca plays a role only at small values of BCL, whereas intracellular Ca²⁺ cycling does not play any significant role in the restitution portrait. In conclusion, we have shown that the restitution portrait is a powerful technique to investigate the restitution properties of periodically paced cardiac myocytes, and the onset of alternans, in particular. We also demonstrated that the calcium current plays a crucial role in the restitution portrait.