The development of L-type Ca2+ current mediated alternans does not depend on the restitution slope in canine ventricular myocardium

Cardiac alternans have crucial importance in the onset of ventricular fibrillation. The early explanation for alternans development was the voltage-driven mechanism, where the action potential (AP) restitution steepness was considered as crucial determining factor. Recent results suggest that restitution slope is an inadequate predictor for alternans development, but several studies still claim the role of membrane potential as underlying mechanism of alternans. These controversial data indicate that the relationship of restitution and alternans development is not completely understood. APs were measured by conventional microelectrode technique from canine right ventricular papillary muscles. Ionic currents combined with fluorescent measurements were recorded by patch-clamp technique. APs combined with fluorescent measurements were monitored by sharp microelectrodes. Rapid pacing evoked restitution-independent AP duration (APD) alternans. When non-alternating AP voltage command was used, Ca2+i-transient (CaT) alternans were not observed. When alternating rectangular voltage pulses were applied, CaT alternans were proportional to ICaL amplitude alternans. Selective ICaL inhibition did not influence the fast phase of APD restitution. In this study we found that ICaL has minor contribution in shaping the fast phase of restitution curve suggesting that ICaL—if it plays important role in the alternans mechanism—could be an additional factor that attenuates the reliability of APD restitution slope to predict alternans.

Determination of the action potential parameters in canine multicellular papillary muscle. Beagle dogs (obtained from a licensed supplier, licence number: XXXV./2018) from both sex weighing 10-15 kg were used for conventional microelectrode experiments. The animals were anesthetized and sacrificed with pentobarbital (60 mg/kg iv), then the heart was removed through a right lateral thoracotomy.
APs were recorded at 37 °C from the surface of right ventricular papillary muscles using conventional microelectrode technique. For measuring tissue APs similar protocol was applied as described earlier with minor modifications 23,24 . Briefly, the preparations were mounted in a custom made Plexiglas chamber, allowing continuous super-fusion with Locke's solution (130 mM NaCl, 21.5 mM NaHCO 3 , 4.5 mM KCl, 12 mM glucose, 0.4 mM MgCl 2 , 1.8 mM CaCl 2 , ph 7.35 ± 0.05) and stimulated with constant pulses of 5 ms duration at a rate of 1 Hz through a pair of bipolar platinum electrodes using an electro-stimulator (EX-ST-A2, Experimetria Ltd). Sharp microelectrodes with tip resistance of 10-20 MΩ, when filled with 3 M KCl, were connected to an amplifier (Biologic Amplifier, model VF 102). Voltage output from the amplifier was sampled using an AD converter (NI 6025, Unisip Ltd). APs were monitored and evaluated by using Evokewave v1.49 (Unisip Ltd).
APD alternans protocol. APD alternans were measured by rapid pacing using cycle lengths of 250-230-210-190-160 ms. 20 consecutive stimuli were used at each frequency. APD differences were calculated between long and short AP pairs along at least 6 consecutive pulses at 25, 50 and 90% of repolarization (APD 25, APD 50 and APD 90 , respectively) and were averaged providing APD alternans amplitude.
Conventional S1S2 restitution protocol. The basic cycle length (BCL) was 1000 and 500 ms. Extra delays for S2 stimuli ranged from − 50 to 1000 ms related to the baseline APD 90 . 15 consecutive stimuli were applied (S1) between all S2 stimuli. Diastolic intervals (DI) refer to the proximity of S2 stimuli (extra beat) to the APD 90 of the basic beat evoked by S1.
Dynamic restitution protocol. Following a pre-pacing at 1 Hz, the basic cycle length was gradually decreased from 1000 to 500 ms by 100 ms steps, from 500 to 300 ms by 50 ms steps. When the cycle length reached the 250 ms the action potential started to alternate and the AP alternation was constantly maintained from 250 to 160 ms. In this cycle length interval, we applied the previously described cycle length pattern for alternans. During these measurements the APD 90 was plotted against the preceding diastolic interval at each cycle length.
Previous study reported that standard S1S2 restitution method is not suitable tool to predict alternans since the slope in most cases < 1 25 . However, we observed restitution slopes larger and smaller than 1 in approximately 50-50% of our experiments, providing an average value of 1.12 ± 0.1 (BCL: 1000 ms; n = 20) and 1.08 ± 0.1 (BCL: 500 ms; n = 20). Therefore, we considered standard S1S2 restitution protocol as an appropriate tool to assess restitution slope.
Voltage-clamp measurements combined with fluorescent recordings. The isolation of canine left ventricular cardiomyocytes of Beagle dogs' hearts was performed as described previously 26 . In brief, cardiac myocytes were isolated from the left ventricle, containing an arterial branch through which the segment was perfused on a Langendorff apparatus with solutions in the following sequence: normal isolation solution (containing in mM: 135 mM NaCl, 4.7 mM KCl, 1.2 mM KH 2 PO 4 , 1.2 mM MgSO 4 , 1 mM CaCl 2 , 10 mM Glucose, 10 mM HEPES, 20 mM taurine, 4.4 mM NaHCO 3 , 5 mM Na-pyruvic acid, pH 7.2 adjusted with NaOH) for 10 min, Ca 2+ -free isolation solution for 10 min and isolation solution containing collagenase (Worthington type II, 0.66 mg/mL) and 33 µM CaCl 2 . To the final perfusion solution protease (type XIV, 0.12 mg/mL) was added at the 15th minutes for digestion. The isolated cardiomyocytes were loaded with Fluo-4-AM (1-2 μM, Molecular Probes, USA; AM is the membrane permeable acetoxymethyl ester conjugated form of the dye) for 20 min at room temperature in dark. The loaded cells were placed in a low volume imaging chamber (RC47FSLP, Warner Instruments, USA), and the cells were then continuously perfused with normal Tyrode solution at 37 °C (1 mL/ min). Data acquisition and analysis were performed using Axon Digidata 1550B System (Molecular Devices, Sunnyvale, CA, USA). Parallel with the current measurements, the fluorescent recordings were performed on a stage of an inverted fluorescent microscope (IX71, Olympus, Japan) and the signal was recorded by a photomul- www.nature.com/scientificreports/ tiplier module (H7828, Hamamatsu, Japan), sampled at 1 kHz. Data acquisition and analysis were (both current and Ca 2+ transient) performed using the pClamp 11.0 software (Molecular Devices, Sunnyvale, CA, USA). Calcium alternans were based on six consecutive CaTs, where the average CaT amplitude was computed for even and odd beats. The amplitude of a single CaT was estimated as the difference between the peak and the minimum directly preceding the first analyzed CaT (i.e., it is the CaT upstroke amplitude).

Parallel measurement of AP and CaT with current clamp technique.
Single cell AP measurements were performed as described previously 27 . Rod-shaped viable ventricular cardiomyocytes, showing clear striation, were placed in a 1 ml volume experimental chamber mounted on the stage of an inverted microscope (Nikon Diaphot 300; Nikon Co., Tokyo, Japan). After sedimentation, cardiomyocytes were continuously superfused with at 37 °C Tyrode solution at a rate of 1-2 mL/min. Cells were impaled with 3 M KCl filled conventional borosilicate microelectrodes having tip resistances between 20 and 40 MΩ, connected to the input of a Multiclamp 700A amplifier (Molecular Devices, Sunnyvale, CA, USA). Action potentials (AP) were elicited through these intracellular electrodes by applying 2 ms wide rectangular current pulses having amplitudes of twice the diastolic threshold. The membrane potential signal was digitalized at 50 kHz using Digidata 1440A A/D card, recorded with pClamp 10 software (both from Molecular Devices) and stored for later analysis. APs were recorded at pacing cycle lengths of 1000, 500, 300, 250, 230, 210 ms in this respective order. Cardiomyocytes were loaded with 5 µM Fura-2 AM for 30 min at room temperature in a Pluronic F-127 containing Tyrode solution. 25 mg Pluronic F-127 was dissolved in 1 mL DMSO and this solvent was used to make a Fura-2 AM stock solution of 1 mM. After loading, the cells were washed twice with Tyrode solution, and were allowed to rest for 30 min at room temperature to de-esterify the dye, and then they were stored at 15 °C before the experiments. Fluorescence was measured using an alternating dual beam excitation fluorescence photometry setup (RatioMaster; Photon Technology International, New Brunswick, NJ, USA) coupled to the inverted microscope. Fluorescence signals of Ca 2+ -bound and Ca 2+ -free Fura-2 dye were detected at excitation wavelengths of 340 nm (F 340 ) and 380 nm (F 380 ), respectively. Emitted photons were detected at 510 nm with an R1527P photomultiplier tube (Hamamatsu Photonics K.K., Hamamatsu, Japan). This signal was digitalized at 200 Hz using the FelixGX software (Photon Technology International) and stored for offline analysis. Background fluorescence was measured by moving the cell out of the field of view, and it was subtracted from total fluorescence in order to obtain fluorescence originating exclusively from the preparation. Fluorescence ratio of F 340 /F 380 was used to assess intracellular Ca 2+ transients (CaT). The CaT was recorded in parallel with AP and CL.

Measurement of I CaL .
The L-type calcium current (I CaL ) was recorded in HEPES-buffered Tyrode's solution, supplemented with 3 mM 4-aminopyridine under perforated patch (Fig. 2) or whole-cell configuration (Fig. 3).
To obtain I CaL current and alternans ( Recovery characteristic of I CaL was obtained by activation of the I CaL current by rectangular pulses from a holding potential of − 80 mV to 0 mV for 400 ms. Subsequently interpulse intervals were used from 25 to 500 ms before the second rectangular pulse that was identical with the initial pulse. The I CaL recovery was calculated by comparing the initial I CaL peaks evoked by the initial pulse with I CaL pulse elicited by the second pulse, and were plotted against the corresponding interpulse intervals. During these experiments the Ca 2+ handling was intact. The cells were loaded with Fluo-4-AM fluorescent dye, and experiments were performed by whole-cell patch-clamp technique. All chemicals were purchased from Sigma (USA). All experiments were carried out at 37 °C.
Statistics. Normal distribution of the data was verified by using Shapiro-Wilk test. Statistical significance (p < 0.05) was assessed using Student's t-test. Data are presented as mean ± S.E.M.

Results
Action potential alternans and restitution measurements in intact subendocardial right ventricular papillary muscle. In the first set of experiments APD restitution (S1S2 protocol) and APD alternans protocol were measured and compared from the same intact subendocardial tissue (right ventricular papillary muscle). Figure 1 represents the summary of 20 experiments (from 11 dogs) of control S1S2 restitution-alternans experiments. Figure 1a illustrates the applied S1S2 restitution protocol. The S1S2 restitution was recorded at BCL of 1000 then 500 ms. The APD alternans amplitude was defined from at least 6 consecutive, regular short-long APs at APD 90 , APD 50 and APD 25 as APD difference. Alternans could be evoked in all cases (n = 20) with clear threshold, i.e. when the pacing length became equal or shorter than 250 ms (action potential waveforms can be seen in Supplementary Fig. S1). When AP alternans developed, they were maintained during the entire pacing protocol without any decline in the magnitude of APD oscillation. Figure 1b represents comparisons between restitution slopes and the corresponding magnitude of APD alternans. Left side of the panel represents S1S2 restitutions at BCL of 500 ms, right side illustrates restitutions at 1000 ms (restitution was analyzed at APD 90 level). Alternans measured at 210 ms cycle length (odd columns) and www.nature.com/scientificreports/ 160 ms (even columns) were highlighted. The first row represents alternans amplitudes measured at APD 90 level, middle row shows alternans recorded at APD 50 level, and bottom row illustrates alternans at 25% of repolarization. Our results indicate that alternans developed even if the restitution slope was smaller than 1, furthermore, data show mainly weak and in some cases moderate correlations between variables. We also analyzed the S1S2 restitutions at APD 50 and APD 25 and these values were plotted against the corresponding alternans magnitude. Weak or moderate correlations were found ( Supplementary Fig. S2). Figure 2 demonstrates comparisons of restitution slopes obtained from dynamic restitution and alternans amplitude. Figure 2a depicts the applied dynamic restitution protocol: the pacing cycle length was gradually decreased. At cycle length of 250 ms the APD started to alternate.
Functions of restitution slope-alternans amplitude are illustrated in Fig. 2b. Left column represents alternans at cycle length of 210 ms, right column represents the same at cycle length of 160 ms. The first row shows alternans amplitudes measured at APD 90 level, middle row represents alternans recorded at APD 50 level, and bottom row illustrates alternans at 25% of repolarization. Similarly to the S1S2 restitution, we found that alternans developed even if the slope was smaller than 1, and data exerted weak or no correlations between restitution slope and alternans.
The temporal relationship of alternans and restitution slopes was further illustrated in Supplementary Fig. S3. It can be observable that alternans could be evoked at slower pacing cycle lengths (i.e. 250 ms) where the corresponding restitution curves were slow, indicating that alternans can be evoked even if the restitution slope is smaller than 1 (Supplementary Fig. S3).
Non-alternating AP sequence failed to elicit CaT alternans. In order to further address the relationship between AP and CaT alternans, current clamp experiments by using sharp microelectrodes were performed Relationship between action potential alternans and S1S2 restitution. (a) Illustrates the applied protocol for S1S2 restitution. The basic cycle length for restitution was 1000 and 500 ms. The diastolic intervals increased from − 50 to 1000 ms (relative to APD 90 ) and the slope of APD 90 restitution was calculated at both 500 and 1000 ms BCLs. After the restitution protocols, alternans were measured from a cycle length of 250 ms to 160 ms. The magnitude of alternans was measured at APD 90 , APD 50 , and APD 25 . (b) Demonstrates correlation tests between S1S2 restitution slope and alternans. The left 6 panels show S1S2 restitutions at BCL of 500 ms, in the right 6 panels the BCL was 1000 ms. The first row demonstrates alternans at APD 90 level, middle row at APD 50 , bottom row at APD 25 . Our results indicate that alternans developed even if the restitution slope was smaller than 1, furthermore, data show mainly weak and in some cases moderate correlations between variables. www.nature.com/scientificreports/ in single cells (Fig. 3a). Stimulus pattern from a cycle length of 250 to 210 ms was applied. The CaT amplitude oscillations were plotted against the corresponding APD 90 difference (Fig. 3b) within the range of 250-210 ms stimulus cycle length. A close relationship between APD and CaT amplitude alternans was found: larger APD alternans were associated with larger CaT amplitude alternans (n = 15). In order to elucidate the initiator mechanism of alternans, a non-alternating AP sequence having a BCL of 210 ms was applied under voltage-clamp mode (Fig. 3c upper panel). During measurements, the ionic currents ( Fig. 3c middle panel) and CaT (Fig. 3c lower panel) were monitored. The experiments were performed by perforated patch-clamp method to preserve the intracellular milieu. Here we found that the inward ionic currents (other currents were inhibited, see Methods) as well as CaT exerted (6.7 ± 2.2%, n = 9) negligible alternans. These results suggest that in our experiments the action potential alternans are required for CaT alternans. I CaL kinetics during alternating voltage pulses. Among transmembrane ionic currents I CaL could be the most obvious candidate that may have important role in the alternans mechanism. As a trigger of the Ca 2+ release it can directly influence the magnitude of the actual Ca 2+ transient, and its kinetic is strongly influenced by the membrane potential.
In order to address the contribution of I CaL in alternans, we applied 3 alternating voltage pulse protocols to produce different extent of I CaL alternans due to alternans of the recovery time (Fig. 4a). The measurements were performed by using perforated patch clamp method. The magnitude of corresponding CaT amplitude alternans was analyzed and compared to the I CaL amplitude alternans. The BCL of all protocols was 220 ms in all cases (see description in the "Methods" section).

Figure 2.
Relationship between action potential alternans and dynamic restitution. (a) Illustrates the applied protocol for dynamic restitution. The basic cycle length for restitution was progressively decreased from 1000 to 160 ms. When BCL was 250 ms or shorter the action potential started to alternate. APD 90 was plotted against the preceding diastolic interval in both long and short AP during alternans. (b) The slope of APD 90 restitution was calculated and was plotted against the magnitude of alternans. The first row demonstrates alternans at APD 90 level, middle row at APD 50 , bottom row at APD 25 . Similarly to the S1S2 restitution, we found that alternans developed even if the slope was smaller than 1, and data exerted weak or no correlations between restitution slope and alternans. www.nature.com/scientificreports/ In these experiments a close correlation between I CaL amplitude alternans and corresponding CaT amplitude alternans was found (Fig. 4d). It implies that CaT alternans were marginal when I CaL alternans were small even though the high pacing frequency. Thus, these results are in agreement with the observed failure of the high pacing rate to produce alternans (Fig. 3c) and the close relationship between APD and CaT alternans demonstrated in Fig. 3a,b.
The Ca 2+ release channel recovery is also sensitive to membrane potential oscillations 9 . Therefore, there is a possibility that an alternating Ca 2+ release controlled by ryanodine recovery could also directly contribute to the observed I CaL alternans. In order to assess this issue, whole cell patch clamp experiments were devised where 10 mM EGTA was employed to buffer Ca 2+ i (Supplementary Fig. S4). In the absence of Ca 2+ release the average of I CaL alternans did not differ from those that were measured in the presence of intact Ca 2+ handling (presented in Fig. 4) indicating major role of membrane potential in the development of I CaL alternans (140 ms-EGTAfree: 7.3 ± 1.2% vs EGTA: 6.5 ± 1.3%. 180 ms-EGTA-free: 25.7 ± 6% vs EGTA: 21.3 + 3%. 200 ms-EGTA-free: 41.4 + 4% vs EGTA: 45.5 ± 7%. n(EGTA-free) = 9, n(EGTA) = 6)).

Recovery of the I CaL .
A further important question is the behavior of I CaL during the fast phase of the restitution curve. This issue was investigated by whole-cell patch clamp omitting Ca 2+ buffer from the pipette solution (Fig. 5). The description of the recovery protocol can be found in the Methods section. We found that during the first 30 ms of the DI, where the APD restitution is the fastest, the I CaL recovers only 20.7 ± 2.4% www.nature.com/scientificreports/ (n = 11) providing relatively small (0.6 ± 0.08 pA/pF, n = 11) current (Fig. 5b,c). These results indicate that I CaL has restricted contribution to the initial, rapid phase of restitution.

I CaL inhibition suppresses alternans without influencing the initial phase of restitution.
In order to further investigate the role of I CaL in the restitution, action potential measurements were performed in multicellular tissue. 1 µM nisoldipine was employed to inhibit selectively the I CaL (Fig. 6). At first, the restitution protocol was applied at 500 ms of BCL then the alternans protocol was used from 250 to 190 ms BCLs. Administration of 1 µM nisoldipine suppressed the APD 90 alternans at 250 ms of BCL (7.5 ± 1.2 ms vs 3.8 ± 0.8 ms; p < 0.05, n = 7, not shown in the figure). The APD 25 alternans were reduced at 250 ms (14.7 ± 4.6 ms vs 4.4 ± 0.9 ms; p < 0.05, n = 7/7 hearts), at 230 ms (13 ± 3.1 ms vs 3.1 ± 1 ms; p < 0.05, n = 7), and at 210 ms (10.8 ± 2.6 ms vs 4.7 ± 0.7 ms; p < 0.05, n = 7, Fig. 6a,b). We found that 1 µM nisoldipine significantly shortened the baseline APD 90 (187 ± 5 ms vs 159 ± 5 ms; p < 0.05, n = 7, bar graphs). In contrast, I CaL inhibition failed to change the initial phase of the restitution steepness but changed it at DIs larger than 60 ms (Fig. 6b,c). Dynamic restitution was calculated from the APD alternans protocol and the effect of nisoldipine was investigated on the restitution slope. It was found that 1 µM nisoldipine does not alter the dynamic restitution slope (1.31 ± 0.1 vs 1.2 ± 0.1; n = 7; Figure not shown).

Discussion
The major findings of this study are the followings: (1) in tissue AP measurements, the development of AP alternans could be evoked irrespective of the restitution slope, suggesting a minor fidelity of restitution curve in prediction of alternans.  www.nature.com/scientificreports/

Has any role of restitution in the alternans development?
The general view is that membrane voltage-driven alternans are determined by a single parameter: APD restitution 5 . The restitution quantifies the relationship between APD and preceding DI. The major factors governing APD restitution are recovery from inactivation of the inward currents and deactivation of outward currents, as well as Ca 2+ cycling also affects restitution through Ca 2+ dependent currents 28 . Our results, similar to those that were reported in other previous studies 1, 18 , do not support previous assumption by Nolasco and Dahlen suggesting that the steepness of restitution reflects the susceptibility of alternans 17 . The restitution hypothesis claims that alternans will occur when the restitution slope is larger than 1. In our tissue AP measurements, the restitution steepness did not influence the development of alternans (i.e. could be triggered regardless of the restitution steepness), rather the basic cycle length: alternans occurred in all cases (20/20 experiments) when the BCL was 250 ms or shorter. In our experiments, alternans occurred even if the restitution steepness (S1S2 or dynamic) was smaller than 1, however, the extent of alternans was weakly/moderately connected to restitution steepness. These results suggest that restitution steepness may have little fidelity in prediction of development of cardiac alternans. At the same time, it is important to note that several transmembrane ionic currents having potential role in alternans development do not contribute to the rapid restitution phase equally 29 . The idea that alternans may have a restitution-independent cause has been recognized by Wu and Patwardhan. Using a feedback-based pacing protocol where diastolic intervals were selected explicitly and independently of APDs it was possible to investigate whether alternans occur when diastolic intervals preceding each AP do not change 30 . It was shown that identical diastolic intervals were also followed by APD alternans claiming that diastolic interval dependent restitution may not be directly linked to alternans development 30 . Do CaT alternans require action potential alternans? Our current clamp experiments (Fig. 3) revealed a close relationship between APD and CaT alternans. This correlation implies that membrane potential www.nature.com/scientificreports/ or Ca 2+ could be a potential driver of the alternans, however when membrane potential did not alternate the beat-to-beat CaT remained also unaltered. A bidirectional coupling exists between AP and Ca 2+ -handling, and I CaL is a major determinant of both actual APD and Ca 2+transients. When the Ca 2+ i alternates, it significantly alters the APD via the balance of I CaL and I NCX causing positive or negative Ca 2+ to Vm coupling 31 .
Several voltage-clamp studies reported that notable Ca 2+ transient alternans were observed in the presence of non-alternating AP sequence [13][14][15][16] . These results were interpreted as the alternans were arose directly from the Ca 2+ handling dynamics and not only the passive response of the beat-to-beat alternans of the AP 13 . In contrast, the data of this study indicate that membrane potential (i.e. AP alternans) is required for the development of CaT alternans in our experiments, and may support the important role of I CaL and the bidirectional coupling between AP and Ca 2+ handling in the development of alternans. I CaL fluctuation is able to ignite CaT alternans. Previous results are controversial regarding the role of I CaL in APD alternans initiation: the incomplete time-dependent recovery of I CaL was found to cause alternans in several studies 8,21,32,33 . In a computer modelling study of ischaemic myocytes, alternans have been proposed to appear due to the interplay of I CaL and potassium transient outward currents 34 . In our previous study we found that selective Na + /Ca 2+ exchanger inhibition decreased alternans without influencing the restitution slope while indirectly inhibits I CaL 35 .
In contrast, several papers found in both atrial and ventricular myocytes that alternans can occur while peak I CaL remained unchanged from beat to beat [14][15][16]36,37 . Additionally, numerous papers demonstrated mechanical and CaT alternans in the absence of AP alternans 2,13,14,16,37 . . Nisoldipine reduced the steady-state APD 90 (bar graphs) measured at 500 ms BCL. (b) Represents a comparison between nisoldipine effect on restitution steepness (left y-axis) and on APD 25 alternans (right y-axis) at a BCL of 500 ms. The nisoldipine reduced the slope of the restitution (green versus red curves) only in a slow phase, at DIs larger than 70 ms (significance marked with *). The APD 25 alternans were significantly reduced at 250, 230, and 210 ms (green versus red symbols, significance marked with #). (c) Depicts APD 90 restitution under control (red curve) and in the presence of 1 µM nisoldipine (green curve) at a BCL of 500 ms. However, the APD 90 shortening after nisoldipine administration is clear, we can observe that the steepness of the curve primarily reduced at the slow phase. www.nature.com/scientificreports/ In our experiments we found that oscillation of the I CaL recovery time (that is often developed during alternans) is able to induce I CaL peak fluctuation-as was expected, and the relationship between I CaL and CaT amplitude alternans was closely coupled (Fig. 4). In line with previous results demonstrated in Fig. 3, the high pacing rate per se was insufficient again to induce CaT alternans, since when I CaL alternans were small the corresponding CaT alternans were also restricted. The magnitude of I CaL alternans was not altered even if the Ca 2+ i was buffered ( Supplementary Fig. S4) indicating the membrane potential origin of the I CaL fluctuations.
At the same time, it is important to note that AP morphology and alternans influence the SR Ca 2+ content and the efficiency of the excitation-contraction coupling 21 . Therefore, the actual SR Ca 2+ content-together with I CaL -may have important contribution to the development of alternans 15 , however, this was out of the scope of this study.

Does I CaL contribute to alternans development in a restitution independent manner?
Since previous experiment showed that I CaL can induce CaT alternans via alterations of the recovery period (i.e. voltage-dependent manner) the relationship of I CaL with the restitution slope was investigated. Several papers reported that I CaL is an important contributor of the restitution slope [38][39][40] .
In order to address this question the I CaL kinetics was investigated under different recovery intervals. Our current measurement in the presence of unbuffered intracellular solution revealed that under short diastolic intervals-that corresponds to the fast phase of restitution-the recovered fraction of the I CaL is relatively low (Fig. 5). Similarly, our tissue AP experiments with 1 µM nisoldipine (Fig. 6) demonstrated that selective I CaL inhibition does not influence the fast phase of the restitution curve. This fact, in line with previous report 41 , may indicate that I CaL has a minor role in shaping the fast phase of the restitution, presumably because highly incomplete recovery allows small I CaL during short diastolic intervals. Furthermore, according to previous study 42 , the failure of nisoldipine to change restitution steepness could be also attributable to the relatively small effect on the baseline APD (~ 20%). Previous paper also reported no change in the time constant of electrical restitution of human ventricle after application of 1 µM nisoldipine in human 29 . At the same time, in line with our results, a numerical simulation demonstrated that I CaL suppression reduces alternans 32 .
Previous studies reported that I CaL blocker verapamil flattened the restitution curve 38,39 , however it is known that it also inhibits the I Kr in submicromolar level 43,44 that was not taken into account in those studies. I Kr suppression was reported to flatten restitution 42 , while in contrast, dihydropyridines did not inhibit the I Kr 43,44 . Therefore, verapamil could not be considered as a suitable tool to assess the role of I CaL in restitution, and its additional I Kr suppressing effect makes the data interpretation difficult.
Possible role of cardiac memory. Cardiac memory is a term introduced by Rosenbaum et al. 45 . The short term cardiac memory reflects the effect of pacing "history" on the APD, therefore, the relationship of alternans and APD restitution is complicated by the possible presence of the short-term cardiac memory. In our measurements the S1S2 restitutions measured at different BCLs and dynamic restitutions are different ( Supplementary  Fig. S3), indicating the presence of memory in the system. Several studies claimed that the presence of cardiac memory decreases the reliability of the restitution in prediction of alternans 46,47 . Therefore in our experiments the cardiac memory could be also an important contributor that reduces the coupling between alternans and restitution slope.

Conclusion
In this study we found that I CaL has minor contribution in shaping the fast phase of restitution curve. This suggest that I CaL -if it contributes to the mechanism of alternans-could be an additional factor that attenuates the reliability of APD restitution slope to predict alternans.
Since I CaL can induce alternans in voltage-dependent manner (i.e. by the change of the recovery period) it could contribute to the development of a voltage-driven alternans that are largely independent of restitution.

Limitations
The alternans-restitution comparison was investigated in endocardial tissue therefore it does not represent the whole heart. Other cell layers, such as midmyocardial cells or Purkinje fibers may exert different behavior.