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(Circulation Research. 2004;94:650.)
© 2004 American Heart Association, Inc.

Cellular Biology

Sarcoplasmic Reticulum Calcium Content Fluctuation Is the Key to Cardiac Alternans

Mary E. Díaz, Stephen C. O’Neill, David A. Eisner

From the Unit of Cardiac Physiology, School of Medicine, University of Manchester, Manchester, UK.

Correspondence to David A. Eisner and Mary E. Díaz, Unit of Cardiac Physiology, School of Medicine, University of Manchester, 1.524 Stopford Building, Oxford Road, Manchester M13 9PT, UK. E-mail eisner{at}man.ac.uk and mary.e.diaz@man.ac.uk

	Abstract

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The aim of this work was to investigate whether beat-to-beat alternation in the amplitude of the systolic Ca²⁺ transient (Ca²⁺ alternans) is due to changes of sarcoplasmic reticulum (SR) Ca²⁺ content, and if so, whether the alternans arises due to a change in the gain of the feedback controlling SR Ca²⁺ content. We found that, in rat ventricular myocytes, stimulating with small (20 mV) depolarizing pulses produced alternans of the amplitude of the Ca²⁺ transient. Confocal measurements showed that the larger transients resulted from propagation of Ca²⁺ waves. SR Ca²⁺ content (measured from caffeine-evoked membrane currents) alternated in phase with the alternans of Ca²⁺ transient amplitude. After a large transient, if SR Ca²⁺ content was elevated by brief exposure of the cell to a Na⁺-free solution, then the alternans was interrupted and the next transient was also large. This shows that changes of SR Ca²⁺ content are sufficient to produce alternans. The dependence of Ca²⁺ transient amplitude on SR content was steeper under alternating than under control conditions. During alternation, the Ca²⁺ efflux from the cell was also a steeper function of SR Ca²⁺ content than under control. We attribute these steeper relationships to the fact that the larger responses in alternans depend on wave propagation and that wave propagation is a steep function of SR Ca²⁺ content. In conclusion, alternans of systolic Ca²⁺ appears to depend on alternation of SR Ca²⁺ content. This, in turn results from the steep dependence on SR Ca²⁺ content of Ca²⁺ release and therefore Ca²⁺ efflux from the cell as a consequence of wave propagation.

Key Words: calcium • excitation-contraction coupling • alternans • sarcoplasmic reticulum

	Introduction

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Sudden death due to arrhythmias accounts for up to 50% of deaths in heart failure.¹ These arrhythmias may be due to problems of Ca²⁺ handling^2,3 by the sarcoplasmic reticulum (SR), the main source of Ca²⁺ for cardiac contraction. Ca²⁺ release occurs via Ca²⁺-induced Ca²⁺ release (CICR) triggered by Ca²⁺ entry on L-type Ca²⁺ channels.⁴ One abnormality of Ca²⁺ handling is mechanical alternans where large and small contractions follow each other^5–7 due to alternation of systolic Ca²⁺.^8,9 Alternans is prominent in heart failure^5,10,11 and is induced by ischemia and acidosis.^7,12,13 Action potential alternans (T-wave alternans) predisposes to arrhythmias^14,15 and may be due to changes of Ca²⁺ handling.¹⁶

Despite the importance of Ca²⁺ alternans, there is no consensus as to its origin. Recent work has shown that the Ca²⁺ transient is not spatially homogenous throughout the cell during alternans. Work on atrial cells,¹⁷ where there are no transverse tubules, found that alternans could be induced by metabolic inhibition. Under these conditions the Ca²⁺ transient in the periphery of the cell occurred on both the large and small responses. However, normal propagation into the center of the cell was only seen on the large response.¹⁷ In ventricular cells, depression of the activity of the ryanodine receptor (RyR) with either tetracaine or acidosis resulted in alternans.¹³ Under these conditions, depolarization produced an initial, relatively uniform increase of [Ca²⁺]_i throughout the cell. This was, however, followed by a further rise in certain regions of the cell that then propagated as a "mini wave" through part of the cell. Alternation occurred because a region with a large release on one stimulus had a small one on the next. These studies therefore implicate the RyR in the genesis of alternans.

The above work leaves unanswered the fundamental question of what causes alternans? Alternation of the amount of Ca²⁺ released from the SR could be due to beat-to-beat changes in either (1) SR Ca²⁺ content or (2) the properties of the Ca²⁺ release process. On the former model, SR content could change because less Ca²⁺ is pumped out of the cell on the small compared with the large Ca²⁺ transient, and therefore, more Ca²⁺ is available for release on the next beat. This might therefore account for the fact that the next beat is large and hence for the alternation. The steeper the dependence of Ca²⁺ release on SR Ca²⁺ content, the more likely alternans would be to occur.^18,19 However, in cat atrial cells it has been reported that the SR Ca²⁺ content (as judged by the amplitude of the caffeine-evoked increase of cytoplasmic Ca²⁺ concentration) is the same after the small and large transients.¹⁷ In our studies of alternans produced by tetracaine, we estimated the likely size of the changes of SR Ca²⁺ content by measuring the fluxes on Na⁺-Ca²⁺ exchange (NCX). We concluded that a change of only a few percent of the SR Ca²⁺ content would occur. However, as mentioned earlier, the large release in alternans is due to a wave of Ca²⁺ and previous work has shown the existence of a clear threshold for wave initiation.²⁰ It is therefore possible that small changes of SR content may be very important.

The purpose of the work in this article was therefore to measure changes of SR Ca²⁺ content and sarcolemmal fluxes in alternans. In order to do this, we have produced a simple reliable means to initiate alternans using small depolarizing pulses. The results show that systolic Ca²⁺ alternans correlates with alternating SR Ca²⁺ content. Depression of RyR opening results in Ca²⁺ waves producing steep dependence of Ca²⁺ release on SR Ca²⁺ content resulting in alternans of systolic Ca²⁺ transient amplitude. Alternans is favored because the threshold nature of waves makes Ca²⁺ release a steep function of SR content.

	Materials and Methods

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Ventricular myocytes were isolated from adult Wistar rats with a standard (collagenase/protease) digestion technique.¹³ Membrane currents were monitored using the perforated patch technique with amphotericin-B.²¹ The pipette solution contained (in mmol/L) KCH₃O₃S₃ 125, KCl 20, NaCl 10, HEPES 10, and MgCl₂ 5; titrated to pH 7.2 with KOH and amphotericin-B (added to a final concentration, 240 µg/mL). The extracellular solution contained (in mmol/L) NaCl 135, Glucose 11, CaCl₂ 1 or 5, HEPES 10, MgCl₂ 1, and KCl 4; titrated to pH 7.4 with NaOH. To avoid interference from outward currents, the control solution also contained 5 mmol/L 4-aminopiridine and 0.1 BaCl₂. Membrane potential was held at -40 mV. Test depolarizing pulses of 100 ms duration from -40 to 0 mV (control pulses) or from -40 to -20 mV (reduced trigger pulses) were applied at 0.33 to 0.5 Hz. Resulting signals were digitized at 2.5 kHz and stored using pCLAMP software (Axon Instruments). Changes in cytoplasmic-free Ca²⁺ ([Ca²⁺]_i) were monitored using fluo-3 or fluo-5F. The myocytes were loaded with the acetoxymethyl form of these Ca²⁺ indicators. Where applicable, fluorescence was calibrated in terms of [Ca²⁺]_i as previously described.²² Confocal image acquisition was performed on a confocal microscope (BioRad MRC 1024) with a 100 mW Argon Ion laser attached to an inverted Nikon microscope (Nikon Diaphot) and a Nikon 60x oil immersion objective (NA 1.4). Fluorescence was excited at 488 nm, and the emission was collected at wavelengths longer than 515 nm. Scanning was performed in linescan mode. Confocal imaging and electrophysiological signal acquisition were synchronized such that each depolarizing step took place 100 ms after the beginning of the corresponding linescan. All experiments were performed at room temperature. The image data were analyzed using Confocal Assistant (brelje@lenti.med.umn.edu) and ImageJ (NIH Image software) as well as custom written software. Ca²⁺ fluxes were calculated by integrating membrane currents as described previously²³ and the SR Ca²⁺ content by adding 10 mmol/L caffeine to release Ca²⁺ from the SR and integrating the resulting NCX current.²⁴ In the experiment of Figure 3, the gain of Ca²⁺ by the SR was calculated by adding up, on a pulse-by-pulse basis, the measured Ca²⁺ efflux on NCX and an assumed Ca²⁺ influx.²⁵

View larger version (15K): [in this window] [in a new window]   Figure 3. SR content changes during alternans development. A, Original record. Caffeine (10 mmol/L) was applied before the record began to empty the SR. After removal of caffeine, stimulation was recommenced at the start of the record. B, Calculated efflux on each pulse from the integral of the NCX current (see Figure 1C).23 C, Estimated SR Ca2+ content (see text; an influx of 4.6 µmol/L was assumed to balance the mean efflux during alternans).

View larger version (45K): [in this window] [in a new window]   Figure 1. Systolic Ca2+ alternans. A, Linescans in response to 3 consecutive voltage pulses (top). Linescans are aligned with time horizontally. B, Ca2+ transients obtained by measuring the mean cellular fluorescence from 10 consecutive Ca2+ transients. C, Averaged membrane current records corresponding to large (black) and small (red) Ca2+ transients. Note that the L-type Ca2+ current is the first downward deflection on the current trace. NCX current develops after repolarization. Inset shows the L-type Ca2+ current on an expanded time scale.

	Results

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Stimulation With Low Amplitude Pulses Produces Alternans
Previous work has shown that agents that decrease the ryanodine receptor (RyR) open probability (P_o) such as the local anesthetic tetracaine or acidification produce alternans.¹³ We wished to avoid using pharmacological interventions and reasoned that we could reduce RyR P_o using a small (20 mV) depolarizing pulse, to reduce the L-type Ca²⁺ trigger. Using a small pulse decreases the amplitude of the Ca²⁺ transient, and we therefore restored it by elevating external Ca²⁺ concentration from 1 to 5 mmol/L. The confocal image of Figure 1A shows that this protocol did, indeed, produce alternans of systolic Ca²⁺. A large Ca²⁺ release is observed in the first and third images but is absent in the second, where only sparks of Ca²⁺ release are present. This also demonstrates that the large responses are not uniform but, rather, begin in discrete places and then spread as waves throughout the rest of the cell. Alternans of contraction is evident by the lack of shortening of the cell (vertical direction of the linescan) in the middle panel. The Ca²⁺ alternans is emphasized by Figure 1B, which shows the profile of release obtained for the whole of the image for 10 consecutive pulses. Figure 1C shows also that the Ca²⁺ current (I_Ca) is identical for big and small transients (emphasized in inset). Note that the small amplitude of the current is due to the small size of the depolarizing pulse. In six of the cells studied, we compared the amplitude of the Ca²⁺ current at -20 mV with that at 0 mV and found peak amplitudes of 29±5 and 355±67 pA, respectively. The big releases, however, are associated with greater loss of Ca²⁺ on NCX. These differences in Ca²⁺ efflux show that the cell loses more Ca²⁺ during the large than the small transients.

Measurement of SR Ca²⁺ Content During Alternans
The measurement of extra Ca²⁺ efflux during the large releases raises the possibility that this decreases the SR Ca²⁺ content and accounts for the alternans. Therefore, the next series of experiments was designed to measure the SR Ca²⁺ content associated with big and with small releases. In other words, is the content of the SR larger before a big than before a small Ca²⁺ release? A typical example is shown in Figure 2A. In this study, we interrupted stimulation and applied 10 mmol/L caffeine either at the time that a small (left) or large (right) release was expected and measured both changes in cytoplasmic Ca²⁺ (Figure 2A) and the associated membrane currents as Ca²⁺ is pumped out of the cell (Figure 2B). Because under these conditions Ca²⁺ extrusion takes place mainly on NCX and this is electrogenic, we calculated SR Ca²⁺ load by integrating the resulting NCX current and correcting for nonelectrogenic Ca²⁺ efflux pathways and cell volume.²⁰ The results (Figure 2C) show that the SR Ca²⁺ content associated with a large release is 1.24±0.04-fold (mean±SEM, n=10; P<0.01) greater than that with a small release. This change of SR Ca²⁺ is associated with a 5.1±0.7-fold difference (n=10) in the amplitude of the systolic transient (Figure 2D).

View larger version (21K): [in this window] [in a new window]   Figure 2. SR Ca2+ content changes during alternans. A, Stimulation was stopped after either a large (left) or small (right) transient. Caffeine (10 mmol/L) was applied at the time when the next stimulus would have occurred. Caffeine-evoked increase of [Ca2+]i is greater in the right panel when a large transient would have been expected. B, Caffeine-evoked NCX currents (top) and their integrals (bottom). C, Mean data. SR Ca2+ content measured from the integrated NCX current is greater before a big than a small transient. D, Histogram showing the mean amplitudes of small and large transients during alternans.

Is the measured increase of SR content sufficient to account for that of systolic [Ca²⁺]_i? Previous work has found that the Ca²⁺ transient amplitude is proportional to the third power of SR Ca²⁺ content.²⁵ However, the data of Figures 2C and 2D show that the apparent dependence of Ca²⁺ transient amplitude on SR Ca²⁺ content during alternans is much steeper (proportional to 7.2±1.3 power of SR Ca²⁺). The question therefore arises as to the origin of this steep dependence during alternans?

Relationship Between SR Content, Ca²⁺ Transient Amplitude, and Ca²⁺ Efflux
In the experiment of Figure 3, the SR had been emptied by exposure to 10 mmol/L caffeine. Caffeine was then removed in the absence of stimulation. Stimulation initially produced a very small Ca²⁺ transient which then slowly increased in amplitude (Figure 3A). Eventually the amplitude of the Ca²⁺ transient began to alternate. Figure 3B shows that the Ca²⁺ efflux from the cell was initially very small, then gradually increased before finally beginning to alternate in parallel with the amplitude of the Ca²⁺ transient. We assume that by the end of the record of Figure 3B the cell is in a steady state with respect to Ca²⁺, and therefore, the mean entry of Ca²⁺ is equal to the mean efflux. The mean efflux can be calculated from the average of the efflux on the small and large transients and here is equal to 4.6 µmol/L cell per pulse. We assume that the influx per cycle is constant and equal to this value. From this calculated Ca²⁺ influx and the measured effluxes, we can calculate the gain of Ca²⁺ by the SR (Figure 3C). Comparison of Figures 3A and 3C predicts that, as SR Ca²⁺ rises from 0 to 80 µmol/L, there is a small increase of systolic Ca²⁺ but then a modest further increase of SR Ca²⁺ is associated with larger transients and marked alternans. The expanded SR content trace (Figure 3C, inset) shows that alternans in the Ca²⁺ transient amplitude is associated with a predicted small alternans of SR content. Again, however, small fractional changes of SR content occur with much larger changes of systolic Ca²⁺.

Figure 4A shows the amplitude of the Ca²⁺ transient plotted as a function of SR content. It is clear that before alternans begins (open circles) the Ca²⁺ efflux is a smooth function of SR content but that, during alternans (filled circles), the transient becomes a much steeper function of content. The origin of this increased steepness is suggested by the linescans of Figure 1A. The larger Ca²⁺ transients involve wave propagation and previous work has shown that wave propagation only occurs above a threshold SR Ca²⁺ content.²⁰ It is likely that it is this threshold nature of wave propagation that produces the steep dependence of amplitude on SR content.

View larger version (16K): [in this window] [in a new window]   Figure 4. The dependence on SR Ca2+ content of the amplitude of the systolic Ca2+ transient (A) and the efflux on NCX (B). Data for A were from the experiment of Figure 3 and for B from another experiment.

Previous modeling has suggested that alternans is favored if the gain of the processes controlling SR Ca²⁺ content increases.¹⁸ An increase of SR Ca²⁺ content increases the amplitude of the systolic Ca²⁺ transient^26,27 and therefore the Ca²⁺ efflux from the cell on NCX.²³ This feedback normally serves to control the SR Ca²⁺ content.²⁸ However, as is the case for other feedback mechanisms, if the feedback gain (in this case the dependence of Ca²⁺ efflux on SR content) is too steep, then the feedback becomes unstable as small SR content changes will produce large fluxes of Ca²⁺ across the cell membrane thereby leading to big changes of SR content and consequently instability. Does this occur in alternans? Figure 4B plots the Ca²⁺ efflux from the cell as a function of SR content for an experiment similar to that of Figure 3. Before alternans occurs (open circles) this relationship can be approximated to a straight line that had a mean slope of 0.020±0.003 in 6 cells. In other words, the change of Ca²⁺ efflux is only 2% of the initiating change of SR content, a low feedback gain. In contrast, when alternans begins, the slope increases to 0.93±0.2 (n=6). These data therefore show that alternans is, indeed associated with an increase of the gain of the feedback.

If alternans is due to a steep dependence of efflux on SR content, one would predict that increasing SR Ca²⁺ following a large Ca²⁺ transient should interrupt the alternans and make the next transient also large. This was examined in Figure 5A by removing external Na⁺ after a large pulse. In this experiment, Na⁺ was removed from the superfusing solution for 160 ms. However the finite time for solution exchange means that the cell will be exposed to an intermediate Na⁺ concentration. There is an outward shift of holding current (not shown), indicating that the Na⁺ concentration sensed by the cell decreased 400 ms before the next pulse. Integrating this current gave a mean charge of 12.0±2.8 pC. If this corresponds to Ca²⁺ entering the cell on NCX, then we calculate a Ca²⁺ gain of 5.3±1.3 µmol/L (n=6). Previous work found that not all of this shift of current is due to NCX²⁹ and therefore this integral gives an overestimate of the increase of cell Ca²⁺. We conclude that an increase of cell Ca²⁺ of less than 5 µmol/L is sufficient to remove alternans and therefore that the measured changes of SR Ca²⁺ content are sufficient to account for alternans.

View larger version (19K): [in this window] [in a new window]   Figure 5. Na+ removal between pulses removes alternans. A, External Na+ was removed (replaced by LiCl) as indicated. B, Specimen records corresponding to the indicated transients in A.

	Discussion

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The data in this article show that in a model of alternans produced by decreasing the amplitude of the depolarizing pulse, alternans is accompanied by a measurable change in the SR Ca²⁺ content. In turn, these changes of SR content are due to changes in the Ca²⁺ efflux from the cell as a consequence of the alternation of Ca²⁺ transient amplitude. We suggest that alternans is favored because, due to the reduced opening of L-type Ca²⁺ channels, most of the RyRs are not activated directly by Ca²⁺ entering the cell via the L-type current but, instead, by Ca²⁺ waves. These waves can only occur above a threshold SR content and the alternans results as the efflux associated with the large Ca²⁺ transients decreases SR content below the threshold. Finally, we show that the dependence of Ca²⁺ efflux from the cell on SR Ca²⁺ content is greatly increased under alternating conditions. These results provide experimental evidence in support of the hypothesis¹⁸ that alternans arises because of increased feedback gain in the processes normally responsible for controlling SR Ca²⁺ content. To the best of our knowledge, this is the first study to quantify SR Ca²⁺ content or the relationship between content and Ca²⁺ efflux from the cell under alternating conditions.

Small Depolarizing Pulses as a Means of Producing Alternans
Our experiments show that decreasing the amplitude of the voltage clamp pulse (in the presence of 5 mmol/L external Ca²⁺) results in a highly stable and reproducible alternans. This is a convenient model for two reasons: (1) it does not require pharmacological interventions and therefore is simple to analyze, and (2) in contrast to high frequency stimulation, which is often used to induce alternans,⁶ the interval between pulses is sufficient to permit measurements of SR Ca²⁺ content using the caffeine-release technique. One interesting feature of this model is that the entry of Ca²⁺ on the Ca²⁺ current in these experiments is less than the efflux via NCX. It is likely that with such small Ca²⁺ currents, the balance is due to a continuous entry of Ca²⁺ into the cell on some other mechanism.

The confocal measurements (Figure 1) show that the larger Ca²⁺ transients in the alternation are not spatially uniform but, rather, begin in discrete points in the cell and propagate as waves throughout the cell. In contrast, the smaller Ca²⁺ transients show no waves and only an increased frequency of Ca²⁺ sparks. The involvement of Ca²⁺ waves in this model of alternans is similar to that observed previously in alternans produced by tetracaine or acid intracellular pH,¹³ maneuvers that decrease the RyR P_o. We have suggested that tetracaine or acid decrease the number of RyRs activated by the L-type Ca²⁺ current such that only a small number of RyRs are initially opened. If the SR Ca²⁺ content is above a threshold level, then a wave of Ca²⁺ release will propagate resulting in a large response. This large response will result in a large Ca²⁺ efflux from the cell and thereby decrease SR content such that no wave occurs on the next pulse, and therefore the Ca²⁺ transient is small. In the case of depolarization with small pulses, only a small number of L-type channels open resulting, therefore, in the opening of only a small number of RyRs. If the SR Ca²⁺ content is sufficient, then a wave occurs. Again, the consequent loss of Ca²⁺ from the cell decreases SR Ca²⁺ content such that no wave occurs on the next pulse. One important question is whether the number of L-type Ca²⁺ channels that open is small enough to account for the observed initiation of only a small number of waves. Ideally, we would like to know the probability of opening of these channels at -20 mV with Ca²⁺ as a charge carrier. Unfortunately, there is little data in the literature and the open probability at -20 mV is very sensitive to small shifts in the activation curve. Values of the order of 0.03 have been obtained,^30,31 and the mean channel open time is 0.27 ms. The initial sparks that result in waves occur within about 10 ms of the start of the depolarization. The low open probability means that it is unlikely that a given channel will have opened more than once during this period. The single channel current is about 0.4 pA.^30,32 Assuming a mean channel open time of 0.27 ms, then each pC of charge carried by the L-type channel corresponds to the opening of 9300 channels. At -20 mV, the L-type channel has a peak amplitude of 29 pA. Ignoring the activation time, then this means that after 10 ms, 0.29 pC of charge will have moved, and therefore, 2685 L-type channels in the cell will have opened. Ca²⁺ sparks are of the order of 2 µm in diameter, and therefore, the confocal scan line will sample any spark occurring within a cross-sectional area of about 3 square µm.³³ A rat myocyte has width and depth of 32 and 13 um³⁴ giving a cross-sectional area of 416 µm² such that 3/416=0.7% of sparks will be seen by a single scan line. We would therefore expect 20 sparks per linescan. In a cell 150 µm in length, this corresponds to one spark every three or so sarcomeres. There are many uncertainties in this calculation but it does show that it is reasonable that small depolarizing pulses should only activate a small number of sparks.

One interesting difference between alternans produced by small depolarizing pulses compared with that seen in tetracaine or acidosis is that, in tetracaine, there is a regional alternans that can differ in phase between different regions of the cell, whereas with small depolarizing pulses, the alternans is more global. Our hypothesis for alternans is that the L-type Ca²⁺ channels activate a group of nearby (coupled) RyRs and that Ca²⁺ release from these coupled RyRs will then activate more distant RyRs. On this hypothesis, small depolarizing pulses will decrease the probability of the coupled RyRs opening but will not affect the more remote RyRs. Therefore, the small depolarizing pulse should not interfere with the ability of Ca²⁺ release from coupled RyRs leading to wave propagation. In contrast, tetracaine will affect all RyRs and may therefore depress wave propagation throughout the cell. This may result in waves failing to propagate beyond a certain point and, therefore, to the local responses seen in tetracaine.

Role of SR Ca²⁺ Content in Alternans
In our previous work on tetracaine or acid-induced alternans, the alternans was inhomogeneous throughout the cell and different regions of the same cell alternated out of phase with each other.¹³ This meant that global measurements of SR Ca²⁺ content would have had no relevance to the origin of alternans. In the present model, however, the alternans is much more homogeneous. We find that the SR Ca²⁺ content, as assessed by the caffeine-evoked NCX current integral is greater at the time of the large than the small Ca²⁺ transient (Figure 2). That the change of SR Ca²⁺ has a causal role in producing alternans is shown by the result (Figure 5) that increasing Ca²⁺ entry into the cell (by exposure to Na⁺-free solution) following a large response interrupts the alternans and makes the next response large. Because this maneuver has no effect on resting [Ca²⁺]_i, we conclude that only SR Ca²⁺ has increased and therefore that the calculated small change of SR Ca²⁺ is, indeed, sufficient to account for alternans. It is noteworthy that the alternans of SR content differs from the result found in cat atrial cells where no change of SR content was reported.¹⁷ This may reflect a difference between the mechanisms that produce alternans in the atrium compared with the ventricle. However, it should also be noted that the atrial study used the caffeine-evoked rise of fluo-3 fluorescence that may be a less sensitive measure of SR content than the integrated NCX current used in the present study.

Our data show that, on average, during alternans, the amplitude of the systolic Ca²⁺ transient is a steep (7.2 power) function of SR Ca²⁺ content. This is a much steeper dependence than is seen under nonalternating conditions.²⁵ The steepness of the dependence of the Ca²⁺ transient amplitude on SR content in alternans is confirmed by the indirect estimates of SR content obtained from membrane fluxes in Figure 4 showing that the slope changes abruptly when alternans begins. We suggest that this increased steepness is due to the threshold-like dependence on SR Ca²⁺ content of wave propagation.

Feedback Gain in Alternans
Under normal conditions, the SR Ca²⁺ content is controlled by the fact that an increase of content results in increased efflux from and decreased influx into the cell.^18,23 This constitutes a feedback system in which the feedback gain can be defined as follows:

Note that this feedback gain should not be confused with the "gain" of calcium-induced calcium release from the SR. The higher this feedback gain is, the more tightly one would expect SR content to be controlled. However, modeling has suggested that too high a feedback gain may lead to alternans.^18,19 In the present study, we have measured this feedback gain directly and found that, indeed, it is greater under alternating conditions. This result does not mean that other factors are not also important in determining whether alternans occurs¹⁹ but lends support to the idea that the feedback gain is, indeed, relevant.

Relevance to Other Models of Alternans
As discussed earlier, we suggest that alternation occurs because the threshold nature of wave propagation makes Ca²⁺ release and therefore efflux from the cell a steep function of SR content. If SR Ca²⁺ content is below a threshold value, Ca²⁺ release will be localized to the regions near the few L-type channels that open. If the SR Ca²⁺ is greater, then waves of Ca²⁺ release can spread throughout the cell from the sites of initial release thereby activating a larger Ca²⁺ transient. In this article, we have only studied alternans produced by small depolarizing pulses. However, decreasing RyR P_o, with either tetracaine or acidification,¹³ also produces alternans accompanied by wave propagation, and it is therefore likely that the model of increased feedback gain due to wave propagation accompanying alternation of SR Ca²⁺ content would also be valid under such conditions. An important question concerns whether these conclusions are relevant to clinically observed mechanical alternans. In this context, it is important to note that some work has found that heart failure is associated with either decreased expression of the RyR^35,36 or decreased coupling between the sarcolemmal L-type Ca²⁺ current and the RyR^37,38 associated with spatially nonuniform Ca²⁺ release.³⁹ Furthermore, ischemic regions will be acidotic, and this would be expected to decrease RyR P_o. These changes might be expected to produce the conditions required for Ca²⁺ alternans.

In summary, decreasing the opening of the RyR, either by direct modulation with tetracaine or acidosis¹³ or, indirectly, by decreasing the number of L-type channels that open (this study), leads to a situation where large amplitude Ca²⁺ transients can only occur as a result of wave propagation. The Ca²⁺ loss from the cell on these waves decreases SR Ca²⁺ content to a level insufficient for wave propagation resulting in the next transient having a small amplitude and alternans therefore develops.

	Acknowledgments

 
This work was supported by grants from the British Heart Foundation.

	Footnotes

 
Original received December 11, 2003; revision received January 15, 2004; accepted January 22, 2004.

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