Mechanisms Underlying the Formation and Dynamics of Subcellular Calcium Alternans in the Intact Rat Heart
Optical mapping of intact cardiac tissue reveals that, in some cases, intracellular calcium (Ca) release can alternate from one beat to the next in a large-small-large sequence, also referred to as Ca transient (CaT) alternans. CaT alternans can also become spatially phase-mismatched within a single cell, when one part of the cell alternates in a large-small-large sequence, whereas a different part alternates in a small-large-small sequence, a phenomenon known as subcellular discordant alternans. The mechanisms for the formation and spatiotemporal evolution of these phase-mismatched patterns are not known. We used confocal Ca imaging to measure CaT alternans at the sarcomeric level within individual myocytes in the intact rat heart. After a sudden change in cycle length (CL), 2 distinct spatial patterns of CaT alternans emerge. CaTs can form spatially phase-mismatched alternans patterns after the first few beats following the change in CL. The phase mismatch persists for many beats, after which it gradually becomes phase matched via the movement of nodes, which are junctures between phase-mismatched cell regions. In other examples, phase-matched alternans gradually become phase-mismatched, via the formation and movement of nodes. In these examples, we observed large beat-to-beat variations in the cell activation times, despite constant CL pacing. Using computer simulations, we explored the underlying mechanisms for these dynamical phenomena. Our results show how heterogeneity at the sarcomeric level, in conjunction with the dynamics of Ca cycling and membrane voltage, can lead to complex spatiotemporal phenomena within myocytes of the intact heart.
Calcium release within a cardiac myocyte occurs within thousands of spatially distributed microdomains where membrane-bound L-type Ca channel (LCC) openings trigger the activation of ryanodine receptor (RyR) channels.1 During a normal beat, the action potential (AP) ensures that Ca release is synchronized throughout the cell, whereas electrotonic coupling between cells ensures that Ca release is synchronized between neighboring cells. However, optical Ca-imaging techniques have revealed that intracellular Ca can, under certain conditions, exhibit rich spatiotemporal properties within single myocytes2,3 and in cardiac tissue.4,5 Aistrup et al3 used high-resolution confocal microscopy to image intracellular Ca release in whole heart and found that Ca transients (CaTs) could vary substantially within different parts of the cell and also between neighboring cells during rapid pacing. It is not yet understood why, and under what conditions, these asynchronous release patterns emerge.
During rapid pacing, CaTs can alternate in a large-small-large-small (L-S-L-S) sequence from one beat to the next.6–8 CaT alternans are thought to originate from a period-doubling instability,9,10 which can occur because of the dependence of the AP duration (APD) on the previous diastolic interval or via a steep Ca release versus sarcoplasmic reticulum (SR) load relationship, ie, a nonlinearity that originates because of Ca-cycling dynamics.11,12 Confocal microscopic studies2,3,13 have shown that CaT alternans in a region of a cell can alternate in a L-S-L-S sequence, whereas a neighboring region can alternate in a S-L-S-L sequence, a phenomenon known as subcellular discordant alternans. These patterns can be complex because several regions of the cell can alternate with different temporal sequences.2,3 In this article, we refer to this phenomenon as phase-mismatched CaT alternans, as opposed to phase-matched CaT alternans where all regions of the cell alternate with the same temporal sequence. The presence of phase-mismatched CaT alternans is potentially arrhythmogenic because large intracellular Ca gradients are formed between phase-mismatched regions. The presence of these large gradients may then induce Ca waves14 to propagate between cellular regions, which could induce triggered activity such as delayed afterdepolarizations.15,16 Furthermore, subcellular heterogeneity attributable to phase-mismatched alternans may induce voltage heterogeneities on the tissue scale. This can happen, for instance, if the density and distribution of phase-mismatched regions vary substantially between different cardiac regions. Because subcellular Ca influences membrane voltage via Ca-sensitive currents such as the sodium/calcium exchanger (NCX) and the LCC current, spatial heterogeneity of Ca can induce heterogeneities in membrane voltage. These heterogeneities of voltage may then contribute to impulse propagation abnormalities.17
Little is known about the properties of phase-mismatched alternans in cardiac cells. Numeric simulation studies have investigated the mechanisms underlying these patterns and have shown that they have rich dynamical properties that are governed by the bidirectional coupling between intracellular Ca release and membrane voltage.18,19 However, much of this work has not been experimentally validated and the underlying mechanisms are not established. In this study, we applied a combined experimental and mathematical modeling approach to investigate the spatiotemporal dynamics of subcellular Ca cycling during rapid pacing. We hypothesized that phase-mismatched CaT patterns arise because of heterogeneities in Ca-cycling properties at the sarcomeric level. To test this hypothesis, we measured Ca release at the single sarcomere level within cardiac myocytes in the intact heart. Our findings show that dynamical factors such as CaT and cycle length (CL) alternans can amplify spatial heterogeneities in the cell to yield phase-mismatched CaT alternans. Moreover, the patterns of subcellular CaTs are dynamic and evolve in a manner that is dictated by the bidirectional coupling between membrane voltage and Ca.
Materials and Methods
Real-Time Confocal Ca Fluorescence (CaT) Acquisition
The whole rat heart preparation and recording of CaTs at sarcomeric-level resolution in ventricular myocytes of intact epicardium have been described in detail elsewhere.3 Additional details are provided in the expanded Materials and Methods section in the online data supplement, available at http://circres.ahajournals.org.
To model the subcellular spatial organization of CaT alternans, we divided the cell into 100 sarcomeres, and each sarcomere was modeled using a set of ordinary differential equations describing Ca cycling within that sarcomere. The essential elements of the local Ca-cycling machinery are based on the model of Shiferaw et al12 and are given in detail in the online data supplement.
Subcellular CaT Alternans Development After an Abrupt Change to Rapid Pacing
Line scan recordings of CaTs obtained in individual myocytes (36 cells from 11 hearts) during episodic pacing demonstrated that CaT alternans formed after an abrupt increase in rate. In all cases, if CaT alternans formed, they were phase-matched across the whole cell for the first 2 beats after the change in CL. For intermediate CLs (typically 160 to 140 ms at 35°C, 300 to 260 ms at 24°C), subcellular alternans remained phase matched throughout the rapid pacing epoch, whereas at faster pacing (typically CLs=140 to 100 ms at 35°C, 260 to 180 ms at 24°C), the CaT alternans evolved toward a phase-mismatched pattern in the subsequent ≈3 to 10 beats. Once formed, phase-mismatched CaT alternans persisted for varying duration of rapid pacing, which depended on both temperature and pacing CL. The X-t line scan in Figure 1A illustrates this subcellular CaT alternans development-persistence-cessation process in a myocyte consisting of 67 “sarcomeres” (2-μm partitions) after an abrupt change in pacing CL from 500 ms to 120 ms. Sarcomeric CaTs are periodic and exhibit no alternans during baseline pacing but, during the first 3 cycles of rapid pacing, sarcomeric CaTs immediately exhibit varying degrees of alternans with a matched L-S spatiotemporal phase. Within several cycles, however, the spatiotemporal phases of the alternans of various sarcomeric CaTs become mismatched. This is illustrated in the selected sarcomeric CaT fluorescence versus time profiles shown in Figure 1B. During cycles 1 to 4, sarcomeric CaT nos. 66 and 2 exhibit alternans of L-S-L-S, whereas sarcomeric CaT no. 22 exhibits L-S-L-L. Thus, after cycle 3 (t0), the alternans of sarcomeric CaT no. 22 is out of phase with those of nos. 2 and 66. Within the limits of our resolution, the alternans of sarcomeric CaT nos. 6 to 55 are phase-matched after cycle 3 but phase-mismatched with those of sarcomeric CaT nos. 1 to 5 and nos. 56 to 67. At least 2 nodes,20,21 junctures of mismatched phases, develop after cycle 3 (at t0). However, as is depicted by the dashed white lines overlaying the X-t line scan image in Figure 1A, the nodes are not stationary and travel to the cell ends and disappear, at t1 for the “lower” node and at t2 for the “upper” node. Phase reversal of the alternans of sarcomeric CaT nos. 1 to 5 and nos. 56 to 67 occurs when the respective nodes pass through them. Note that in the example average fluorescence versus time profiles of sarcomeric CaT nos. 2 and 66, little if any alternans are exhibited at the moment (2 cycles) each node passes through. After t2, the alternans of all sarcomeric CaTs are phase-matched again.
By plotting poststimulus latencies of CaT initiation, peak and duration at 90% recovery (TD90) versus each “sarcomere,” and aligning the plot with the corresponding X-t line scan image (Figure 1C), it is clear that there is significant spatiotemporal heterogeneity in sarcomere SR Ca release and reuptake along the length of the myocyte during baseline pacing in this example (and in all cells examined). However, heterogeneity in latency of Ca release does not predict the specific location of node development and movement, indicating that static heterogeneities alone are insufficient to explain the dynamic movement of phase-mismatched Ca alternans. Some nominal predictive power seemed to be offered by plotting sarcomeric CaT integrals (Figure 1D) (ie, high, narrow distributions of CaT integral measures seem to coincide with the initial location of node development) perhaps because this parameter encompasses both amplitude and time.
Late Development of Phase-Mismatched CaT Alternans During Rapid Pacing
In some myocytes, sarcomeric CaT alternans that are phase-matched across the whole cell after many beats can gradually become phase-mismatched. This behavior is distinct from that observed in Figure 1A, where CaT alternans were phase-mismatched shortly after the change in CL but then became phase-matched for the remainder of pacing. This behavior is shown in Figure 2A, where we observe the same mapping field as that shown in Figure 1, with baseline pacing CL=500 ms and rapid pacing CL=115 ms. The myocyte in this example is adjacent to that shown in Figure 1, illustrating that distinct spatiotemporal phenomena can emerge in response to small changes in CL. Alternans are phase-matched for the first 55 beats, and on the 55th beat, 2 nodes emerge from the top and bottom of the cell and drift toward the center of the cell (Figure 2A). A multinodal example of this behavior is shown in Figure 2B. The line scan in Figure 2C is a time-expanded version of Figure 2B, from which select sarcomeric average fluorescence versus time profiles are displayed in Figure 2D. As in Figure 1, the initial period of multinodal subcellular CaT alternans begins immediately after changing to rapid pacing, and extinguishes over t0 to t1 as the alternans of all sarcomeric CaTs eventually become spatiotemporally phase-matched when the nodes travel and collide with each other or with the ends of the cell, followed by 5 cycles of phase-matched CaT alternans. Starting at time t2, however, sarcomeric CaTs in 3 different regions (dashed yellow circles) again begin to exhibit phase-mismatched alternans. In this case 2 “inner” nodes form spontaneously inside the cell and travel toward opposite ends of the cell, whereas 2 “outer” nodes traveled toward the center of the cell. Again, the phase of the sarcomeric CaT alternans reverses as the nodes pass through their respective regions, and eventually inner and outer nodes meet at times t3 and t4, after which all sarcomeric CaT alternans are once again phase-matched.
A close inspection of these and other examples of more complex CaT alternans dynamics revealed that the timing of Ca activation varied significantly from beat-to-beat. However, because we have not measured the local membrane voltage, we can only infer the time of activation from the sarcomere CaTs. Our rationale is that when an electrical wavefront passes through the cell in the mapping field, the local membrane voltage will rise rapidly on a time scale <1 ms. This rapid rise of the membrane voltage induces the opening of LCCs distributed throughout the cell. Activation of LCCs is a fast process and occurs on a time scale of roughly 1 to 5 ms and triggers Ca release throughout the cell via Ca-induced Ca release (CICR).1 Because CICR is also a fast process (5 to 10 ms), we can estimate the time of cell activation by simply identifying that time when subcellular regions of uniform Ca release occur. Uniform Ca release across the >20-μm subcellular regions typically observed during image acquisition cannot be explained by simple diffusion of Ca, because it is too slow to correlate activation times across such intracellular spans. Using the examples of Figure 2A and 2B, we have illustrated our estimations of cell activation in Figure 3A and 3B. Note that we verify these measurements of cell activation of very small whole-cell or subcellular CaTs by measuring the initiation of Ca release in adjacent cells that gave sufficiently large CaTs during these same cycles, an interaction between neighboring myocytes that may also have some bearing on the formation of discordant CaT alternans at the cellular and/or regional level.22 Our analysis of rapid pacing epochs indicated that whereas the CLs of the electrical stimuli delivered were precisely those set, the local CLs for actual Ca release in the recording site often developed beat-to-beat short-long alternations (or CL alternans) that grew with time, often becoming >10 ms.
Evolution of Phase-Mismatched Alternans: Constant CL
Our experimental results revealed a variety of distinct spatiotemporal properties associated with both CaT and CL alternans. Here, we will apply mathematical modeling to simulate these properties and elucidate their underlying mechanisms. As a starting point, we examine Figure 1 and note that sarcomeric CaTs exhibit heterogeneities in their beat-to-beat characteristics after the change in CL. Based on this observation, we hypothesized that the initial alternans phase for a given sarcomere depends on the Ca-cycling characteristics of that sarcomere. Thus, the phase mismatch that developed over the next few beats should be a direct consequence of differences in Ca-cycling properties across sarcomeres, which could be attributable to a variety of factors such as spatial variations in expression levels of NCX, SERCA2a (sarco-/endoplasmic reticulum Ca-ATPase), or LCC.
To test the role of heterogeneity in the formation of phase-mismatched Ca alternans, we modeled a cell as a collection of coupled sarcomeres and endowed each sarcomere with different Ca-cycling characteristics. Heterogeneity can arise because of any number of factors that influence Ca cycling, such as variations in protein expression. In these studies, we modeled variations in SR Ca release properties, because this is the variable which has the most direct effect on Ca cycling and should vary to some degree between sarcomeres. To modulate Ca release, we allow each sarcomere to have specific Ca release properties by simply controlling the slope (u) of the SR Ca release versus SR Ca load relationship,12 which in our simplified model includes the combined effect of RyR channel density, dyadic junction spacing, and RyR Ca sensitivity on both the cytosolic and luminal sides. Heterogeneity in Ca cycling was incorporated into a simulated myocyte such that sarcomeres 1 to 20 and sarcomeres 80 to 100 have a slope u=12 sec−1, whereas sarcomeres 21 to 79 have slope u=14 sec−1 (Figure 4A). We then simulated the dynamical response of this heterogeneous distribution of sarcomeres after a jump from baseline pacing (CL=400 ms) to rapid pacing (CL=200 ms). Plotting the intracellular Ca concentrations ([Ca]i) versus time across the whole cell shows that phase-mismatched alternans form after the first few beats following the change in CL. Two nodes form at the junctures between subcellular regions of lower and higher u, and each node travels toward opposing cell ends. In Figure 4B, we plot the [Ca]i versus time profiles for selected individual sarcomeres 15, 50, and 90. The first 6 cycles after the rate increase show that sarcomeres 15 and 90 both exhibit the CaT alternans sequence L-S-L-S-L, whereas sarcomere 50 displays an alternans sequence L-S-S-L-S-L. Thus the spatiotemporal phase of the alternans in sarcomere 50 is mismatched with those of sarcomeres 15 and 90 after only 2 short cycles. This phase-mismatched pattern persists for 30 short cycles, indicating that Ca diffusion between sarcomeres was insufficient to disperse the phase-mismatch. However, the phase-mismatched pattern was dynamic and the nodes that form at the heterogeneities drift and extinguish at the cell boundaries.
Evolution of Phase-Mismatched Alternans: Alternating CL
Our modeling studies showed that the spatiotemporal dynamics observed in Figure 1A can be reproduced simply by incorporating heterogeneity between sarcomeres. In contrast, we found that it is necessary to incorporate CL alternans in combination with heterogeneity between sarcomeres to reproduce the dynamic behavior seen in Figure 2A and 2B. To model heterogeneity, we let the release load slope vary across the cell so that u=15 sec−1 for sarcomeres 1 to 19 and 81 to 100 and u=10 sec−1 for sarcomeres 20 to 80. We paced the cell with an alternating CL defined as CL(n)=CL+(−1)nΔCL, where CL(n) is the CL on the nth beat, following a change in CL from 500 to 200 ms. In Figure 5A, we plot [Ca]i versus time across the cell, and in Figure 5B we plot [Ca]i versus time for sarcomeres 15, 50, and 90. In this case, we let ΔCL increase linearly from 0 to 9 ms over 50 beats. In Figure 5B, CaT alternans are phase-matched over the first 25 beats but gradually diminish in amplitude and then eventually reverse phase. However, sarcomere 50 reverses phase at time t1, whereas sarcomeres 15 and 90 reverse phase at time t2. On examining the node positions in the line scan image in Figure 5A (white dashed lines), the nodes form at time t1 at the boundaries separating the 2 regions of different release load slope. These nodes then gradually drift toward the cell boundaries and extinguish, leaving phase-matched alternans throughout the cell.
Change in CL in Conjunction With Ca-Cycling Heterogeneity Leads to Phase-Mismatched CaT Alternans
Our experimental studies revealed that when the CL is suddenly decreased, the beat-to-beat evolution of CaT alternans can differ substantially between sarcomeres. Therefore, as CaT alternans develop during rapid pacing, sarcomeres in different regions of the cell can become phase-mismatched. Subcellular alternans can develop within just the first 3 to 4 beats after the change in cycle length, which is reproduced by our mathematical model of coupled sarcomeres. The mechanism for this is simply that the phase of CaT alternans is chosen by the dynamical response of Ca cycling during the first few beats, and because Ca-cycling characteristics differ between sarcomeres, different sarcomeres are likely to develop CaT alternans that are phase-mismatched. Moreover, once CaT alternans develop, Ca diffusion between sarcomeres is not sufficient to resynchronize these phase-mismatched sarcomeres.
There have been few studies of the intrinsic heterogeneity in Ca release properties that could explain these observations. The use of confocal microscopy to study CaTs in cardiac myocytes allowed the identification of substantial variation in release magnitude and timing along the cell length.23 However, it was only recently that the heterogeneity in virtually all characteristics of intracellular Ca cycling was recognized in intact heart (Figure 1C and 1D).3 This study shows that these characteristics have important influences on physiological behavior, especially during rapid pacing.
A key ingredient in the formation of phase-mismatched CaT alternans is the presence of variations of Ca-cycling properties across the cell. We modeled this effect in the numeric simulations by letting the SR Ca release properties vary across the cell. However, we found similar results when we varied LCC, NCX, or SERCA channel density (results not shown). The crucial requirement is simply that there are differences in the Ca-cycling response of different sarcomeres, which can arise because of a multitude of factors which influence Ca cycling. This is expected because Ca cycling is dependent on both Ca release from the SR and the Ca flux balance across the cell membrane, which is dependent on a wide variety of channels and pumps. Experimentally, it is also difficult to identify the specific protein(s) responsible for the observed heterogeneities but such spatial variations in RyR, SERCA, NCX, or LCC protein density are not unexpected. The novel finding in this article is that these differences can induce phase-mismatched Ca release patterns.
Node Movement Is Dictated by the Membrane Potential
Our experiments have shown that the spatial distribution of CaT alternans within a cell is time-dependent. In particular, nodes that mark the boundaries between regions of the cell that are phase-mismatched can drift across the cell. In Figure 6A and 6B, we show 2 examples where nodes move across a cell. To uncover the underlying mechanism for this effect, we first note that because cardiac cells in tissue are electrically coupled, the voltage across the membrane of a given cell is the spatial average of all cells within the electrotonic space constant. Thus, to a good approximation, the cell in the field of view is essentially driven by a voltage clamp. Furthermore, we expect that the voltage time course driving a cell can itself exhibit APD alternans. This is expected because a close examination of the pseudo-ECG reveals repolarization alternans, which suggests that beat-to-beat alternations exist in the local AP. Also, because Ca release is coupled to voltage via membrane currents, CaT alternans will induce APD alternans.8 Furthermore, there is increasing evidence that repolarization alternans recorded in single cells of intact tissue reflects T-wave alternans at the level of intact myocardium, so that cellular phenomena reflect electrical behavior in the heart.24 Note that the magnitude of APD alternans is sensitive to the average over all cells within the electrotonic space constant, which need not average to 0. Investigating the effect of APD alternans on the spatiotemporal dynamics of CaT alternans reveals that the movement of nodes is dictated by the phase of APD alternans driving that cell. To support this claim, we simulated a cardiac cell that is paced by an alternating voltage clamp waveform. Within this cell, we form phase-mismatched alternans by simply choosing initial conditions so that half of the cell is phase-mismatched with the other half. As shown in Figure 6C, when the cell is paced with a periodic AP waveform, the CaT node does not move. However, if the AP wave form exhibits alternans with a given phase of L-S-L-S or S-L-S-L, then the node moves either up or down, respectively (Figure 6D and 6E). Once the node reaches the cell boundary, all sarcomeres in the cell are phase-matched, such that a large (small) CaT corresponds to a long (short) APD.
Our numeric simulations demonstrate that the presence of APD alternans leads to node movement. The mechanism for this effect is that when APD alternans of a given phase drive a sarcomere, that sarcomere will reverse its phase to match the phase of the APD alternans, such that CaT alternans will synchronize to the APD alternans. Thus, if the APD alternates in a L-S-L-S duration, then CaT alternans at the sarcomeric level will adjust to a L-S-L-S phase. This response is attributable to the fact that a large APD is followed by a short diastolic interval, reducing the recovery from inactivation of the LCC. Therefore, in the subsequent beat, there are fewer LCC openings, leading to decreased Ca release. APD alternans will then “force” sarcomere CaT alternans to synchronize their phase. If there is phase mismatch attributable to subcellular heterogeneities, then nodes will move so that the phase synchronized with the APD alternans driving the cell will gradually dominate. In contrast, in the absence of APD alternans and the AP is periodic from beat-to-beat, there is no mechanism to dictate which phase a particular sarcomere will obey, and the nodes remain fixed at the location at which they are formed. Dynamical changes in local Ca-cycling properties can only serve to enhance or diminish local CaT alternans amplitude but cannot impose a particular phase. Therefore, it is essential to invoke alternans in the AP waveform to explain node movement.
CL Alternans Are Necessary for Late Development of Phase-Mismatched CaT Alternans
Our experimental results also revealed that subcellular CaT alternans can exhibit a variety of distinct spatiotemporal dynamics. We found numerous instances where phase-matched alternans was established after many beats, after which multiple nodes formed spontaneously at the ends (and centers) of the cells and drifted toward the centers (and ends). Now the mechanism for node movement presented in the previous section could not explain these features because once APD alternans is synchronized with the CaT alternans throughout the cell, there is no mechanism for phase reversal and the cell should remain phase-matched. In these examples, however, we found a beat-to-beat CL alternans so that these cells were not paced at a truly constant CL. CL alternans is not unexpected because the conduction velocity of an electrical wave in cardiac tissue is sensitive to the diastolic interval. Therefore, if the APD alternates from beat-to-beat, then so will the diastolic interval, and this will lead to an alternation of the conduction velocity in cardiac tissue. The result is that the time of arrival of a wavefront at the cell within the mapping field will typically alternate between beats. The mechanism for the transition from phase-matched to phase-mismatched and then back to phase-matched CaT alternans is attributable to a combination of CL alternans and the differences in Ca cycling between different sarcomeres. As illustrated in Figure 7A, let us first assume that a cell is paced at a constant cycle length CL0 and that CaT alternans are present (indicated by the black line). In this case, the magnitude of alternans is determined simply by the relationship between SR Ca load and release. Now let us assume that this cell is then paced with a CL that alternates between a long (CL1) and short (CL2) duration. Here, the timing of the current stimulus is such that an early stimulus is delivered just before (after) the small (large) CaT. This choice of timing will serve to diminish the magnitude of alternans because the short CL favors a decrease in Ca release because that sarcomere will have less time to reload its SR. On the other hand, the long CL will lead to an increase in the small CaT because that sarcomere will have more time for reloading. Thus, the effect of an alternating CL on the Ca-cycling dynamics will be to diminish alternans and subsequently to reverse the phase of the alternans sequence as the amplitude of CL alternans is increased. For CL alternans to reverse the phase of CaT alternans, they must be out-of-phase in the sense that a long (short) CL must correspond to a small (large) Ca release. A close examination of the line scan images in Figure 3A and 3B is consistent with this prediction.
To explain the formation of subcellular CaT alternans, it is necessary to invoke the intrinsic differences between sarcomeres. In Figure 7B, we pace 2 sarcomeres with different Ca-cycling characteristics in which sarcomere 1 exhibits a larger degree of CaT alternans than sarcomere 2 at steady state. If we now pace these 2 sarcomeres with an alternating CL, then CaT alternans in both sarcomeres gradually diminish and reverse phase via the mechanism discussed above. However, the amplitude of alternans in sarcomere 1 decreases more slowly than that in sarcomere 2 and the phase-reversal points, as indicated by the vertical dashed lines, occur at different time points. Therefore, CaT alternans in both sarcomeres will be phase-mismatched during that time interval. Thus, the spatiotemporal dynamics observed in Figure 3A and 3B is caused by the interplay between CL alternans and the spatial variation of Ca-cycling characteristics.
This result highlights, for the first time, how dynamic factors, such as CaT and CL alternans, interact with heterogeneities at the sarcomere scale to form subcellular CaT alternans. These mechanisms could be of considerable clinical importance because subcellular alternans could promote the development of intracellular Ca gradients and resulting Ca waves, thus providing a mechanism for triggered activity and arrhythmias.2,14
Sources of Funding
Supported, in part, by The Everett-O'Connor Trust (A.H.K.). Computer simulations conducted by Yohannes Shiferaw were funded, in part, by American Heart Association Grant 0830298N.
↵*Both authors contributed equally to this work.
Original received June 19, 2008; revision received January 4, 2009; accepted January 7, 2009.
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