Voltage and Calcium Dynamics Both Underlie Cellular Alternans in Cardiac Myocytes

Cardiac alternans, a putative trigger event for cardiac reentry, is a beat-to-beat alternation in membrane potential and calcium transient. Alternans was originally attributed to instabilities in transmembrane ion channel dynamics (i.e., the voltage mechanism). As of this writing, the predominant view is that instabilities in subcellular calcium handling are the main underlying mechanism. That being said, because the voltage and calcium systems are bidirectionally coupled, theoretical studies have suggested that both mechanisms can contribute. To date, to our knowledge, no experimental evidence of such a dual role within the same cell has been reported. Here, a combined electrophysiological and calcium imaging approach was developed and used to illuminate the contributions of voltage and calcium dynamics to alternans. An experimentally feasible protocol, quantification of subcellular calcium alternans and restitution slope during cycle-length ramping alternans control, was designed and validated. This approach allows simultaneous illumination of the contributions of voltage and calcium-driven instability to total cellular instability as a function of cycle-length. Application of this protocol in in vitro guinea-pig left-ventricular myocytes demonstrated that both voltage- and calcium-driven instabilities underlie alternans, and that the relative contributions of the two systems change as a function of pacing rate.     

Characterizing the contribution of voltage- and calcium-dependent coupling to action potential stability: implications for repolarization alternans

Experiments have provided suggestive but inconclusive insights into the relative contributions of transmembrane voltage and intracellular calcium handling to the development of cardiac electrical instabilities such as repolarization alternans. In this study, we applied a novel combination of techniques (action potential voltage clamping, calcium-transient clamping, and stability analysis) to cardiac cell models to more clearly determine the roles that voltage- and calcium-dependent coupling play in regulating action potential stability and the development of alternans subsequent to the loss of stability. Using these techniques, we are able to demonstrate that voltage- and calcium-dependent coupling exhibit varying degrees of influence on action potential stability across models. Our results indicate that cellular dynamic instabilities such as alternans may be initiated by either voltage- or calcium-dependent mechanisms or by some combination of the two. Based on these modeling results, we propose novel single-cell experiments that incorporate action-potential voltage clamping, calcium imaging, and real-time measurement of action potential stability. These experiments will make it possible to experimentally determine the relative contribution of voltage coupling to the regulation of action potential stability in real cardiac myocytes, thereby providing further insights into the mechanism of alternans.     

Feedback-control induced pattern formation in cardiac myocytes: A mathematical modeling study

Cardiac alternans is a dangerous rhythm disturbance of the heart, in which rapid stimulation elicits a beat-to-beat alternation in the action potential duration (APD) and calcium (Ca) transient amplitude of individual myocytes. Recently, “subcellular alternans”, in which the Ca transients of adjacent regions within individual myocytes alternate out-of-phase, has been observed. A previous theoretical study suggested that subcellular alternans may result during static pacing from a Turing-type symmetry breaking instability, but this was only predicted in a subset of cardiac myocytes (with negative Ca to voltage (Ca→V_m) coupling) and has never been directly verified experimentally. A recent experimental study, however, showed that subcellular alternans is dynamically induced in the remaining subset of myocytes during pacing with a simple feedback control algorithm (“alternans control”). Here we show that alternans control pacing changes the effective coupling between the APD and the Ca transient (V_m→Ca coupling), such that subcellular alternans is predicted to occur by a Turing instability in cells with positive Ca→V_m coupling. In addition to strengthening the understanding of the proposed mechanism for subcellular alternans formation, this work (in concert with previous theoretical and experimental results) illuminates subcellular alternans as a striking example of a biological Turing instability in which the diffusing morphogens can be clearly identified.     

Formation of Spatially Discordant Alternans Due to Fluctuations and Diffusion of Calcium

Spatially discordant alternans (SDA) of action potential duration (APD) is a phenomenon where different regions of cardiac tissue exhibit an alternating sequence of APD that are out-of-phase. SDA is arrhythmogenic since it can induce spatial heterogeneity of refractoriness, which can cause wavebreak and reentry. However, the underlying mechanisms for the formation of SDA are not completely understood. In this paper, we present a novel mechanism for the formation of SDA in the case where the cellular instability leading to alternans is caused by intracellular calcium (Ca) cycling, and where Ca transient and APD alternans are electromechanically concordant. In particular, we show that SDA is formed when rapidly paced cardiac tissue develops alternans over many beats due to Ca accumulation in the sarcoplasmic reticulum (SR). The mechanism presented here relies on the observation that Ca cycling fluctuations dictate Ca alternans phase since the amplitude of Ca alternans is small during the early stages of pacing. Thus, different regions of a cardiac myocyte will typically develop Ca alternans which are opposite in phase at the early stages of pacing. These subcellular patterns then gradually coarsen due to interactions with membrane voltage to form steady state SDA of voltage and Ca on the tissue scale. This mechanism for SDA is distinct from well-known mechanisms that rely on conduction velocity restitution, and a Turing-like mechanism known to apply only in the case where APD and Ca alternans are electromechanically discordant. Furthermore, we argue that this mechanism is robust, and is likely to underlie a wide range of experimentally observed patterns of SDA.     

Dependency of Calcium Alternans on Ryanodine Receptor Refractoriness

Background

Rapid pacing rates induce alternations in the cytosolic calcium concentration caused by fluctuations in calcium released from the sarcoplasmic reticulum (SR). However, the relationship between calcium alternans and refractoriness of the SR calcium release channel (RyR2) remains elusive.

Methodology/Principal Findings

To investigate how ryanodine receptor (RyR2) refractoriness modulates calcium handling on a beat-to-beat basis using a numerical rabbit cardiomyocyte model. We used a mathematical rabbit cardiomyocyte model to study the beat-to-beat calcium response as a function of RyR2 activation and inactivation. Bi-dimensional maps were constructed depicting the beat-to-beat response. When alternans was observed, a novel numerical clamping protocol was used to determine whether alternans was caused by oscillations in SR calcium loading or by RyR2 refractoriness. Using this protocol, we identified regions of RyR2 gating parameters where SR calcium loading or RyR2 refractoriness underlie the induction of calcium alternans, and we found that at the onset of alternans both mechanisms contribute. At low inactivation rates of the RyR2, calcium alternans was caused by alternation in SR calcium loading, while at low activation rates it was caused by alternation in the level of available RyR2s.

Conclusions/Significance

We have mapped cardiomyocyte beat-to-beat responses as a function of RyR2 activation and inactivation, identifying domains where SR calcium load or RyR2 refractoriness underlie the induction of calcium alternans. A corollary of this work is that RyR2 refractoriness due to slow recovery from inactivation can be the cause of calcium alternans even when alternation in SR calcium load is present.     

Cardiac cellular coupling and the spread of early instabilities in intracellular Ca2+

Recent experimental and modeling studies demonstrate the fine spatial scale, complex nature, and independent contribution of Ca²⁺ dynamics as a proarrhythmic factor in the heart. The mechanism of progression of cell-level Ca²⁺ instabilities, known as alternans, to tissue-level arrhythmias is not well understood. Because gap junction coupling dictates cardiac syncytial properties, we set out to elucidate its role in the spatiotemporal evolution of Ca²⁺ instabilities. We experimentally perturbed cellular coupling in cardiac syncytium in vitro. Coupling was quantified by fluorescence recovery after photobleaching, and related to function, including subtle fine-scale Ca²⁺ alternans, captured by optical mapping. Conduction velocity and threshold for alternans monotonically increased with coupling. Lower coupling enhanced Ca²⁺ alternans amplitude, but the spatial spread of early (<2 Hz) alternation was the greatest under intermediate (not low) coupling. This nonmonotonic relationship was closely matched by the percent of samples exhibiting large-scale alternans at higher pacing rates. Computer modeling corroborated these experimental findings for strong but not weak electromechanical (voltage-Ca²⁺) coupling, and offered mechanistic insight. In conclusion, using experimental and modeling approaches, we reveal a general mechanism for the spatial spread of subtle cellular Ca²⁺ alternans that relies on a combination of gap-junctional and voltage-Ca²⁺ coupling.     

Model of intracellular calcium cycling in ventricular myocytes

We present a mathematical model of calcium cycling that takes into account the spatially localized nature of release events that correspond to experimentally observed calcium sparks. This model naturally incorporates graded release by making the rate at which calcium sparks are recruited proportional to the whole cell L-type calcium current, with the total release of calcium from the sarcoplasmic reticulum (SR) being just the sum of local releases. The dynamics of calcium cycling is studied by pacing the model with a clamped action potential waveform. Experimentally observed calcium alternans are obtained at high pacing rates. The results show that the underlying mechanism for this phenomenon is a steep nonlinear dependence of the calcium released from the SR on the diastolic SR calcium concentration (SR load) and/or the diastolic calcium level in the cytosol, where the dependence on diastolic calcium is due to calcium-induced inactivation of the L-type calcium current. In addition, the results reveal that the calcium dynamics can become chaotic even though the voltage pacing is periodic. We reduce the equations of the model to a two-dimensional discrete map that relates the SR and cytosolic concentrations at one beat and the previous beat. From this map, we obtain a condition for the onset of calcium alternans in terms of the slopes of the release-versus-SR load and release-versus-diastolic-calcium curves. From an analysis of this map, we also obtain an understanding of the origin of chaotic dynamics.     

Electrophysiology of Heart Failure Using a Rabbit Model: From the Failing Myocyte to Ventricular Fibrillation

Heart failure is a leading cause of death, yet its underlying electrophysiological (EP) mechanisms are not well understood. In this study, we use a multiscale approach to analyze a model of heart failure and connect its results to features of the electrocardiogram (ECG). The heart failure model is derived by modifying a previously validated electrophysiology model for a healthy rabbit heart. Specifically, in accordance with the heart failure literature, we modified the cell EP by changing both membrane currents and calcium handling. At the tissue level, we modeled the increased gap junction lateralization and lower conduction velocity due to downregulation of Connexin 43. At the biventricular level, we reduced the apex-to-base and transmural gradients of action potential duration (APD). The failing cell model was first validated by reproducing the longer action potential, slower and lower calcium transient, and earlier alternans characteristic of heart failure EP. Subsequently, we compared the electrical wave propagation in one dimensional cables of healthy and failing cells. The validated cell model was then used to simulate the EP of heart failure in an anatomically accurate biventricular rabbit model. As pacing cycle length decreases, both the normal and failing heart develop T-wave alternans, but only the failing heart shows QRS alternans (although moderate) at rapid pacing. Moreover, T-wave alternans is significantly more pronounced in the failing heart. At rapid pacing, APD maps show areas of conduction block in the failing heart. Finally, accelerated pacing initiated wave reentry and breakup in the failing heart. Further, the onset of VF was not observed with an upregulation of SERCA, a potential drug therapy, using the same protocol. The changes introduced at the cell and tissue level have increased the failing heart’s susceptibility to dynamic instabilities and arrhythmias under rapid pacing. However, the observed increase in arrhythmogenic potential is not due to a steepening of the restitution curve (not present in our model), but rather to a novel blocking mechanism.     

Calcium instabilities in mammalian cardiomyocyte networks

The degeneration of a regular heart rhythm into fibrillation (a chaotic or chaos-like sequence) can proceed via several classical routes described by nonlinear dynamics: period-doubling, quasiperiodicity, or intermittency. In this study, we experimentally examine one aspect of cardiac excitation dynamics, the long-term evolution of intracellular calcium signals in cultured cardiomyocyte networks subjected to increasingly faster pacing rates via field stimulation. In this spatially extended system, we observed alternans and higher-order periodicities, extra beats, and skipped beats or blocks. Calcium instabilities evolved nonmonotonically with the prevalence of phase-locking or Wenckebach rhythm, low-frequency magnitude modulations (signature of quasiperiodicity), and switches between patterns with occasional bursts (signature of intermittency), but period-doubling bifurcations were rare. Six ventricular-fibrillation-resembling episodes were pace-induced, for which significantly higher complexity was confirmed by approximate entropy calculations. The progressive destabilization of the heart rhythm by coexistent frequencies, seen in this study, can be related to theoretically predicted competition of control variables (voltage and calcium) at the single-cell level, or to competition of excitation and recovery at the cell network level. Optical maps of the response revealed multiple local spatiotemporal patterns, and the emergence of longer-period global rhythms as a result of wavebreak-induced reentries.     

Model of mechanical alternans in the mammalian myocardium

A model is proposed to elucidate the cause and mechanism of mechanical alternans in cardiac muscle in terms of discrete calcium movements. Mechanical alternans, the cause of which lies within the borders of excitation-contraction-coupling (ECC), is analyzed. In this case, the "input" of the ECC system (the action potentials and intervals) is constant while the "output" (contractile force) oscillates between two constant values, indicating that the system has a "memory" with two "internal states". It is proposed that these two "states" are associated with a part of the sarcoplasmic reticulum ("releasable terminal") containing the readily releasable calcium. A mechanism of "calcium-concentration-dependent threshold" is suggested to govern the "release function", i.e. the release of calcium from the "releasable terminal" to the myofilaments. The "release function" is analyzed in both the linear and the non-linear cases and its implication on the initiation of sustained and transient mechanical alternans are described. The dependence of mechanical alternans on a disturbance is also explained. The model response resembles the experimental observations of mechanical alternans in mammalian myocardium in the following manners: abrupt transition from low to high heart rates, slow progressive acceleration of rate, variations in persistence at subthreshold rates, effect of premature and delayed beat following the small and large beats, restitution curves, and transient mechanical alternans initiated by a delayed beat.     

Uncovering the dynamics of cardiac systems using stochastic pacing and frequency domain analyses

Alternans of cardiac action potential duration (APD) is a well-known arrhythmogenic mechanism which results from dynamical instabilities. The propensity to alternans is classically investigated by examining APD restitution and by deriving APD restitution slopes as predictive markers. However, experiments have shown that such markers are not always accurate for the prediction of alternans. Using a mathematical ventricular cell model known to exhibit unstable dynamics of both membrane potential and Ca²⁺ cycling, we demonstrate that an accurate marker can be obtained by pacing at cycle lengths (CLs) varying randomly around a basic CL (BCL) and by evaluating the transfer function between the time series of CLs and APDs using an autoregressive-moving-average (ARMA) model. The first pole of this transfer function corresponds to the eigenvalue (λ_alt) of the dominant eigenmode of the cardiac system, which predicts that alternans occurs when λ_alt≤−1. For different BCLs, control values of λ_alt were obtained using eigenmode analysis and compared to the first pole of the transfer function estimated using ARMA model fitting in simulations of random pacing protocols. In all versions of the cell model, this pole provided an accurate estimation of λ_alt. Furthermore, during slow ramp decreases of BCL or simulated drug application, this approach predicted the onset of alternans by extrapolating the time course of the estimated λ_alt. In conclusion, stochastic pacing and ARMA model identification represents a novel approach to predict alternans without making any assumptions about its ionic mechanisms. It should therefore be applicable experimentally for any type of myocardial cell.     

Contrasting effects of ischemia on the kinetics of membrane voltage and intracellular calcium transient underlie electrical alternans

Repolarization alternans has been considered a strong marker of electrical instability. The objective of this study was to investigate the hypothesis that ischemia-induced contrasting effects on the kinetics of membrane voltage and intracellular calcium transient (Ca(i)T) can explain the vulnerability of the ischemic heart to repolarization alternans. Ischemia-induced changes in action potential (AP) and Ca(i)T resulting in alternans were investigated in perfused Langendorff guinea pig hearts subjected to 10-15 min of global no-flow ischemia followed by 10-15 min of reperfusion. The heart was stained with 100 microl of rhod-2 AM and 25 microl of RH-237, and AP and Ca(i)T were simultaneously recorded with an optical mapping system of two 16 x 16 photodiode arrays. Ischemia was associated with shortening of AP duration (D) but delayed upstroke, broadening of peak, and slowed decay of Ca(i)T resulting in a significant increase of Ca(i)T-D. The changes in APD were spatially heterogeneous in contrast to a more spatially homogeneous lengthening of Ca(i)T-D. Ca(i)T alternans could be consistently induced with the introduction of a shorter cycle when the upstroke of the AP occurred before complete relaxation of the previous Ca(i)T and generated a reduced Ca(i)T. However, alternans of Ca(i)T was not necessarily associated with alternans of APD, and this was correlated with the degree of spatially heterogeneous shortening of APD. Sites with less shortening of APD developed alternans of both Ca(i)T and APD, whereas sites with greater shortening of APD could develop a similar degree of Ca(i)T alternans but slight or no APD alternans. This resulted in significant spatial dispersion of APD. The study shows that the contrasting effects of ischemia on the duration of AP and Ca(i)T and, in particular, on their spatial distribution explain the vulnerability of ischemic heart to alternans and the increased dispersion of repolarization during alternans.     

Inferring the cellular origin of voltage and calcium alternans from the spatial scales of phase reversal during discordant alternans

Beat-to-beat alternation of the action potential duration (APD) in paced cardiac cells has been linked to the onset of lethal arrhythmias. Both experimental and theoretical studies have shown that alternans at the single cell level can be caused by unstable membrane voltage (V(m)) dynamics linked to steep APD-restitution, or unstable intracellular calcium (Ca) cycling linked to high sensitivity of Ca release from the sarcoplasmic reticulum on sarcoplasmic reticulum Ca load. Identifying which of these two mechanisms is the primary cause of cellular alternans, however, has remained difficult since Ca and V(m) are bidirectionally coupled. Here, we use numerical simulations of a physiologically detailed ionic model to show that the origin of alternans can be inferred by measuring the length scales over which APD and Ca(i) alternans reverse phase during spatially discordant alternans. The main conclusion is that these scales are comparable to a few millimeters and equal when alternans is driven by APD restitution, but differ markedly when alternans is driven predominantly by unstable Ca cycling. In the latter case, APD alternans still reverses phase on a millimeter tissue scale due to electrotonic coupling, while Ca alternans reverses phase on a submillimeter cellular scale. These results show that experimentally accessible measurements of Ca(i) and V(m) in cardiac tissue can be used to shed light on the cellular origin of alternans.     

Cellular and subcellular alternans in the canine left ventricle

Previous studies indicate that action potential duration (APD) alternans is initiated in the endocardial (END) and midmyocardial (MID) regions rather than the epicardium (EPI) in the canine left ventricle (LV). This study examines regional differences in the rate dependence of Ca(2+) transient characteristics under conditions that give rise to APD and associated T wave alternans. The role of the sarcoplasmic reticulum (SR) was further evaluated by studying Ca(2+) transient characteristics in myocytes isolated from neonates, where an organized SR is poorly developed. All studies were performed in cells and tissues isolated from the canine LV. Isolated canine ENDO, MID, and EPI LV myocytes were either field stimulated or voltage clamped, and Ca(2+) transients were measured by confocal microscopy. In LV wedge preparations, increasing the basic cycle length (BCL) from 800 to 250 ms caused alternans to appear mainly in the ENDO and MID region; alternans were not observed in EPI under these conditions. Ca(2+) transient alternans developed in response to rapid pacing, appearing in EPI cells at shorter BCL compared with MID and ENDO cells (BCL=428 +/- 17 vs. 517 +/- 29 and 514 +/- 21, respectively, P < 0.05). Further increases in pacing rate resulted in the appearance of subcellular alternans of Ca(2+) transient amplitude, which also appeared in EPI at shorter BCL than in ENDO and MID cells. Ca(2+) transient alternans was not observed in neonate myocytes. We conclude that 1) there are distinct regional differences in the vulnerability to rate-dependent Ca(2+) alternans in dog LV that may be related to regional differences in SR function and Ca(2+) cycling; 2) the development of subcellular Ca(2+) alternans suggests the presence of intracellular heterogeneities in Ca(2+) cycling; and 3) the failure of neonatal cells to develop Ca(2+) alternans provides further support that SR Ca(2+) cycling is a major component in the development of these phenomena.     

Alternans and 2:1 rhythms in an ionic model of heart cells

ECG alternans is commonly held to be an indicator of electrical instability of the heart, but the development of alternans has not yet been fully understood theoretically. We investigate the onset of alternans and 2:1 rhythms for stimulation at increasing frequencies in the Beeler-Reuter model, a simple ionic model of cardiac tissue. We find hysteresis and bistability at the onset of alternans; well-timed stimuli can switch between the two limit cycles. We determine quantitatively the effect of blocking specific ionic currents. Moreover, we find that calcium buffers generally promote alternans.     

Voltage-mediated mechanism for calcium wave synchronization and arrhythmogenesis in atrial tissue

A wide range of atrial arrythmias are caused by molecular defects in proteins that regulate calcium (Ca) cycling. In many cases, these defects promote the propagation of subcellular Ca waves in the cell, which can perturb the voltage time course and induce dangerous perturbations of the action potential (AP). However, subcellular Ca waves occur randomly in cells and, therefore, electrical coupling between cells substantially decreases their effect on the AP. In this study, we present evidence that Ca waves in atrial tissue can synchronize in-phase owing to an order-disorder phase transition. In particular, we show that, below a critical pacing rate, Ca waves are desynchronized and therefore do not induce substantial AP fluctuations in tissue. However, above this critical pacing rate, Ca waves gradually synchronize over millions of cells, which leads to a dramatic amplification of AP fluctuations. We exploit an underlying Ising symmetry of paced cardiac tissue to show that this transition exhibits universal properties common to a wide range of physical systems in nature. Finally, we show that in the heart, phase synchronization induces spatially out-of-phase AP duration alternans which drives wave break and reentry. These results suggest that cardiac tissue exhibits a phase transition that is required for subcellular Ca cycling defects to induce a life-threatening arrhythmia.     

The labile brain. II. Transients, complexity and selection

The successive expression of neuronal transients is related to dynamic correlations and, as shown in this paper, to dynamic instability. Dynamic instability is a form of complexity, typical of neuronal systems, which may be crucial for adaptive brain function from two perspectives. The first is from the point of view of neuronal selection and self-organizing systems: if selective mechanisms underpin the emergence of adaptive neuronal responses then dynamic instability is, itself, necessarily adaptive. This is because dynamic instability is the source of diversity on which selection acts and is therefore subject to selective pressure. In short, the emergence of order, through selection, depends almost paradoxically on the instabilities that characterize the diversity of brain dynamics. The second perspective is provided by information theory.     

Dynamic origin of spatially discordant alternans in cardiac tissue

Alternans, a condition in which there is a beat-to-beat alternation in the electromechanical response of a periodically stimulated cardiac cell, has been linked to the genesis of life-threatening ventricular arrhythmias. Optical mapping of membrane voltage (V_m) and intracellular calcium (Ca_i) on the surface of animal hearts reveals complex spatial patterns of alternans. In particular, spatially discordant alternans has been observed in which regions with a large-small-large action potential duration (APD) alternate out-of-phase adjacent to regions of small-large-small APD. However, the underlying mechanisms that lead to the initiation of discordant alternans and govern its spatiotemporal properties are not well understood. Using mathematical modeling, we show that dynamic changes in the spatial distribution of discordant alternans can be used to pinpoint the underlying mechanisms. Optical mapping of V_m and Ca_i in paced rabbit hearts revealed that spatially discordant alternans induced by rapid pacing exhibits properties consistent with a purely dynamical mechanism as shown in theoretical studies. Our results support the viewpoint that spatially discordant alternans in the heart can be formed via a dynamical pattern formation process which does not require tissue heterogeneity.