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.     

Remodeling Promotes Proarrhythmic Disruption of Calcium Homeostasis in Failing Atrial Myocytes

It is well known that heart failure (HF) typically coexists with atrial fibrillation (AF). However, until now, no clear mechanism has been established that relates HF to AF. In this study, we apply a multiscale computational framework to establish a mechanistic link between atrial myocyte structural remodeling in HF and AF. Using a spatially distributed model of calcium (Ca) signaling, we show that disruption of the spatial relationship between L-type Ca channels (LCCs) and ryanodine receptors results in markedly increased Ca content of the sarcoplasmic reticulum (SR). This increase in SR load is due to changes in the balance between Ca entry via LCCs and Ca extrusion due to the sodium-calcium exchanger after an altered spatial relationship between these signaling proteins. Next, we show that the increased SR load in atrial myocytes predisposes these cells to subcellular Ca waves that occur during the action potential (AP) and are triggered by LCC openings. These waves are common in atrial cells because of the absence of a well-developed t-tubule system in most of these cells. This distinct spatial architecture allows for the presence of a large pool of orphaned ryanodine receptors, which can fire and sustain Ca waves during the AP. Finally, we incorporate our atrial cell model in two-dimensional tissue simulations and demonstrate that triggered wave generation in cells leads to electrical waves in tissue that tend to fractionate to form wavelets of excitation. This fractionation is driven by the underlying stochasticity of subcellular Ca waves, which perturbs AP repolarization and consequently induces localized conduction block in tissue. We outline the mechanism for this effect and argue that it may explain the propensity for atrial arrhythmias in HF.     

A mathematical model of spontaneous calcium release in cardiac myocytes

In cardiac myocytes, calcium (Ca) can be released from the sarcoplasmic reticulum independently of Ca influx from voltage-dependent membrane channels. This efflux of Ca, referred to as spontaneous Ca release (SCR), is due to Ryanodine receptor fluctuations, which can induce spontaneous Ca sparks, which propagate to form Ca waves. This release of Ca can then induce delayed after-depolarizations (DADs), which can lead to arrhythmogenic-triggered activity in the heart. However, despite its importance, to date there is no mathematical model of SCR that accounts for experimentally observed features of subcellular Ca. In this article, we present an experimentally based model of SCR that reproduces the timing distribution of spontaneous Ca sparks and key features of the propagation of Ca waves emanating from these spontaneous sparks. We have coupled this model to an ionic model for the rabbit ventricular action potential to simulate SCR within several thousand cells in cardiac tissue. We implement this model to study the formation of an ectopic beat on a cable of cells that exhibit SCR-induced DADs.     

Calcium-Voltage Coupling in the Genesis of Early and Delayed Afterdepolarizations in Cardiac Myocytes

Early afterdepolarizations (EADs) and delayed afterdepolarizations (DADs) are voltage oscillations known to cause cardiac arrhythmias. EADs are mainly driven by voltage oscillations in the repolarizing phase of the action potential (AP), while DADs are driven by spontaneous calcium (Ca) release during diastole. Because voltage and Ca are bidirectionally coupled, they modulate each other’s behaviors, and new AP and Ca cycling dynamics can emerge from this coupling. In this study, we performed computer simulations using an AP model with detailed spatiotemporal Ca cycling incorporating stochastic openings of Ca channels and ryanodine receptors to investigate the effects of Ca-voltage coupling on EAD and DAD dynamics. Simulations were complemented by experiments in mouse ventricular myocytes. We show that: 1) alteration of the Ca transient due to increased ryanodine receptor leakiness and/or sarco/endoplasmic reticulum Ca ATPase activity can either promote or suppress EADs due to the complex effects of Ca on ionic current properties; 2) spontaneous Ca waves also exhibit complex effects on EADs, but cannot induce EADs of significant amplitude without the participation of I_Ca,L; 3) lengthening AP duration and the occurrence of EADs promote DADs by increasing intracellular Ca loading, and two mechanisms of DADs are identified, i.e., Ca-wave-dependent and Ca-wave-independent; and 4) Ca-voltage coupling promotes complex EAD patterns such as EAD alternans that are not observed for solely voltage-driven EADs. In conclusion, Ca-voltage coupling combined with the nonlinear dynamical behaviors of voltage and Ca cycling play a key role in generating complex EAD and DAD dynamics observed experimentally in cardiac myocytes, whose mechanisms are complex but analyzable.     

Mechanistic link between CaM-RyR2 interactions and the genesis of cardiac arrhythmia

In this study, we develop a computational model of the interaction between ryanodine receptor type 2 (RyR2) and calmodulin (CaM) to explore the mechanistic link between CaM-RyR2 interactions and cardiac arrhythmia. Our starting point is a biophysically based computational model of CaM binding to a single RyR2 subunit, which reproduces single-channel RyR2 measurements in lipid bilayers. We then integrate this CaM-RyR2 model into a spatially distributed whole-cell model of Ca cycling, which is used to investigate the relationship between CaM and Ca cycling homeostasis. We show that a reduction in CaM concentration leads to a substantial increase in the rate of spontaneous Ca sparks, and this induces a marked reduction in sarcoplasmic reticulum Ca load during steady-state pacing. Also, we show that a reduction in CaM modifies the RyR2 open probability, which makes the cell more prone to Ca wave propagation. These results indicate that aberrant Ca cycling activity during pacing is determined by the interplay between sarcoplasmic reticulum load reduction and the threshold for Ca wave propagation. Based on these results, we show that when CaM is reduced, Ca waves can occur in a cell and induce action potential perturbations that are arrhythmogenic. Thus, this study outlines a novel, to our knowledge, mechanistic link between CaM-RyR2 binding kinetics and the induction of arrhythmias in the heart.     

Intracellular Ca(2+) dynamics and the stability of ventricular tachycardia

Ventricular fibrillation (VF), the major cause of sudden cardiac death, is typically preceded by ventricular tachycardia (VT), but the mechanisms underlying the transition from VT to VF are poorly understood. Intracellular Ca(2+) overload occurs during rapid heart rates typical of VT and is also known to promote arrhythmias. We therefore studied the role of intracellular Ca(2+) dynamics in the transition from VT to VF, using a combined experimental and mathematical modeling approach. Our results show that 1) rapid pacing of rabbit ventricular myocytes at 35 degrees C led to increased intracellular Ca(2+) levels and complex patterns of action potential (AP) configuration and the intracellular Ca(2+) transients; 2) the complex patterns of the Ca(2+) transient arose directly from the dynamics of intracellular Ca(2+) cycling, and were not merely passive responses to beat-to-beat alterations in AP; 3) the complex Ca(2+) dynamics were simulated in a modified version of the Luo-Rudy (LR) ventricular action potential with improved intracellular Ca(2+) dynamics, and showed good agreement with the experimental findings in isolated myocytes; and 4) when incorporated into simulated two-dimensional cardiac tissue, this action potential model produced a form of spiral wave breakup from VT to a VF-like state in which intracellular Ca(2+) dynamics played a key role through its influence on Ca(2+)-sensitive membrane currents such as I(Ca), I(NaCa), and I(ns(Ca)). To the extent that spiral wave breakup is useful as a model for the transition from VT to VF, these findings suggest that intracellular Ca(2+) dynamics may play an important role in the destabilization of VT and its degeneration into VF.     

A Comparative Study of Early Afterdepolarization-Mediated Fibrillation in Two Mathematical Models for Human Ventricular Cells

Early afterdepolarizations (EADs), which are abnormal oscillations of the membrane potential at the plateau phase of an action potential, are implicated in the development of cardiac arrhythmias like Torsade de Pointes. We carry out extensive numerical simulations of the TP06 and ORd mathematical models for human ventricular cells with EADs. We investigate the different regimes in both these models, namely, the parameter regimes where they exhibit (1) a normal action potential (AP) with no EADs, (2) an AP with EADs, and (3) an AP with EADs that does not go back to the resting potential. We also study the dependence of EADs on the rate of at which we pace a cell, with the specific goal of elucidating EADs that are induced by slow or fast rate pacing. In our simulations in two- and three-dimensional domains, in the presence of EADs, we find the following wave types: (A) waves driven by the fast sodium current and the L-type calcium current (Na-Ca-mediated waves); (B) waves driven only by the L-type calcium current (Ca-mediated waves); (C) phase waves, which are pseudo-travelling waves. Furthermore, we compare the wave patterns of the various wave-types (Na-Ca-mediated, Ca-mediated, and phase waves) in both these models. We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca-mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves. However, there are quantitative differences in the wave patterns of each wave type. The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not. The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model.     

Action potential and contractility changes in [Na(+)](i) overloaded cardiac myocytes: a simulation study

Sodium overload of cardiac cells can accompany various pathologies and induce fatal cardiac arrhythmias. We investigate effects of elevated intracellular sodium on the cardiac action potential (AP) and on intracellular calcium using the Luo-Rudy model of a mammalian ventricular myocyte. The results are: 1) During rapid pacing, AP duration (APD) shortens in two phases, a rapid phase without Na(+) accumulation and a slower phase that depends on [Na(+)](i). 2) The rapid APD shortening is due to incomplete deactivation (accumulation) of I(Ks). 3) The slow phase is due to increased repolarizing currents I(NaK) and reverse-mode I(NaCa), secondary to elevated [Na(+)](i). 4) Na(+)-overload slows the rate of AP depolarization, allowing time for greater I(Ca(L)) activation; it also enhances reverse-mode I(NaCa). The resulting increased Ca(2+) influx triggers a greater [Ca(2+)](i) transient. 5) Reverse-mode I(NaCa) alone can trigger Ca(2+) release in a voltage and [Na(+)](i)-dependent manner. 6) During I(NaK) block, Na(+) and Ca(2+) accumulate and APD shortens due to enhanced reverse-mode I(NaCa); contribution of I(K(Na)) to APD shortening is negligible. By slowing AP depolarization (hence velocity) and shortening APD, Na(+)-overload acts to enhance inducibility of reentrant arrhythmias. Shortened APD with elevated [Ca(2+)](i) (secondary to Na(+)-overload) also predisposes the myocardium to arrhythmogenic delayed afterdepolarizations.     

The statistics of calcium-mediated focal excitations on a one-dimensional cable

It is well known that various cardiac arrhythmias are initiated by an ill-timed excitation that originates from a focal region of the heart. However, up to now, it is not known what governs the timing, location, and morphology of these focal excitations. Recent studies have shown that these excitations can be caused by abnormalities in the calcium (Ca) cycling system. However, the cause-and-effect relationships linking subcellular Ca dynamics and focal activity in cardiac tissue is not completely understood. In this article, we present a minimal model of Ca-mediated focal excitations in cardiac tissue. This model accounts for the stochastic nature of spontaneous Ca release on a one-dimensional cable of cardiac cells. Using this model, we show that the timing of focal excitations is equivalent to a first passage time problem in a spatially extended system. In particular, we find that for a short cable the mean first passage time increases exponentially with the number of cells in tissue, and is critically dependent on the ratio of inward to outward currents near the threshold for an action potential. For long cables excitations occurs due to ectopic foci that occur on a length scale determined by the minimum length of tissue that can induce an action potential. Furthermore, we find that for long cables the mean first passage time decreases as a power law in the number cells. These results provide precise criteria for the occurrence of focal excitations in cardiac tissue, and will serve as a guide to determine the propensity of Ca-mediated triggered arrhythmias in the heart.     

Complete Atrial-Specific Knockout of Sodium-Calcium Exchange Eliminates Sinoatrial Node Pacemaker Activity

The origin of sinoatrial node (SAN) pacemaker activity in the heart is controversial. The leading candidates are diastolic depolarization by “funny” current (I_f) through HCN4 channels (the “Membrane Clock“ hypothesis), depolarization by cardiac Na-Ca exchange (NCX1) in response to intracellular Ca cycling (the "Calcium Clock" hypothesis), and a combination of the two (“Coupled Clock”). To address this controversy, we used Cre/loxP technology to generate atrial-specific NCX1 KO mice. NCX1 protein was undetectable in KO atrial tissue, including the SAN. Surface ECG and intracardiac electrograms showed no atrial depolarization and a slow junctional escape rhythm in KO that responded appropriately to β-adrenergic and muscarinic stimulation. Although KO atria were quiescent they could be stimulated by external pacing suggesting that electrical coupling between cells remained intact. Despite normal electrophysiological properties of I_f in isolated patch clamped KO SAN cells, pacemaker activity was absent. Recurring Ca sparks were present in all KO SAN cells, suggesting that Ca cycling persists but is uncoupled from the sarcolemma. We conclude that NCX1 is required for normal pacemaker activity in murine SAN.     

Muscarinic modulation of cardiac activity

The goal of the present review is to report information concerning cardiac innervation or more precisely to approach the modulation of cardiac electrical and mechanical activity by parasympathetic innervation. Acetylcholine (ACh) release by nerve endings from the vagus nerve hyperpolarizes the membrane, shortens action potential (AP) duration and has a negative inotropic effect on cardiac muscle. Toxins are usefull tools in the study of membrane signals. The Caribbean ciguatoxin (C-CTX-1) has a muscarinic effect on frog atrial fibres. The toxin evokes the release of ACh from motoneuron nerve terminals innervating this tissue which allows us to propose a model, similar to the one of the neuromuscular junction (nmj), to describe the events occurring during the triggering and release of ACh. Trachynilysin (TLY) is a proteic toxin which causes an influx of Ca2+ into the cells and releases ACh from nmj synaptic vesicles. TLY has a muscarinic effect on atrial fibres which is explicated in the release of neurotransmitter from the nerve endings generated by the TLY-induced Ca2+ influx. It is known that ACh release from nmj is known to be due to exocytosis of synaptic vesicles via the activation of a proteic complex blocked by botulinum toxins. One of these proteins SNAP-25 is the target of type A botulinum toxin (BoNT/A). The study of hearts isolated from BoNT/A poisoned frogs show that atrial AP is lengthened and reveals the presence of SNAP-25 in nerve endings of this tissue. Moreover, the electrical activity of ventricular muscle is markedly altered; in BoNT/A treated frog, an important outward current activated by internal Ca2+ develops. ACh released from nerve terminals binds to a G protein coupled membrane receptor and activates a K+ channel and other effectors. Five subtypes of muscarinic receptors have been cloned from different tissue (M1, M2, M3, M4) subtypes have been identified in cardiac tissues throughout many species. These receptors coupled with different G-proteins activate different effectors. M1 receptors modulate the cardiac plateau and therefore the magnitude of the peak contraction. M2 receptors are mainly involved in the repolarization phase of the AP and modulate the duration of the peak contraction. The roles of M3 and M4 are not yet clearly defined; however, they may activate K+ currents. In conclusion, ACh releases from parasympathetic nerve endings which innervate cardiac cells follows to similar events (Ca2+ influx; presence of a SNAP-25 protein) to those which produce ACh release from nmj, stimulates different G proteins coupled muscarinic receptors, and activates different effectors involved in the modulation of cardiac electrical and mechanical activity.     

Simulations of propagated mouse ventricular action potentials: effects of molecular heterogeneity

The molecular heterogeneity of repolarizing currents produces significant spatial heterogeneity and/or dispersion of repolarization in many mammalian cardiac tissues. Transgenic mice are prominent experimental models for the study of the molecular basis of repolarization and arrhythmias. However, it is debated whether the small mouse heart can sustain physiologically relevant heterogeneity of repolarization. We used a comprehensive model of the mouse action potential (AP) to predict how small a region of the cardiac tissue can maintain spatial gradients of repolarization due to differential expression of channels. Our simulations of a one-dimensional multicellular ring or cable predict that substantial gradients in repolarization and intracellular Ca(2+) concentration transients can be maintained through heterogeneity of expression of K(+) channels in distances of approximately 10 cells that are sufficient to block propagation. The abruptness of expression gradients and the site of stimulation can cause Ca(2+) transient oscillations and affect the stability of Ca(2+) dynamics and AP propagation. Two different mechanisms of instability of AP propagation in one-dimensional cable occur at fast pacing rates. Transitions from periodic activity to alternans or to irregular behavior were observed. Abrupt gradients of channel expression can cause alternans at slower pacing rates than gradual changes. Our simulations demonstrate the importance of incorporating realistic Ca(2+) dynamics and current densities into models of propagated AP. They also emphasize that microscopic aspects of tissue organization are important for predicting large-scale propagation phenomena. Finally, our results predict that the mouse heart should be able to sustain substantial molecularly based heterogeneity of repolarization.     

Propagation of the apoptotic signal by mitochondrial waves

Generation of mitochondrial signals is believed to be important in the commitment to apoptosis, but the mechanisms coordinating the output of individual mitochondria remain elusive. We show that in cardiac myotubes exposed to apoptotic agents, Ca2+ spikes initiate depolarization of mitochondria in discrete subcellular regions, and these mitochondria initiate slow waves of depolarization and Ca2+ release propagating through the cell. Traveling mitochondrial waves are prevented by Bcl-x(L), involve permeability transition pore (PTP) opening, and yield cytochrome c release, caspase activation and nuclear apoptosis. Mitochondrial Ca2+ uptake is critical for wave propagation, and mitochondria at the origin of waves take up Ca2+ particularly effectively, providing a mechanism that may underlie selection of the initiation sites. Thus, apoptotic agents transform the mitochondria into an excitable state by sensitizing PTP to Ca2+. Expansion of the local excitation by mitochondrial waves propagating through the whole cell can be especially important in activation of the apoptotic machinery in large cells.     

3D virtual human atria: A computational platform for studying clinical atrial fibrillation

Despite a vast amount of experimental and clinical data on the underlying ionic, cellular and tissue substrates, the mechanisms of common atrial arrhythmias (such as atrial fibrillation, AF) arising from the functional interactions at the whole atria level remain unclear. Computational modelling provides a quantitative framework for integrating such multi-scale data and understanding the arrhythmogenic behaviour that emerges from the collective spatio-temporal dynamics in all parts of the heart. In this study, we have developed a multi-scale hierarchy of biophysically detailed computational models for the human atria - the 3D virtual human atria. Primarily, diffusion tensor MRI reconstruction of the tissue geometry and fibre orientation in the human sinoatrial node (SAN) and surrounding atrial muscle was integrated into the 3D model of the whole atria dissected from the Visible Human dataset. The anatomical models were combined with the heterogeneous atrial action potential (AP) models, and used to simulate the AP conduction in the human atria under various conditions: SAN pacemaking and atrial activation in the normal rhythm, break-down of regular AP wave-fronts during rapid atrial pacing, and the genesis of multiple re-entrant wavelets characteristic of AF. Contributions of different properties of the tissue to mechanisms of the normal rhythm and arrhythmogenesis were investigated. Primarily, the simulations showed that tissue heterogeneity caused the break-down of the normal AP wave-fronts at rapid pacing rates, which initiated a pair of re-entrant spiral waves; and tissue anisotropy resulted in a further break-down of the spiral waves into multiple meandering wavelets characteristic of AF. The 3D virtual atria model itself was incorporated into the torso model to simulate the body surface ECG patterns in the normal and arrhythmic conditions. Therefore, a state-of-the-art computational platform has been developed, which can be used for studying multi-scale electrical phenomena during atrial conduction and AF arrhythmogenesis. Results of such simulations can be directly compared with electrophysiological and endocardial mapping data, as well as clinical ECG recordings. The virtual human atria can provide in-depth insights into 3D excitation propagation processes within atrial walls of a whole heart in vivo, which is beyond the current technical capabilities of experimental or clinical set-ups.     

Criticality in intracellular calcium signaling in cardiac myocytes

Calcium (Ca) is a ubiquitous second messenger that regulates many biological functions. The elementary events of local Ca signaling are Ca sparks, which occur randomly in time and space, and integrate to produce global signaling events such as intra- and intercellular Ca waves and whole-cell Ca oscillations. Despite extensive experimental characterization in many systems, the transition from local random to global synchronous events is still poorly understood. Here we show that criticality, a ubiquitous dynamical phenomenon in nature, is responsible for the transition from local to global Ca signaling. We demonstrate this first in a computational model of Ca signaling in a cardiac myocyte and then experimentally in mouse ventricular myocytes, complemented by a theoretical agent-based model to delineate the underlying dynamics. We show that the interaction between the Ca release units via Ca-induced Ca release causes self-organization of Ca spark clusters. When the coupling between Ca release units is weak, the cluster-size distribution is exponential. As the interactions become strong, the cluster-size distribution changes to a power-law distribution, which is characteristic of criticality in thermodynamic and complex nonlinear systems, and facilitates the formation and propagation of Ca waves and whole-cell Ca oscillations. Our findings illustrate how criticality is harnessed by a biological cell to regulate Ca signaling via self-organization of random subcellular events into cellular-scale oscillations, and provide a general theoretical framework for the transition from local Ca signaling to global Ca signaling in biological cells.     

Early development of intracellular calcium cycling defects in intact hearts of spontaneously hypertensive rats

Defects in excitation-contraction coupling have been reported in failing hearts, but little is known about the relationship between these defects and the development of heart failure (HF). We compared the early changes in intracellular Ca(2+) cycling to those that underlie overt pump dysfunction and arrhythmogenesis found later in HF. Laser-scanning confocal microscopy was used to measure Ca(2+) transients in myocytes of intact hearts in Wistar-Kyoto (WKY) rats and spontaneously hypertensive rats (SHRs) at different ages. Early compensatory mechanisms include a positive inotropic effect in SHRs at 7.5-9 mo compared with 6 mo. Ca(2+) transient duration increased at 9 mo in SHRs, indicating changes in Ca(2+) reuptake during decompensation. Cell-to-cell variability in Ca(2+) transient duration increased at 7.5 mo, decreased at 9 mo, and increased again at 22 mo (overt HF), indicating extensive intercellular variability in Ca(2+) transient kinetics during disease progression. Vulnerability to intercellular concordant Ca(2+) alternans increased at 9-22 mo in SHRs and was mirrored by a slowing in Ca(2+) transient restitution, suggesting that repolarization alternans and the resulting repolarization gradients might promote reentrant arrhythmias early in disease development. Intercellular discordant and subcellular Ca(2+) alternans increased as early as 7.5 mo in SHRs and may also promote arrhythmias during the compensated phase. The incidence of spontaneous and triggered Ca(2+) waves was increased in SHRs at all ages, suggesting a higher likelihood of triggered arrhythmias in SHRs compared with WKY rats well before HF develops. Thus serious and progressive defects in Ca(2+) cycling develop in SHRs long before symptoms of HF occur. Defective Ca(2+) cycling develops early and affects a small number of myocytes, and this number grows with age and causes the transition from asymptomatic to overt HF. These defects may also underlie the progressive susceptibility to Ca(2+) alternans and Ca(2+) wave activity, thus increasing the propensity for arrhythmogenesis in HF.     

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.     

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.     

Mechanisms of Transition from Normal to Reentrant Electrical Activity in a Model of Rabbit Atrial Tissue: Interaction of Tissue Heterogeneity and Anisotropy

Experimental evidence suggests that regional differences in action potential (AP) morphology can provide a substrate for initiation and maintenance of reentrant arrhythmias in the right atrium (RA), but the relationships between the complex electrophysiological and anatomical organization of the RA and the genesis of reentry are unclear. In this study, a biophysically detailed three-dimensional computer model of the right atrial tissue was constructed to study the role of tissue heterogeneity and anisotropy in arrhythmogenesis. The model of Lindblad et al. for a rabbit atrial cell was modified to incorporate experimental data on regional differences in several ionic currents (primarily, I_Na, I_CaL, I_K1, I_to, and I_sus) between the crista terminalis and pectinate muscle cells. The modified model was validated by its ability to reproduce the AP properties measured experimentally. The anatomical model of the rabbit RA (including tissue geometry and fiber orientation) was based on a recent histological reconstruction. Simulations with the resultant electrophysiologically and anatomically detailed three-dimensional model show that complex organization of the RA tissue causes breakdown of regular AP conduction patterns at high pacing rates (>11.75 Hz): as the AP in the crista terminalis cells is longer, and electrotonic coupling transverse to fibers of the crista terminalis is weak, high-frequency pacing at the border between the crista terminalis and pectinate muscles results in a unidirectional conduction block toward the crista terminalis and generation of reentry. Contributions of the tissue heterogeneity and anisotropy to reentry initiation mechanisms are quantified by measuring action potential duration (APD) gradients at the border between the crista terminalis and pectinate muscles: the APD gradients are high in areas where both heterogeneity and anisotropy are high, such that intrinsic APD differences are not diminished by electrotonic interactions. Thus, our detailed computer model reconstructs complex electrical activity in the RA, and provides new insights into the mechanisms of transition from focal atrial tachycardia into reentry.     

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.