Subcellular Ca2+ alternans represents a novel mechanism for the generation of arrhythmogenic Ca2+ waves in cat atrial myocytes

Role of Mitochondrial ROS for Calcium Alternans in Atrial Myocytes

Atrial calcium transient (CaT) alternans is defined as beat-to-beat alternations in CaT amplitude and is causally linked to atrial fibrillation (AF). Mitochondria play a significant role in cardiac excitation-contraction coupling and Ca signaling through redox environment regulation. In isolated rabbit atrial myocytes, ROS production is enhanced during CaT alternans, measured by fluorescence microscopy. Exogenous ROS (tert-butyl hydroperoxide) enhanced CaT alternans, whereas ROS scavengers (dithiothreitol, MnTBAP, quercetin, tempol) alleviated CaT alternans. While the inhibition of cellular NADPH oxidases had no effect on CaT alternans, interference with mitochondrial ROS (ROSm) production had profound effects: (1) the superoxide dismutase mimetic MitoTempo diminished CaT alternans and shifted the pacing threshold to higher frequencies; (2) the inhibition of cyt c peroxidase by SS-31, and inhibitors of ROSm production by complexes of the electron transport chain S1QEL1.1 and S3QEL2, decreased the severity of CaT alternans; however (3) the impairment of mitochondrial antioxidant defense by the inhibition of nicotinamide nucleotide transhydrogenase with NBD-Cl and thioredoxin reductase-2 with auranofin enhanced CaT alternans. Our results suggest that intact mitochondrial antioxidant defense provides crucial protection against pro-arrhythmic CaT alternans. Thus, modulating the mitochondrial redox state represents a potential therapeutic approach for alternans-associated arrhythmias, including AF.

Calcium- and voltage-driven atrial alternans: Insight from [Ca]i and Vm asynchrony

Cardiac alternans is defined as beat-to-beat alternations in contraction strength, action potential duration (APD), and Ca transient (CaT) amplitude. Cardiac excitation-contraction coupling relies on the activity of two bidirectionally coupled excitable systems, membrane voltage (Vm ) and Ca release. Alternans has been classified as Vm - or Ca-driven, depending whether a disturbance of Vm or [Ca]i regulation drives the alternans. We determined the primary driver of pacing induced alternans in rabbit atrial myocytes, using combined patch clamp and fluorescence [Ca]i and Vm measurements. APD and CaT alternans are typically synchronized; however, uncoupling between APD and CaT regulation can lead to CaT alternans in the absence of APD alternans, and APD alternans can fail to precipitate CaT alternans, suggesting a considerable degree of independence of CaT and APD alternans. Using alternans AP voltage clamp protocols with extra APs showed that most frequently the pre-existing CaT alternans pattern prevailed after the extra-beat, indicating that alternans is Ca-driven. In electrically coupled cell pairs, dyssynchrony of APD and CaT alternans points to autonomous regulation of CaT alternans. Thus, with three novel experimental protocols, we collected evidence for Ca-driven alternans; however, the intimately intertwined regulation of Vm and [Ca]i precludes entirely independent development of CaT and APD alternans.

Targeted Atrial Fibrillation Therapy and Risk Stratification Using Atrial Alternans

Atrial fibrillation (AF) is the most persistent arrhythmia today, with its prevalence increasing exponentially with the rising age of the population. Particularly at elevated heart rates, a functional abnormality known as cardiac alternans can occur prior to the onset of lethal arrhythmias. Cardiac alternans are a beat-to-beat oscillation of electrical activity and the force of cardiac muscle contraction. Extensive evidence has demonstrated that microvolt T-wave alternans can predict ventricular fibrillation vulnerability and the risk of sudden cardiac death. The majority of our knowledge of the mechanisms of alternans stems from studies of ventricular electrophysiology, although recent studies offer promising evidence of the potential of atrial alternans in predicting the risk of AF. Exciting preclinical and clinical studies have demonstrated a link between atrial alternans and the onset of atrial tachyarrhythmias. Here, we provide a comprehensive review of the clinical utility of atrial alternans in identifying the risk and guiding treatment of AF.

Cardiac Alternans: From Bedside to Bench and Back

Cardiac alternans arises from dynamical instabilities in the electrical and calcium cycling systems of the heart, and often precedes ventricular arrhythmias and sudden cardiac death. In this review, we integrate clinical observations with theory and experiment to paint a holistic portrait of cardiac alternans: the underlying mechanisms, arrhythmic manifestations and electrocardiographic signatures. We first summarize the cellular and tissue mechanisms of alternans that have been demonstrated both theoretically and experimentally, including 3 voltage-driven and 2 calcium-driven alternans mechanisms. Based on experimental and simulation results, we describe their relevance to mechanisms of arrhythmogenesis under different disease conditions, and their link to electrocardiographic characteristics of alternans observed in patients. Our major conclusion is that alternans is not only a predictor, but also a causal mechanism of potentially lethal ventricular and atrial arrhythmias across the full spectrum of arrhythmia mechanisms that culminate in functional reentry, although less important for anatomic reentry and focal arrhythmias.

The 'Reverse FDUF' Mechanism of Atrial Excitation-Contraction Coupling Sustains Calcium Alternans-A Hypothesis

Cardiac calcium alternans is defined as beat-to-beat alternations of Ca transient (CaT) amplitude and has been linked to cardiac arrhythmia, including atrial fibrillation. We investigated the mechanism of atrial alternans in isolated rabbit atrial myocytes using high-resolution line scan confocal Ca imaging. Alternans was induced by increasing the pacing frequency until stable alternans was observed (1.6-2.5 Hz at room temperature). In atrial myocytes, action potential-induced Ca release is initiated in the cell periphery and subsequently propagates towards the cell center by Ca-induced Ca release (CICR) in a Ca wave-like fashion, driven by the newly identified 'fire-diffuse-uptake-fire' (FDUF) mechanism. The development of CaT alternans was accompanied by characteristic changes of the spatio-temporal organization of the CaT. During the later phase of the CaT, central [Ca]_i exceeded peripheral [Ca]_i that was indicative of a reversal of the subcellular [Ca]_i gradient from centripetal to centrifugal. This gradient reversal resulted in a reversal of CICR propagation, causing a secondary Ca release during the large-amplitude alternans CaT, thereby prolonging the CaT, enhancing Ca-release refractoriness and reducing Ca release on the subsequent beat, thus enhancing the degree of CaT alternans. Here, we propose the 'reverse FDUF' mechanism as a novel cellular mechanism of atrial CaT alternans, which explains how the uncoupling of central from peripheral Ca release leads to the reversal of propagating CICR and to alternans.

The physics of heart rhythm disorders

The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.

Synchronization of spatially discordant voltage and calcium alternans in cardiac tissue

The heart is an excitable medium which is excited by membrane potential depolarization and propagation. Membrane potential depolarization brings in calcium (Ca) through the Ca channels to trigger intracellular Ca release for contraction of the heart. Ca also affects voltage via Ca-dependent ionic currents, and thus, voltage and Ca are bidirectionally coupled. It has been shown that the voltage subsystem or the Ca subsystem can generate its own dynamical instabilities which are affected by their bidirectional couplings, leading to complex dynamics of action potential and Ca cycling. Moreover, the dynamics become spatiotemporal in tissue in which cells are diffusively coupled through voltage. A widely investigated spatiotemporal dynamics is spatially discordant alternans (SDA) in which action potential duration (APD) or Ca amplitude exhibits temporally period-2 and spatially out-of-phase patterns, i.e., APD-SDA and Ca-SDA patterns, respectively. However, the mechanisms of formation, stability, and synchronization of APD-SDA and Ca-SDA patterns remain incompletely understood. In this paper, we use cardiac tissue models described by an amplitude equation, coupled iterated maps, and reaction-diffusion equations with detailed physiology (the ionic model) to perform analytical and computational investigations. We show that, when the Ca subsystem is stable, the Ca-SDA pattern always follows the APD-SDA pattern, and thus, they are always synchronized. When the Ca subsystem is unstable, synchronization of APD-SDA and Ca-SDA patterns depends on the stabilities of both subsystems, their coupling strengths, and the spatial scales of the initial Ca-SDA patterns. Spontaneous (initial condition-independent) synchronization is promoted by enhancing APD instability and reducing Ca instability as well as stronger Ca-to-APD and APD-to-Ca coupling, a pattern formation caused by dynamical instabilities. When Ca is more unstable and APD is less unstable or APD-to-Ca coupling is weak, synchronization of APD-SDA and Ca-SDA patterns is promoted by larger initially synchronized Ca-SDA clusters, i.e., initial condition-dependent synchronization. The synchronized APD-SDA and Ca-SDA patterns can be locked in-phase, antiphase, or quasiperiodic depending on the coupling relationship between APD and Ca. These theoretical and simulation results provide mechanistic insights into the APD-SDA and Ca-SDA dynamics observed in experimental studies.

Cardiac Alternans Occurs through the Synergy of Voltage- and Calcium-Dependent Mechanisms

Cardiac alternans is characterized by alternating weak and strong beats of the heart. This signaling at the cellular level may appear as alternating long and short action potentials (APs) that occur in synchrony with alternating large and small calcium transients, respectively. Previous studies have suggested that alternans manifests itself through either a voltage dependent mechanism based upon action potential restitution or as a calcium dependent mechanism based on refractoriness of calcium release. We use a novel model of cardiac excitation-contraction (EC) coupling in the rat ventricular myocyte that includes 20,000 calcium release units (CRU) each with 49 ryanodine receptors (RyR2s) and 7 L-type calcium channels that are all stochastically gated. The model suggests that at the cellular level in the case of alternans produced by rapid pacing, the mechanism requires a synergy of voltage- and calcium-dependent mechanisms. The rapid pacing reduces AP duration and magnitude reducing the number of L-type calcium channels activating individual CRUs during each AP and thus increases the population of CRUs that can be recruited stochastically. Elevated myoplasmic and sarcoplasmic reticulum (SR) calcium, [Ca2+]myo and [Ca2+]SR respectively, increases ryanodine receptor open probability (Po) according to our model used in this simulation and this increased the probability of activating additional CRUs. A CRU that opens in one beat is less likely to open the subsequent beat due to refractoriness caused by incomplete refilling of the junctional sarcoplasmic reticulum (jSR). Furthermore, the model includes estimates of changes in Na+ fluxes and [Na+]i and thus provides insight into how changes in electrical activity, [Na+]i and sodium-calcium exchanger activity can modulate alternans. The model thus tracks critical elements that can account for rate-dependent changes in [Na+]i and [Ca2+]myo and how they contribute to the generation of Ca2+ signaling alternans in the heart.

Excitation-contraction coupling and calcium release in atrial muscle

In cardiac muscle, the process of excitation-contraction coupling (ECC) describes the chain of events that links action potential induced myocyte membrane depolarization, surface membrane ion channel activation, triggering of Ca²⁺ induced Ca²⁺ release from the sarcoplasmic reticulum (SR) Ca²⁺ store to activation of the contractile machinery that is ultimately responsible for the pump function of the heart. Here we review similarities and differences of structural and functional attributes of ECC between atrial and ventricular tissue. We explore a novel "fire-diffuse-uptake-fire" paradigm of atrial ECC and Ca²⁺ release that assigns a novel role to the SR SERCA pump and involves a concerted "tandem" activation of the ryanodine receptor Ca²⁺ release channel by cytosolic and luminal Ca²⁺. We discuss the contribution of the inositol 1,4,5-trisphosphate (IP₃) receptor Ca²⁺ release channel as an auxiliary pathway to Ca²⁺ signaling, and we review IP₃ receptor-induced Ca²⁺ release involvement in beat-to-beat ECC, nuclear Ca²⁺ signaling, and arrhythmogenesis. Finally, we explore the topic of electromechanical and Ca²⁺ alternans and its ramifications for atrial arrhythmia.

Delayed global feedback in the genesis and stability of spatiotemporal excitation patterns in paced biological excitable media

Biological excitable media, such as cardiac or neural cells and tissue, exhibit memory in which a change in the present excitation may affect the behaviors in the next excitation. For example, a change in calcium (Ca²⁺) concentration in a cell in the present excitation may affect the Ca²⁺ dynamics in the next excitation via bi-directional coupling between voltage and Ca²⁺, forming a delayed feedback loop. Since the Ca²⁺ dynamics inside the excitable cells are spatiotemporal while the membrane voltage is a global signal, the feedback loop is then a delayed global feedback (DGF) loop. In this study, we investigate the roles of DGF in the genesis and stability of spatiotemporal excitation patterns in periodically-paced excitable media using mathematical models with different levels of complexity: a model composed of coupled FitzHugh-Nagumo units, a 3-dimensional physiologically-detailed ventricular myocyte model, and a coupled map lattice model. We investigate the dynamics of excitation patterns that are temporal period-2 (P2) and spatially concordant or discordant, such as subcellular concordant or discordant Ca²⁺alternans in cardiac myocytes or spatially concordant or discordant Ca²⁺ and repolarization alternans in cardiac tissue. Our modeling approach allows both computer simulations and rigorous analytical treatments, which lead to the following results and conclusions. When DGF is absent, concordant and discordant P2 patterns occur depending on initial conditions with the discordant P2 patterns being spatially random. When the DGF is negative, only concordant P2 patterns exist. When the DGF is positive, both concordant and discordant P2 patterns can occur. The discordant P2 patterns are still spatially random, but they satisfy that the global signal exhibits a temporal period-1 behavior. The theoretical analyses of the coupled map lattice model reveal the underlying instabilities and bifurcations for the genesis, selection, and stability of spatiotemporal excitation patterns.

Understanding the mechanisms of pattern formation in biological systems is of great importance. Here we investigate the dynamical mechanisms by which delayed global feedback affects excitation pattern formation and stability in periodically-paced biological excitable media, such as cardiac or neural cells and tissue. We focus on the formation and stability of the temporal period-2 and spatially in-phase and out-of-phase excitation patterns. Using models of different levels of complexity, we show that when the delayed global feedback is negative, only the spatially in-phase patterns are stable. When the feedback is positive, both spatially in-phase and out-of-phase patterns are stable, and the out-of-phase patterns are spatially random but satisfy that the global signals are temporal period-1 solutions.

Dual regulation by subcellular calcium heterogeneity and heart rate variability on cardiac electromechanical dynamics

Heart rate constantly varies under physiological conditions, termed heart rate variability (HRV), and in clinical studies, low HRV is associated with a greater risk of cardiac arrhythmias. Prior work has shown that HRV influences the temporal patterns of electrical activity, specifically the formation of pro-arrhythmic alternans, a beat-to-beat alternation in the action potential duration (APD), or intracellular calcium (Ca) levels. We previously showed that HRV may be anti-arrhythmic by disrupting APD and Ca alternations in a homogeneous cardiac myocyte. Here, we expand on our previous work, incorporating variation in subcellular Ca handling (also known to influence alternans) into a nonlinear map model of a cardiac myocyte composed of diffusively coupled Ca release units (CRUs). Ca-related parameters and initial conditions of each CRU are varied to mimic subcellular Ca heterogeneity, and a stochastic pacing sequence reproduces HRV. We find that subcellular Ca heterogeneity promotes the formation of spatially discordant subcellular alternans patterns, which decreases whole cell Ca and APD alternation for low and moderate HRV, while high subcellular Ca heterogeneity and HRV both promote electromechanical desynchronization. Finally, we find that for low and moderate HRV, both the specific subcellular Ca-related parameters and the pacing sequences influence measures of electromechanical dynamics, while for high HRV, these measures depend predominantly on the pacing sequence. Our results suggest that pro-arrhythmic subcellular discordant alternans tend to form for low levels of HRV, while high HRV may be anti-arrhythmic due to mitigated influence from subcellular Ca heterogeneity and desynchronization of APD from Ca instabilities.

Mitochondrial calcium uniporter complex activation protects against calcium alternans in atrial myocytes

Cardiac alternans, defined as beat-to-beat alternations in action potential duration, cytosolic Ca transient (CaT) amplitude, and cardiac contraction is associated with atrial fibrillation (AF) and sudden cardiac death. At the cellular level, cardiac alternans is linked to abnormal intracellular calcium handling during excitation-contraction coupling. We investigated how pharmacological activation or inhibition of cytosolic Ca sequestration via mitochondrial Ca uptake and mitochondrial Ca retention affects the occurrence of pacing-induced CaT alternans in isolated rabbit atrial myocytes. Cytosolic CaTs were recorded using Fluo-4 fluorescence microscopy. Alternans was quantified as the alternans ratio (AR = 1 - CaT_small/CaT_large, where CaT_small and CaT_large are the amplitudes of the small and large CaTs of a pair of alternating CaTs). Inhibition of mitochondrial Ca sequestration via mitochondrial Ca uniporter complex (MCUC) with Ru360 enhanced the severity of CaT alternans (AR increase) and lowered the pacing frequency threshold for alternans. In contrast, stimulation of MCUC mediated mitochondrial Ca uptake with spermine-rescued alternans (AR decrease) and increased the alternans pacing threshold. Direct measurement of mitochondrial [Ca] in membrane permeabilized myocytes with Fluo-4 loaded mitochondria revealed that spermine enhanced and accelerated mitochondrial Ca uptake. Stimulation of mitochondrial Ca retention by preventing mitochondrial Ca efflux through the mitochondrial permeability transition pore with cyclosporin A also protected from alternans and increased the alternans pacing threshold. Pharmacological manipulation of MCUC activity did not affect sarcoplasmic reticulum Ca load. Our results suggest that activation of Ca sequestration by mitochondria protects from CaT alternans and could be a potential therapeutic target for cardiac alternans and AF prevention.NEW & NOTEWORTHY This study provides conclusive evidence that mitochondrial Ca uptake and retention protects from Ca alternans, whereas uptake inhibition enhances Ca alternans. The data suggest pharmacological mitochondrial Ca cycling modulation as a potential therapeutic strategy for alternans-related cardiac arrhythmia prevention.

Linking cellular energy state to atrial fibrillation pathogenesis: Potential role of adenosine monophosphate-activated protein kinase

Adenosine monophosphate-activated protein kinase (AMPK) is the cellular stress-sensing molecule. Apart from maintaining cellular energy balance, AMPK controls expression and regulation of ion channels and ion transporters, including cytosolic Ca²⁺ handling proteins. Emerging evidence suggests that metabolic impairment plays a crucial role in the pathogenesis of atrial fibrillation. AMPK activation is thought to be protective by preventing metabolic stress, favorably modulating membrane electrophysiology including cytosolic Ca²⁺ dynamics; preventing cellular growth; and hypertrophic remodeling. This review considers current concepts and evidence from clinical and experimental studies regarding the role of AMPK in atrial fibrillation.

Complex patterns of subcellular cardiac alternans

Cardiac alternans, in which the membrane potential and the intracellular calcium concentration exhibit alternating durations and peak amplitudes at consecutive beats, constitute a precursor to fatal cardiac arrhythmia such as sudden cardiac death. A crucial question therefore concerns the onset of cardiac alternans. Typically, alternans are only reported when they are fully developed. Here, we present a modelling approach to explore recently discovered microscopic alternans, which represent one of the earliest manifestations of cardiac alternans. In this case, the regular periodic dynamics of the local intracellular calcium concentration is already unstable, while the whole-cell behaviour suggests a healthy cell state. In particular, we use our model to investigate the impact of calcium diffusion in both the cytosol and the sarcoplasmic reticulum on the formation of microscopic calcium alternans. We find that for dominant cytosolic coupling, calcium alternans emerge via the traditional period doubling bifurcation. In contrast, dominant luminal coupling leads to a novel route to calcium alternans through a saddle-node bifurcation at the network level. Combining semi-analytical and computational approaches, we compute areas of stability in parameter space and find that as we cross from stable to unstable regions, the emergent patterns of the intracellular calcium concentration change abruptly in a fashion that is highly dependent upon position along the stability boundary. Our results demonstrate that microscopic calcium alternans may possess a much richer dynamical repertoire than previously thought and further strengthen the role of luminal calcium in shaping cardiac calcium dynamics.

German Cardiac Society Working Group on Cellular Electrophysiology state-of-the-art paper: impact of molecular mechanisms on clinical arrhythmia management

Cardiac arrhythmias remain a common challenge and are associated with significant morbidity and mortality. Effective and safe rhythm control strategies are a primary, yet unmet need in everyday clinical practice. Despite significant pharmacological and technological advances, including catheter ablation and device-based therapies, the development of more effective alternatives is of significant interest to increase quality of life and to reduce symptom burden, hospitalizations and mortality. The mechanistic understanding of pathophysiological pathways underlying cardiac arrhythmias has advanced profoundly, opening up novel avenues for mechanism-based therapeutic approaches. Current management of arrhythmias, however, is primarily guided by clinical and demographic characteristics of patient groups as opposed to individual, patient-specific mechanisms and pheno-/genotyping. With this state-of-the-art paper, the Working Group on Cellular Electrophysiology of the German Cardiac Society aims to close the gap between advanced molecular understanding and clinical decision-making in cardiac electrophysiology. The significance of cellular electrophysiological findings for clinical arrhythmia management constitutes the main focus of this document. Clinically relevant knowledge of pathophysiological pathways of arrhythmias and cellular mechanisms of antiarrhythmic interventions are summarized. Furthermore, the specific molecular background for the initiation and perpetuation of atrial and ventricular arrhythmias and mechanism-based strategies for therapeutic interventions are highlighted. Current "hot topics" in atrial fibrillation are critically appraised. Finally, the establishment and support of cellular and translational electrophysiology programs in clinical rhythmology departments is called for to improve basic-science-guided patient management.

On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling

The correspondence between mathematical structures and experimental systems is the basis of the generalizability of results found with specific systems and is the basis of the predictive power of theoretical physics. While physicists have confidence in this correspondence, it is less recognized in cellular biophysics. On the one hand, the complex organization of cellular dynamics involving a plethora of interacting molecules and the basic observation of cell variability seem to question its possibility. The practical difficulties of deriving the equations describing cellular behaviour from first principles support these doubts. On the other hand, ignoring such a correspondence would severely limit the possibility of predictive quantitative theory in biophysics. Additionally, the existence of functional modules (like pathways) across cell types suggests also the existence of mathematical structures with comparable universality. Only a few cellular systems have been sufficiently investigated in a variety of cell types to follow up these basic questions. IP₃ induced Ca²⁺signalling is one of them, and the mathematical structure corresponding to it is subject of ongoing discussion. We review the system's general properties observed in a variety of cell types. They are captured by a reaction diffusion system. We discuss the phase space structure of its local dynamics. The spiking regime corresponds to noisy excitability. Models focussing on different aspects can be derived starting from this phase space structure. We discuss how the initial assumptions on the set of stochastic variables and phase space structure shape the predictions of parameter dependencies of the mathematical models resulting from the derivation.

Transverse tubular network structures in the genesis of intracellular calcium alternans and triggered activity in cardiac cells

RATIONALE

The major role of a transverse-tubular (TT) network in a cardiac cell is to facilitate effective excitation-contraction coupling and signaling. The TT network structures are heterogeneous within a single cell, and vary between different types of cells and species. They are also remodeled in cardiac diseases. However, how different TT network structures predispose cardiac cells to arrhythmogenesis remains to be revealed.

OBJECTIVE

To systematically investigate the roles of TT network structure and the underlying mechanisms in the genesis of intracellular calcium (Ca2+) alternans and triggered activity (TA).

METHODS AND RESULTS

Based on recent experimental observations, different TT network structures, including uniformly and non-uniformly random TT distributions, were modeled in a cardiac cell model consisting of a three-dimensional network of Ca2+ release units (CRUs). Our simulations showed that both Ca2+ alternans and Ca2+ wave-mediated TA were promoted when the fraction of orphaned CRUs was in an intermediate range, but suppressed in cells exhibiting either well-organized TT networks or low TT densities. Ca2+ alternans and TA could be promoted by low TT densities when the cells were small or the CRU coupling was strong. Both alternans and TA occurred more easily in uniformly random TT networks than in non-uniformly random TT networks. Subcellular spatially discordant Ca2+ alternans was promoted by non-uniformly random TT networks but suppressed by increasing CRU coupling strength. These mechanistic insights provide a holistic understanding of the effects of TT network structure on the susceptibility to arrhythmogenesis.

CONCLUSIONS

The TT network plays important roles in promoting Ca2+ alternans and TA, and different TT network structures may predispose cardiac cells differently to arrhythmogenesis.

Spatiotemporally Non-Uniform Ca2+ Dynamics of Cardiac Purkinje Fibers in Mouse Myocardial Infarct

Surviving Purkinje fibers in myocardial infarct are regarded as an important substrate in arrhythmogenesis. However, poorly understood are functional properties of Purkinje fibers in the infarcted heart. We sought to visualize intracellular Ca²⁺ ([Ca²⁺]_i) dynamics of Purkinje fiber networks in the mouse myocardial infarct. Using 3- to 4-day-old or 7- to 9-day-old infarcted hearts after the left coronary-artery ligation corresponding, respectively, to acute or healing phase, we conducted rapid fluo4-fluorescence imaging on the endocardial surface of the left ventricular septum by macro-zoom fluorescence microscopy and rapid-scanning confocal microscopy. In contrast with the intact heart, where uniform Ca²⁺ transients propagated rapidly, the infarcted heart exhibited slow, non-uniform impulse propagations. On confocal microscopy, Purkinje fibers in the peri-infarct zone exhibited non-uniform [Ca²⁺]_i dynamics: beat-to-beat alternans of the Ca²⁺ transient amplitude in and among the individual fibers, whereas the intact fibers exhibited uniform Ca²⁺ transients. Such non-uniform [Ca²⁺]_i dynamics were more conspicuous in the acute infarcted hearts than in the healing ones. In accordance with [Ca²⁺]_i dynamics, fixed fluo4-loaded heart preparations exhibited definitive connexin-40 plaques in the peri-infarct Purkinje fibers, whereas the subjacent myocardium presented coagulative necrosis and granulation tissues, respectively. The surviving Purkinje fibers in the peri-infarct zone exhibited non-uniform [Ca²⁺]_i dynamics, which may lead to arrhythmogenesis.

Dynamics of spatiotemporal line defects and chaos control in complex excitable systems

Spatiotemporal pattern formation governs dynamics and functions in various biological systems. In the heart, excitable waves can form complex oscillatory and chaotic patterns even at an abnormally higher frequency than normal heart beats, which increase the risk of fatal heart conditions by inhibiting normal blood circulation. Previous studies suggested that line defects (nodal lines) play a critical role in stabilizing those undesirable patterns. However, it remains unknown if the line defects are static or dynamically changing structures in heart tissue. Through in vitro experiments of heart tissue observation, we reveal the spatiotemporal dynamics of line defects in rotating spiral waves. We combined a novel signaling over-sampling technique with a multi-dimensional Fourier analysis, showing that line defects can translate, merge, collapse and form stable singularities with even and odd parity while maintaining a stable oscillation of the spiral wave in the tissue. These findings provide insights into a broad class of complex periodic systems, with particular impact to the control and understanding of heart diseases.

Alternans in atria: Mechanisms and clinical relevance

Atrial fibrillation is the most common sustained arrhythmia and its prevalence is rapidly rising with the aging of the population. Cardiac alternans, defined as cyclic beat-to-beat alternations in contraction force, action potential (AP) duration and intracellular Ca²⁺ release at constant stimulation rate, has been associated with the development of ventricular arrhythmias. Recent clinical data also provide strong evidence that alternans plays a central role in arrhythmogenesis in atria. The aim of this article is to review the mechanisms that are responsible for repolarization alternans and contribute to the transition from spatially concordant alternans to the more arrhythmogenic spatially discordant alternans in atria.

Rate-dependent force, intracellular calcium, and action potential voltage alternans are modulated by sarcomere length and heart failure induced-remodeling of thin filament regulation in human heart failure: A myocyte modeling study

Microvolt T-wave alternans (MTWA) testing identifies heart failure patients at risk for lethal ventricular arrhythmias at near-resting heart rates (<110 beats per minute). Since pressure alternans occurs simultaneously with MTWA and has a higher signal to noise ratio, it may be a better predictor of arrhythmia, although the mechanism remains unknown. Therefore, we investigated the relationship between force alternans (FORCE-ALT), the cellular manifestation of pressure alternans, and action potential voltage alternans (APV-ALT), the cellular driver of MTWA. Our goal was to uncover the mechanisms linking APV-ALT and FORCE-ALT in failing human myocytes and to investigate how the link between those alternans was affected by pacing rate and by physiological conditions such as sarcomere length and heart failure induced-remodeling of mechanical parameters. To achieve this, a mechanically-based, strongly coupled human electromechanical myocyte model was constructed. Reducing the sarcoplasmic reticulum calcium uptake current (Iup) to 27% was incorporated to simulate abnormal calcium handling in human heart failure. Mechanical remodeling was incorporated to simulate altered thin filament activation and crossbridge (XB) cycling rates. A dynamical pacing protocol was used to investigate the development of intracellular calcium concentration ([Ca]i), voltage, and active force alternans at different pacing rates. FORCE-ALT only occurred in simulations incorporating reduced Iup, demonstrating that alternans in the intracellular calcium concentration (CA-ALT) induced FORCE-ALT. The magnitude of FORCE-ALT was found to be largest at clinically relevant pacing rates (<110 bpm), where APV-ALT was smallest. We found that the magnitudes of FORCE-ALT, CA-ALT and APV-ALT were altered by heart failure induced-remodeling of mechanical parameters and sarcomere length due to the presence of myofilament feedback. These findings provide important insight into the relationship between heart-failure-induced electrical and mechanical alternans and how they are altered by physiological conditions at near-resting heart rates.

Prevention of adenosine A2A receptor activation diminishes beat-to-beat alternation in human atrial myocytes

Atrial fibrillation (AF) has been associated with increased spontaneous calcium release from the sarcoplasmic reticulum and linked to increased adenosine A2A receptor (A2AR) expression and activation. Here we tested whether this may favor atrial arrhythmogenesis by promoting beat-to-beat alternation and irregularity. Patch-clamp and confocal calcium imaging was used to measure the beat-to-beat response of the calcium current and transient in human atrial myocytes. Responses were classified as uniform, alternating or irregular and stimulation of Gs-protein coupled receptors decreased the frequency where a uniform response could be maintained from 1.0 ± 0.1 to 0.6 ± 0.1 Hz; p < 0.01 for beta-adrenergic receptors and from 1.4 ± 0.1 to 0.5 ± 0.1 Hz; p < 0.05 for A2ARs. The latter was linked to increased spontaneous calcium release and after-depolarizations. Moreover, A2AR activation increased the fraction of non-uniformly responding cells in HL-1 myocyte cultures from 19 ± 3 to 51 ± 9 %; p < 0.02, and electrical mapping in perfused porcine atria revealed that adenosine induced electrical alternans at longer cycle lengths, doubled the fraction of electrodes showing alternation, and increased the amplitude of alternations. Importantly, protein kinase A inhibition increased the highest frequency where uniform responses could be maintained from 0.84 ± 0.12 to 1.86 ± 0.11 Hz; p < 0.001 and prevention of A2AR-activation with exogenous adenosine deaminase selectively increased the threshold from 0.8 ± 0.1 to 1.2 ± 0.1 Hz; p = 0.001 in myocytes from patients with AF. In conclusion, A2AR-activation promotes beat-to-beat irregularities in the calcium transient in human atrial myocytes, and prevention of A2AR activation may be a novel means to maintain uniform beat-to-beat responses at higher beating frequencies in patients with atrial fibrillation.

Absence of the Regulator of G-protein Signaling, RGS4, Predisposes to Atrial Fibrillation and Is Associated with Abnormal Calcium Handling

The description of potential molecular substrates for predisposition to atrial fibrillation (AF) is incomplete, and it is unknown what role regulators of G-protein signaling might play. We address whether the attenuation of RGS4 function may promote AF and the mechanism through which this occurs. For this purpose, we studied a mouse with global genetic deletion of RGS4 (RGS4(-/-)) and the normal littermate controls (RGS4(+/+)). In vivo electrophysiology using atrial burst pacing revealed that mice with global RGS4 deletion developed AF more frequently than control littermates. Isolated atrial cells from RGS4(-/-) mice show an increase in Ca(2+) spark frequency under basal conditions and after the addition of endothelin-1 and abnormal spontaneous Ca(2+) release events after field stimulation. Isolated left atria studied on a multielectrode array revealed modest changes in path length for re-entry but abnormal electrical events after a pacing train in RGS4(-/-) mice. RGS4 deletion results in a predisposition to atrial fibrillation from enhanced activity in the Gαq/11-IP3 pathway, resulting in abnormal Ca(2+) release and corresponding electrical events.

Cardiac alternans and intracellular calcium cycling

Cardiac alternans refers to a condition in which there is a periodic beat-to-beat oscillation in electrical activity and the strength of cardiac muscle contraction at a constant heart rate. Clinically, cardiac alternans occurs in settings that are typical for cardiac arrhythmias and has been causally linked to these conditions. At the cellular level, alternans is defined as beat-to-beat alternations in contraction amplitude (mechanical alternans), action potential duration (APD; electrical or APD alternans) and Ca(2+) transient amplitude (Ca(2+) alternans). The cause of alternans is multifactorial; however, alternans always originate from disturbances of the bidirectional coupling between membrane voltage (Vm ) and intracellular calcium ([Ca(2+) ]i ). Bidirectional coupling refers to the fact that, in cardiac cells, Vm depolarization and the generation of action potentials cause the elevation of [Ca(2+) ]i that is required for contraction (a process referred to as excitation-contraction coupling); conversely, changes of [Ca(2+) ]i control Vm because important membrane currents are Ca(2+) dependent. Evidence is mounting that alternans is ultimately caused by disturbances of cellular Ca(2+) signalling. Herein we review how two key factors of cardiac cellular Ca(2+) cycling, namely the release of Ca(2+) from internal stores and the capability of clearing the cytosol from Ca(2+) after each beat, determine the conditions under which alternans occurs. The contributions from key Ca(2+) -handling proteins (i.e. surface membrane channels, ion pumps and transporters and internal Ca(2+) release channels) are discussed.

Cardiac myocyte alternans in intact heart: Influence of cell-cell coupling and β-adrenergic stimulation

BACKGROUND

Cardiac alternans are proarrhythmic and mechanistically link cardiac mechanical dysfunction and sudden cardiac death. Beat-to-beat alternans occur when beats with large Ca(2+) transients and long action potential duration (APD) alternate with the converse. APD alternans are typically driven by Ca(2+) alternans and sarcoplasmic reticulum (SR) Ca(2+) release alternans. But the effect of intercellular communication via gap junctions (GJ) on alternans in the intact heart remains unknown.

OBJECTIVE

We assessed the effects of cell-to-cell coupling on local alternans in intact Langendorff-perfused mouse hearts, measuring single myocyte [Ca(2+)] alternans synchronization among neighboring cells, and effects of β-adrenergic receptor (β-AR) activation and reduced GJ coupling.

METHODS AND RESULTS

Mouse hearts (C57BL/6) were retrogradely perfused and loaded with Fluo8-AM to record cardiac myocyte [Ca(2+)] in situ with confocal microscopy. Single cell resolution allowed analysis of alternans within the intact organ during alternans induction. Carbenoxolone (25 μM), a GJ inhibitor, significantly increased the occurrence and amplitude of alternans in single cells within the intact heart. Alternans were concordant between neighboring cells throughout the field of view, except transiently during onset. β-AR stimulation only reduced Ca(2+) alternans in tissue that had reduced GJ coupling, matching effects seen in isolated myocytes.

CONCLUSIONS

Ca(2+) alternans among neighboring myocytes is predominantly concordant, likely because of electrical coupling between cells. Consistent with this, partial GJ uncoupling increased propensity and amplitude of Ca(2+) alternans, and made them more sensitive to reversal by β-AR activation, as in isolated myocytes. Electrical coupling between myocytes may thus limit the alternans initiation, but also allow alternans to be more stable once established.

Early subcellular Ca2+ remodelling and increased propensity for Ca2+ alternans in left atrial myocytes from hypertensive rats

AIMS

Hypertension is a major risk factor for atrial fibrillation. We hypothesized that arterial hypertension would alter atrial myocyte calcium (Ca2+) handling and that these alterations would serve to trigger atrial tachyarrhythmias.

METHODS AND RESULTS

Left atria or left atrial (LA) myocytes were isolated from spontaneously hypertensive rats (SHR) or normotensive Wistar-Kyoto (WKY) controls. Early after the onset of hypertension, at 3 months of age, there were no differences in Ca2+ transients (CaTs) or expression and phosphorylation of Ca2+ handling proteins between SHR and WKY. At 7 months of age, when left ventricular (LV) hypertrophy had progressed and markers of fibrosis were increased in left atrium, CaTs (at 1 Hz stimulation) were still unchanged. Subcellular alterations in Ca2+ handling were observed, however, in SHR atrial myocytes including (i) reduced expression of the α1C subunit of and reduced Ca2+ influx through L-type Ca2+ channels, (ii) reduced expression of ryanodine receptors with increased phosphorylation at Ser2808, (iii) decreased activity of the Na+ / Ca2+ exchanger (at unaltered intracellular Na+ concentration), and (iv) increased SR Ca2+ load with reduced fractional release. These changes were associated with an increased propensity of SHR atrial myocytes to develop frequency-dependent, arrhythmogenic Ca2+ alternans.

CONCLUSIONS

In SHR, hypertension induces early subcellular LA myocyte Ca2+ remodelling during compensated LV hypertrophy. In basal conditions, atrial myocyte CaTs are not changed. At increased stimulation frequency, however, SHR atrial myocytes become more prone to arrhythmogenic Ca2+ alternans, suggesting a link between hypertension, atrial Ca2+ homeostasis, and development of atrial tachyarrhythmias.

The mechanisms of calcium cycling and action potential dynamics in cardiac alternans

RATIONALE

Alternans is a risk factor for cardiac arrhythmia, including atrial fibrillation. At the cellular level alternans manifests as beat-to-beat alternations in contraction, action potential duration (APD), and magnitude of the Ca(2+) transient (CaT). Electromechanical and CaT alternans are highly correlated, however, it has remained controversial whether the primary cause of alternans is a disturbance of cellular Ca(2+) signaling or electrical membrane properties.

OBJECTIVE

To determine whether a primary failure of intracellular Ca(2+) regulation or disturbances in membrane potential and AP regulation are responsible for the occurrence of alternans in atrial myocytes.

METHODS AND RESULTS

Pacing-induced APD and CaT alternans were studied in single rabbit atrial and ventricular myocytes using combined [Ca(2+)]i and electrophysiological measurements. In current-clamp experiments, APD and CaT alternans strongly correlated in time and magnitude. CaT alternans was observed without alternation in L-type Ca(2+) current, however, elimination of intracellular Ca(2+) release abolished APD alternans, indicating that [Ca(2+)]i dynamics have a profound effect on the occurrence of CaT alternans. Trains of 2 distinctive voltage commands in form of APs recorded during large and small alternans CaTs were applied to voltage-clamped cells. CaT alternans was observed with and without alternation in the voltage command shape. During alternans AP-clamp large CaTs coincided with both long and short AP waveforms, indicating that CaT alternans develop irrespective of AP dynamics.

CONCLUSIONS

The primary mechanism underlying alternans in atrial cells, similarly to ventricular cells, resides in a disturbance of Ca(2+) signaling, whereas APD alternans are a secondary consequence, mediated by Ca(2+)-dependent AP modulation.

Cellular mechanism of cardiac alternans: an unresolved chicken or egg problem

T-wave alternans, a specific form of cardiac alternans, has been associated with the increased susceptibility to cardiac arrhythmias and sudden cardiac death (SCD). Plenty of evidence has related cardiac alternans at the tissue level to the instability of voltage kinetics or Ca(2+) handling dynamics at the cellular level. However, to date, none of the existing experiments could identify the exact cellular mechanism of cardiac alternans due to the bi-directional coupling between voltage kinetics and Ca(2+) handling dynamics. Either of these systems could be the origin of alternans and the other follows as a secondary change, therefore making the cellular mechanism of alternans a difficult chicken or egg problem. In this context, theoretical analysis combined with experimental techniques provides a possibility to explore this problem. In this review, we will summarize the experimental and theoretical advances in understanding the cellular mechanism of alternans. We focus on the roles of action potential duration (APD) restitution and Ca(2+) handling dynamics in the genesis of alternans and show how the theoretical analysis combined with experimental techniques has provided us a new insight into the cellular mechanism of alternans. We also discuss the possible reasons of increased propensity for alternans in heart failure (HF) and the new possible therapeutic targets. Finally, according to the level of electrophysiological recording techniques and theoretical strategies, we list some critical experimental or theoretical challenges which may help to determine the origin of alternans and to find more effective therapeutic targets in the future.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

Calcium waves initiating from the anomalous subdiffusive calcium sparks

The objective of the study is to investigate the propagation of Ca(2+) waves in full-width cardiac myocytes and carry out sensitivity analysis to study the effects of various physiological parameters on global Ca(2+) waves. Based on the anomalous subdiffusion of Ca(2+) sparks, a mathematical model was proposed to characterize the Ca(2+) waves. The computed results were in agreement with the experimental measurements using confocal microscopy. This model includes variables of current through the Ca(2+) release unit (CRU; ICRU), duration of current flow through CRU (Topen), Ca(2+) sensitivity parameter (K), the longitudinal and transverse spatial separation of CRUs (lx and ly, where x denotes longitudinal direction (x-axis) and y denotes transverse direction (y-axis)) and Ca(2+) diffusion coefficients (Dx, Dy). The spatio-temporal mechanism of the anomalous Ca(2+) sparks led to results that were different from those based on Fick's law. The major findings were reported as: ICRU affected the dynamic properties of Ca(2+) waves more significantly than Topen; the effect of K on the properties of Ca(2+) waves was negligible; ly affected the amplitude significantly, but lx affected the longitudinal velocity significantly; in turn, the limitation and significance of the study are discussed.

Calcium alternans in cardiac myocytes: order from disorder

Calcium alternans is associated with T-wave alternans and pulsus alternans, harbingers of increased mortality in the setting of heart disease. Recent experimental, computational, and theoretical studies have led to new insights into the mechanisms of Ca alternans, specifically how disordered behaviors dominated by stochastic processes at the subcellular level become organized into ordered periodic behaviors. In this article, we summarize the recent progress in this area, outlining a holistic theoretical framework in which the complex effects of Ca cycling proteins on Ca alternans are linked to three key properties of the cardiac Ca cycling network: randomness, refractoriness, and recruitment. We also illustrate how this '3R theory' can reconcile many seemingly contradictory experimental observations.

Ca(2+) release events in cardiac myocytes up close: insights from fast confocal imaging

The spatio-temporal properties of Ca²⁺ transients during excitation-contraction coupling and elementary Ca²⁺ release events (Ca²⁺ sparks) were studied in atrial and ventricular myocytes with ultra-fast confocal microscopy using a Zeiss LSM 5 LIVE system that allows sampling rates of up to 60 kHz. Ca²⁺ sparks which originated from subsarcolemmal junctional sarcoplasmic reticulum (j-SR) release sites in atrial myocytes were anisotropic and elongated in the longitudinal direction of the cell. Ca²⁺ sparks in atrial cells originating from non-junctional SR and in ventricular myocytes were symmetrical. Ca²⁺ spark recording in line scan mode at 40,000 lines/s uncovered step-like increases of [Ca²⁺]_i. 2-D imaging of Ca²⁺ transients revealed an asynchronous activation of release sites and allowed the sequential recording of Ca²⁺ entry through surface membrane Ca²⁺ channels and subsequent activation of Ca²⁺-induced Ca²⁺ release. With a latency of 2.5 ms after application of an electrical stimulus, Ca²⁺ entry could be detected that was followed by SR Ca²⁺ release after an additional 3 ms delay. Maximum Ca²⁺ release was observed 4 ms after the beginning of release. The timing of Ca²⁺ entry and release was confirmed by simultaneous [Ca²⁺]_i and membrane current measurements using the whole cell voltage-clamp technique. In atrial cells activation of discrete individual release sites of the j-SR led to spatially restricted Ca²⁺ release events that fused into a peripheral ring of elevated [Ca²⁺]_i that subsequently propagated in a wave-like fashion towards the center of the cell. In ventricular myocytes asynchronous Ca²⁺ release signals from discrete sites with no preferential subcellular location preceded the whole-cell Ca²⁺ transient. In summary, ultra-fast confocal imaging allows investigation of Ca²⁺ signals with a time resolution similar to patch clamp technique, however in a less invasive fashion.

Chronic myocardial infarction promotes atrial action potential alternans, afterdepolarizations, and fibrillation

Aims

Atrial fibrillation (AF) is increased in patients with heart failure resulting from myocardial infarction (MI). We aimed to determine the effects of chronic ventricular MI in rabbits on the susceptibility to AF, and underlying atrial electrophysiological and Ca²⁺-handling mechanisms.

Methods and results

In Langendorff-perfused rabbit hearts, under β-adrenergic stimulation with isoproterenol (ISO; 1 µM), 8 weeks MI decreased AF threshold, indicating increased AF susceptibility. This was associated with increased atrial action potential duration (APD)-alternans at 90% repolarization, by 147%, and no significant change in the mean APD or atrial global conduction velocity (CV; n = 6–13 non-MI hearts, 5–12 MI). In atrial isolated myocytes, also under β-stimulation, L-type Ca²⁺ current (I_CaL) density and intracellular Ca²⁺-transient amplitude were decreased by MI, by 35 and 41%, respectively, and the frequency of spontaneous depolarizations (SDs) was substantially increased. MI increased atrial myocyte size and capacity, and markedly decreased transverse-tubule density. In non-MI hearts perfused with ISO, the I_CaL-blocker nifedipine, at a concentration (0.02 µM) causing an equivalent I_CaL reduction (35%) to that from the MI, did not affect AF susceptibility, and decreased APD.

Conclusion

Chronic MI in rabbits remodels atrial structure, electrophysiology, and intracellular Ca²⁺ handling. Increased susceptibility to AF by MI, under β-adrenergic stimulation, may result from associated production of atrial APD alternans and SDs, since steady-state APD and global CV were unchanged under these conditions, and may be unrelated to the associated reduction in whole-cell I_CaL. Future studies may clarify potential contributions of local conduction changes, and cellular and subcellular mechanisms of alternans, to the increased AF susceptibility.

Effects of mitochondrial uncoupling on Ca(2+) signaling during excitation-contraction coupling in atrial myocytes

Mitochondria play an important role in intracellular Ca(2+) concentration ([Ca(2+)]i) regulation in the heart. We studied sarcoplasmic reticulum (SR) Ca(2+) release in cat atrial myocytes during depolarization of mitochondrial membrane potential (ΔΨm) induced by the protonophore FCCP. FCCP caused an initial decrease of action potential-induced Ca(2+) transient amplitude and frequency of spontaneous Ca(2+) waves followed by partial recovery despite partially depleted SR Ca(2+) stores. In the presence of oligomycin, FCCP only exerted a stimulatory effect on Ca(2+) transients and Ca(2+) wave frequency, suggesting that the inhibitory effect of FCCP was mediated by ATP consumption through reverse-mode operation of mitochondrial F1F0-ATPase. ΔΨm depolarization was accompanied by cytosolic acidification, increases of diastolic [Ca(2+)]i, intracellular Na(+) concentration ([Na(+)]i), and intracellular Mg(2+) concentration ([Mg(2+)]i), and a decrease of intracellular ATP concentration ([ATP]i); however, glycolytic ATP production partially compensated for the exhaustion of mitochondrial ATP supplies. In conclusion, the initial inhibition of Ca(2+) transients and waves resulted from suppression of ryanodine receptor SR Ca(2+) release channel activity by a decrease in [ATP], an increase of [Mg(2+)]i, and cytoplasmic acidification. The later stimulation resulted from reduced mitochondrial Ca(2+) buffering and cytosolic Na(+) and Ca(2+) accumulation, leading to enhanced Ca(2+)-induced Ca(2+) release and spontaneous Ca(2+) release in the form of Ca(2+) waves. ΔΨm depolarization and the ensuing consequences of mitochondrial uncoupling observed here (intracellular acidification, decrease of [ATP]i, increase of [Na(+)]i and [Mg(2+)]i, and Ca(2+) overload) are hallmarks of ischemia. These findings may therefore provide insight into the consequences of mitochondrial uncoupling for ion homeostasis, SR Ca(2+) release, and excitation-contraction coupling in ischemia at the cellular and subcellular level.

Regulation of cardiac alternans by β-adrenergic signaling pathways

In cat atrial myocytes, β-adrenergic receptor (β-AR) stimulation exerts profound effects on excitation-contraction coupling and cellular Ca(2+) cycling that are mediated by β(1)- and β(2)-AR subtypes coupled to G proteins (G(s) and G(i)). In this study, we determined the effects of β-AR stimulation on pacing-induced Ca(2+) alternans. Ca(2+) alternans was recorded from single cat atrial myocytes with the fluorescent Ca(2+) indicator indo-1. Stable Ca(2+) alternans occurred at an average pacing frequency of 1.7 Hz at room temperature with a mean alternans ratio of 0.43. Nonselective β-AR stimulation as well as selective stimulation of β(1)/G(s), β(2)/G(s) + G(i), and β(2)/G(s) coupled pathways all abolished pacing-induced Ca(2+) alternans. β(1)-AR stimulation abolished alternans through stimulation of PKA and Ca(2+)/calmodulin-dependent protein kinase II, whereas β(2)-AR stimulation exclusively involved PKA and was mediated via G(s), whereas a known second pathway in cat atrial myocytes acting through G(i) and nitric oxide production was not involved in alternans regulation. Inhibition of various mitochondrial functions (dissipation of the mitochondrial membrane potential or inhibition of mitochondrial F(1)/F(0)-ATP synthase, mitochondrial Ca(2+) uptake via the mitochondrial Ca(2+) uniporter, and Ca(2+) extrusion via mitochondrial Na(+)/Ca(2+) exchange) enhanced Ca(2+) alternans; however, β-AR stimulation still abrogated alternans, provided that sufficient cellular ATP was available. Selective inhibition of mitochondrial or glycolytic ATP production did not prevent β-AR stimulation from abolishing Ca(2+) alternans. However, when both ATP sources were depleted, β-AR stimulation failed to decrease Ca(2+) alternans. These results indicate that in atrial myocytes, β-AR stimulation protects against pacing-induced alternans by acting through parallel and complementary signaling pathways.

Refractoriness of sarcoplasmic reticulum Ca2+ release determines Ca2+ alternans in atrial myocytes

Cardiac alternans is a recognized risk factor for cardiac arrhythmia and sudden cardiac death. At the cellular level, Ca(2+) alternans appears as cytosolic Ca(2+) transients of alternating amplitude at regular beating frequency. Cardiac alternans is a multifactorial process but has been linked to disturbances in intracellular Ca(2+) regulation. In atrial myocytes, we tested the role of voltage-gated Ca(2+) current, sarcoplasmic reticulum (SR) Ca(2+) load, and restitution properties of SR Ca(2+) release for the occurrence of pacing-induced Ca(2+) alternans. Voltage-clamp experiments revealed that peak Ca(2+) current was not affected during alternans, and alternans of end-diastolic SR Ca(2+) load, evaluated by application of caffeine or measured directly with an intra-SR fluorescent Ca(2+) indicator (fluo-5N), were not a requirement for cytosolic Ca(2+) alternans. Restitution properties and kinetics of refractoriness of Ca(2+) release after activation during alternans were evaluated by four different approaches: measurements of 1) the delay (latency) of occurrence of spontaneous global Ca(2+) releases and 2) Ca(2+) spark frequency, both during rest after a large and small alternans Ca(2+) transient; 3) the magnitude of premature action potential-induced Ca(2+) transients after a large and small beat; and 4) the efficacy of a photolytically induced Ca(2+) signal (Ca(2+) uncaging from DM-nitrophen) to trigger additional Ca(2+) release during alternans. The results showed that the latency of global spontaneous Ca(2+) release was prolonged and Ca(2+) spark frequency was decreased after the large Ca(2+) transient during alternans. Furthermore, the restitution curve of the Ca(2+) transient elicited by premature action potentials or by photolysis-induced Ca(2+) release from the SR lagged behind after a large-amplitude transient during alternans compared with the small-amplitude transient. The data demonstrate that beat-to-beat alternation of the time-dependent restitution properties and refractory kinetics of the SR Ca(2+) release mechanism represents a key mechanism underlying cardiac alternans.

Non-linear dynamics of cardiac alternans: subcellular to tissue-level mechanisms of arrhythmia

Cardiac repolarization alternans is a rhythm disturbance of the heart in which rapid stimulation elicits a beat-to-beat alternation in the duration of action potentials and magnitude of intracellular calcium transients in individual cardiac myocytes. Although this phenomenon has been identified as a potential precursor to dangerous reentrant arrhythmias and sudden cardiac death, significant uncertainty remains regarding its mechanism and no clinically practical means of halting its occurrence or progression currently exists. Cardiac alternans has well-characterized tissue, cellular, and subcellular manifestations, the mechanisms and interplay of which are an active area of research.

Nonlinear dynamics in cardiology

The dynamics of many cardiac arrhythmias, as well as the nature of transitions between different heart rhythms, have long been considered evidence of nonlinear phenomena playing a direct role in cardiac arrhythmogenesis. In most types of cardiac disease, the pathology develops slowly and gradually, often over many years. In contrast, arrhythmias often occur suddenly. In nonlinear systems, sudden changes in qualitative dynamics can, counterintuitively, result from a gradual change in a system parameter-this is known as a bifurcation. Here, we review how nonlinearities in cardiac electrophysiology influence normal and abnormal rhythms and how bifurcations change the dynamics. In particular, we focus on the many recent developments in computational modeling at the cellular level that are focused on intracellular calcium dynamics. We discuss two areas where recent experimental and modeling work has suggested the importance of nonlinearities in calcium dynamics: repolarization alternans and pacemaker cell automaticity.

Prevention of postoperative atrial fibrillation: novel and safe strategy based on the modulation of the antioxidant system

Postoperative atrial fibrillation (AF) is the most common arrhythmia following cardiac surgery with extracorporeal circulation. The pathogenesis of postoperative AF is multifactorial. Oxidative stress, caused by the unavoidable ischemia-reperfusion event occurring in this setting, is a major contributory factor. Reactive oxygen species (ROS)-derived effects could result in lipid peroxidation, protein carbonylation, or DNA oxidation of cardiac tissue, thus leading to functional and structural myocardial remodeling. The vulnerability of myocardial tissue to the oxidative challenge is also dependent on the activity of the antioxidant system. High ROS levels, overwhelming this system, should result in deleterious cellular effects, such as the induction of necrosis, apoptosis, or autophagy. Nevertheless, tissue exposure to low to moderate ROS levels could trigger a survival response with a trend to reinforce the antioxidant defense system. Administration of n-3 polyunsaturated fatty acids (PUFA), known to involve a moderate ROS production, is consistent with a diminished vulnerability to the development of postoperative AF. Accordingly, supplementation of n-3 PUFA successfully reduced the incidence of postoperative AF after coronary bypass grafting. This response is due to an up-regulation of antioxidant enzymes, as shown in experimental models. In turn, non-enzymatic antioxidant reinforcement through vitamin C administration prior to cardiac surgery has also reduced the postoperative AF incidence. Therefore, it should be expected that a mixed therapy result in an improvement of the cardioprotective effect by modulating both components of the antioxidant system. We present novel available evidence supporting the hypothesis of an effective prevention of postoperative AF including a two-step therapeutic strategy: n-3 PUFA followed by vitamin C supplementation to patients scheduled for cardiac surgery with extracorporeal circulation. The present study should encourage the design of clinical trials aimed to test the efficacy of this strategy to offer new therapeutic opportunities to patients challenged by ischemia-reperfusion events not solely in heart, but also in other organs such as kidney or liver in transplantation surgeries.

Mechanisms by which cytoplasmic calcium wave propagation and alternans are generated in cardiac atrial myocytes lacking T-tubules-insights from a simulation study

This study investigated the mechanisms underlying the propagation of cytoplasmic calcium waves and the genesis of systolic Ca(2+) alternans in cardiac myocytes lacking transverse tubules (t-tubules). These correspond to atrial cells of either small mammals or large mammals that have lost their t-tubules due to disease-induced structural remodeling (e.g., atrial fibrillation). A mathematical model was developed for a cluster of ryanodine receptors distributed on the cross section of a cell that was divided into 13 elements with a spatial resolution of 2 μm. Due to the absence of t-tubules, L-type Ca(2+) channels were only located in the peripheral elements close to the cell-membrane surface and produced Ca(2+) signals that propagated toward central elements by triggering successive Ca(2+)-induced Ca(2+) release (CICR) via Ca(2+) diffusion between adjacent elements. Under control conditions, the Ca(2+) signals did not fully propagate to the central region of the cell. However, with modulation of several factors responsible for Ca(2+) handling, such as the L-type Ca(2+) channels (Ca(2+) influx), SERCA pumps (sarcoplasmic reticulum (SR) Ca(2+) uptake), and ryanodine receptors (SR Ca(2+) release), Ca(2+) wave propagation to the center of the cell could occur. These simulation results are consistent with previous experimental data from atrial cells of small mammals. The model further reveals that spatially functional heterogeneity in Ca(2+) diffusion within the cell produced a steep relationship between the SR Ca(2+) content and the cytoplasmic Ca(2+) concentration. This played an important role in the genesis of Ca(2+) alternans that were more obvious in central than in peripheral elements. Possible association between the occurrence of Ca(2+) alternans and the model parameters of Ca(2+) handling was comprehensively explored in a wide range of one- and two-parameter spaces. In addition, the model revealed a spontaneous second Ca(2+) release in response to a single voltage stimulus pulse with SR Ca(2+) overloading and augmented Ca(2+) influx. This study provides what to our knowledge are new insights into the genesis of Ca(2+) alternans and spontaneous second Ca(2+) release in cardiac myocytes that lack t-tubules.

Properties of Ca2+ sparks revealed by four-dimensional confocal imaging of cardiac muscle

Parameters (amplitude, width, kinetics) of Ca²⁺ sparks imaged confocally are affected by errors when the spark source is not in focus. To identify sparks that were in focus, we used fast scanning (LSM 5 LIVE; Carl Zeiss) combined with fast piezoelectric focusing to acquire x–y images in three planes at 1-µm separation (x-y-z-t mode). In 3,000 x–y scans in each of 34 membrane-permeabilized cat atrial cardiomyocytes, 6,906 sparks were detected. 767 sparks were in focus. They had greater amplitude, but their spatial width and rise time were similar compared with all sparks recorded. Their distribution of amplitudes had a mode at ΔF/F₀ = 0.7. The Ca²⁺ release current underlying in-focus sparks was 11 pA, requiring 20 to 30 open channels, a number at the high end of earlier estimates. Spark frequency was greater than in earlier imaging studies of permeabilized ventricular cells, suggesting a greater susceptibility to excitation, which could have functional relevance for atrial cells. Ca²⁺ release flux peaked earlier than the time of peak fluorescence and then decayed, consistent with significant sarcoplasmic reticulum (SR) depletion. The evolution of fluorescence and release flux were strikingly similar for in-focus sparks of different rise time (T). Spark termination involves both depletion of Ca²⁺ in the SR and channel closure, which may be synchronized by depletion. The observation of similar flux in sparks of different T requires either that channel closure and other termination processes be independent of the determinants of flux (including [Ca²⁺]_SR) or that different channel clusters respond to [Ca²⁺]_SR with different sensitivity.

A novel method for spatially complex diffraction-limited photoactivation and photobleaching in living cells

Photoactivated probes have gained interest as experimental tools to study intracellular signalling pathways all the way to the molecular level. However technical limitations of the means to activate such compounds have put constraints on their use in spatially highly restricted subcellular areas. The Mosaic digital illumination system uses a high-speed array of individually addressable, tiltable micromirrors to direct continuous-wave laser light onto a specimen with diffraction-limited precision. The system, integrated into a Nikon A1R confocal microscope, was used to uncage Ca²⁺ or IP3 and conduct photobleaching experiments from multiple geometrically complex subcellular regions while simultaneously measuring [Ca²⁺]i with high-speed confocal imaging.

Calsequestrin 2 deletion shortens the refractoriness of Ca²⁺ release and reduces rate-dependent Ca²⁺-alternans in intact mouse hearts

Calsequestrin (Casq2) is a low affinity Ca(2+)-binding protein located in sarcoplasmic reticulum (SR) of cardiac myocytes. Casq2 acts as a Ca(2+) buffer regulating free Ca(2+) concentration in the SR lumen and plays a significant role in the regulation of Ca(2+) release from this intracellular organelle. In addition, there is experimental evidence supporting the hypothesis that Casq2 also modulates the activity of the cardiac Ca(2+) release channels, ryanodine receptors (RyR2). In this study, Casq2 knockout mice (Casq2-/-) were used as a model to evaluate the effects of the Casq2 on the cytosolic and intra-SR Ca(2+) dynamics, and the electrical activity in the ventricular epicardial layer of intact beating hearts. Casq2-/- mice have accelerated intra-SR Ca(2+) refilling kinetics (76 ± 22 vs. 136.5 ± 15 ms) and a reduced refractoriness of Ca(2+) release (182 ± 32 ms Casq2+/+ and 111 ± 22 ms Casq2-/- ). In addition, mice display reduced Ca(2+) alternans (67% decline in the amplitude of Ca(2+) alternans at 7 Hz, 21oC) and less T-wave alternans at the electrocardiographic level. The results presented in this paper support the idea of Casq2 acting both as a buffer and a direct regulator of the Ca(2+) release process. Finally, we propose that alterations in Ca(2+) release refractoriness shown here could explain the relationship between Casq2 function and an increase in the risk for ventricular arrhythmias.

Sarcoplasmic reticulum and L-type Ca²⁺ channel activity regulate the beat-to-beat stability of calcium handling in human atrial myocytes

Irregularities in intracellular calcium on a beat-to-beat basis can precede cardiac arrhythmia, but the mechanisms inducing such irregularities remain elusive. This study tested the hypothesis that sarcoplasmic reticulum (SR) and L-type calcium channel activity determine the beat-to-beat response and its rate dependency. For this purpose, patch-clamp technique and confocal calcium imaging was used to record L-type calcium current (ICa) and visualize calcium in human atrial myocytes subjected to increasing stimulation frequencies (from 0.2 to 2 Hz). The beat-to-beat response was heterogeneous among a population of 133 myocytes, with 30 myocytes responding uniformly at all frequencies, while alternating and irregular responses were induced in 78 and 25 myocytes, respectively. Myocytes with uniform responses had the lowest frequency of calcium wave-induced transient inward currents (ITI; 0.4 ± 0.2 min⁻¹), ICa density (1.8 ± 0.3 pA pF⁻¹) and caffeine-releasable calcium load (6.2 ± 0.5 amol pF⁻¹), while those with alternating responses had the highest ITI frequency (1.8 ± 0.3 min⁻¹,P =0.003) and ICa density (2.4 ± 0.2 pA pF⁻¹, P =0.04). In contrast, the calcium load was highest in myocytes with irregular responses (8.5 ± 0.7 amol pF⁻¹, P =0.01). Accordingly, partial ICa inhibition reduced the incidence (from 78 to 44%, P <0.05) and increased the threshold frequency for beat-to-beat alternation (from 1.3 ± 0.2 to 1.9 ± 0.2 Hz, P <0.05). Partial inhibition of SR calcium release reduced the ITI frequency, increased calcium loading and favoured induction of irregular responses, while complete inhibition abolished beat-to-beat alternation at all frequencies. In conclusion, the beat-to-beat response was heterogeneous among human atrial myocytes subjected to increasing stimulation frequencies, and the nature and stability of the response were determined by the SR and L-type calcium channel activities, suggesting that these mechanisms are key to controlling cardiac beat-to-beat stability.

Glycolytic inhibition causes spontaneous ventricular fibrillation in aged hearts

Selective glycolytic inhibition (GI) promotes electromechanical alternans and triggered beats in isolated cardiac myocytes. We sought to determine whether GI promotes triggered activity by early afterdepolarization (EAD) or delayed afterdepolarizations in intact hearts isolated from adult and aged rats. Dual voltage and intracellular calcium ion (Ca(i)(2+)) fluorescent optical maps and single cell glass microelectrode recordings were made from the left ventricular (LV) epicardium of isolated Langendorff-perfused adult (∼4 mo) and aged (∼24 mo) rat hearts. GI was induced by replacing glucose with 10 mM pyruvate in oxygenated Tyrode's. Within 20 min, GI slowed Ca(i)(2+) transient decline rate and shortened action potential duration in both groups. These changes were associated with ventricular fibrillation (VF) in the aged hearts (64 out of 66) but not in adult hearts (0 out of 18; P < 0.001). VF was preceded by a transient period of focal ventricular tachycardia caused by EAD-mediated triggered activity leading to VF within seconds. The VF was suppressed by the ATP-sensitive K (K(ATP)) channel blocker glibenclamide (1 μM) but not (0 out of 7) by mitochondrial K(ATP) block. The Ca-calmodulin-dependent protein kinase II (CaMKII) blocker KN-93 (1 μM) prevented GI-mediated VF (P < 0.05). Block of Na-Ca exchanger (NCX) by SEA0400 (2 μM) prevented GI-mediated VF (3 out of 6), provided significant bradycardia did not occur. Aged hearts had significantly greater LV fibrosis and reduced connexin 43 than adult hearts (P < 0.05). We conclude that in aged fibrotic unlike in adult rat hearts, GI promotes EADs, triggered activity, and VF by activation of K(ATP) channels CaMKII and NCX.

Understanding cardiac alternans: a piecewise linear modeling framework

Cardiac alternans is a beat-to-beat alternation in action potential duration (APD) and intracellular calcium (Ca(2+)) cycling seen in cardiac myocytes under rapid pacing that is believed to be a precursor to fibrillation. The cellular mechanisms of these rhythms and the coupling between cellular Ca(2+) and voltage dynamics have been extensively studied leading to the development of a class of physiologically detailed models. These have been shown numerically to reproduce many of the features of myocyte response to pacing, including alternans, and have been analyzed mathematically using various approximation techniques that allow for the formulation of a low dimensional map to describe the evolution of APDs. The seminal work by Shiferaw and Karma is of particular interest in this regard [Shiferaw, Y. and Karma, A., "Turing instability mediated by voltage and calcium diffusion in paced cardiac cells," Proc. Natl. Acad. Sci. U.S.A. 103, 5670-5675 (2006)]. Here, we establish that the key dynamical behaviors of the Shiferaw-Karma model are arranged around a set of switches. These are shown to be the main elements for organizing the nonlinear behavior of the model. Exploiting this observation, we show that a piecewise linear caricature of the Shiferaw-Karma model, with a set of appropriate switching manifolds, can be constructed that preserves the physiological interpretation of the original model while being amenable to a systematic mathematical analysis. In illustration of this point, we formulate the dynamics of Ca(2+) cycling (in response to pacing) and compute the properties of periodic orbits in terms of a stroboscopic map that can be constructed without approximation. Using this, we show that alternans emerge via a period-doubling instability and track this bifurcation in terms of physiologically important parameters. We also show that when coupled to a spatially extended model for Ca(2+) transport, the model supports spatially varying patterns of alternans. We analyze the onset of this instability with a generalization of the master stability approach to accommodate the nonsmooth nature of our system.

The role of mitochondria for the regulation of cardiac alternans

Electro-mechanical and Ca alternans is a beat-to-beat alternation of action potential duration, contraction strength and Ca transient amplitude observed in cardiac myocytes at regular stimulation frequency. Ca alternans is a multifactorial process that is causally linked to cardiac arrhythmias. At the cellular level, conditions that increase fractional release from the sarcoplasmic reticulum or reduce diastolic Ca sequestration favor the occurrence of alternans. Mitochondria play a significant role in cardiac excitation–contraction coupling and Ca signaling by providing the energy for contraction and ATP-dependent processes and possibly by serving as Ca buffering organelles. Here we tested the hypothesis that impairment of mitochondrial function generates conditions that favor the occurrence of Ca alternans. Alternans were elicited by electrical pacing (>1 Hz) in single cat atrial myocytes and intracellular Ca ([Ca]_i) was measured with the fluorescent Ca indicator Indo-1. The degree of alternans was quantified as the alternans ratio (AR = 1 − S/L, where S/L is the ratio of the small to the large amplitude of a pair of alternating Ca transients). Dissipation of mitochondrial membrane potential (with FCCP) as well as inhibition of mitochondrial F₁/F₀-ATP synthase (oligomycin), electron transport chain (rotenone, antimycin, CN⁻), Ca-dependent dehydrogenases and mitochondrial Ca uptake or extrusion, all enhanced AR and lowered the threshold for the occurrence of Ca alternans. The data indicate that impairment of mitochondrial function adversely affects cardiac Ca cycling leading to proarrhythmic Ca 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.