Restitution of Ca(2+) release and vulnerability to arrhythmias

Role of ryanodine receptor cooperativity in Ca2+-wave-mediated triggered activity in cardiomyocytes

Ca2+ waves are known to trigger delayed after-depolarizations that can cause malignant cardiac arrhythmias. However, modelling Ca2+ waves using physiologically realistic models has remained a major challenge. Existing models with low Ca2+ sensitivity of ryanodine receptors (RyRs) necessitate large release currents, leading to an unrealistically large Ca2+ transient amplitude incompatible with the experimental observations. Consequently, current physiologically detailed models of delayed after-depolarizations resort to unrealistic cell architectures to produce Ca2+ waves with a normal Ca2+ transient amplitude. Here, we address these challenges by incorporating RyR cooperativity into a physiologically detailed model with a realistic cell architecture. We represent RyR cooperativity phenomenologically through a Hill coefficient within the sigmoid function of RyR open probability. Simulations in permeabilized myocytes with high Ca2+ sensitivity reveal that a sufficiently large Hill coefficient is required for Ca2+ wave propagation via the fire-diffuse-fire mechanism. In intact myocytes, propagating Ca2+ waves can occur only within an intermediate Hill coefficient range. Within this range, the spark rate is neither too low, enabling Ca2+ wave propagation, nor too high, allowing for the maintenance of a high sarcoplasmic reticulum load during diastole of the action potential. Moreover, this model successfully replicates other experimentally observed manifestations of Ca2+-wave-mediated triggered activity, including phase 2 and phase 3 early after-depolarizations and high-frequency voltage-Ca2+ oscillations. These oscillations feature an elevated take-off potential with depolarization mediated by the L-type Ca2+ current. The model also sheds light on the roles of luminal gating of RyRs and the mobile buffer ATP in the genesis of these arrhythmogenic phenomena. KEY POINTS: Existing mathematical models of Ca2+ waves use an excessively large Ca2+-release current or unrealistic diffusive coupling between release units. Our physiologically realistic model, using a Hill coefficient in the ryanodine receptor (RyR) gating function to represent RyR cooperativity, addresses these limitations and generates organized Ca2+ waves at Hill coefficients ranging from ∼5 to 10, as opposed to the traditional value of 2. This range of Hill coefficients gives a spark rate neither too low, thereby enabling Ca2+ wave propagation, nor too high, allowing for the maintenance of a high sarcoplasmic reticulum load during the plateau phase of the action potential. Additionally, the model generates Ca2+-wave-mediated phase 2 and phase 3 early after-depolarizations, and coupled membrane voltage with Ca2+ oscillations mediated by the L-type Ca2+ current. This study suggests that pharmacologically targeting RyR cooperativity could be a promising strategy for treating cardiac arrhythmias linked to Ca2+-wave-mediated triggered activity.

Tissue-resident memory T cells in epicardial adipose tissue comprise transcriptionally distinct subsets that are modulated in atrial fibrillation

Atrial fibrillation (AF) is the most common sustained arrhythmia and carries an increased risk of stroke and heart failure. Here we investigated how the immune infiltrate of human epicardial adipose tissue (EAT), which directly overlies the myocardium, contributes to AF. Flow cytometry analysis revealed an enrichment of tissue-resident memory T (TRM) cells in patients with AF. Cellular indexing of transcriptomes and epitopes by sequencing (CITE-seq) and single-cell T cell receptor (TCR) sequencing identified two transcriptionally distinct CD8+ TRM cells that are modulated in AF. Spatial transcriptomic analysis of EAT and atrial tissue identified the border region between the tissues to be a region of intense inflammatory and fibrotic activity, and the addition of TRM populations to atrial cardiomyocytes demonstrated their ability to differentially alter calcium flux as well as activate inflammatory and apoptotic signaling pathways. This study identified EAT as a reservoir of TRM cells that can directly modulate vulnerability to cardiac arrhythmia.

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.

Ventricular Repolarization and Calcium Transient Show Resonant Behavior under Oscillatory Pacing Rate

Cardiac EC coupling is triggered by rhythmic depolarizing current fronts originating from the sino-atrial node, and the way variability in rhythm is associated with variability in action potential duration (APD) and, in turn, in the variability of calcium transient amplitude (CTA) and contraction is a key determinant of beating stability. Sinusoidal-varying pacing rate is adopted here in order to establish whether APD and CTA oscillations, elicited in a human ventricular AP model (OR) under oscillatory pacing, are consistent with the dynamics of two coupled harmonic oscillators, e.g., a two-degree-of-freedom system of mass and springs (MS model). I show evidence that this is the case, and that the MS model, preliminarily fitted to OR behavior, retains key features of the physiological system, such as the dependence of APD and CTA oscillation amplitudes from average value and from beat-to-beat changes in pacing rate, and the phase relationship between them. The bi-directionality of coupling between APD and CTA makes it difficult to discriminate which one leads EC coupling dynamics under variable pacing. The MS model suggests that the calcium cycling, with its greater inertia chiefly determined by the SR calcium release, is the leading mechanism. I propose the present approach to also be relevant at the whole organ level, where the need of compact representations of electromechanical interaction, particularly in clinical practice, remains urgent.

In silico simulations reveal that RYR distribution affects the dynamics of calcium release in cardiac myocytes

The dyads of cardiac myocytes contain ryanodine receptors (RYRs) that generate calcium sparks upon activation. To test how geometric factors of RYR distribution contribute to the formation of calcium sparks, which cannot be addressed experimentally, we performed in silico simulations on a large set of models of calcium release sites (CRSs). Our models covered the observed range of RYR number, density, and spatial arrangement. The calcium release function of CRSs was modeled by RYR openings, with an open probability dependent on concentrations of free Ca2+ and Mg2+ ions, in a rapidly buffered system, with a constant open RYR calcium current. We found that simulations of spontaneous sparks by repeatedly opening one of the RYRs in a CRS produced three different types of calcium release events (CREs) in any of the models. Transformation of simulated CREs into fluorescence signals yielded calcium sparks with characteristics close to the observed ones. CRE occurrence varied broadly with the spatial distribution of RYRs in the CRS but did not consistently correlate with RYR number, surface density, or calcium current. However, it correlated with RYR coupling strength, defined as the weighted product of RYR vicinity and calcium current, so that CRE characteristics of all models followed the same state-response function. This finding revealed the synergy between structure and function of CRSs in shaping dyad function. Lastly, rearrangements of RYRs simulating hypothetical experiments on splitting and compaction of a dyad revealed an increased propensity to generate spontaneous sparks and an overall increase in calcium release in smaller and more compact dyads, thus underlying the importance and physiological role of RYR arrangement in cardiac myocytes.

Stability of spatially discordant repolarization alternans in cardiac tissue

Cardiac alternans, a period-2 behavior of excitation and contraction of the heart, is a precursor of ventricular arrhythmias and sudden cardiac death. One form of alternans is repolarization or action potential duration alternans. In cardiac tissue, repolarization alternans can be spatially in-phase, called spatially concordant alternans, or spatially out-of-phase, called spatially discordant alternans (SDA). In SDA, the border between two out-of-phase regions is called a node in a one-dimensional cable or a nodal line in a two-dimensional tissue. In this study, we investigate the stability and dynamics of the nodes and nodal lines of repolarization alternans driven by voltage instabilities. We use amplitude equation and coupled map lattice models to derive theoretical results, which are compared with simulation results from the ionic model. Both conduction velocity restitution induced SDA and non-conduction velocity restitution induced SDA are investigated. We show that the stability and dynamics of the SDA nodes or nodal lines are determined by the balance of the tensions generated by conduction velocity restitution, convection due to action potential propagation, curvature of the nodal lines, and repolarization and coupling heterogeneities. Our study provides mechanistic insights into the different SDA behaviors observed in experiments.

Gene polymorphisms in calcium-calmodulin pathway: Focus on cardiovascular disease

Cardiovascular disease is the leading cause of death in industrialized countries and affects an increasing number of people. Several risk factors play an important role in the etiology of this disease, such as an unhealthy lifestyle. It is increasingly clear that genetic factors influencing the molecular basis of excitation-contraction mechanisms in the heart could contribute to modify the individual's risk. Thanks to the progress that has been made in understanding calcium signaling in the heart, it is assumed that calmodulin can play a crucial role in the excitation-contraction coupling. In fact, calmodulin (CaM) binds calcium and consequently regulates calcium channels. Several works show how some polymorphic variants can be considered predisposing factors to complex pathologies. Therefore, we hypothesize that the identification of polymorphic variants of proteins involved in the CaM pathway could be important for understanding how genetic traits can influence predisposition to myocardial infarction. This review considers each pathway of the three different isoforms of calmodulin (CaM1; CaM2; CaM3) and focuses on some common proteins involved in the three pathways, with the aim of analyzing the polymorphisms studied in the literature and understanding if they are associated with cardiovascular disease.

Altered Intracellular Calcium Homeostasis and Arrhythmogenesis in the Aged Heart

Aging of the heart is associated with a blunted response to sympathetic stimulation, reduced contractility, and increased propensity for arrhythmias, with the risk of sudden cardiac death significantly increased in the elderly population. The altered cardiac structural and functional phenotype, as well as age-associated prevalent comorbidities including hypertension and atherosclerosis, predispose the heart to atrial fibrillation, heart failure, and ventricular tachyarrhythmias. At the cellular level, perturbations in mitochondrial function, excitation-contraction coupling, and calcium homeostasis contribute to this electrical and contractile dysfunction. Major determinants of cardiac contractility are the intracellular release of Ca²⁺ from the sarcoplasmic reticulum by the ryanodine receptors (RyR2), and the following sequestration of Ca²⁺ by the sarco/endoplasmic Ca²⁺-ATPase (SERCa2a). Activity of RyR2 and SERCa2a in myocytes is not only dependent on expression levels and interacting accessory proteins, but on fine-tuned regulation via post-translational modifications. In this paper, we review how aberrant changes in intracellular Ca²⁺ cycling via these proteins contributes to arrhythmogenesis in the aged heart.

Proarrhythmic Remodeling of Calcium Homeostasis in Cardiac Disease; Implications for Diabetes and Obesity

A rapid growth in the incidence of diabetes and obesity has transpired to a major heath issue and economic burden in the postindustrial world, with more than 29 million patients affected in the United States alone. Cardiovascular defects have been established as the leading cause of mortality and morbidity of diabetic patients. Over the last decade, significant progress has been made in delineating mechanisms responsible for the diminished cardiac contractile function and enhanced propensity for malignant cardiac arrhythmias characteristic of diabetic disease. Rhythmic cardiac contractility relies upon the precise interplay between several cellular Ca²⁺ transport protein complexes including plasmalemmal L-type Ca²⁺ channels (LTCC), Na⁺-Ca²⁺ exchanger (NCX1), Sarco/endoplasmic Reticulum (SR) Ca²⁺-ATPase (SERCa2a) and ryanodine receptors (RyR2s), the SR Ca²⁺ release channels. Here we provide an overview of changes in Ca²⁺ homeostasis in diabetic ventricular myocytes and discuss the therapeutic potential of targeting Ca²⁺ handling proteins in the prevention of diabetes-associated cardiomyopathy and arrhythmogenesis.

Proarrhythmic Remodeling of Calcium Homeostasis in Cardiac Disease; Implications for Diabetes and Obesity

A rapid growth in the incidence of diabetes and obesity has transpired to a major heath issue and economic burden in the postindustrial world, with more than 29 million patients affected in the United States alone. Cardiovascular defects have been established as the leading cause of mortality and morbidity of diabetic patients. Over the last decade, significant progress has been made in delineating mechanisms responsible for the diminished cardiac contractile function and enhanced propensity for malignant cardiac arrhythmias characteristic of diabetic disease. Rhythmic cardiac contractility relies upon the precise interplay between several cellular Ca²⁺ transport protein complexes including plasmalemmal L-type Ca²⁺ channels (LTCC), Na⁺-Ca²⁺ exchanger (NCX1), Sarco/endoplasmic Reticulum (SR) Ca²⁺-ATPase (SERCa2a) and ryanodine receptors (RyR2s), the SR Ca²⁺ release channels. Here we provide an overview of changes in Ca²⁺ homeostasis in diabetic ventricular myocytes and discuss the therapeutic potential of targeting Ca²⁺ handling proteins in the prevention of diabetes-associated cardiomyopathy and arrhythmogenesis.

Proarrhythmic Remodeling of Calcium Homeostasis in Cardiac Disease; Implications for Diabetes and Obesity

A rapid growth in the incidence of diabetes and obesity has transpired to a major heath issue and economic burden in the postindustrial world, with more than 29 million patients affected in the United States alone. Cardiovascular defects have been established as the leading cause of mortality and morbidity of diabetic patients. Over the last decade, significant progress has been made in delineating mechanisms responsible for the diminished cardiac contractile function and enhanced propensity for malignant cardiac arrhythmias characteristic of diabetic disease. Rhythmic cardiac contractility relies upon the precise interplay between several cellular Ca²⁺ transport protein complexes including plasmalemmal L-type Ca²⁺ channels (LTCC), Na⁺-Ca²⁺ exchanger (NCX1), Sarco/endoplasmic Reticulum (SR) Ca²⁺-ATPase (SERCa2a) and ryanodine receptors (RyR2s), the SR Ca²⁺ release channels. Here we provide an overview of changes in Ca²⁺ homeostasis in diabetic ventricular myocytes and discuss the therapeutic potential of targeting Ca²⁺ handling proteins in the prevention of diabetes-associated cardiomyopathy and arrhythmogenesis.

NCX-Mediated Subcellular Ca2+ Dynamics Underlying Early Afterdepolarizations in LQT2 Cardiomyocytes

Long QT syndrome type 2 (LQT2) is a congenital disease characterized by loss of function mutations in hERG potassium channels (I_Kr). LQT2 is associated with fatal ventricular arrhythmias promoted by triggered activity in the form of early afterdepolarizations (EADs). We previously demonstrated that intracellular Ca²⁺ handling is remodeled in LQT2 myocytes. Remodeling leads to aberrant late RyR-mediated Ca²⁺ releases that drive forward-mode Na⁺-Ca²⁺ exchanger (NCX) current and slow repolarization to promote reopening of L-type calcium channels and EADs. Forward-mode NCX was found to be enhanced despite the fact that these late releases do not significantly alter the whole-cell cytosolic calcium concentration during a vulnerable period of phase 2 of the action potential corresponding to the onset of EADs. Here, we use a multiscale ventricular myocyte model to explain this finding. We show that because the local NCX current is a saturating nonlinear function of the local submembrane calcium concentration, a larger number of smaller-amplitude discrete Ca²⁺ release events can produce a large increase in whole-cell forward-mode NCX current without increasing significantly the whole-cell cytosolic calcium concentration. Furthermore, we develop novel insights, to our knowledge, into how alterations of stochastic RyR activity at the single-channel level cause late aberrant Ca²⁺ release events. Experimental measurements in transgenic LTQ2 rabbits confirm the critical arrhythmogenic role of NCX and identify this current as a potential target for antiarrhythmic therapies in LQT2.

A unified theory of calcium alternans in ventricular myocytes

Intracellular calcium (Ca²⁺) alternans is a dynamical phenomenon in ventricular myocytes, which is linked to the genesis of lethal arrhythmias. Iterated map models of intracellular Ca²⁺ cycling dynamics in ventricular myocytes under periodic pacing have been developed to study the mechanisms of Ca²⁺ alternans. Two mechanisms of Ca²⁺ alternans have been demonstrated in these models: one relies mainly on fractional sarcoplasmic reticulum Ca²⁺ release and uptake, and the other on refractoriness and other properties of Ca²⁺ sparks. Each of the two mechanisms can partially explain the experimental observations, but both have their inconsistencies with the experimental results. Here we developed an iterated map model that is composed of two coupled iterated maps, which unifies the two mechanisms into a single cohesive mathematical framework. The unified theory can consistently explain the seemingly contradictory experimental observations and shows that the two mechanisms work synergistically to promote Ca²⁺ alternans. Predictions of the theory were examined in a physiologically-detailed spatial Ca²⁺ cycling model of ventricular myocytes.

Ryanodine receptor sensitivity governs the stability and synchrony of local calcium release during cardiac excitation-contraction coupling

Calcium-induced calcium release is the principal mechanism that triggers the cell-wide [Ca(2+)]i transient that activates muscle contraction during cardiac excitation-contraction coupling (ECC). Here, we characterize this process in mouse cardiac myocytes with a novel mathematical action potential (AP) model that incorporates realistic stochastic gating of voltage-dependent L-type calcium (Ca(2+)) channels (LCCs) and sarcoplasmic reticulum (SR) Ca(2+) release channels (the ryanodine receptors, RyR2s). Depolarization of the sarcolemma during an AP stochastically activates the LCCs elevating subspace [Ca(2+)] within each of the cell's 20,000 independent calcium release units (CRUs) to trigger local RyR2 opening and initiate Ca(2+) sparks, the fundamental unit of triggered Ca(2+) release. Synchronization of Ca(2+) sparks during systole depends on the nearly uniform cellular activation of LCCs and the likelihood of local LCC openings triggering local Ca(2+) sparks (ECC fidelity). The detailed design and true SR Ca(2+) pump/leak balance displayed by our model permits investigation of ECC fidelity and Ca(2+) spark fidelity, the balance between visible (Ca(2+) spark) and invisible (Ca(2+) quark/sub-spark) SR Ca(2+) release events. Excess SR Ca(2+) leak is examined as a disease mechanism in the context of "catecholaminergic polymorphic ventricular tachycardia (CPVT)", a Ca(2+)-dependent arrhythmia. We find that that RyR2s (and therefore Ca(2+) sparks) are relatively insensitive to LCC openings across a wide range of membrane potentials; and that key differences exist between Ca(2+) sparks evoked during quiescence, diastole, and systole. The enhanced RyR2 [Ca(2+)]i sensitivity during CPVT leads to increased Ca(2+) spark fidelity resulting in asynchronous systolic Ca(2+) spark activity. It also produces increased diastolic SR Ca(2+) leak with some prolonged Ca(2+) sparks that at times become "metastable" and fail to efficiently terminate. There is a huge margin of safety for stable Ca(2+) handling within the cell and this novel mechanistic model provides insight into the molecular signaling characteristics that help maintain overall Ca(2+) stability even under the conditions of high SR Ca(2+) leak during CPVT. Finally, this model should provide tools for investigators to examine normal and pathological Ca(2+) signaling characteristics in the heart.

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.

Mechanisms of ventricular arrhythmias: from molecular fluctuations to electrical turbulence

Ventricular arrhythmias have complex causes and mechanisms. Despite extensive investigation involving many clinical, experimental, and computational studies, effective biological therapeutics are still very limited. In this article, we review our current understanding of the mechanisms of ventricular arrhythmias by summarizing the state of knowledge spanning from the molecular scale to electrical wave behavior at the tissue and organ scales and how the complex nonlinear interactions integrate into the dynamics of arrhythmias in the heart. We discuss the challenges that we face in synthesizing these dynamics to develop safe and effective novel therapeutic approaches.

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 transients closely reflect prolonged action potentials in iPSC models of inherited cardiac arrhythmia

Long-QT syndrome mutations can cause syncope and sudden death by prolonging the cardiac action potential (AP). Ion channels affected by mutations are various, and the influences of cellular calcium cycling on LQTS cardiac events are unknown. To better understand LQTS arrhythmias, we performed current-clamp and intracellular calcium ([Ca(2+)]i) measurements on cardiomyocytes differentiated from patient-derived induced pluripotent stem cells (iPS-CM). In myocytes carrying an LQT2 mutation (HERG-A422T), APs and [Ca(2+)]i transients were prolonged in parallel. APs were abbreviated by nifedipine exposure and further lengthened upon releasing intracellularly stored Ca(2+). Validating this model, control iPS-CM treated with HERG-blocking drugs recapitulated the LQT2 phenotype. In LQT3 iPS-CM, expressing NaV1.5-N406K, APs and [Ca(2+)]i transients were markedly prolonged. AP prolongation was sensitive to tetrodotoxin and to inhibiting Na(+)-Ca(2+) exchange. These results suggest that LQTS mutations act partly on cytosolic Ca(2+) cycling, potentially providing a basis for functionally targeted interventions regardless of the specific mutation site.

The emergence of subcellular pacemaker sites for calcium waves and oscillations

Calcium (Ca(2+)) waves generating oscillatory Ca(2+) signals are widely observed in biological cells. Experimental studies have shown that under certain conditions, initiation of Ca(2+) waves is random in space and time, while under other conditions, waves occur repetitively from preferred locations (pacemaker sites) from which they entrain the whole cell. In this study, we use computer simulations to investigate the self-organization of Ca(2+) sparks into pacemaker sites generating Ca(2+) oscillations. In both ventricular myocyte experiments and computer simulations of a heterogeneous Ca(2+) release unit (CRU) network model, we show that Ca(2+) waves occur randomly in space and time when the Ca(2+) level is low, but as the Ca(2+) level increases, waves occur repetitively from the same sites. Our analysis indicates that this transition to entrainment can be attributed to the fact that random Ca(2+) sparks self-organize into Ca(2+) oscillations differently at low and high Ca(2+) levels. At low Ca(2+), the whole cell Ca(2+) oscillation frequency of the coupled CRU system is much slower than that of an isolated single CRU. Compared to a single CRU, the distribution of interspike intervals (ISIs) of the coupled CRU network exhibits a greater variation, and its ISI distribution is asymmetric with respect to the peak, exhibiting a fat tail. At high Ca(2+), however, the coupled CRU network has a faster frequency and lesser ISI variation compared to an individual CRU. The ISI distribution of the coupled network no longer exhibits a fat tail and is well-approximated by a Gaussian distribution. This same Ca(2+) oscillation behaviour can also be achieved by varying the number of ryanodine receptors per CRU or the distance between CRUs. Using these results, we develop a theory for the entrainment of random oscillators which provides a unified explanation for the experimental observations underlying the emergence of pacemaker sites and Ca(2+) oscillations.

Ca²⁺ waves in the heart

Ca(2+) waves were probably first observed in the early 1940s. Since then Ca(2+) waves have captured the attention of an eclectic mixture of mathematicians, neuroscientists, muscle physiologists, developmental biologists, and clinical cardiologists. This review discusses the current state of mathematical models of Ca(2+) waves, the normal physiological functions Ca(2+) waves might serve in cardiac cells, as well as how the spatial arrangement of Ca(2+) release channels shape Ca(2+) waves, and we introduce the idea of Ca(2+) phase waves that might provide a useful framework for understanding triggered arrhythmias.

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.

Electrophysiological and contractile function of cardiomyocytes derived from human embryonic stem cells

Human embryonic stem cells have emerged as the prototypical source from which cardiomyocytes can be derived for use in drug discovery and cell therapy. However, such applications require that these cardiomyocytes (hESC-CMs) faithfully recapitulate the physiology of adult cells, especially in relation to their electrophysiological and contractile function. We review what is known about the electrophysiology of hESC-CMs in terms of beating rate, action potential characteristics, ionic currents, and cellular coupling as well as their contractility in terms of calcium cycling and contraction. We also discuss the heterogeneity in cellular phenotypes that arises from variability in cardiac differentiation, maturation, and culture conditions, and summarize present strategies that have been implemented to reduce this heterogeneity. Finally, we present original electrophysiological data from optical maps of hESC-CM clusters.

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.

Multiscale modeling of calcium cycling in cardiac ventricular myocyte: macroscopic consequences of microscopic dyadic function

In cardiac ventricular myocytes, calcium (Ca) release occurs at distinct structures (dyads) along t-tubules, where L-type Ca channels (LCCs) appose sarcoplasmic reticulum (SR) Ca release channels (RyR2s). We developed a model of the cardiac ventricular myocyte that simulates local stochastic Ca release processes. At the local Ca release level, the model reproduces Ca spark properties. At the whole-cell level, the model reproduces the action potential, Ca currents, and Ca transients. Changes in microscopic dyadic properties (e.g., during detubulation in heart failure) affect whole-cell behavior in complex ways, which we investigated by simulating changes in the dyadic volume and number of LCCs/RyR2s in the dyad, and effects of calsequestrin (CSQN) as a Ca buffer (CSQN buffer) or a luminal Ca sensor (CSQN regulator). We obtained the following results: 1), Increased dyadic volume and reduced LCCs/RyR2s decrease excitation-contraction coupling gain and cause asynchrony of SR Ca release, and interdyad coupling partially compensates for the reduced synchrony. 2), Impaired CSQN buffer depresses Ca transients without affecting the synchrony of SR Ca release. 3), When CSQN regulator function is impaired, interdyad coupling augments diastolic Ca release activity to form Ca waves and long-lasting Ca release events.

Recovery of cardiac calcium release is controlled by sarcoplasmic reticulum refilling and ryanodine receptor sensitivity

AIMS

In heart cells, the mechanisms underlying refractoriness of the elementary units of sarcoplasmic reticulum (SR) Ca(2+) release, Ca(2+) sparks, remain unclear. We investigated local recovery of SR Ca(2+) release using experimental measurements and mathematical modelling.

METHODS AND RESULTS

Repeated Ca(2+) sparks were induced from individual clusters of ryanodine receptors (RyRs) in quiescent rat ventricular myocytes, and we examined how changes in RyR gating influenced the time-dependent recovery of Ca(2+) spark amplitude and triggering probability. Repeated Ca(2+) sparks from individual sites were analysed in the presence of 50 nM ryanodine with: (i) no additional agents (control); (ii) 50 µM caffeine to sensitize RyRs; (iii) 50 µM tetracaine to inhibit RyRs; or (iv) 100 nM isoproterenol to activate β-adrenergic receptors. Sensitization and inhibition of RyR clusters shortened and lengthened, respectively, the median interval between consecutive Ca(2+) sparks (caffeine 239 ms; control 280 ms; tetracaine 453 ms). Recovery of Ca(2+) spark amplitude, however, was exponential with a time constant of ∼100 ms in all cases. Isoproterenol both accelerated the recovery of Ca(2+) spark amplitude (τ = 58 ms) and shortened the median interval between Ca(2+) sparks (192 ms). The results were recapitulated by a mathematical model in which SR [Ca(2+)] depletion terminates Ca(2+) sparks, but not by an alternative model based on limited depletion and Ca(2+)-dependent inactivation of RyRs.

CONCLUSION

Together, the results strongly suggest that: (i) local SR refilling controls Ca(2+) spark amplitude recovery; (ii) Ca(2+) spark triggering depends on both refilling and RyR sensitivity; and (iii) β-adrenergic stimulation influences both processes.

T-wave alternans and arrhythmogenesis in cardiac diseases

T-wave alternans, a manifestation of repolarization alternans at the cellular level, is associated with lethal cardiac arrhythmias and sudden cardiac death. At the cellular level, several mechanisms can produce repolarization alternans, including: (1) electrical restitution resulting from collective ion channel recovery, which usually occurs at fast heart rates but can also occur at normal heart rates when action potential is prolonged resulting in a short diastolic interval; (2) the transient outward current, which tends to occur at normal or slow heart rates; (3) the dynamics of early after depolarizations, which tends to occur during bradycardia; and (4) intracellular calcium cycling alternans through its interaction with membrane voltage. In this review, we summarize the cellular mechanisms of alternans arising from these different mechanisms, and discuss their roles in arrhythmogenesis in the setting of cardiac disease.

A computational model of Purkinje fibre single cell electrophysiology: implications for the long QT syndrome

Computer modelling has emerged as a particularly useful tool in understanding the physiology and pathophysiology of cardiac tissues. Models of ventricular, atrial and nodal tissue have evolved and include detailed ion channel kinetics and intercellular Ca(2+) handling. Purkinje fibre cells play a central role in the electrophysiology of the heart and in the genesis of cardiac arrhythmias. In this study, a new computational model has been constructed that incorporates the major membrane currents that have been isolated in recent experiments using Purkinje fibre cells. The model, which integrates mathematical models of human ion channels based on detailed biophysical studies of their kinetic and voltage-dependent properties, recapitulates distinct electrophysiological characteristics unique to Purkinje fibre cells compared to neighbouring ventricular myocytes. These characteristics include automaticity, hyperpolarized voltage range of the action potential plateau potential, and prolonged action potential duration. Simulations of selective ion channel blockade reproduce responses to pharmacological challenges characteristic of isolated Purkinje fibres in vitro, and importantly, the model predicts that Purkinje fibre cells are prone to severe arrhythmogenic activity in patients harbouring long QT syndrome 3 but much less so for other common forms of long QT. This new Purkinje cellular model can be a useful tool to study tissue-specific drug interactions and the effects of disease-related ion channel dysfunction on the cardiac conduction system.

Spark-induced sparks as a mechanism of intracellular calcium alternans in cardiac myocytes

RATIONALE

Intracellular calcium (Ca) alternans has been widely studied in cardiac myocytes and tissue, yet the underlying mechanism remains controversial.

OBJECTIVE

In this study, we used computational modeling and simulation to study how randomly occurring Ca sparks interact collectively to result in whole-cell Ca alternans.

METHODS AND RESULTS

We developed a spatially distributed intracellular Ca cycling model in which Ca release units (CRUs) are locally coupled by Ca diffusion throughout the myoplasm and sarcoplasmic reticulum (SR) network. Ca sparks occur randomly in the CRU network when periodically paced with a clamped voltage waveform, but Ca alternans develops as the pacing speeds up. Combining computational simulation with theoretical analysis, we show that Ca alternans emerges as a collective behavior of Ca sparks, determined by 3 critical properties of the CRU network from which Ca sparks arise: "randomness" (of Ca spark activation), "refractoriness" (of a CRU after a Ca spark), and "recruitment" (Ca sparks inducing Ca sparks in adjacent CRUs). We also show that the steep nonlinear relationship between fractional SR Ca release and SR Ca load arises naturally as a collective behavior of Ca sparks, and Ca alternans can occur even when SR Ca is held constant.

CONCLUSIONS

We present a general theory for the mechanisms of intracellular Ca alternans, which mechanistically links Ca sparks to whole-cell Ca alternans, and is applicable to Ca alternans in both physiological and pathophysiological conditions.

Calsequestrin-mediated mechanism for cellular calcium transient alternans

Intracellular calcium transient alternans (CTA) has a recognized role in arrhythmogenesis, but its origin is not yet fully understood. Recent models of CTA are based on a steep relationship between calcium release from the sarcoplasmic reticulum (SR) and its calcium load before release. This mechanism alone, however, does not explain recent observations of CTA without diastolic SR calcium content alternations. In addition, nanoscopic imaging of calcium dynamics has revealed that the elementary calcium release units of the SR can become refractory independently of their local calcium content. Here we show using a new physiologically detailed mathematical model of calcium cycling that luminal gating of the calcium release channels (RyRs) mediated by the luminal buffer calsequestrin (CSQN) can cause CTA independently of the steepness of the release-load relationship. In this complementary mechanism, CTA is caused by a beat-to-beat alternation in the number of refractory RyR channels and can occur with or without diastolic SR calcium content alternans depending on pacing conditions and uptake dynamics. The model has unique features, in that it treats a realistic number of spatially distributed and diffusively coupled dyads, each one with a realistic number of RyR channels, and that luminal CSQN buffering and gating is incorporated based on experimental data that characterizes the effect of the conformational state of CSQN on its buffering properties. In addition to reproducing observed features of CTA, this multiscale model is able to describe recent experiments in which CSQN expression levels were genetically altered as well as to reproduce nanoscopic measurements of spark restitution properties. The ability to link microscopic properties of the calcium release units to whole cell behavior makes this model a powerful tool to investigate the arrhythmogenic role of abnormal calcium handling in many pathological settings.

Ca2+-mobility in the sarcoplasmic reticulum of ventricular myocytes is low

The sarcoplasmic reticulum (SR) in ventricular myocytes contains releasable Ca(2+) for activating cellular contraction. Recent measurements of intra-SR (luminal) Ca(2+) suggest a high diffusive Ca(2+)-mobility constant (D(CaSR)). This could help spatially to unify SR Ca(2+)-content ([Ca(2+)](SRT)) and standardize Ca(2+)-release throughout the cell. But measurements of localized depletions of luminal Ca(2+) (Ca(2+)-blinks), associated with local Ca(2+)-release (Ca(2+)-sparks), suggest D(CaSR) may actually be low. Here we describe a novel method for measuring D(CaSR). Using a cytoplasmic Ca(2+)-fluorophore, we estimate regional [Ca(2+)](SRT) from localized, caffeine-induced SR Ca(2+)-release. Caffeine microperfusion of one end of a guinea pig or rat myocyte diffusively empties the whole SR at a rate indicating D(CaSR) is 8-9 microm(2)/s, up to tenfold lower than previous estimates. Ignoring background SR Ca(2+)-leakage in our measurement protocol produces an artifactually high D(CaSR) (>40 microm(2)/s), which may also explain the previous high values. Diffusion-reaction modeling suggests that a low D(CaSR) would be sufficient to support local SR Ca(2+)-signaling within sarcomeres during excitation-contraction coupling. Low D(CaSR) also implies that [Ca(2+)](SRT) may readily become spatially nonuniform, particularly under pathological conditions of spatially nonuniform Ca(2+)-release. Local control of luminal Ca(2+), imposed by low D(CaSR), may complement the well-established local control of SR Ca(2+)-release by Ca(2+)-channel/ryanodine receptor couplons.

Allosterically coupled calcium and magnesium binding sites are unmasked by ryanodine receptor chimeras

We studied cation regulation of wild-type ryanodine receptor type 1 ((WT)RyR1), type 3 ((WT)RyR3), and RyR3/RyR1 chimeras (Ch) expressed in 1B5 dyspedic myotubes. Using [(3)H]ryanodine binding to sarcoplasmic reticulum (SR) membranes, Ca(2+) titrations with (WT)RyR3 and three chimeras show biphasic activation that is allosterically coupled to an attenuated inhibition relative to (WT)RyR1. Chimeras show biphasic Mg(2+) inhibition profiles at 3 and 10 microM Ca(2+), no observable inhibition at 20 microM Ca(2+) and monophasic inhibition at 100 microM Ca(2+). Ca(2+) imaging of intact myotubes expressing Ch-4 exhibit caffeine-induced Ca(2+) transients with inhibition kinetics that are significantly slower than those expressing (WT)RyR1 or (WT)RyR3. Four new aspects of RyR regulation are evident: (1) high affinity (H) activation and low affinity (L) inhibition sites are allosterically coupled, (2) Ca(2+) facilitates removal of the inherent Mg(2+) block, (3) (WT)RyR3 exhibits reduced cooperativity between H activation sites when compared to (WT)RyR1, and (4) uncoupling of these sites in Ch-4 results in decreased rates of inactivation of caffeine-induced Ca(2+) transients.

Neuronal firing sensitivity to morphologic and active membrane parameters

Both the excitability of a neuron's membrane, driven by active ion channels, and dendritic morphology contribute to neuronal firing dynamics, but the relative importance and interactions between these features remain poorly understood. Recent modeling studies have shown that different combinations of active conductances can evoke similar firing patterns, but have neglected how morphology might contribute to homeostasis. Parameterizing the morphology of a cylindrical dendrite, we introduce a novel application of mathematical sensitivity analysis that quantifies how dendritic length, diameter, and surface area influence neuronal firing, and compares these effects directly against those of active parameters. The method was applied to a model of neurons from goldfish Area II. These neurons exhibit, and likely contribute to, persistent activity in eye velocity storage, a simple model of working memory. We introduce sensitivity landscapes, defined by local sensitivity analyses of firing rate and gain to each parameter, performed globally across the parameter space. Principal directions over which sensitivity to all parameters varied most revealed intrinsic currents that most controlled model output. We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain. Application of our method, and its characterization of which models were sensitive to general morphologic features, will lead to advances in understanding how realistic morphology participates in functional homeostasis. Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function. Our method can be adapted to analyze any computational model. Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.

Homeostasis is a process that allows a system to maintain a certain level of output over a long time, even though the inputs controlling the output are changing. Recently, studies of neurons and neuronal networks have shown that the “active” parameters that describe the movement of ions across the cell membrane contribute to homeostasis, since these parameters can be combined in different ways to maintain a specific output. There is also evidence that the physical shape (“morphology”) of the neuron may play a role in homeostasis, but this possibility has not been explored in computational models. We have developed a method that uses sensitivity analysis to evaluate how different kinds of parameters, like active and morphologic ones, affect model output. Across a multi-dimensional parameter space, we identified both local and global trends in parameter sensitivities that indicate regions where different parameters, even morphologic ones, contribute strongly to homeostasis. Significantly, the authors used sensitivities to predict which parameters should change, and by how much, to compensate for changes in another parameter to restore normal function. These predictions may prove important to neuronal aging, disease, and trauma research, but the method can be used to analyze any computational model.

Nonlinear dynamics of cardiac excitation-contraction coupling: an iterated map study

Cardiac myocytes are excitable cells in which an external current stimulus depolarizes the membrane potential to elicit an action potential. This action potential then triggers calcium release from intracellular stores, which mediates contraction. Conversely, intracellular calcium also modulates membrane currents, affecting action potential morphology and action potential duration (APD). The interactions between action potential and calcium, termed excitation-contraction coupling, give rise to a rich spectrum of nonlinear dynamics, especially at rapid heart rates, which are important for cardiac contraction and the development of lethal arrhythmias. In this study, we developed a nonlinear iterated map model to investigate the dynamics of cardiac excitation-contraction coupling in a periodically stimulated cell. We first studied the nonlinear dynamics due to APD restitution, a functional relation between APD and its preceding diastolic interval. We then studied the nonlinear dynamics due to intracellular calcium cycling when total cell calcium is constant or varies at a beat-to-beat basis. Finally, we studied the nonlinear dynamics due to the bidirectional coupling of the two dynamical systems. Saddle-node bifurcations leading to bistability, period-doubling bifurcations leading to alternans, and period-doubling routes to chaos can independently occur in both action potential or intracellular calcium cycling subsystems as heart rate increases. A Hopf bifurcation leading to quasiperiodicity occurs when the two dynamical systems are coupled. Although these dynamics are predicted from low-dimensional iterated maps, the approach here provides valuable information which can be used as a basis to explore dynamical features of physiologically detailed ionic models, to illuminate experimental findings, and to design experimentally testable predictions for new biological experiments.