How does stochastic ryanodine receptor-mediated Ca leak fail to initiate a Ca spark?

Computational Modeling of Cardiac Electrophysiology

Mathematical modeling and simulation are well-established and powerful tools to integrate experimental data of individual components of cardiac electrophysiology, excitation-contraction coupling, and regulatory signaling pathways, to gain quantitative and mechanistic insight into pathophysiological processes and guide therapeutic strategies. Here, we briefly describe the processes governing cardiac myocyte electrophysiology and Ca2+ handling and their regulation, as well as action potential propagation in tissue. We discuss the models and methods used to describe these phenomena, including procedures for model parameterization and validation, in addition to protocols for model interrogation and analysis and techniques that account for phenotypic variability and parameter uncertainty. Our objective is to provide a summary of basic concepts and approaches as a resource for scientists training in this discipline and for all researchers aiming to gain an understanding of cardiac modeling studies.

Elementary intracellular Ca signals approximated as a transition of release channel system from a metastable state

Cardiac muscle contraction is initiated by an elementary Ca signal (called Ca spark) which is achieved by collective action of Ca release channels in a cluster. The mechanism of this synchronization remains uncertain. We approached Ca spark activation as an emergent phenomenon of an interactive system of release channels. We constructed a weakly lumped Markov chain that applies an Ising model formalism to such release channel clusters and probable open channel configurations and demonstrated that spark activation is described as a system transition from a metastable to an absorbing state, analogous to the pressure required to overcome surface tension in bubble formation. This yielded quantitative estimates of the spark generation probability as a function of various system parameters. We performed numerical simulations to find spark probabilities as a function of sarcoplasmic reticulum Ca concentration, obtaining similar values for spark activation threshold as our analytic model, as well as those reported in experimental studies. Our parametric sensitivity analyses also showed that the spark activation threshold decreased as Ca sensitivity of RyR activation and RyR cluster size increased.

Mechanisms of spontaneous Ca2+ release-mediated arrhythmia in a novel 3D human atrial myocyte model: II. Ca2+ -handling protein variation

Disruption of the transverse-axial tubule system (TATS) in diseases such as heart failure and atrial fibrillation occurs in combination with changes in the expression and distribution of key Ca2+ -handling proteins. Together this ultrastructural and ionic remodelling is associated with aberrant Ca2+ cycling and electrophysiological instabilities that underlie arrhythmic activity. However, due to the concurrent changes in TATs and Ca2+ -handling protein expression and localization that occur in disease it is difficult to distinguish their individual contributions to the arrhythmogenic state. To investigate this, we applied our novel 3D human atrial myocyte model with spatially detailed Ca2+ diffusion and TATS to investigate the isolated and interactive effects of changes in expression and localization of key Ca2+ -handling proteins and variable TATS density on Ca2+ -handling abnormality driven membrane instabilities. We show that modulating the expression and distribution of the sodium-calcium exchanger, ryanodine receptors and the sarcoplasmic reticulum (SR) Ca2+ buffer calsequestrin have varying pro- and anti-arrhythmic effects depending on the balance of opposing influences on SR Ca2+ leak-load and Ca2+ -voltage relationships. Interestingly, the impact of protein remodelling on Ca2+ -driven proarrhythmic behaviour varied dramatically depending on TATS density, with intermediately tubulated cells being more severely affected compared to detubulated and densely tubulated myocytes. This work provides novel mechanistic insight into the distinct and interactive consequences of TATS and Ca2+ -handling protein remodelling that underlies dysfunctional Ca2+ cycling and electrophysiological instability in disease. KEY POINTS: In our companion paper we developed a 3D human atrial myocyte model, coupling electrophysiology and Ca2+ handling with subcellular spatial details governed by the transverse-axial tubule system (TATS). Here we utilize this model to mechanistically examine the impact of TATS loss and changes in the expression and distribution of key Ca2+ -handling proteins known to be remodelled in disease on Ca2+ homeostasis and electrophysiological stability. We demonstrate that varying the expression and localization of these proteins has variable pro- and anti-arrhythmic effects with outcomes displaying dependence on TATS density. Whereas detubulated myocytes typically appear unaffected and densely tubulated cells seem protected, the arrhythmogenic effects of Ca2+ handling protein remodelling are profound in intermediately tubulated cells. Our work shows the interaction between TATS and Ca2+ -handling protein remodelling that underlies the Ca2+ -driven proarrhythmic behaviour observed in atrial fibrillation and may help to predict the effects of antiarrhythmic strategies at varying stages of ultrastructural remodelling.

Mechanisms of spontaneous Ca2+ release-mediated arrhythmia in a novel 3D human atrial myocyte model: I. Transverse-axial tubule variation

Intracellular calcium (Ca2+ ) cycling is tightly regulated in the healthy heart ensuring effective contraction. This is achieved by transverse (t)-tubule membrane invaginations that facilitate close coupling of key Ca2+ -handling proteins such as the L-type Ca2+ channel and Na+ -Ca2+ exchanger (NCX) on the cell surface with ryanodine receptors (RyRs) on the intracellular Ca2+ store. Although less abundant and regular than in the ventricle, t-tubules also exist in atrial myocytes as a network of transverse invaginations with axial extensions known as the transverse-axial tubule system (TATS). In heart failure and atrial fibrillation, there is TATS remodelling that is associated with aberrant Ca2+ -handling and Ca2+ -induced arrhythmic activity; however, the mechanism underlying this is not fully understood. To address this, we developed a novel 3D human atrial myocyte model that couples electrophysiology and Ca2+ -handling with variable TATS organization and density. We extensively parameterized and validated our model against experimental data to build a robust tool examining TATS regulation of subcellular Ca2+ release. We found that varying TATS density and thus the localization of key Ca2+ -handling proteins has profound effects on Ca2+ handling. Following TATS loss, there is reduced NCX that results in increased cleft Ca2+ concentration through decreased Ca2+ extrusion. This elevated Ca2+ increases RyR open probability causing spontaneous Ca2+ releases and the promotion of arrhythmogenic waves (especially in the cell interior) leading to voltage instabilities through delayed afterdepolarizations. In summary, the present study demonstrates a mechanistic link between TATS remodelling and Ca2+ -driven proarrhythmic behaviour that probably reflects the arrhythmogenic state observed in disease. KEY POINTS: Transverse-axial tubule systems (TATS) modulate Ca2+ handling and excitation-contraction coupling in atrial myocytes, with TATS remodelling in heart failure and atrial fibrillation being associated with altered Ca2+ cycling and subsequent arrhythmogenesis. To investigate the poorly understood mechanisms linking TATS variation and spontaneous Ca2+ release, we built, parameterized and validated a 3D human atrial myocyte model coupling electrophysiology and spatially-detailed subcellular Ca2+ handling governed by the TATS. Simulated TATS loss causes diastolic Ca2+ and voltage instabilities through reduced Na+ -Ca2+ exchanger-mediated Ca2+ removal, cleft Ca2+ accumulation and increased ryanodine receptor open probability, resulting in spontaneous Ca2+ release and promotion of arrhythmogenic waves and delayed afterdepolarizations. At fast electrical rates typical of atrial tachycardia/fibrillation, spontaneous Ca2+ releases are larger and more frequent in the cell interior than at the periphery. Our work provides mechanistic insight into how atrial TATS remodelling can lead to Ca2+ -driven instabilities that may ultimately contribute to the arrhythmogenic state in disease.

Preserved cardiac performance and adrenergic response in a rabbit model with decreased ryanodine receptor 2 expression

Ryanodine receptor 2 (RyR2) is an ion channel in the heart responsible for releasing into the cytosol most of the Ca2+ required for contraction. Proper regulation of RyR2 is critical, as highlighted by the association between channel dysfunction and cardiac arrhythmia. Lower RyR2 expression is also observed in some forms of heart disease; however, there is limited information on the impact of this change on excitation-contraction (e-c) coupling, Ca2+-dependent arrhythmias, and cardiac performance. We used a constitutive knock-out of RyR2 in rabbits (RyR2-KO) to assess the extent to which a stable decrease in RyR2 expression modulates Ca2+ handling in the heart. We found that homozygous knock-out of RyR2 in rabbits is embryonic lethal. Remarkably, heterozygotes (KO+/-) show ~50% loss of RyR2 protein without developing an overt phenotype at the intact animal and whole heart levels. Instead, we found that KO+/- myocytes show (1) remodeling of RyR2 clusters, favoring smaller groups in which channels are more densely arranged; (2) lower Ca2+ spark frequency and amplitude; (3) slower rate of Ca2+ release and mild but significant desynchronization of the Ca2+ transient; and (4) a significant decrease in the basal phosphorylation of S2031, likely due to increased association between RyR2 and PP2A. Our data show that RyR2 deficiency, although remarkable at the molecular and subcellular level, has only a modest impact on global Ca2+ release and is fully compensated at the whole-heart level. This highlights the redundancy of RyR2 protein expression and the plasticity of the e-c coupling apparatus.

Multi-Scale Computational Modeling of Spatial Calcium Handling From Nanodomain to Whole-Heart: Overview and Perspectives

Regulation of intracellular calcium is a critical component of cardiac electrophysiology and excitation-contraction coupling. The calcium spark, the fundamental element of the intracellular calcium transient, is initiated in specialized nanodomains which co-locate the ryanodine receptors and L-type calcium channels. However, calcium homeostasis is ultimately regulated at the cellular scale, by the interaction of spatially separated but diffusively coupled nanodomains with other sub-cellular and surface-membrane calcium transport channels with strong non-linear interactions; and cardiac electrophysiology and arrhythmia mechanisms are ultimately tissue-scale phenomena, regulated by the interaction of a heterogeneous population of coupled myocytes. Recent advances in imaging modalities and image-analysis are enabling the super-resolution reconstruction of the structures responsible for regulating calcium homeostasis, including the internal structure of nanodomains themselves. Extrapolating functional and imaging data from the nanodomain to the whole-heart is non-trivial, yet essential for translational insight into disease mechanisms. Computational modeling has important roles to play in relating structural and functional data at the sub-cellular scale and translating data across the scales. This review covers recent methodological advances that enable image-based modeling of the single nanodomain and whole cardiomyocyte, as well as the development of multi-scale simulation approaches to integrate data from nanometer to whole-heart. Firstly, methods to overcome the computational challenges of simulating spatial calcium dynamics in the nanodomain are discussed, including image-based modeling at this scale. Then, recent whole-cell models, capable of capturing a range of different structures (such as the T-system and mitochondria) and cellular heterogeneity/variability are discussed at two different levels of discretization. Novel methods to integrate the models and data across the scales and simulate stochastic dynamics in tissue-scale models are then discussed, enabling elucidation of the mechanisms by which nanodomain remodeling underlies arrhythmia and contractile dysfunction. Perspectives on model differences and future directions are provided throughout.

Three-Dimensional Model of Sub-Plasmalemmal Ca2+ Microdomains Evoked by T Cell Receptor/CD3 Complex Stimulation

Ca²⁺ signalling plays an essential role in T cell activation, which is a key step to start an adaptive immune response. During the transition from a quiescent to a fully activated state, Ca²⁺ microdomains of reduced spatial and temporal extents develop in the junctions between the plasma membrane and the endoplasmic reticulum (ER). These microdomains rely on Ca²⁺ entry from the extracellular medium, via the ORAI1/STIM1/STIM2 system that mediates store operated Ca²⁺ entry Store operated calcium entry. The mechanism leading to local store depletion and subsequent Ca²⁺ entry depends on the activation state of the cells. The initial, smaller microdomains are triggered by D-myo-inositol 1,4,5-trisphosphate (IP₃) signalling in response to T cell adhesion. T cell receptor (TCR)/CD3 stimulation then initiates nicotinic acid adenine dinucleotide phosphate signalling, which activates ryanodine receptors (RYR). We have recently developed a mathematical model to elucidate the spatiotemporal Ca²⁺ dynamics of the microdomains triggered by IP₃ signalling in response to T cell adhesion (Gil et al., 2021). This reaction-diffusion model describes the evolution of the cytosolic and endoplasmic reticulum Ca²⁺ concentrations in a three-dimensional ER-PM junction and was solved using COMSOL Multiphysics. Modelling predicted that adhesion-dependent microdomains result from the concerted activity of IP₃ receptors and pre-formed ORAI1-STIM2 complexes. In the present study, we extend this model to include the role of RYRs rapidly after TCR/CD3 stimulation. The involvement of STIM1, which has a lower K_D for Ca²⁺ than STIM2, is also considered. Detailed 3D spatio-temporal simulations show that these Ca²⁺ microdomains rely on the concerted opening of ∼7 RYRs that are simultaneously active in response to the increase in NAADP induced by T cell stimulation. Opening of these RYRs provoke a local depletion of ER Ca²⁺ that triggers Ca²⁺ flux through the ORAI1 channels. Simulations predict that RYRs are most probably located around the junction and that the increase in junctional Ca²⁺ concentration results from the combination between diffusion of Ca²⁺ released through the RYRs and Ca²⁺ entry through ORAI1 in the junction. The computational model moreover provides a tool allowing to investigate how Ca²⁺ microdomains occur, extend and interact in various states of T cell activation.

Increasing SERCA function promotes initiation of calcium sparks and breakup of calcium waves

KEY POINTS

Increasing sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) pump activity enhances sarcoplasmic reticulum calcium (Ca) load, which increases both ryanodine receptor opening and driving force of Ca release flux. Both of these effects promote Ca spark formation and wave propagation. However, increasing SERCA activity also accelerates local cytosolic Ca decay as the wave front travels to the next cluster, which limits wave propagation. As a result, increasing SERCA pump activity has a biphasic effect on the propensity of arrhythmogenic Ca waves, but a monotonic effect to increase Ca spark frequency and amplitude.

ABSTRACT

Waves of sarcoplasmic reticulum (SR) calcium (Ca) release can cause arrhythmogenic afterdepolarizations in cardiac myocytes. Ca waves propagate when Ca sparks at one Ca release unit (CRU) recruit new Ca sparks in neighbouring CRUs. Under normal conditions, Ca sparks are too small to recruit neighbouring Ca sparks where Ca sensitivity is also low. However, under pathological conditions such as a Ca overload or ryanodine receptor (RyR) sensitization, Ca sparks can be larger and propagate more readily as macro-sparks or full Ca waves. Increasing SERCA pump activity promotes SR Ca load, which promotes RyR opening and increases driving force of the Ca release flux from SR to cytosol, promoting Ca waves. However, high sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) activity can also decrease local cytosolic [Ca] as it approaches the next CRU, thereby reducing wave appearance and propagation. In this study, we use a physiologically detailed model of subcellular Ca cycling and experiments in phospholamban-knockout mice, to show how Ca waves are initiated and propagate and how different conditions contribute to the generation and propagation of Ca waves. We show that reducing diffusive coupling between Ca sparks by increasing SERCA activity prevents Ca waves by reducing [Ca] at the next CRU, as do Ca buffers, low intra-SR Ca diffusion and distance between CRUs. Increasing SR Ca uptake rate has a biphasic effect on Ca wave propagation; initially it enhances Ca spark probability and amplitude and CRU coupling, thereby promoting arrhythmogenic Ca wave propagation, but at higher levels SR Ca uptake can abort those arrhythmogenic Ca waves.

Recruiting RyRs to Open in a Ca2+ Release Unit: Single-RyR Gating Properties Make RyR Group Dynamics

In cardiac myocytes, clusters of type-2 ryanodine receptors (RyR2s) release Ca²⁺ from the sarcoplasmic reticulum (SR) via a positive feedback mechanism in which fluxed Ca²⁺ activates nearby RyRs. Although the general principles of this are understood, less is known about how single-RyR gating properties define the RyR group dynamics in an array of many channels. Here, we examine this using simulations with three models of RyR gating that have identical open probabilities: the commonly used two-state Markov gating model, one that utilizes multiple exponentials to fit single-channel open time (OT) and closed time (CT) distributions, and an extension of this multiexponential model that also includes experimentally measured correlations between single-channel OTs and CTs. The simulations of RyR clusters that utilize the multiexponential gating model produce infrequent Ca²⁺ release events with relatively few open RyRs. Ca²⁺ release events become even smaller when OT/CT correlations are included. This occurs because the correlations produce a small but consistent bias against recruiting more RyRs to open during the middle of a Ca²⁺ release event, between the initiation and termination phases (which are unaltered compared to the uncorrelated simulations). In comparison, the two-state model produces frequent, large, and long Ca²⁺ release events because it had a recruitment bias in favor of opening more RyRs. This difference stems from the two-state model's single-RyR OT and CT distributions being qualitatively different from the experimental ones. Thus, the details of single-RyR gating can profoundly affect SR Ca²⁺ release even if open probability and mean OTs and CTs are identical. We also show that Ca²⁺ release events can terminate spontaneously without any reduction in SR [Ca²⁺], luminal regulation, Ca²⁺-dependent inactivation, or physical coupling between RyRs when Ca²⁺ flux is below a threshold value. This supports and extends the pernicious attrition/induction decay hypothesis that SR Ca²⁺ release events terminate below a threshold Ca²⁺ flux.

Mechanisms of Calcium Leak from Cardiac Sarcoplasmic Reticulum Revealed by Statistical Mechanics

Heart muscle contraction is normally activated by a synchronized Ca release from sarcoplasmic reticulum (SR), a major intracellular Ca store. However, under abnormal conditions, Ca leaks from the SR, decreasing heart contraction amplitude and increasing risk of life-threatening arrhythmia. The mechanisms and regimes of SR operation generating the abnormal Ca leak remain unclear. Here, we employed both numerical and analytical modeling to get mechanistic insights into the emergent Ca leak phenomenon. Our numerical simulations using a detailed realistic model of the Ca release unit reveal sharp transitions resulting in Ca leak. The emergence of leak is closely mapped mathematically to the Ising model from statistical mechanics. The system steady-state behavior is determined by two aggregate parameters: the analogs of magnetic field (h) and the inverse temperature (β) in the Ising model, for which we have explicit formulas in terms of SR [Ca] and release channel opening and closing rates. The classification of leak regimes takes the shape of a phase β-h diagram, with the regime boundaries occurring at h = 0 and a critical value of β (β^∗) that we estimate using a classical Ising model and mean field theory. Our theory predicts that a synchronized Ca leak will occur when h > 0 and β >β^∗, and a disordered leak occurs when β <β^∗ and h is not too negative. The disorder leak is distinguished from synchronized leak (in long-lasting sparks) by larger Peierls contour lengths, an output parameter reflecting degree of disorder. Thus, in addition to our detailed numerical model approach, we also offer an instantaneous computational tool using analytical formulas of the Ising model for respective ryanodine receptor parameters and SR Ca load that describe and classify phase transitions and leak emergence.

Size Matters: Ryanodine Receptor Cluster Size Heterogeneity Potentiates Calcium Waves

Ryanodine receptors (RyRs) mediate calcium (Ca)-induced Ca release and intracellular Ca homeostasis. In a cardiac myocyte, RyRs group into clusters of variable size from a few to several hundred RyRs, creating a spatially nonuniform intracellular distribution. It is unclear how heterogeneity of RyR cluster size alters spontaneous sarcoplasmic reticulum (SR) Ca releases (Ca sparks) and arrhythmogenic Ca waves. Here, we tested the impact of heterogeneous RyR cluster size on the initiation of Ca waves. Experimentally, we measured RyR cluster sizes at Ca spark sites in rat ventricular myocytes and further tested functional impacts using a physiologically detailed computational model with spatial and stochastic intracellular Ca dynamics. We found that the spark frequency and amplitude increase nonlinearly with the size of RyR clusters. Larger RyR clusters have lower SR Ca release threshold for local Ca spark initiation and exhibit steeper SR Ca release versus SR Ca load relationship. However, larger RyR clusters tend to lower SR Ca load because of the higher Ca leak rate. Conversely, smaller clusters have a higher threshold and a lower leak, which tends to increase SR Ca load. At the myocyte level, homogeneously large or small RyR clusters limit Ca waves (because of low load for large clusters but low excitability for small clusters). Mixtures of large and small RyR clusters potentiates Ca waves because the enhanced SR Ca load driven by smaller clusters enables Ca wave initiation and propagation from larger RyR clusters. Our study suggests that a spatially heterogeneous distribution of RyR cluster size under pathological conditions may potentiate Ca waves and thus afterdepolarizations and triggered arrhythmias.

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.

Size Matters: Ryanodine Receptor Cluster Size Affects Arrhythmogenic Sarcoplasmic Reticulum Calcium Release

BACKGROUND

Ryanodine receptors (RyR) mediate sarcoplasmic reticulum calcium (Ca2+) release and influence myocyte Ca2+ homeostasis and arrhythmias. In cardiac myocytes, RyRs are found in clusters of various sizes and shapes, and RyR cluster size may critically influence normal and arrhythmogenic Ca2+ spark and wave formation. However, the actual RyR cluster sizes at specific Ca2+ spark sites have never been measured in the physiological setting.

METHODS AND RESULTS

Here we measured RyR cluster size and Ca2+ sparks simultaneously to assess how RyR cluster size influences Ca2+ sparks and sarcoplasmic reticulum Ca2+ leak. For small RyR cluster sizes (<50), Ca2+ spark frequency is very low but then increases dramatically at larger cluster sizes. In contrast, Ca2+ spark amplitude is nearly maximal even at relatively small RyR cluster size (≈10) and changes little at larger cluster size. These properties agreed with computational simulations of RyR gating within clusters.

CONCLUSIONS

Our study explains how this combination of properties may limit arrhythmogenic Ca2+ sparks and wave propagation (at many junctions) while preserving the efficacy and spatial synchronization of Ca2+-induced Ca2+-release during normal excitation-contraction coupling. However, variations in RyR cluster size among individual junctions and RyR sensitivity could exacerbate heterogeneity of local sarcoplasmic reticulum Ca2+ release and arrhythmogenesis under pathological conditions.

Effects of rogue ryanodine receptors on Ca2+ sparks in cardiac myocytes

Ca2+ sparks and Ca2+ quarks, arising from clustered and rogue ryanodine receptors (RyRs), are significant Ca2+ release events from the junctional sarcoplasmic reticulum (JSR). Based on the anomalous subdiffusion of Ca2+ in the cytoplasm, a mathematical model was developed to investigate the effects of rogue RyRs on Ca2+ sparks in cardiac myocytes. Ca2+ quarks and sparks from the stochastic opening of rogue and clustered RyRs are numerically reproduced and agree with experimental measurements. It is found that the stochastic opening Ca2+ release units (CRUs) of clustered RyRs are regulated by free Ca2+ concentration in the JSR lumen (i.e. [Ca2+]lumen). The frequency of spontaneous Ca2+ sparks is remarkably increased by the rogue RyRs opening at high [Ca2+]lumen, but not at low [Ca2+]lumen. Hence, the opening of rogue RyRs contributes to the formation of Ca2+ sparks at high [Ca2+]lumen. The interplay of Ca2+ sparks and Ca2+ quarks has been discussed in detail. This work is of significance to provide insight into understanding Ca2+ release mechanisms in cardiac myocytes.

A model for cooperative gating of L-type Ca2+ channels and its effects on cardiac alternans dynamics

In ventricular myocytes, membrane depolarization during the action potential (AP) causes synchronous activation of multiple L-type CaV1.2 channels (LTCCs), which trigger the release of calcium (Ca2+) from the sarcoplasmic reticulum (SR). This results in an increase in intracellular Ca2+ (Cai) that initiates contraction. During pulsus alternans, cardiac contraction is unstable, going from weak to strong in successive beats despite a constant heart rate. These cardiac alternans can be caused by the instability of membrane potential (Vm) due to steep AP duration (APD) restitution (Vm-driven alternans), instability of Cai cycling (Ca2+-driven alternans), or both, and may be modulated by functional coupling between clustered CaV1.2 (e.g. cooperative gating). Here, mathematical analysis and computational models were used to determine how changes in the strength of cooperative gating between LTCCs may impact membrane voltage and intracellular Ca2+ dynamics in the heart. We found that increasing the degree of coupling between LTCCs increases the amplitude of Ca2+ currents (ICaL) and prolongs AP duration (APD). Increased AP duration is known to promote cardiac alternans, a potentially arrhythmogenic substrate. In addition, our analysis shows that increasing the strength of cooperative activation of LTCCs makes the coupling of Ca2+ on the membrane voltage (Cai→Vm coupling) more positive and destabilizes the Vm-Cai dynamics for Vm-driven alternans and Cai-driven alternans, but not for quasiperiodic oscillation. These results suggest that cooperative gating of LTCCs may have a major impact on cardiac excitation-contraction coupling, not only by prolonging APD, but also by altering Cai→Vm coupling and potentially promoting cardiac arrhythmias.

Calcium-Dependent Arrhythmogenic Foci Created by Weakly Coupled Myocytes in the Failing Heart

RATIONALE

Intercellular uncoupling and Ca²⁺ (Ca) mishandling can initiate triggered ventricular arrhythmias. Spontaneous Ca release activates inward current which depolarizes membrane potential (V_m) and can trigger action potentials in isolated myocytes. However, cell-cell coupling in intact hearts limits local depolarization and may protect hearts from this arrhythmogenic mechanism. Traditional optical mapping lacks the spatial resolution to assess coupling of individual myocytes.

OBJECTIVE

We investigate local intercellular coupling in Ca-induced depolarization in intact hearts, using confocal microscopy to measure local V_m and intracellular [Ca] simultaneously.

METHODS AND RESULTS

We used isolated Langendorff-perfused hearts from control (CTL) and heart failure (HF) mice (HF induced by transaortic constriction). In CTL hearts, 1.4% of myocytes were poorly synchronized with neighboring cells and exhibited asynchronous (AS) Ca transients. These AS myocytes were much more frequent in HF (10.8% of myocytes, P<0.05 versus CTL). Local Ca waves depolarized V_m in HF but not CTL hearts, suggesting weaker gap junction coupling in HF-AS versus CTL-AS myocytes. Cell-cell coupling was assessed by calcein fluorescence recovery after photobleach during intracellular [Ca] recording. All regions in CTL hearts exhibited faster calcein diffusion than in HF, with HF-AS myocyte being slowest. In HF-AS, enhancing gap junction conductance (with rotigaptide) increased coupling and suppressed V_m depolarization during Ca waves. Conversely, in CTL hearts, gap junction inhibition (carbenoxolone) decreased coupling and allowed Ca wave-induced depolarizations. Synchronization of Ca wave initiation and triggered action potentials were observed in HF hearts and computational models.

CONCLUSIONS

Well-coupled CTL myocytes are effectively voltage-clamped during Ca waves, protecting the heart from triggered arrhythmias. Spontaneous Ca waves are much more common in HF myocytes and these AS myocytes are also poorly coupled, enabling local Ca-induced inward current of sufficient source strength to overcome a weakened current sink to depolarize V_m and trigger action potentials.

Ambiguous interactions between diastolic and SR Ca2+ in the regulation of cardiac Ca2+ release

Sobie et al. highlight unresolved issues concerning the regulation of sarcoplasmic reticulum calcium release in cardiac myocytes.

Sarcoplasmic Reticulum Structure and Functional Properties that Promote Long-Lasting Calcium Sparks

Calcium (Ca) sparks are the fundamental sarcoplasmic reticulum (SR) Ca release events in cardiac myocytes, and they have a typical duration of 20-40 ms. However, when a fraction of ryanodine receptors (RyRs) are blocked by tetracaine or ruthenium red, Ca sparks lasting hundreds of milliseconds have been observed experimentally. The fundamental mechanism underlying these extremely prolonged Ca sparks is not understood. In this study, we use a physiologically detailed mathematical model of subcellular Ca cycling to examine how Ca spark duration is influenced by the number of functional RyRs in a junctional cluster (which is reduced by tetracaine or ruthenium red) and other SR Ca handling properties. One RyR cluster contains a few to several hundred RyRs, and we use a four-state Markov RyR gating model. Each RyR opens stochastically and is regulated by cytosolic and luminal Ca. We varied the number of functional RyRs in the single cluster, diffusion within the SR network, diffusion between network and junctional SR, cytosolic Ca diffusion, SERCA uptake activity, and RyR open probability. For long-lasting Ca release events, opening events within the cluster must occur continuously because the typical open time of the RyR is only a few milliseconds. We found the following: 1) if the number of RyRs is too small, it is difficult to maintain consecutive openings and stochastic attrition terminates the release; 2) if the number of RyRs is too large, the depletion of Ca from the junctional SR terminates the release; and 3) very long release events require relatively small-sized RyR clusters (reducing flux as seen experimentally with tetracaine) and sufficiently rapid intra-SR Ca diffusion, such that local junctional intra-SR [Ca] can be maintained by intra-SR diffusion and overall SR Ca reuptake.

Oxidative stress and ca(2+) release events in mouse cardiomyocytes

Cellular oxidative stress, associated with a variety of common cardiac diseases, is well recognized to affect the function of several key proteins involved in Ca(2+) signaling and excitation-contraction coupling, which are known to be exquisitely sensitive to reactive oxygen species. These include the Ca(2+) release channels of the sarcoplasmic reticulum (ryanodine receptors or RyR2s) and the Ca(2+)/calmodulin-dependent protein kinase II (CaMKII). Oxidation of RyR2s was found to increase the open probability of the channel, whereas CaMKII can be activated independent of Ca(2+) through oxidation. Here, we investigated how oxidative stress affects RyR2 function and SR Ca(2+) signaling in situ, by analyzing Ca(2+) sparks in permeabilized mouse cardiomyocytes under a broad range of oxidative conditions. The results show that with increasing oxidative stress Ca(2+) spark duration is prolonged. In addition, long and very long-lasting (up to hundreds of milliseconds) localized Ca(2+) release events started to appear, eventually leading to sarcoplasmic reticulum (SR) Ca(2+) depletion. These changes of release duration could be prevented by the CaMKII inhibitor KN93 and did not occur in mice lacking the CaMKII-specific S2814 phosphorylation site on RyR2. The appearance of long-lasting Ca(2+) release events was paralleled by an increase of RyR2 oxidation, but also by RyR-S2814 phosphorylation, and by CaMKII oxidation. Our results suggest that in a strongly oxidative environment oxidation-dependent activation of CaMKII leads to RyR2 phosphorylation and thereby contributes to the massive prolongation of SR Ca(2+) release events.

Superresolution modeling of calcium release in the heart

Stable calcium-induced calcium release (CICR) is critical for maintaining normal cellular contraction during cardiac excitation-contraction coupling. The fundamental element of CICR in the heart is the calcium (Ca²⁺) spark, which arises from a cluster of ryanodine receptors (RyR). Opening of these RyR clusters is triggered to produce a local, regenerative release of Ca²⁺ from the sarcoplasmic reticulum (SR). The Ca²⁺ leak out of the SR is an important process for cellular Ca²⁺ management, and it is critically influenced by spark fidelity, i.e., the probability that a spontaneous RyR opening triggers a Ca²⁺ spark. Here, we present a detailed, three-dimensional model of a cardiac Ca²⁺ release unit that incorporates diffusion, intracellular buffering systems, and stochastically gated ion channels. The model exhibits realistic Ca²⁺ sparks and robust Ca²⁺ spark termination across a wide range of geometries and conditions. Furthermore, the model captures the details of Ca²⁺ spark and nonspark-based SR Ca²⁺ leak, and it produces normal excitation-contraction coupling gain. We show that SR luminal Ca²⁺-dependent regulation of the RyR is not critical for spark termination, but it can explain the exponential rise in the SR Ca²⁺ leak-load relationship demonstrated in previous experimental work. Perturbations to subspace dimensions, which have been observed in experimental models of disease, strongly alter Ca²⁺ spark dynamics. In addition, we find that the structure of RyR clusters also influences Ca²⁺ release properties due to variations in inter-RyR coupling via local subspace Ca²⁺ concentration ([Ca²⁺]_ss). These results are illustrated for RyR clusters based on super-resolution stimulated emission depletion microscopy. Finally, we present a believed-novel approach by which the spark fidelity of a RyR cluster can be predicted from structural information of the cluster using the maximum eigenvalue of its adjacency matrix. These results provide critical insights into CICR dynamics in heart, under normal and pathological conditions.

Phospholamban ablation rescues the enhanced propensity to arrhythmias of mice with CaMKII-constitutive phosphorylation of RyR2 at site S2814

KEY POINTS

Mice with Ca(2+) -calmodulin-dependent protein kinase (CaMKII) constitutive pseudo-phosphorylation of the ryanodine receptor RyR2 at Ser2814 (S2814D(+/+) mice) exhibit a higher open probability of RyR2, higher sarcoplasmic reticulum (SR) Ca(2+) leak in diastole and increased propensity to arrhythmias under stress conditions. We generated phospholamban (PLN)-deficient S2814D(+/+) knock-in mice by crossing two colonies, S2814D(+/+) and PLNKO mice, to test the hypothesis that PLN ablation can prevent the propensity to arrhythmias of S2814D(+/+) mice. PLN ablation partially rescues the altered intracellular Ca(2+) dynamics of S2814D(+/+) hearts and myocytes, but enhances SR Ca(2+) sparks and leak on confocal microscopy. PLN ablation diminishes ventricular arrhythmias promoted by CaMKII phosphorylation of S2814 on RyR2. PLN ablation aborts the arrhythmogenic SR Ca(2+) waves of S2814D(+/+) and transforms them into non-propagating events. A mathematical human myocyte model replicates these results and predicts the increase in SR Ca(2+) uptake required to prevent the arrhythmias induced by a CaMKII-dependent leaky RyR2.

ABSTRACT

Mice with constitutive pseudo-phosphorylation at Ser2814-RyR2 (S2814D(+/+) ) have increased propensity to arrhythmias under β-adrenergic stress conditions. Although abnormal Ca(2+) release from the sarcoplasmic reticulum (SR) has been linked to arrhythmogenesis, the role played by SR Ca(2+) uptake remains controversial. We tested the hypothesis that an increase in SR Ca(2+) uptake is able to rescue the increased arrhythmia propensity of S2814D(+/+) mice. We generated phospholamban (PLN)-deficient/S2814D(+/+) knock-in mice by crossing two colonies, S2814D(+/+) and PLNKO mice (SD(+/+) /KO). SD(+/+) /KO myocytes exhibited both increased SR Ca(2+) uptake seen in PLN knock-out (PLNKO) myocytes and diminished SR Ca(2+) load (relative to PLNKO), a characteristic of S2814D(+/+) myocytes. Ventricular arrhythmias evoked by catecholaminergic challenge (caffeine/adrenaline) in S2814D(+/+) mice in vivo or programmed electric stimulation and high extracellular Ca(2+) in S2814D(+) /(-) hearts ex vivo were significantly diminished by PLN ablation. At the myocyte level, PLN ablation converted the arrhythmogenic Ca(2+) waves evoked by high extracellular Ca(2+) provocation in S2814D(+/+) mice into non-propagated Ca(2+) mini-waves on confocal microscopy. Myocyte Ca(2+) waves, typical of S2814D(+/+) mice, could be evoked in SD(+/+) /KO cells by partially inhibiting SERCA2a. A mathematical human myocyte model replicated these results and allowed for predicting the increase in SR Ca(2+) uptake required to prevent the arrhythmias induced by a Ca(2+) -calmodulin-dependent protein kinase (CaMKII)-dependent leaky RyR2. Our results demonstrate that increasing SR Ca(2+) uptake by PLN ablation can prevent the arrhythmic events triggered by SR Ca(2+) leak due to CaMKII-dependent phosphorylation of the RyR2-S2814 site and underscore the benefits of increasing SERCA2a activity on SR Ca(2+) -triggered arrhythmias.

Modeling calcium regulation of contraction, energetics, signaling, and transcription in the cardiac myocyte

Calcium (Ca(2+)) plays many important regulatory roles in cardiac muscle cells. In the initial phase of the action potential, influx of Ca(2+) through sarcolemmal voltage-gated L-type Ca(2+) channels (LCCs) acts as a feed-forward signal that triggers a large release of Ca(2+) from the junctional sarcoplasmic reticulum (SR). This Ca(2+) drives heart muscle contraction and pumping of blood in a process known as excitation-contraction coupling (ECC). Triggered and released Ca(2+) also feed back to inactivate LCCs, attenuating the triggered Ca(2+) signal once release has been achieved. The process of ECC consumes large amounts of ATP. It is now clear that in a process known as excitation-energetics coupling, Ca(2+) signals exert beat-to-beat regulation of mitochondrial ATP production that closely couples energy production with demand. This occurs through transport of Ca(2+) into mitochondria, where it regulates enzymes of the tricarboxylic acid cycle. In excitation-signaling coupling, Ca(2+) activates a number of signaling pathways in a feed-forward manner. Through effects on their target proteins, these interconnected pathways regulate Ca(2+) signals in complex ways to control electrical excitability and contractility of heart muscle. In a process known as excitation-transcription coupling, Ca(2+) acting primarily through signal transduction pathways also regulates the process of gene transcription. Because of these diverse and complex roles, experimentally based mechanistic computational models are proving to be very useful for understanding Ca(2+) signaling in the cardiac myocyte.

On the Adjacency Matrix of RyR2 Cluster Structures

In the heart, electrical stimulation of cardiac myocytes increases the open probability of sarcolemmal voltage-sensitive Ca2+ channels and flux of Ca2+ into the cells. This increases Ca2+ binding to ligand-gated channels known as ryanodine receptors (RyR2). Their openings cause cell-wide release of Ca2+, which in turn causes muscle contraction and the generation of the mechanical force required to pump blood. In resting myocytes, RyR2s can also open spontaneously giving rise to spatially-confined Ca2+ release events known as "sparks." RyR2s are organized in a lattice to form clusters in the junctional sarcoplasmic reticulum membrane. Our recent work has shown that the spatial arrangement of RyR2s within clusters strongly influences the frequency of Ca2+ sparks. We showed that the probability of a Ca2+ spark occurring when a single RyR2 in the cluster opens spontaneously can be predicted from the precise spatial arrangements of the RyR2s. Thus, "function" follows from "structure." This probability is related to the maximum eigenvalue (λ1) of the adjacency matrix of the RyR2 cluster lattice. In this work, we develop a theoretical framework for understanding this relationship. We present a stochastic contact network model of the Ca2+ spark initiation process. We show that λ1 determines a stability threshold for the formation of Ca2+ sparks in terms of the RyR2 gating transition rates. We recapitulate these results by applying the model to realistic RyR2 cluster structures informed by super-resolution stimulated emission depletion (STED) microscopy. Eigendecomposition of the linearized mean-field contact network model reveals functional subdomains within RyR2 clusters with distinct sensitivities to Ca2+. This work provides novel perspectives on the cardiac Ca2+ release process and a general method for inferring the functional properties of transmembrane receptor clusters from their structure.

Cytosolic Ca²⁺ buffering determines the intra-SR Ca²⁺ concentration at which cardiac Ca²⁺ sparks terminate

Single ryanodine receptor (RyR) Ca(2+) flux amplitude (i(Ca-RyR)) decreases as intra-sarcoplasmic reticulum (SR) Ca(2+) levels fall during a cardiac Ca(2+) spark. Since i(Ca-RyR) drives the inter-RyR Ca(2+)-induced Ca(2+) release (CICR) that underlies the spark, decreasing i(Ca-RyR) may contribute to spark termination because RyRs that spontaneously close may stay closed. To test this possibility, we simultaneously measured local cytosolic and intra-SR ([Ca(2+)]cyto and [Ca(2+)]SR) during Ca(2+) sparks in permeabilized rabbit ventricular myocytes. Local cytosolic or intra-SR Ca(2+) dynamics were manipulated using Ca(2+) buffers. Buffer manipulations applied in cells had no effect on individual RyR channels reconstituted in planar lipid bilayers. Presence of a fast cytosolic Ca(2+) buffer (BAPTA) significantly suppressed Ca(2+) spark activity and sparks terminated earlier at a higher than usual [Ca(2+)]SR level (∼80% vs. ∼62%). When cytosolic Ca(2+) buffer power was reduced (i.e. cytosolic EGTA level decreased), sparks terminated later and at a lower than usual [Ca(2+)]SR level (∼45% vs. ∼62%). When intra-SR Ca(2+) buffer power was increased, sparks also terminated later and at a lower than usual [Ca(2+)]SR (∼48% vs. ∼62%). These results suggest that cytosolic local control of inter-RyR CICR by i(Ca-RyR) plays a substantial role during the spark termination process. Thus, alterations in local cytosolic Ca(2+) handling dynamics in the dyadic cleft (Ca(2+) buffering, extrusion, etc.) likely influence Ca(2+) spark termination.

Depolarization of cardiac membrane potential synchronizes calcium sparks and waves in tissue

The diastolic membrane potential (Vm) can be hyperpolarized or depolarized by various factors such as hyperkalemia or hypokalemia in the long term, or by delayed afterdepolarizations in the short term. In this study, we investigate how Vm affects Ca sparks and waves. We use a physiologically detailed mathematical model to investigate individual factors that affect Ca spark generation and wave propagation. We focus on the voltage range of -90 ∼ -70 mV, which is just below the Vm for sodium channel activation. We find that Vm depolarization promotes Ca wave propagation and hyperpolarization prevents it. This finding is directly validated in voltage clamp experiments with Ca waves using isolated rat ventricular myocytes. Ca transport by the sodium-calcium exchanger (NCX) is determined by Vm as well as Na and Ca concentrations. Depolarized Vm reduces NCX-mediated efflux, elevating [Ca]i, and thus promoting Ca wave propagation. Moreover, depolarized Vm promotes spontaneous Ca releases that can cause initiation of multiple Ca waves. This indicates that during delayed afterdepolarizations, Ca release units (CRUs) interact with not just the immediately adjacent CRUs via Ca diffusion, but also further CRUs via fast (∼0.1 ms) changes in Vm mediated by the voltage and Ca-sensitive NCX. This may contribute significantly to synchronization of Ca waves among multiple cells in tissue.

The role of dyadic organization in regulation of sarcoplasmic reticulum Ca(2+) handling during rest in rabbit ventricular myocytes

The dyadic organization of ventricular myocytes ensures synchronized activation of sarcoplasmic reticulum (SR) Ca(2+) release during systole. However, it remains obscure how the dyadic organization affects SR Ca(2+) handling during diastole. By measuring intraluminal SR Ca(2+) ([Ca(2+)]SR) decline during rest in rabbit ventricular myocytes, we found that ∼76% of leaked SR Ca(2+) is extruded from the cytosol and only ∼24% is pumped back into the SR. Thus, the majority of Ca(2+) that leaks from the SR is removed from the cytosol before it can be sequestered back into the SR by the SR Ca(2+)-ATPase (SERCA). Detubulation decreased [Ca(2+)]SR decline during rest, thus making the leaked SR Ca(2+) more accessible for SERCA. These results suggest that Ca(2+) extrusion systems are localized in T-tubules. Inhibition of Na(+)-Ca(2+) exchanger (NCX) slowed [Ca(2+)]SR decline during rest by threefold, however did not prevent it. Depolarization of mitochondrial membrane potential during NCX inhibition completely prevented the rest-dependent [Ca(2+)]SR decline. Despite a significant SR Ca(2+) leak, Ca(2+) sparks were very rare events in control conditions. NCX inhibition or detubulation increased Ca(2+) spark activity independent of SR Ca(2+) load. Overall, these results indicate that during rest NCX effectively competes with SERCA for cytosolic Ca(2+) that leaks from the SR. This can be explained if the majority of SR Ca(2+) leak occurs through ryanodine receptors in the junctional SR that are located closely to NCX in the dyadic cleft. Such control of the dyadic [Ca(2+)] by NCX play a critical role in suppressing Ca(2+) sparks during rest.

Disrupted calcium release as a mechanism for atrial alternans associated with human atrial fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia, but our knowledge of the arrhythmogenic substrate is incomplete. Alternans, the beat-to-beat alternation in the shape of cardiac electrical signals, typically occurs at fast heart rates and leads to arrhythmia. However, atrial alternans have been observed at slower pacing rates in AF patients than in controls, suggesting that increased vulnerability to arrhythmia in AF patients may be due to the proarrythmic influence of alternans at these slower rates. As such, alternans may present a useful therapeutic target for the treatment and prevention of AF, but the mechanism underlying alternans occurrence in AF patients at heart rates near rest is unknown. The goal of this study was to determine how cellular changes that occur in human AF affect the appearance of alternans at heart rates near rest. To achieve this, we developed a computational model of human atrial tissue incorporating electrophysiological remodeling associated with chronic AF (cAF) and performed parameter sensitivity analysis of ionic model parameters to determine which cellular changes led to alternans. Of the 20 parameters tested, only decreasing the ryanodine receptor (RyR) inactivation rate constant (ki_Ca) produced action potential duration (APD) alternans seen clinically at slower pacing rates. Using single-cell clamps of voltage, fluxes, and state variables, we determined that alternans onset was Ca²⁺-driven rather than voltage-driven and occurred as a result of decreased RyR inactivation which led to increased steepness of the sarcoplasmic reticulum (SR) Ca²⁺ release slope. Iterated map analysis revealed that because SR Ca²⁺ uptake efficiency was much higher in control atrial cells than in cAF cells, drastic reductions in ki_Ca were required to produce alternans at comparable pacing rates in control atrial cells. These findings suggest that RyR kinetics may play a critical role in altered Ca²⁺ homeostasis which drives proarrhythmic APD alternans in patients with AF.

Atrial fibrillation is an irregular heart rhythm affecting millions of people worldwide. Effective treatment of this cardiac disorder relies upon our detailed knowledge and understanding of the mechanisms that lead to arrhythmia. Recent clinical observations have suggested that alternans, a phenomenon where the shape of the electrical signal in the heart alternates from beat to beat, may play an important role in this process, but the underlying mechanisms remain unknown. In this study, we use computational models to conduct a detailed examination of the causes and contributors to alternans associated with human atrial fibrillation. We find that in atria remodeled by atrial fibrillation, alternans appears near resting heart rates because several aspects of calcium cycling are disrupted in the atrial cells. In particular, the release and uptake of calcium from the cellular storage compartment, the sarcoplasmic reticulum, becomes imbalanced, leading to alternation in calcium signals from beat to beat. These findings provide important insights into the mechanisms of proarrhythmic alternans in human atrial fibrillation which may be used to develop novel therapeutic targets and treatment strategies in the future.

Ca handling during excitation-contraction coupling in heart failure

In the heart, coupling between excitation of the surface membrane and activation of contractile apparatus is mediated by Ca released from the sarcoplasmic reticulum (SR). Several components of Ca machinery are perfectly arranged within the SR network and the T-tubular system to generate a regular Ca cycling and thereby rhythmic beating activity of the heart. Among these components, ryanodine receptor (RyR) and SR Ca ATPase (SERCA) complexes play a particularly important role and their dysfunction largely underlies abnormal Ca homeostasis in diseased hearts such as in heart failure. The abnormalities in Ca regulation occur at practically all main steps of Ca cycling in the failing heart, including activation and termination of SR Ca release, diastolic SR Ca leak, and SR Ca uptake. The contributions of these different mechanisms to depressed contractile function and enhanced arrhythmogenesis may vary in different HF models. This brief review will therefore focus on modifications in RyR and SERCA structure that occur in the failing heart and how these molecular modifications affect SR Ca regulation and excitation-contraction coupling.

Cardiac sarcoplasmic reticulum calcium leak: basis and roles in cardiac dysfunction

Synchronized SR calcium (Ca) release is critical to normal cardiac myocyte excitation-contraction coupling, and ideally this release shuts off completely between heartbeats. However, other SR Ca release events are referred to collectively as SR Ca leak (which includes Ca sparks and waves as well as smaller events not detectable as Ca sparks). Much, but not all, of the SR Ca leak occurs via ryanodine receptors and can be exacerbated in pathological states such as heart failure. The extent of SR Ca leak is important because it can (a) reduce SR Ca available for release, causing systolic dysfunction; (b) elevate diastolic [Ca]i, contributing to diastolic dysfunction; (c) cause triggered arrhythmias; and (d) be energetically costly because of extra ATP used to repump Ca. This review addresses quantitative aspects and manifestations of SR Ca leak and its measurement, and how leak is modulated by Ca, associated proteins, and posttranslational modifications in health and disease.

Determinants of beat-to-beat variability of repolarization duration in the canine ventricular myocyte: a computational analysis

Beat-to-beat variability of repolarization duration (BVR) is an intrinsic characteristic of cardiac function and a better marker of proarrhythmia than repolarization prolongation alone. The ionic mechanisms underlying baseline BVR in physiological conditions, its rate dependence, and the factors contributing to increased BVR in pathologies remain incompletely understood. Here, we employed computer modeling to provide novel insights into the subcellular mechanisms of BVR under physiological conditions and during simulated drug-induced repolarization prolongation, mimicking long-QT syndromes type 1, 2, and 3. We developed stochastic implementations of 13 major ionic currents and fluxes in a model of canine ventricular-myocyte electrophysiology. Combined stochastic gating of these components resulted in short- and long-term variability, consistent with experimental data from isolated canine ventricular myocytes. The model indicated that the magnitude of stochastic fluctuations is rate dependent due to the rate dependence of action-potential (AP) duration (APD). This process (the “active” component) and the intrinsic nonlinear relationship between membrane current and APD (“intrinsic component”) contribute to the rate dependence of BVR. We identified a major role in physiological BVR for stochastic gating of the persistent Na⁺ current (I_Na) and rapidly activating delayed-rectifier K⁺ current (I_Kr). Inhibition of I_Kr or augmentation of I_Na significantly increased BVR, whereas subsequent β-adrenergic receptor stimulation reduced it, similar to experimental findings in isolated myocytes. In contrast, β-adrenergic stimulation increased BVR in simulated long-QT syndrome type 1. In addition to stochastic channel gating, AP morphology, APD, and beat-to-beat variations in Ca²⁺ were found to modulate single-cell BVR. Cell-to-cell coupling decreased BVR and this was more pronounced when a model cell with increased BVR was coupled to a model cell with normal BVR. In conclusion, our results provide new insights into the ionic mechanisms underlying BVR and suggest that BVR reflects multiple potentially proarrhythmic parameters, including increased ion-channel stochasticity, prolonged APD, and abnormal Ca²⁺ handling.

Every heartbeat has an electrical recovery (repolarization) interval that varies in duration from beat to beat. Excessive beat-to-beat variability of repolarization duration has been shown to be a risk marker of potentially fatal heart-rhythm disorders, but the contributing subcellular mechanisms remain incompletely understood. Computational models have greatly enhanced our understanding of several basic electrophysiological mechanisms. We developed a detailed computer model of the ventricular myocyte that can simulate beat-to-beat changes in repolarization duration by taking into account stochastic changes in the opening and closing of individual ion channels responsible for all main ion currents. The model accurately reproduced experimental data from isolated myocytes under both physiological and pathological conditions. Using the model, we identified several mechanisms contributing to repolarization variability, including stochastic gating of ion channels, duration and morphology of the repolarization phase, and intracellular calcium handling, thereby providing insights into its basis as a proarrhythmic marker. Our computer model provides a detailed framework to study the dynamics of cardiac electrophysiology and arrhythmias.

Parameter sensitivity analysis of stochastic models provides insights into cardiac calcium sparks

We present a parameter sensitivity analysis method that is appropriate for stochastic models, and we demonstrate how this analysis generates experimentally testable predictions about the factors that influence local Ca(2+) release in heart cells. The method involves randomly varying all parameters, running a single simulation with each set of parameters, running simulations with hundreds of model variants, then statistically relating the parameters to the simulation results using regression methods. We tested this method on a stochastic model, containing 18 parameters, of the cardiac Ca(2+) spark. Results show that multivariable linear regression can successfully relate parameters to continuous model outputs such as Ca(2+) spark amplitude and duration, and multivariable logistic regression can provide insight into how parameters affect Ca(2+) spark triggering (a probabilistic process that is all-or-none in a single simulation). Benchmark studies demonstrate that this method is less computationally intensive than standard methods by a factor of 16. Importantly, predictions were tested experimentally by measuring Ca(2+) sparks in mice with knockout of the sarcoplasmic reticulum protein triadin. These mice exhibit multiple changes in Ca(2+) release unit structures, and the regression model both accurately predicts changes in Ca(2+) spark amplitude (30% decrease in model, 29% decrease in experiments) and provides an intuitive and quantitative understanding of how much each alteration contributes to the result. This approach is therefore an effective, efficient, and predictive method for analyzing stochastic mathematical models to gain biological insight.

Mechanism of calsequestrin regulation of single cardiac ryanodine receptor in normal and pathological conditions

Release of Ca²⁺ from the sarcoplasmic reticulum (SR) drives contractile function of cardiac myocytes. Luminal Ca²⁺ regulation of SR Ca²⁺ release is fundamental not only in physiology but also in physiopathology because abnormal luminal Ca²⁺ regulation is known to lead to arrhythmias, catecholaminergic polymorphic ventricular tachycardia (CPVT), and/or sudden cardiac arrest, as inferred from animal model studies. Luminal Ca²⁺ regulates ryanodine receptor (RyR)2-mediated SR Ca²⁺ release through mechanisms localized inside the SR; one of these involves luminal Ca²⁺ interacting with calsequestrin (CASQ), triadin, and/or junctin to regulate RyR2 function.

CASQ2-RyR2 regulation was examined at the single RyR2 channel level. Single RyR2s were incorporated into planar lipid bilayers by the fusion of native SR vesicles isolated from either wild-type (WT), CASQ2 knockout (KO), or R33Q-CASQ2 knock-in (KI) mice. KO and KI mice have CPVT-like phenotypes. We show that CASQ2(WT) action on RyR2 function (either activation or inhibition) was strongly influenced by the presence of cytosolic MgATP. Function of the reconstituted CASQ2(WT)–RyR2 complex was unaffected by changes in luminal free [Ca²⁺] (from 0.1 to 1 mM). The inhibition exerted by CASQ2(WT) association with the RyR2 determined a reduction in cytosolic Ca²⁺ activation sensitivity. RyR2s from KO mice were significantly more sensitive to cytosolic Ca²⁺ activation and had significantly longer mean open times than RyR2s from WT mice. Sensitivity of RyR2s from KI mice was in between that of RyR2 channels from KO and WT mice. Enhanced cytosolic RyR2 Ca²⁺ sensitivity and longer RyR2 open times likely explain the CPVT-like phenotype of both KO and KI mice.

Calcium movements inside the sarcoplasmic reticulum of cardiac myocytes

Sarcoplasmic reticulum (SR) Ca content ([Ca]SRT) is critical to both normal cardiac function and electrophysiology, and changes associated with pathology contribute to systolic and diastolic dysfunction and arrhythmias. The intra-SR free [Ca] ([Ca]SR) dictates the [Ca]SRT, the driving force for Ca release and regulates release channel gating. We discuss measurement of [Ca]SR and [Ca]SRT, how [Ca]SR regulates activation and termination of release, and how Ca diffuses within the SR and influences SR Ca release during excitation-contraction coupling, Ca sparks and Cac waves. The entire SR network is connected and its lumen is also continuous with the nuclear envelope. Rapid Ca diffusion within the SR could stabilize and balance local [Ca]SR within the myocyte, but restrictions to diffusion can create spatial inhomogeneities. Experimental measurements and mathematical models of [Ca]SR to date have greatly enriched our understanding of these [Ca]SR dynamics, but controversies exist and may stimulate new measurements and analysis.

Extraction of sub-microscopic Ca fluxes from blurred and noisy fluorescent indicator images with a detailed model fitting approach

The release of Ca from intracellular stores is key to cardiac muscle function; however, the molecular control of intracellular Ca release remains unclear. Depletion of the intracellular Ca store (sarcoplasmic reticulum, SR) may play an important role, but the ability to measure local SR Ca with fluorescent Ca indicators is limited by the microscope optical resolution and properties of the indicator. This leads to an uncertain degree of spatio-temporal blurring, which is not easily corrected (by deconvolution methods) due to the low signal-to-noise ratio of the recorded signals. In this study, a 3D computer model was constructed to calculate local Ca fluxes and consequent dye signals, which were then blurred by a measured microscope point spread function. Parameter fitting was employed to adjust a release basis function until the model output fitted recorded (2D) Ca spark data. This ‘forward method’ allowed us to obtain estimates of the time-course of Ca release flux and depletion within the sub-microscopic local SR associated with a number of Ca sparks. While variability in focal position relative to Ca spark sites causes more out-of-focus events to have smaller calculated fluxes (and less SR depletion), the average SR depletion was to 20±10% (s.d.) of the resting level. This focus problem implies that the actual SR depletion is likely to be larger and the five largest depletions analyzed were to 8±6% of the resting level. This profound depletion limits SR release flux during a Ca spark, which peaked at 8±3 pA and declined with a half time of 7±2 ms. By comparison, RyR open probability declined more slowly, suggesting release termination is dominated by neither SR Ca depletion nor intrinsic RyR gating, but results from an interaction of these processes.

Calcium levels inside myocytes regulate the heart's force of contraction. Calcium is released from the primary intracellular store called the sarcoplasmic reticulum. Calcium release was directly observed as ‘calcium sparks’ using fluorescent calcium indicators inside the cell. More recently, calcium levels inside the store have been measured as calcium ‘blinks’. These suggest that some depletion of store calcium occurs during cell excitation; however, the actual extent of depletion is made uncertain by the complex sarcoplasmic reticulum shape, dye saturation and optical properties of the microscope. While previous studies have assumed idealized microscope properties, we measured microscope blurring and applied it to a computer model of calcium movements inside the cell. In this model, calcium release was adjusted to match the simulated blurred calcium signals to experimental results. The calculations show that the depth of local sarcoplasmic reticulum calcium depletion is much greater than inferred from calcium blinks and that the time-course of calcium release is affected by this depletion. An estimate for the time-course of gating of the ion channels that regulate calcium release inside the cell was also calculated. We suggest that the time-course of SR Ca release arises from a complex interaction of Ca depletion and channel gating.

β-adrenergic stimulation activates early afterdepolarizations transiently via kinetic mismatch of PKA targets

Sympathetic stimulation regulates cardiac excitation-contraction coupling in hearts but can also trigger ventricular arrhythmias caused by early afterdepolarizations (EADs) in pathological conditions. Isoproterenol (ISO) stimulation can transiently cause EADs which could result from differential kinetics of L-type Ca current (ICaL) vs. delayed rectifier potassium current (IKs) effects, but multiple PKA targets complicate mechanistic analysis. Utilizing a biophysically detailed model integrating Ca and β-adrenergic signaling, we investigate how different phosphorylation kinetics and targets influence β-adrenergic-induced transient EADs. We found that: 1) The faster time course of ICaL vs. IKs increases recapitulates experimentally observed ISO-induced transient EADs (which are due to ICaL reactivation). These EADs disappear at steady state ISO and do not occur during more gradual ISO application. 2) This ICaL vs. IKs kinetic mismatch with ISO can also induce transient EADs due to spontaneous sarcoplasmic reticulum (SR) Ca release and Na/Ca exchange current. The increased ICaL, SR Ca uptake and action potential duration (APD) raise SR Ca to cause spontaneous SR Ca release, but eventual IKs activation and APD shortening abolish these EADs. 3) Phospholemman (PLM) phosphorylation decreases both types of EADs by increasing outward Na/K-ATPase current (INaK) for ICaL-mediated EADs, and reducing intracellular Na and Ca loading for SR Ca-release-mediated EADs. Slowing PLM phosphorylation kinetics abolishes this protective effect. 4) Blocking phospholamban (PLB) phosphorylation has little effect on ICaL-mediated transient EADs, but abolishes SR Ca-release-mediated transient EADs by limiting SR Ca loading. 5) RyR phosphorylation has little effect on either transient EAD type. Our study emphasizes the importance of understanding non-steady state kinetics of several systems in mediating β-adrenergic-induced EADs and arrhythmias.

Alterations in T-tubule and dyad structure in heart disease: challenges and opportunities for computational analyses

Compelling recent experimental results make clear that sub-cellular structures are altered in ventricular myocytes during the development of heart failure, in both human samples and diverse experimental models. These alterations can include, but are not limited to, changes in the clusters of sarcoplasmic reticulum (SR) Ca(2+)-release channels, ryanodine receptors, and changes in the average distance between the cell membrane and ryanodine receptor clusters. In this review, we discuss the potential consequences of these structural alterations on the triggering of SR Ca(2+) release during excitation-contraction coupling. In particular, we describe how mathematical models of local SR Ca(2+) release can be used to predict functional changes resulting from diverse modifications that occur in disease states. We review recent studies that have used simulations to understand the consequences of sub-cellular structural changes, and we discuss modifications that will allow for future modelling studies to address unresolved questions. We conclude with a discussion of improvements in both experimental and mathematical modelling techniques that will be required to provide a stronger quantitative understanding of the functional consequences of changes in sub-cellular structure in heart disease.

Pernicious attrition and inter-RyR2 CICR current control in cardiac muscle

In cardiac muscle cells, ryanodine receptor (RyR) mediated Ca(2+) release from the sarcoplasmic reticulum (SR) drives the contractile apparatus. Spontaneous bouts of inter-RyR Ca(2+) induced Ca(2+) release (CICR) generate an elemental unit of SR Ca(2+) release called a spark. Sparks are localized events that terminate soon after they begin. The local control of sparks is not clearly understood. In this article, we review the potential regulatory role that the changing single RyR Ca(2+) current may play. Moreover, we aggregate RyR data into a working scheme of inter-RyR CICR current control of sparks and a potential inter-RyR CICR termination mechanism that we call pernicious attrition.

Termination of calcium-induced calcium release by induction decay: an emergent property of stochastic channel gating and molecular scale architecture

Calcium-induced calcium release (CICR) is an inherently regenerative process due to the Ca(2+)-dependent gating of ryanodine receptors (RyRs) in the sarco/endoplasmic reticulum (SR) and is critical for cardiac excitation-contraction coupling. This process is seen as Ca(2+) sparks, which reflect the concerted gating of groups of RyRs in the dyad, a specialised junctional signalling domain between the SR and surface membrane. However, the mechanism(s) responsible for the termination of regenerative CICR during the evolution of Ca(2+) sparks remain uncertain. Rat cardiac RyR gating was recorded at physiological Ca(2+), Mg(2+) and ATP levels and incorporated into a 3D model of the cardiac dyad which reproduced the time-course of Ca(2+) sparks, Ca(2+) blinks and Ca(2+) spark restitution. Model CICR termination was robust, relatively insensitive to the number of dyadic RyRs and automatic. This emergent behaviour arose from the rapid development and dissolution of nanoscopic Ca(2+) gradients within the dyad. These simulations show that CICR does not require intrinsic inactivation or SR calcium sensing mechanisms for stability and cessation of regeneration that arises from local control at the molecular scale via a process we call 'induction decay'.

Can the sodium-calcium exchanger initiate or suppress calcium sparks in cardiac myocytes?

Positive feedback of Calcium (Ca)-induced Ca release is the mechanism of Ca spark formation in cardiac myocytes. To initiate this process, a certain amount of Ca in the cleft space is necessary. When the membrane potential becomes higher during excitation-contraction coupling, Ca can enter through both Ca current (I(CaL)) and sodium-calcium exchanger (NCX) and may activate ryanodine receptors to initiate a Ca spark. On the other hand, at the resting membrane potential (V(m) ~-80 mV), NCX removes Ca from the cell (forward mode). If Ca released from the sarcoplasmic reticulum is quickly removed via forward mode NCX before Ca-induced Ca release starts, the Ca release becomes nonspark Ca leak. This would also be influenced by the cleft/noncleft distribution of NCX, which is unknown. Using a physiologically detailed mathematical model of subcellular Ca cycling, we analyze how NCX strength and distribution alter Ca spark formation. During excitation-contraction coupling, most Ca sparks are induced by I(CaL) with very few due to NCX current. At the resting membrane potential if most NCX is localized to the cleft, spontaneous Ca sparks are significantly reduced.

Decoding myocardial Ca²⁺ signals across multiple spatial scales: a role for sensitivity analysis

Numerous studies have employed mathematical modeling to quantitatively understand release of Ca(2+) from the sarcoplasmic reticulum (SR) in the heart. Models have been used to investigate physiologically important phenomena such as triggering of SR Ca(2+) release by Ca(2+) entry across the cell membrane and spontaneous leak of Ca(2+) from the SR in quiescent heart cells. In this review we summarize studies that have modeled myocardial Ca(2+) at different spatial scales: the sub-cellular level, the cellular level, and the multicellular level. We discuss each category of models from the standpoint of parameter sensitivity analysis, a common simulation procedure that can generate quantitative, comprehensive predictions about how changes in conditions influence model output. We propose that this is a useful perspective for conceptualizing models, in part because a sensitivity analysis requires the investigator to define the relevant parameters and model outputs. This procedure therefore helps to illustrate the capabilities and limitations of each model. We further suggest that in future studies, sensitivity analyses will aid in simplifying complex models and in suggesting experiments to differentiate between competing models built with different assumptions. We conclude with a discussion of unresolved questions that are likely to be addressed over the next several years.

Modeling effects of L-type ca(2+) current and na(+)-ca(2+) exchanger on ca(2+) trigger flux in rabbit myocytes with realistic T-tubule geometries

The transverse tubular system of rabbit ventricular myocytes consists of cell membrane invaginations (t-tubules) that are essential for efficient cardiac excitation-contraction coupling. In this study, we investigate how t-tubule micro-anatomy, L-type Ca²⁺ channel (LCC) clustering, and allosteric activation of Na⁺/Ca²⁺ exchanger by L-type Ca²⁺ current affects intracellular Ca²⁺ dynamics. Our model includes a realistic 3D geometry of a single t-tubule and its surrounding half-sarcomeres for rabbit ventricular myocytes. The effects of spatially distributed membrane ion-transporters (LCC, Na⁺/Ca²⁺ exchanger, sarcolemmal Ca²⁺ pump, and sarcolemmal Ca²⁺ leak), and stationary and mobile Ca²⁺ buffers (troponin C, ATP, calmodulin, and Fluo-3) are also considered. We used a coupled reaction-diffusion system to describe the spatio-temporal concentration profiles of free and buffered intracellular Ca²⁺. We obtained parameters from voltage-clamp protocols of L-type Ca²⁺ current and line-scan recordings of Ca²⁺ concentration profiles in rabbit cells, in which the sarcoplasmic reticulum is disabled. Our model results agree with experimental measurements of global Ca²⁺ transient in myocytes loaded with 50 μM Fluo-3. We found that local Ca²⁺ concentrations within the cytosol and sub-sarcolemma, as well as the local trigger fluxes of Ca²⁺ crossing the cell membrane, are sensitive to details of t-tubule micro-structure and membrane Ca²⁺ flux distribution. The model additionally predicts that local Ca²⁺ trigger fluxes are at least threefold to eightfold higher than the whole-cell Ca²⁺ trigger flux. We found also that the activation of allosteric Ca²⁺-binding sites on the Na⁺/Ca²⁺ exchanger could provide a mechanism for regulating global and local Ca²⁺ trigger fluxes in vivo. Our studies indicate that improved structural and functional models could improve our understanding of the contributions of L-type and Na⁺/Ca²⁺ exchanger fluxes to intracellular Ca²⁺ dynamics.

Posttranslational modifications of cardiac ryanodine receptors: Ca(2+) signaling and EC-coupling

In cardiac muscle, a number of posttranslational protein modifications can alter the function of the Ca(2+) release channel of the sarcoplasmic reticulum (SR), also known as the ryanodine receptor (RyR). During every heartbeat RyRs are activated by the Ca(2+)-induced Ca(2+) release mechanism and contribute a large fraction of the Ca(2+) required for contraction. Some of the posttranslational modifications of the RyR are known to affect its gating and Ca(2+) sensitivity. Presently, research in a number of laboratories is focused on RyR phosphorylation, both by PKA and CaMKII, or on RyR modifications caused by reactive oxygen and nitrogen species (ROS/RNS). Both classes of posttranslational modifications are thought to play important roles in the physiological regulation of channel activity, but are also known to provoke abnormal alterations during various diseases. Only recently it was realized that several types of posttranslational modifications are tightly connected and form synergistic (or antagonistic) feed-back loops resulting in additive and potentially detrimental downstream effects. This review summarizes recent findings on such posttranslational modifications, attempts to bridge molecular with cellular findings, and opens a perspective for future work trying to understand the ramifications of crosstalk in these multiple signaling pathways. Clarifying these complex interactions will be important in the development of novel therapeutic approaches, since this may form the foundation for the implementation of multi-pronged treatment regimes in the future. This article is part of a Special Issue entitled: Cardiomyocyte Biology: Cardiac Pathways of Differentiation, Metabolism and Contraction.

CaMKIIδC slows [Ca]i decline in cardiac myocytes by promoting Ca sparks

Acute activation of calcium/calmodulin-dependent protein kinase (CaMKII) in permeabilized phospholamban knockout (PLN-KO) mouse myocytes phosphorylates ryanodine receptors (RyRs) and activates spontaneous local sarcoplasmic reticulum (SR) Ca release events (Ca sparks) even at constant SR Ca load. To assess how CaMKII regulates SR Ca release in intact myocytes (independent of SR Ca content changes or PLN effects), we compared Ca sparks in PLN-KO versus mice, which also have transgenic cardiac overexpression of CaMKIIδC in the PLN-KO background (KO/TG). Compared with PLN-KO mice, these KO/TG cardiomyocytes exhibited 1), increased twitch Ca transient and fractional release (both by ∼35%), but unaltered SR Ca load; 2), increased resting Ca spark frequency (300%) despite a lower diastolic [Ca]i, which also slowed twitch [Ca]i decline (suggesting CaMKII-dependent RyR Ca sensitization); 3), elevated Ca spark amplitude and rate of Ca release (which might indicate that more RyR channels participate in a single spark); 4), prolonged Ca spark rise time (which implies that CaMKII either delays RyR closure or prolongs the time when openings can occur); 5), more frequent repetitive sparks at single release sites. Analysis of repetitive sparks from individual Ca release sites indicates that CaMKII enhanced RyR Ca sensitivity, but did not change the time course of SR Ca refilling. These results demonstrate that there are dramatic CaMKII-mediated effects on RyR Ca release that occur via regulation of both RyR activation and termination processes.

Ankyrin-B reduction enhances Ca spark-mediated SR Ca release promoting cardiac myocyte arrhythmic activity

Ankyrin-B (AnkB) loss-of-function may cause ventricular arrhythmias and sudden cardiac death in humans. Cardiac myocytes from AnkB heterozygous mice (AnkB(+/-)) show reduced expression and altered localization of Na/Ca exchanger (NCX) and Na/K-ATPase (NKA), key players in regulating [Na](i) and [Ca](i). Here we investigate how AnkB reduction affects cardiac [Na](i), [Ca](i) and SR Ca release. We found reduced NCX and NKA transport function but unaltered [Na](i) and diastolic [Ca](i) in myocytes from AnkB(+/-) vs. wild-type (WT) mice. Ca transients, SR Ca content and fractional SR Ca release were larger in AnkB(+/-) myocytes. The frequency of spontaneous, diastolic Ca sparks (CaSpF) was significantly higher in intact myocytes from AnkB(+/-) vs. WT myocytes (with and without isoproterenol), even when normalized for SR Ca load. However, total ryanodine receptor (RyR)-mediated SR Ca leak (tetracaine-sensitive) was not different between groups. Thus, in AnkB(+/-) mice SR Ca leak is biased towards more Ca sparks (vs. smaller release events), suggesting more coordinated openings of RyRs in a cluster. This is due to local cytosolic RyR regulation, rather than intrinsic RyR differences, since CaSpF was similar in saponin-permeabilized myocytes from WT and AnkB(+/-) mice. The more coordinated RyRs openings resulted in an increased propensity of pro-arrhythmic Ca waves in AnkB(+/-) myocytes. In conclusion, AnkB reduction alters cardiac Na and Ca transport and enhances the coupled RyR openings, resulting in more frequent Ca sparks and waves although the total SR Ca leak is unaffected. This could enhance the propensity for triggered arrhythmias in AnkB(+/-) mice.