Predicting local SR Ca(2+) dynamics during Ca(2+) wave propagation in ventricular myocytes

A Stochastic Spatiotemporal Model of Rat Ventricular Myocyte Calcium Dynamics Demonstrated Necessary Features for Calcium Wave Propagation

Calcium (Ca2+) plays a central role in the excitation and contraction of cardiac myocytes. Experiments have indicated that calcium release is stochastic and regulated locally suggesting the possibility of spatially heterogeneous calcium levels in the cells. This spatial heterogeneity might be important in mediating different signaling pathways. During more than 50 years of computational cell biology, the computational models have been advanced to incorporate more ionic currents, going from deterministic models to stochastic models. While periodic increases in cytoplasmic Ca2+ concentration drive cardiac contraction, aberrant Ca2+ release can underly cardiac arrhythmia. However, the study of the spatial role of calcium ions has been limited due to the computational expense of using a three-dimensional stochastic computational model. In this paper, we introduce a three-dimensional stochastic computational model for rat ventricular myocytes at the whole-cell level that incorporate detailed calcium dynamics, with (1) non-uniform release site placement, (2) non-uniform membrane ionic currents and membrane buffers, (3) stochastic calcium-leak dynamics and (4) non-junctional or rogue ryanodine receptors. The model simulates spark-induced spark activation and spark-induced Ca2+ wave initiation and propagation that occur under conditions of calcium overload at the closed-cell condition, but not when Ca2+ levels are normal. This is considered important since the presence of Ca2+ waves contribute to the activation of arrhythmogenic currents.

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.

Excitation-contraction coupling and calcium release in atrial muscle

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

Pharmacological Modulation of Mitochondrial Ca2+ Content Regulates Sarcoplasmic Reticulum Ca2+ Release via Oxidation of the Ryanodine Receptor by Mitochondria-Derived Reactive Oxygen Species

In a physiological setting, mitochondria increase oxidative phosphorylation during periods of stress to meet increased metabolic demand. This in part is mediated via enhanced mitochondrial Ca2+ uptake, an important regulator of cellular ATP homeostasis. In a pathophysiological setting pharmacological modulation of mitochondrial Ca2+ uptake or retention has been suggested as a therapeutic strategy to improve metabolic homeostasis or attenuate Ca2+-dependent arrhythmias in cardiac disease states. To explore the consequences of mitochondrial Ca2+ accumulation, we tested the effects of kaempferol, an activator of mitochondrial Ca2+ uniporter (MCU), CGP-37157, an inhibitor of mitochondrial Na+/Ca2+ exchanger, and MCU inhibitor Ru360 in rat ventricular myocytes (VMs) from control rats and rats with hypertrophy induced by thoracic aortic banding (TAB). In periodically paced VMs under β-adrenergic stimulation, treatment with kaempferol (10 μmol/L) or CGP-37157 (1 μmol/L) enhanced mitochondrial Ca2+ accumulation monitored by mitochondrial-targeted Ca2+ biosensor mtRCamp1h. Experiments with mitochondrial membrane potential-sensitive dye TMRM revealed this was accompanied by depolarization of the mitochondrial matrix. Using redox-sensitive OMM-HyPer and ERroGFP_iE biosensors, we found treatment with kaempferol or CGP-37157 increased the levels of reactive oxygen species (ROS) in mitochondria and the sarcoplasmic reticulum (SR), respectively. Confocal Ca2+ imaging showed that accelerated Ca2+ accumulation reduced Ca2+ transient amplitude and promoted generation of spontaneous Ca2+ waves in VMs paced under ISO, suggestive of abnormally high activity of the SR Ca2+ release channel ryanodine receptor (RyR). Western blot analyses showed increased RyR oxidation after treatment with kaempferol or CGP-37157 vs. controls. Furthermore, in freshly isolated TAB VMs, confocal Ca2+ imaging demonstrated that enhancement of mitochondrial Ca2+ accumulation further perturbed global Ca2+ handling, increasing the number of cells exhibiting spontaneous Ca2+ waves, shortening RyR refractoriness and decreasing SR Ca2+ content. In ex vivo optically mapped TAB hearts, kaempferol exacerbated proarrhythmic phenotype. On the contrary, incubation of cells with MCU inhibitor Ru360 (2 μmol/L, 30 min) normalized RyR oxidation state, improved intracellular Ca2+ homeostasis and reduced triggered activity in ex vivo TAB hearts. These findings suggest facilitation of mitochondrial Ca2+ uptake in cardiac disease can exacerbate proarrhythmic disturbances in Ca2+ homeostasis via ROS and enhanced activity of oxidized RyRs, while strategies to reduce mitochondrial Ca2+ accumulation can be protective.

Calcium Deregulation: Novel Insights to Understand Friedreich's Ataxia Pathophysiology

Friedreich's Ataxia (FRDA) is a neurodegenerative disorder, characterized by degeneration of dorsal root ganglia, cerebellum and cardiomyopathy. Heart failure is one of the most common causes of death for FRDA patients. Deficiency of frataxin, a small mitochondrial protein, is responsible for all clinical and morphological manifestations of FRDA. The focus of our study was to investigate the unexplored Ca²⁺ homeostasis in cerebellar granule neurons (CGNs) and in cardiomyocytes of FRDA cellular models to understand the pathogenesis of degeneration. Ca²⁺ homeostasis in neurons and cardiomyocytes is not only crucial for the cellular wellbeing but more importantly to generate action potential in both neurons and cardiomyocytes. By challenging Ca²⁺ homeostasis in CGNs, and in adult and neonatal cardiomyocytes of FRDA models, we have assessed the impact of frataxin decrease on both neuronal and cardiac physiopathology. Interestingly, we have found that Ca²⁺ homeostasis is altered both cell types. CGNs showed a Ca²⁺ mishandling under depolarizing conditions and this was also reflected in the endoplasmic reticulum (ER) content. In cardiomyocytes we found that the sarcoplasmic reticulum (SR) Ca²⁺ content was pathologically reduced, and that mitochondrial Ca²⁺ uptake was impaired. This phenomenon is due to the excess of oxidative stress under FRDA like conditions and the consequent aberrant modulation of key players at the SR/ER and mitochondrial level that usually restore the Ca²⁺ homeostasis. Our findings demonstrate that in both neurons and cardiomyocytes the decreased Ca²⁺ level within the stores has a comparable detrimental impact in their physiology. In cardiomyocytes, we found that ryanodine receptors (RyRs) may be leaking and expel more Ca²⁺ out from the SR. At the same time mitochondrial uptake was altered and we found that Vitamin E can restore this defect. Moreover, Vitamin E protects from cell death induced by hypoxia-reperfusion injury, revealing novel properties of Vitamin E as potential therapeutic tool for FRDA cardiomyopathy.

Stabilization of Ca2+ signaling in cardiac muscle by stimulation of SERCA

AIMS

In cardiac muscle, phosphorylation of the RyRs is proposed to increase their Ca²⁺ sensitivity. This mechanism could be arrhythmogenic via facilitation of spontaneous Ca²⁺ waves. Surprisingly, the level of Ca²⁺ inside the SR needed to initiate such waves has been reported to increase upon β-adrenergic stimulation, an observation which cannot be easily reconciled with elevated Ca²⁺ sensitivity of the RyRs. We tested the hypothesis that this change of Ca²⁺ wave threshold could occur indirectly, subsequent to SERCA stimulation.

METHODS AND RESULTS

Cytosolic and intra-SR Ca²⁺ waves were simultaneously recorded with confocal line-scan imaging in intact and permeabilized mouse cardiomyocytes using Rhod-2 and Fluo-5-N, respectively. We analyzed changes of several Ca²⁺ signaling parameters during specific SERCA stimulation by ochratoxin A (OTA), jasmonate or the Fab fragment of a phospholamban antibody. SERCA stimulation resulted in a substantial increase of the threshold for Ca²⁺ wave initiation. Faster Ca²⁺ transient decay and SR refilling confirmed SERCA acceleration.

CONCLUSIONS

These results suggest that isolated SERCA stimulation can elevate the intra-SR threshold for the generation of Ca²⁺ waves, independently of RyR phosphorylation. Simultaneously, fractional Ca²⁺ release and wave amplitudes are reduced. Thus, SERCA stimulation appears to exert a negative feed-back on the Ca²⁺-induced Ca²⁺ release mechanisms sustaining the waves. Thereby, it may be profoundly antiarrhythmic. This may be clinically relevant when therapies are applied to stimulate the SERCA activity (e.g. SERCA overexpression with gene therapy, future small molecule SERCA stimulators).

The intricacies of atrial calcium cycling during excitation-contraction coupling

Blatter discusses the initiation and spread of Ca release, Ca store depletion, and release termination in atrial myocytes.

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.

A novel mechanism of tandem activation of ryanodine receptors by cytosolic and SR luminal Ca2+ during excitation-contraction coupling in atrial myocytes

KEY POINTS

In atrial myocytes excitation-contraction coupling is strikingly different from ventricle because atrial myocytes lack a transverse tubule membrane system: Ca²⁺ release starts in the cell periphery and propagates towards the cell centre by Ca²⁺ -induced Ca²⁺ release from the sarcoplasmic reticulum (SR) Ca²⁺ store. The cytosolic Ca²⁺ sensitivity of the ryanodine receptor (RyRs) Ca²⁺ release channel is low and it is unclear how Ca²⁺ release can be activated in the interior of atrial cells. Simultaneous confocal imaging of cytosolic and intra-SR calcium revealed a transient elevation of store Ca²⁺ that we termed 'Ca²⁺ sensitization signal'. We propose a novel paradigm of atrial ECC that is based on tandem activation of the RyRs by cytosolic and luminal Ca²⁺ through a 'fire-diffuse-uptake-fire' (or FDUF) mechanism: Ca²⁺ uptake by SR Ca²⁺ pumps at the propagation front elevates Ca²⁺ inside the SR locally, leading to luminal RyR sensitization and lowering of the cytosolic Ca²⁺ activation threshold.

ABSTRACT

In atrial myocytes Ca²⁺ release during excitation-contraction coupling (ECC) is strikingly different from ventricular myocytes. In many species atrial myocytes lack a transverse tubule system, dividing the sarcoplasmic reticulum (SR) Ca²⁺ store into the peripheral subsarcolemmnal junctional (j-SR) and the much more abundant central non-junctional (nj-SR) SR. Action potential (AP)-induced Ca²⁺ entry activates Ca²⁺ -induced Ca²⁺ release (CICR) from j-SR ryanodine receptor (RyR) Ca²⁺ release channels. Peripheral elevation of [Ca²⁺ ]_i initiates CICR from nj-SR and sustains propagation of CICR to the cell centre. Simultaneous confocal measurements of cytosolic ([Ca²⁺ ]_i ; with the fluorescent Ca²⁺ indicator rhod-2) and intra-SR ([Ca²⁺ ]_SR ; fluo-5N) Ca²⁺ in rabbit atrial myocytes revealed that Ca²⁺ release from j-SR resulted in a cytosolic Ca²⁺ transient of higher amplitude compared to release from nj-SR; however, the degree of depletion of j-SR [Ca²⁺ ]_SR was smaller than nj-SR [Ca²⁺ ]_SR . Similarly, Ca²⁺ signals from individual release sites of the j-SR showed a larger cytosolic amplitude (Ca²⁺ sparks) but smaller depletion (Ca²⁺ blinks) than release from nj-SR. During AP-induced Ca²⁺ release the rise of [Ca²⁺ ]_i detected at individual release sites of the nj-SR preceded the depletion of [Ca²⁺ ]_SR , and during this latency period a transient elevation of [Ca²⁺ ]_SR occurred. We propose that Ca²⁺ release from nj-SR is activated by cytosolic and luminal Ca²⁺ (tandem RyR activation) via a novel 'fire-diffuse-uptake-fire' (FDUF) mechanism. This novel paradigm of atrial ECC predicts that Ca²⁺ uptake by sarco-endoplasmic reticulum Ca²⁺ -ATPase (SERCA) at the propagation front elevates local [Ca²⁺ ]_SR , leading to luminal RyR sensitization and lowering of the activation threshold for cytosolic CICR.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

Calcium Sparks in the Heart: Dynamics and Regulation

Calcium (Ca²⁺) plays a central role in the contraction of the heart. It is the bi-directional link between electrical excitation of the heart and contraction. Electrical excitation initiates Ca²⁺influx across the sarcolemma and T-tubular membrane that triggered calcium release from the sarcoplasmic reticulum. Ca²⁺sparks are the elementary events of calcium release from the sarcoplasmic reticulum. Therefore, understanding the dynamics of Ca²⁺sparks is essential for understanding the function of the heart. To this end, numerous experimental and computational studies have focused on this topic, exploring the mechanisms of calcium spark initiation, termination, and regulation and what role these play in normal and patho-physiology. The proper understanding of Ca²⁺ spark regulation and dynamics serves as the foundation for our insights into a multitude of pathological conditions may develop that can be the result of structural and/or functional changes at the cellular or subcellular level. Computational modeling of Ca²⁺ spark dynamics has proven to be a useful tool to understand Ca²⁺ spark dynamics. This review addresses our current understanding of Ca²⁺ sparks and how synchronized SR Ca²⁺ release, in which Ca²⁺ sparks is a major pathway, is linked to the different cardiac diseases, especially arrhythmias.

Nanoscale analysis of ryanodine receptor clusters in dyadic couplings of rat cardiac myocytes

The contractile properties of cardiac myocytes depend on the calcium (Ca(2+)) released by clusters of ryanodine receptors (RyRs) throughout the myoplasm. Accurate quantification of the spatial distribution of RyRs has previously been challenging due to the comparatively low resolution in optical microscopy. We have combined single-molecule localisation microscopy (SMLM) in a super-resolution modality known as dSTORM with immunofluorescence staining of tissue sections of rat ventricles to resolve a wide, near-exponential size distribution of RyR clusters that lined on average ~57% of the perimeter of each myofibril. The average size of internal couplons is ~63 RyRs (nearly 4 times larger than that of peripheral couplons) and the largest clusters contain many hundreds of RyRs. Similar to previous observations in peripheral couplons, we observe many clusters with one or few receptors; however ≥80% of the total RyRs were detected in clusters containing ≥100 receptors. ~56% of all clusters were within an edge-to-edge distance sufficiently close to co-activate via Ca(2+)-induced Ca(2+) release (100nm) and were grouped into 'superclusters'. The co-location of superclusters with the same or adjacent t-tubular connections in dual-colour super-resolution images suggested that member sub-clusters may be exposed to similar local luminal Ca(2+) levels. Dual-colour dSTORM revealed high co-localisation between the cardiac junctional protein junctophilin-2 (JPH2) and RyR clusters that confirmed that the majority of the RyR clusters observed are dyadic. The increased sensitivity of super-resolution images revealed approximately twice as many RyR clusters (2.2clusters/μm(3)) compared to previous confocal measurements. We show that, in general, the differences of previous confocal estimates are largely attributable to the limited spatial resolution of diffraction-limited imaging. The new data can be used to inform the construction of detailed mechanistic models of cardiac Ca(2+) signalling.

Dantrolene suppresses spontaneous Ca2+ release without altering excitation-contraction coupling in cardiomyocytes of aged mice

Cardiac dysfunction in the aged heart reflects abnormalities in cardiomyocyte Ca(2+) homeostasis including altered Ca(2+) cycling through the sarcoplasmic reticulum (SR). The ryanodine receptor antagonist dantrolene exerts antiarrhythmic effects by preventing spontaneous diastolic Ca(2+) release from the SR. We tested the hypothesis that dantrolene prevents spontaneous Ca(2+) release without altering excitation-contraction coupling in aged myocardium. Left ventricular cardiomyocytes isolated from young (3 to 4 mo) and aged (24-26 mo) C57BL/6 mice were loaded with the Ca(2+) indicator fluo-4. Amplitudes of action potential-induced Ca(2+) transients at 1-Hz pacing were similar between young and aged mice, yet cell shortening was impaired in aged mice. Isoproterenol (1 μM) increased Ca(2+) transient amplitude and cell shortening to identical levels in young and aged; dantrolene (1 μM) had no effect on Ca(2+) transients or cell shortening during pacing. Under Ca(2+) overload conditions induced with 10 mM extracellular Ca(2+) concentration, spontaneous Ca(2+) waves were of diminished amplitude and associated with lower SR Ca(2+) content in aged versus young mice. Despite no effect in young mice, dantrolene increased SR Ca(2+) content and Ca(2+) wave amplitude in aged mice. In the presence of isoproterenol following rest from 1-Hz pacing, Ca(2+) spark frequency was elevated in aged mice, yet the time to spontaneous Ca(2+) wave was similar between young and aged mice; dantrolene decreased Ca(2+) spark frequency and prolonged the time to Ca(2+) wave onset in aged mice with no effect in young mice. Thus dantrolene attenuates diastolic Ca(2+) release in the aged murine heart that may prove useful in preventing cardiac dysfunction.

Abnormal propagation of calcium waves and ultrastructural remodeling in recessive catecholaminergic polymorphic ventricular tachycardia

RATIONALE

The recessive form of catecholaminergic polymorphic ventricular tachycardia is caused by mutations in the cardiac calsequestrin-2 gene; this variant of catecholaminergic polymorphic ventricular tachycardia is less well characterized than the autosomal-dominant form caused by mutations in the ryanodine receptor-2 gene.

OBJECTIVE

We characterized the intracellular Ca²⁺ homeostasis, electrophysiological properties, and ultrastructural features of the Ca²⁺ release units in the homozygous calsequestrin 2-R33Q knock-in mouse model (R33Q) R33Q knock-in mouse model.

METHODS AND RESULTS

We studied isolated R33Q and wild-type ventricular myocytes and observed properties not previously identified in a catecholaminergic polymorphic ventricular tachycardia model. As compared with wild-type cells, R33Q myocytes (1) show spontaneous Ca²⁺ waves unable to propagate as cell-wide waves; (2) show smaller Ca²⁺sparks with shortened coupling intervals, suggesting a reduced refractoriness of Ca²⁺ release events; (3) have a reduction of the area of membrane contact, of the junctions between junctional sarcoplasmic reticulum and T tubules (couplons), and of junctional sarcoplasmic reticulum volume; (4) have a propensity to develop phase 2 to 4 afterdepolarizations that can elicit triggered beats; and (5) involve viral gene transfer with wild-type cardiac calsequestrin-2 that is able to normalize structural abnormalities and to restore cell-wide calcium wave propagation.

CONCLUSIONS

Our data show that homozygous cardiac calsequestrin-2-R33Q myocytes develop spontaneous Ca²⁺ release events with a broad range of intervals coupled to preceding beats, leading to the formation of early and delayed afterdepolarizations. They also display a major disruption of the Ca²⁺ release unit architecture that leads to fragmentation of spontaneous Ca²⁺ waves. We propose that these 2 substrates in R33Q myocytes synergize to provide a new arrhythmogenic mechanism for catecholaminergic polymorphic ventricular tachycardia.

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 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.

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.

Facilitation of cytosolic calcium wave propagation by local calcium uptake into the sarcoplasmic reticulum in cardiac myocytes

The widely accepted paradigm for cytosolic Ca(2+) wave propagation postulates a 'fire-diffuse-fire' mechanism where local Ca(2+)-induced Ca(2+) release (CICR) from the sarcoplasmic reticulum (SR) via ryanodine receptor (RyR) Ca(2+) release channels diffuses towards and activates neighbouring release sites, resulting in a propagating Ca(2+) wave. A recent challenge to this paradigm proposed the requirement for an intra-SR 'sensitization' Ca(2+) wave that precedes the cytosolic Ca(2+) wave and primes RyRs from the luminal side to CICR. Here, we tested this hypothesis experimentally with direct simultaneous measurements of cytosolic ([Ca(2+)](i); rhod-2) and intra-SR ([Ca(2+)](SR); fluo-5N) calcium signals during wave propagation in rabbit ventricular myocytes, using high resolution fluorescence confocal imaging. The increase in [Ca(2+)](i) at the wave front preceded depletion of the SR at each point along the calcium wave front, while during this latency period a transient increase of [Ca(2+)](SR) was observed. This transient elevation of [Ca(2+)](SR) could be identified at individual release junctions and depended on the activity of the sarco-endoplasmic reticulum Ca(2+)-ATPase (SERCA). Increased SERCA activity (β-adrenergic stimulation with 1 μM isoproterenol (isoprenaline)) decreased the latency period and increased the amplitude of the transient elevation of [Ca(2+)](SR), whereas inhibition of SERCA (3 μM cyclopiazonic acid) had the opposite effect. In conclusion, the data provide experimental evidence that local Ca(2+) uptake by SERCA into the SR facilitates the propagation of cytosolic Ca(2+) waves via luminal sensitization of the RyR, and supports a novel paradigm of a 'fire-diffuse-uptake-fire' mechanism for Ca(2+) wave propagation in cardiac myocytes.

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.

β-Adrenergic stimulation increases the intra-sarcoplasmic reticulum Ca2+ threshold for Ca2+ wave generation

β-Adrenergic signalling induces positive inotropic effects on the heart that associate with pro-arrhythmic spontaneous Ca(2+) waves. A threshold level of sarcoplasmic reticulum (SR) Ca(2+) ([Ca(2+)](SR)) is necessary to trigger Ca(2+) waves, and whether the increased incidence of Ca(2+) waves during β-adrenergic stimulation is due to an alteration in this threshold remains controversial. Using the low-affinity Ca(2+) indicator fluo-5N entrapped within the SR of rabbit ventricular myocytes, we addressed this controversy by directly monitoring [Ca(2+)](SR) and Ca(2+) waves during β-adrenergic stimulation. Electrical pacing in elevated extracellular Ca(2+) ([Ca(2+)](o) = 7 mM) was used to increase [Ca(2+)](SR) to the threshold where Ca(2+) waves were consistently observed. The β-adrenergic agonist isoproterenol (ISO; 1 μM) increased [Ca(2+)](SR) well above the control threshold and consistently triggered Ca(2+) waves. However, when [Ca(2+)](SR) was subsequently lowered in the presence of ISO (by lowering [Ca(2+)](o) to 1 mM and partially inhibiting sarcoplasmic/endoplasmic reticulum calcium ATPase with cyclopiazonic acid or thapsigargin), Ca(2+) waves ceased to occur at a [Ca(2+)](SR) that was higher than the control threshold. Furthermore, for a set [Ca(2+)](SR) level the refractoriness of wave occurrence (Ca(2+) wave latency) was prolonged during β-adrenergic stimulation, and was highly dependent on the extent that [Ca](SR) exceeded the wave threshold. These data show that acute β-adrenergic stimulation increases the [Ca(2+)](SR) threshold for Ca(2+) waves, and therefore the primary cause of Ca(2+) waves is the robust increase in [Ca(2+)](SR) above this higher threshold level. Elevation of the [Ca(2+)](SR) wave threshold and prolongation of wave latency represent potentially protective mechanisms against pro-arrhythmogenic Ca(2+) release during β-adrenergic stimulation.

Computational approaches to understand cardiac electrophysiology and arrhythmias

Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.

How cells process information: quantification of spatiotemporal signaling dynamics

Arguably, one of the foremost distinctions between life and non-living matter is the ability to sense environmental changes and respond appropriately--an ability that is invested in every living cell. Within a single cell, this function is largely carried out by networks of signaling molecules. However, the details of how signaling networks help cells make complicated decisions are still not clear. For instance, how do cells read graded, analog stress signals but convert them into digital live-or-die responses? The answer to such questions may originate from the fact that signaling molecules are not static but dynamic entities, changing in numbers and activity over time and space. In the past two decades, researchers have been able to experimentally monitor signaling dynamics and use mathematical techniques to quantify and abstract general principles of how cells process information. In this review, the authors first introduce and discuss various experimental and computational methodologies that have been used to study signaling dynamics. The authors then discuss the different types of temporal dynamics such as oscillations and bistability that can be exhibited by signaling systems and highlight studies that have investigated such dynamics in physiological settings. Finally, the authors illustrate the role of spatial compartmentalization in regulating cellular responses with examples of second-messenger signaling in cardiac myocytes.

Computational modeling and numerical methods for spatiotemporal calcium cycling in ventricular myocytes

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain and the myoplasm domain in each CRU are modeled by 5 × 5 × 5 voxels to maintain proper Ca diffusion. Advanced numerical algorithms implemented on graphical processing units were used for fast computational simulations. For a myocyte containing 100 × 20 × 10 CRUs, a 1-s heart time simulation takes about 10 min of machine time on a single NVIDIA Tesla C2050. Examples of simulated Ca cycling dynamics, such as Ca sparks, Ca waves, and Ca alternans, are shown.

Modelling cardiac calcium sparks in a three-dimensional reconstruction of a calcium release unit

Triggered release of Ca2+ from an individual sarcoplasmic reticulum (SR) Ca(2+) release unit (CRU) is the fundamental event of cardiac excitation–contraction coupling, and spontaneous release events (sparks) are the major contributor to diastolic Ca(2+) leak in cardiomyocytes. Previous model studies have predicted that the duration and magnitude of the spark is determined by the local CRU geometry, as well as the localization and density of Ca(2+) handling proteins. We have created a detailed computational model of a CRU, and developed novel tools to generate the computational geometry from electron tomographic images. Ca(2+) diffusion was modelled within the SR and the cytosol to examine the effects of localization and density of the Na(+)/Ca(2+) exchanger, sarco/endoplasmic reticulum Ca(2+)-ATPase 2 (SERCA), and calsequestrin on spark dynamics. We reconcile previous model predictions of approximately 90% local Ca(2+) depletion in junctional SR, with experimental reports of about 40%. This analysis supports the hypothesis that dye kinetics and optical averaging effects can have a significant impact on measures of spark dynamics. Our model also predicts that distributing calsequestrin within non-junctional Z-disc SR compartments, in addition to the junctional compartment, prolongs spark release time as reported by Fluo5. By pumping Ca(2+) back into the SR during a release, SERCA is able to prolong a Ca(2+) spark, and this may contribute to SERCA-dependent changes in Ca(2+) wave speed. Finally, we show that including the Na(+)/Ca(2+) exchanger inside the dyadic cleft does not alter local [Ca(2+)] during a spark.

Instabilities of the resting state in a mathematical model of calcium handling in cardiac myocytes

We analyze a recently published model of calcium handling in cardiac myocytes in order to find conditions for the presence of instabilities in the resting state of the model. Such instabilities can create calcium waves which in turn may be able to initiate cardiac arrhythmias. The model was developed by Swietach, Spitzer and Vaughan-Jones in order to study the effect, on calcium waves, of varying ryanodine receptor (RyR)-permeability, sarco/endoplasmic reticulum calcium ATPase (SERCA) and calcium diffusion. We study the model using the extracellular calcium concentration c(e) and the maximal velocity of the SERCA-pump v(SERCA) as control parameters. In the (c(e),v(SERCA))-domain we derive an explicit function v∗=v∗(c(e)), and we claim that any resting state based on parameters that lie above the curve (i.e. any pair (c(e),v(SERCA)) such that with v(SERCA) > v∗(c(e))) is unstable in the sense that small perturbations will grow and can eventually turn into a calcium wave. And conversely; any pair (c(e),v(SERCA)) below the curve is stable in the sense that small perturbations to the resting state will decay to rest. This claim is supported by analyzing the stability of the system in terms of computing the eigenmodes of the linearized model. Furthermore, the claim is supported by direct simulations based on the non-linear model. Since the curve separating stable from unstable states is given as an explicit function, we can show how stability depends on other parameters of the model.

Dynamic local changes in sarcoplasmic reticulum calcium: physiological and pathophysiological roles

Evidence obtained in recent years indicates that, in cardiac myocytes, release of Ca(2+) from the sarcoplasmic reticulum (SR) is regulated by changes in the concentration of Ca(2+) within the SR. In this review, we summarize recent advances in our understanding of this regulatory role, with a particular emphasis on dynamic and local changes in SR [Ca(2+)]. We focus on five important questions that are to some extent unresolved and controversial. These questions concern: (1) the importance of SR [Ca(2+)] depletion in the termination of Ca(2+) release; (2) the quantitative extent of depletion during local release events such as Ca(2+) sparks; (3) the influence of SR [Ca(2+)] refilling on release refractoriness and the propensity for pathological Ca(2+) release; (4) dynamic changes in SR [Ca(2+)] during propagating Ca(2+) waves; and (5) the speed of Ca(2+) diffusion within the SR. With each issue, we discuss data supporting alternative viewpoints, and we identify fundamental questions that are being actively investigated. We conclude with a discussion of experimental and computational advances that will help to resolve controversies. This article is part of a special issue entitled "Local Signaling in Myocytes."

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.

Dynamic calcium movement inside cardiac sarcoplasmic reticulum during release

RATIONALE

Intra-sarcoplasmic reticulum (SR) free [Ca] ([Ca](SR)) provides the driving force for SR Ca release and is a key regulator of SR Ca release channel gating during normal SR Ca release or arrhythmogenic spontaneous Ca release events. However, little is known about [Ca](SR) spatiotemporal dynamics.

OBJECTIVE

To directly measure local [Ca](SR) with subsarcomeric spatiotemporal resolution during both normal global SR Ca release and spontaneous Ca sparks and to evaluate the quantitative implications of spatial [Ca](SR) gradients.

METHODS AND RESULTS

Intact and permeabilized rabbit ventricular myocytes were subjected to direct simultaneous measurement of cytosolic [Ca] and [Ca](SR) and FRAP (fluorescence recovery after photobleach). We found no detectable [Ca](SR) gradients between SR release sites (junctional SR) and Ca uptake sites (free SR) during normal global Ca release, clear spatiotemporal [Ca](SR) gradients during isolated Ca blinks, faster intra-SR diffusion in the longitudinal versus transverse direction, 3- to 4-fold slower diffusion of fluorophores in the SR than in cytosol, and that intra-SR Ca diffusion varies locally, dependent on local SR connectivity. A computational model clarified why spatiotemporal gradients are more detectable in isolated local releases versus global releases and provides a quantitative framework for understanding intra-SR Ca diffusion.

CONCLUSIONS

Intra-SR Ca diffusion is rapid, limiting spatial [Ca](SR) gradients during excitation-contraction coupling. Spatiotemporal [Ca](SR) gradients are apparent during Ca sparks, and these observations constrain models of dynamic Ca movement inside the SR. This has important implications for myocyte SR Ca handling, synchrony, and potentially arrhythmogenic spontaneous contraction.

Numerical analysis of Ca2+ signaling in rat ventricular myocytes with realistic transverse-axial tubular geometry and inhibited sarcoplasmic reticulum

The t-tubules of mammalian ventricular myocytes are invaginations of the cell membrane that occur at each Z-line. These invaginations branch within the cell to form a complex network that allows rapid propagation of the electrical signal, and hence synchronous rise of intracellular calcium (Ca²⁺). To investigate how the t-tubule microanatomy and the distribution of membrane Ca²⁺ flux affect cardiac excitation-contraction coupling we developed a 3-D continuum model of Ca²⁺ signaling, buffering and diffusion in rat ventricular myocytes. The transverse-axial t-tubule geometry was derived from light microscopy structural data. To solve the nonlinear reaction-diffusion system we extended SMOL software tool (http://mccammon.ucsd.edu/smol/). The analysis suggests that the quantitative understanding of the Ca²⁺ signaling requires more accurate knowledge of the t-tubule ultra-structure and Ca²⁺ flux distribution along the sarcolemma. The results reveal the important role for mobile and stationary Ca²⁺ buffers, including the Ca²⁺ indicator dye. In agreement with experiment, in the presence of fluorescence dye and inhibited sarcoplasmic reticulum, the lack of detectible differences in the depolarization-evoked Ca²⁺ transients was found when the Ca²⁺ flux was heterogeneously distributed along the sarcolemma. In the absence of fluorescence dye, strongly non-uniform Ca²⁺ signals are predicted. Even at modest elevation of Ca²⁺, reached during Ca²⁺ influx, large and steep Ca²⁺ gradients are found in the narrow sub-sarcolemmal space. The model predicts that the branched t-tubule structure and changes in the normal Ca²⁺ flux density along the cell membrane support initiation and propagation of Ca²⁺ waves in rat myocytes.

In cardiac muscle cells, calcium (Ca²⁺) is best known for its role in contraction activation. A remarkable amount of quantitative data on cardiac cell structure, ion-transporting protein distributions and intracellular Ca²⁺ dynamics has been accumulated. Various alterations in the protein distributions or cell ultra-structure are now recognized to be the primary mechanisms of cardiac dysfunction in a diverse range of common pathologies including cardiac arrhythmias and hypertrophy. Using a 3-D computational model, incorporating more realistic transverse-axial t-tubule geometry and considering geometric irregularities and inhomogeneities in the distribution of ion-transporting proteins, we analyze several important spatial and temporal features of Ca²⁺ signaling in rat ventricular myocytes. This study demonstrates that the computational models could serve as powerful tools for prediction and analyses of how the Ca²⁺ dynamics and cardiac excitation-contraction coupling are regulated under normal conditions or certain pathologies. The use of computational and mathematical approaches will help also to better understand aspects of cell functions that are not currently amenable to experimental investigation.