Modeling calcium waves in cardiac myocytes: importance of calcium diffusion

Oxidative stress in early metabolic syndrome impairs cardiac RyR2 and SERCA2a activity and modifies the interplay of these proteins during Ca2+ waves

We investigated how oxidative stress (OS) alters Ca2+ handling in ventricular myocytes in early metabolic syndrome (MetS) in sucrose-fed rats. The effects of N-acetyl cysteine (NAC) or dl-Dithiothreitol (DTT) on systolic Ca2+ transients (SCaTs), diastolic Ca2+ sparks (CaS) and Ca2+ waves (CaW), recorded by confocal techniques, and L-type Ca2+ current (ICa), assessed by whole-cell patch clamp, were evaluated in MetS and Control cells. MetS myocytes exhibited decreased SCaTs and CaS frequency but unaffected CaW propagation. In Control cells, NAC/DTT reduced RyR2/SERCA2a activity blunting SCaTs, CaS frequency and CaW propagation, suggesting that basal ROS optimised Ca2+ signalling by maintaining RyR2/SERCA2a function and that these proteins facilitate CaW propagation. Conversely, NAC/DTT in MetS recovered RyR2/SERCA2a function, improving SCaTs and CaS frequency, but unexpectedly decreasing CaW propagation. We hypothesised that OS decreases RyR2/SERCA2a activity at early MetS, and while decreased SERCA2a favours CaW propagation, diminished RyR2 restrains it.

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.

Live-cell photo-activated localization microscopy correlates nanoscale ryanodine receptor configuration to calcium sparks in cardiomyocytes

Ca2+ sparks constitute the fundamental units of Ca2+ release in cardiomyocytes. Here we investigate how ryanodine receptors (RyRs) collectively generate these events by employing a transgenic mouse with a photo-activated label on RyR2. This allowed correlative imaging of RyR localization, by super-resolution Photo-Activated Localization Microscopy, and Ca2+ sparks, by high-speed imaging. Two populations of Ca2+ sparks were observed: stationary events and "travelling" events that spread between neighbouring RyR clusters. Travelling sparks exhibited up to 8 distinct releases, sourced from local or distal junctional sarcoplasmic reticulum. Quantitative analyses showed that sparks may be triggered by any number of RyRs within a cluster, and that acute β-adrenergic stimulation augments intra-cluster RyR recruitment to generate larger events. In contrast, RyR "dispersion" during heart failure facilitates the generation of travelling sparks. Thus, RyRs cooperatively generate Ca2+ sparks in a complex, malleable fashion, and channel organization regulates the propensity for local propagation of Ca2+ release.

Generation of myocyte agonal Ca2+ waves and contraction bands in perfused rat hearts following irreversible membrane permeabilisation

Although irreversible cardiomyocyte injury provokes intracellular Ca²⁺ ([Ca²⁺]_i) overload, the underlying dynamics of this response and its effects on cellular morphology remain unknown. We therefore visualised rapid-scanning confocal fluo4-[Ca²⁺]_i dynamics and morphology of cardiomyocytes in Langendorff-perfused rat hearts following saponin-membrane permeabilisation. Our data demonstrate that 0.4% saponin-treated myocytes immediately exhibited high-frequency Ca²⁺ waves (131.3 waves/min/cell) with asynchronous, oscillatory contractions having a mean propagation velocity of 117.8 μm/s. These waves slowly decreased in frequency, developed a prolonged decay phase, and disappeared in 10 min resulting in high-static, fluo4-fluorescence intensity. The myocytes showing these waves displayed contraction bands, i.e., band-like actin-fibre aggregates with disruption of sarcomeric α-actinin. The contraction bands were not attenuated by the abolition of Ca²⁺ waves under pretreatment with ryanodine plus thapsigargin, but were partially attenuated by the calpain inhibitor MDL28170, while mechanical arrest of the myocytes by 2,3-butanedione monoxime completely attenuated contraction-band formation. The depletion of adenosine 5'-triphosphate by the mitochondrial electron uncoupler carbonyl cyanide 4-trifluoromethoxy phenylhydrazone also attenuated Ca²⁺ waves and contraction bands. Overall, saponin-induced myocyte [Ca²⁺]_i overload provokes agonal Ca²⁺ waves and contraction bands. Contraction bands are not the direct consequence of the waves but are caused by cross-bridge interactions of the myocytes under calpain-mediated proteolysis.

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.

Finite element analysis predicts Ca2+ microdomains within tubular-sarcoplasmic reticular junctions of amphibian skeletal muscle

A finite element analysis modelled diffusional generation of steady-state Ca²⁺ microdomains within skeletal muscle transverse (T)-tubular-sarcoplasmic reticular (SR) junctions, sites of ryanodine receptor (RyR)-mediated SR Ca²⁺ release. It used established quantifications of sarcomere and T-SR anatomy (radial diameter [Formula: see text]; axial distance [Formula: see text]). Its boundary SR Ca²⁺ influx densities,[Formula: see text], reflected step impositions of influxes, [Formula: see text] deduced from previously measured Ca²⁺ signals following muscle fibre depolarization. Predicted steady-state T-SR junctional edge [Ca²⁺], [Ca²⁺]_edge, matched reported corresponding experimental cytosolic [Ca²⁺] elevations given diffusional boundary efflux [Formula: see text] established cytosolic Ca²⁺ diffusion coefficients [Formula: see text] and exit length [Formula: see text]. Dependences of predicted [Ca²⁺]_edge upon [Formula: see text] then matched those of experimental [Ca²⁺] upon Ca²⁺ release through their entire test voltage range. The resulting model consistently predicted elevated steady-state T-SR junctional ~ µM-[Ca²⁺] elevations radially declining from maxima at the T-SR junction centre along the entire axial T-SR distance. These [Ca²⁺] heterogeneities persisted through 10⁴- and fivefold, variations in D and w around, and fivefold reductions in d below, control values, and through reported resting muscle cytosolic [Ca²⁺] values, whilst preserving the flux conservation ([Formula: see text] condition, [Formula: see text]. Skeletal muscle thus potentially forms physiologically significant ~ µM-[Ca²⁺] T-SR microdomains that could regulate cytosolic and membrane signalling molecules including calmodulin and RyR, These findings directly fulfil recent experimental predictions invoking such Ca²⁺ microdomains in observed regulatory effects upon Na⁺ channel function, in a mechanism potentially occurring in similar restricted intracellular spaces in other cell types.

Cellular Mechanisms Underlying the Low Cardiotoxicity of Istaroxime

Background

Istaroxime is an inhibitor of Na⁺/K⁺ ATPase with proven efficacy to increase cardiac contractility and to accelerate relaxation attributable to a relief in phospholamban‐dependent inhibition of the sarcoplasmic reticulum Ca²⁺ ATPase. We have previously shown that pharmacologic Na⁺/K⁺ ATPase inhibition promotes calcium/calmodulin‐dependent kinase II activation, which mediates both cardiomyocyte death and arrhythmias. Here, we aim to compare the cardiotoxic effects promoted by classic pharmacologic Na⁺/K⁺ ATPase inhibition versus istaroxime.

Methods and Results

Ventricular cardiomyocytes were treated with ouabain or istaroxime at previously tested equi‐inotropic concentrations to compare their impact on cell viability, apoptosis, and calcium/calmodulin‐dependent kinase II activation. In contrast to ouabain, istaroxime neither promoted calcium/calmodulin‐dependent kinase II activation nor cardiomyocyte death. In addition, we explored the differential behavior promoted by ouabain and istaroxime on spontaneous diastolic Ca²⁺ release. In rat cardiomyocytes, istaroxime did not significantly increase Ca²⁺ spark and wave frequency but increased the proportion of aborted Ca²⁺ waves. Further insight was provided by studying cardiomyocytes from mice that do not express phospholamban. In this model, the lower Ca²⁺ wave incidence observed with istaroxime remains present, suggesting that istaroxime‐dependent relief on phospholamban‐dependent sarcoplasmic reticulum Ca²⁺ ATPase 2A inhibition is not the unique mechanism underlying the low arrhythmogenic profile of this drug.

Conclusions

Our results indicate that, different from ouabain, istaroxime can reach a significant inotropic effect without leading to calcium/calmodulin‐dependent kinase II–dependent cardiomyocyte death. Additionally, we provide novel insights regarding the low arrhythmogenic impact of istaroxime on cardiac Ca²⁺ handling.

Regional acidosis locally inhibits but remotely stimulates Ca2+ waves in ventricular myocytes

Aims

Spontaneous Ca²⁺ waves in cardiomyocytes are potentially arrhythmogenic. A powerful controller of Ca²⁺ waves is the cytoplasmic H⁺ concentration ([H⁺]_i), which fluctuates spatially and temporally in conditions such as myocardial ischaemia/reperfusion. H⁺-control of Ca²⁺ waves is poorly understood. We have therefore investigated how [H⁺]_i co-ordinates their initiation and frequency.

Methods and results

Spontaneous Ca²⁺ waves were imaged (fluo-3) in rat isolated ventricular myocytes, subjected to modest Ca²⁺-overload. Whole-cell intracellular acidosis (induced by acetate-superfusion) stimulated wave frequency. Pharmacologically blocking sarcolemmal Na⁺/H⁺ exchange (NHE1) prevented this stimulation, unveiling inhibition by H⁺. Acidosis also increased Ca²⁺ wave velocity. Restricting acidosis to one end of a myocyte, using a microfluidic device, inhibited Ca²⁺ waves in the acidic zone (consistent with ryanodine receptor inhibition), but stimulated wave emergence elsewhere in the cell. This remote stimulation was absent when NHE1 was selectively inhibited in the acidic zone. Remote stimulation depended on a locally evoked, NHE1-driven rise of [Na⁺]_i that spread rapidly downstream.

Conclusion

Acidosis influences Ca²⁺ waves via inhibitory Hi+ and stimulatory Nai+ signals (the latter facilitating intracellular Ca²⁺-loading through modulation of sarcolemmal Na⁺/Ca²⁺ exchange activity). During spatial [H⁺]_i-heterogeneity, Hi+-inhibition dominates in acidic regions, while rapid Nai+ diffusion stimulates waves in downstream, non-acidic regions. Local acidosis thus simultaneously inhibits and stimulates arrhythmogenic Ca²⁺-signalling in the same myocyte. If the principle of remote H⁺-stimulation of Ca²⁺ waves also applies in multicellular myocardium, it raises the possibility of electrical disturbances being driven remotely by adjacent ischaemic areas, which are known to be intensely acidic.

Calcium Dynamics of Ex Vivo Long-Term Cultured CD8+ T Cells Are Regulated by Changes in Redox Metabolism

T cells reach a state of replicative senescence characterized by a decreased ability to proliferate and respond to foreign antigens. Calcium release associated with TCR engagement is widely used as a surrogate measure of T cell response. Using an ex vivo culture model that partially replicates features of organismal aging, we observe that while the amplitude of Ca2+ signaling does not change with time in culture, older T cells exhibit faster Ca2+ rise and a faster decay. Gene expression analysis of Ca2+ channels and pumps expressed in T cells by RT-qPCR identified overexpression of the plasma membrane CRAC channel subunit ORAI1 and PMCA in older T cells. To test whether overexpression of the plasma membrane Ca2+ channel is sufficient to explain the kinetic information, we adapted a previously published computational model by Maurya and Subramaniam to include additional details on the store-operated calcium entry (SOCE) process to recapitulate Ca2+ dynamics after T cell receptor stimulation. Simulations demonstrated that upregulation of ORAI1 and PMCA channels is not sufficient to explain the observed alterations in Ca2+ signaling. Instead, modeling analysis identified kinetic parameters associated with the IP3R and STIM1 channels as potential causes for alterations in Ca2+ dynamics associated with the long term ex vivo culturing protocol. Due to these proteins having known cysteine residues susceptible to oxidation, we subsequently investigated and observed transcriptional remodeling of metabolic enzymes, a shift to more oxidized redox couples, and post-translational thiol oxidation of STIM1. The model-directed findings from this study highlight changes in the cellular redox environment that may ultimately lead to altered T cell calcium dynamics during immunosenescence or organismal aging.

Ryanodine receptor gating controls generation of diastolic calcium waves in cardiac myocytes

Calcium waves can form and propagate at low frequencies of spontaneous calcium sparks if the calcium dependence of spark frequency is sufficiently steep, or the number of open RyRs is sufficiently large.

The role of cardiac ryanodine receptor (RyR) gating in the initiation and propagation of calcium waves was investigated using a mathematical model comprising a stochastic description of RyR gating and a deterministic description of calcium diffusion and sequestration. We used a one-dimensional array of equidistantly spaced RyR clusters, representing the confocal scanning line, to simulate the formation of calcium sparks. Our model provided an excellent description of the calcium dependence of the frequency of diastolic calcium sparks and of the increased tendency for the production of calcium waves after a decrease in cytosolic calcium buffering. We developed a hypothesis relating changes in the propensity to form calcium waves to changes of RyR gating and tested it by simulation. With a realistic RyR gating model, increased ability of RyR to be activated by Ca²⁺ strongly increased the propensity for generation of calcium waves at low (0.05–0.1-µM) calcium concentrations but only slightly at high (0.2–0.4-µM) calcium concentrations. Changes in RyR gating altered calcium wave formation by changing the calcium sensitivity of spontaneous calcium spark activation and/or the average number of open RyRs in spontaneous calcium sparks. Gating changes that did not affect RyR activation by Ca²⁺ had only a weak effect on the propensity to form calcium waves, even if they strongly increased calcium spark frequency. Calcium waves induced by modulating the properties of the RyR activation site could be suppressed by inhibiting the spontaneous opening of the RyR. These data can explain the increased tendency for production of calcium waves under conditions when RyR gating is altered in cardiac diseases.

What is a Ca(2+) wave? Is it like an Electrical Wave?

Arrhythmia subcellular mechanisms are constantly being explored. Recent knowledge has shown that travelling Ca(2+) waves in cardiac cells are critical for delayed afterdepolarisations and in some cases, early afterdepolarisations. In this review, we comment on the properties of cardiac Ca(2+) waves and abnormal Ca(2+) releases in terms of properties used to describe electrical waves; propagation, excitability and refractoriness.

Synchrony of cardiomyocyte Ca(2+) release is controlled by T-tubule organization, SR Ca(2+) content, and ryanodine receptor Ca(2+) sensitivity

Recent work has demonstrated that cardiomyocyte Ca(2+)release is desynchronized in several pathological conditions. Loss of Ca(2+) release synchrony has been attributed to t-tubule disruption, but it is unknown if other factors also contribute. We investigated this issue in normal and failing myocytes by integrating experimental data with a mathematical model describing spatiotemporal dynamics of Ca(2+) in the cytosol and sarcoplasmic reticulum (SR). Heart failure development in postinfarction mice was associated with progressive t-tubule disorganization, as quantified by fast-Fourier transforms. Data from fast-Fourier transforms were then incorporated in the model as a dyadic organization index, reflecting the proportion of ryanodine receptors located in dyads. With decreasing dyadic-organization index, the model predicted greater dyssynchrony of Ca(2+) release, which exceeded that observed in experimental line-scan images. Model and experiment were reconciled by reducing the threshold for Ca(2+) release in the model, suggesting that increased RyR sensitivity partially offsets the desynchronizing effects of t-tubule disruption in heart failure. Reducing the magnitude of SR Ca(2+) content and release, whether experimentally by thapsigargin treatment, or in the model, desynchronized the Ca(2+) transient. However, in cardiomyocytes isolated from SERCA2 knockout mice, RyR sensitization offset such effects. A similar interplay between RyR sensitivity and SR content was observed during treatment of myocytes with low-dose caffeine. Initial synchronization of Ca(2+) release during caffeine was reversed as SR content declined due to enhanced RyR leak. Thus, synchrony of cardiomyocyte Ca(2+) release is not only determined by t-tubule organization but also by the interplay between RyR sensitivity and SR Ca(2+) content.

Evoked centripetal Ca(2+) mobilization in cardiac Purkinje cells: insight from a model of three Ca(2+) release regions

Despite strong suspicion that abnormal Ca(2+) handling in Purkinje cells (P-cells) is implicated in life-threatening forms of ventricular tachycardias, the mechanism underlying the Ca(2+) cycling of these cells under normal conditions is still unclear. There is mounting evidence that P-cells have a unique Ca(2+) handling system. Notably complex spontaneous Ca(2+) activity was previously recorded in canine P-cells and was explained by a mechanistic hypothesis involving a triple layered system of Ca(2+) release channels. Here we examined the validity of this hypothesis for the electrically evoked Ca(2+) transient which was shown, in the dog and rabbit, to occur progressively from the periphery to the interior of the cell. To do so, the hypothesis was incorporated in a model of intracellular Ca(2+) dynamics which was then used to reproduce numerically the Ca(2+) activity of P-cells under stimulated conditions. The modelling was thus performed through a 2D computational array that encompassed three distinct Ca(2+) release nodes arranged, respectively, into three consecutive adjacent regions. A system of partial differential equations (PDEs) expressed numerically the principal cellular functions that modulate the local cytosolic Ca(2+) concentration (Cai). The apparent node-to-node progression of elevated Cai was obtained by combining Ca(2+) diffusion and 'Ca(2+)-induced Ca(2+) release'. To provide the modelling with a reliable experimental reference, we first re-examined the Ca(2+) mobilization in swine stimulated P-cells by 2D confocal microscopy. As reported earlier for the dog and rabbit, a centripetal Ca(2+) transient was readily visible in 22 stimulated P-cells from six adult Yucatan swine hearts (pacing rate: 0.1 Hz; pulse duration: 25 ms, pulse amplitude: 10% above threshold; 1 mm Ca(2+); 35°C; pH 7.3). An accurate replication of the observed centripetal Ca(2+) propagation was generated by the model for four representative cell examples and confirmed by statistical comparisons of simulations against cell data. Selective inactivation of Ca(2+) release regions of the computational array showed that an intermediate layer of Ca(2+) release nodes with an ~30-40% lower Ca(2+) activation threshold was required to reproduce the phenomenon. Our computational analysis was therefore fully consistent with the activation of a triple layered system of Ca(2+) release channels as a mechanism of centripetal Ca(2+) signalling in P-cells. Moreover, the model clearly indicated that the intermediate Ca(2+) release layer with increased sensitivity for Ca(2+) plays an important role in the specific intracellular Ca(2+) mobilization of Purkinje fibres and could therefore be a relevant determinant of cardiac conduction.

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.

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.

Slow Calcium-Depolarization-Calcium waves may initiate fast local depolarization waves in ventricular tissue

Intercellular calcium waves in cardiac myocytes are a well-recognized, if incompletely understood, phenomenon. In a variety of preparations, investigators have reported multi-cellular calcium waves or triggered propagated contractions, but the mechanisms of propagation and pathological importance of these events remain unclear. Here, we review existing experimental data and present a computational approach to investigate the mechanisms of multi-cellular calcium wave propagation. Over the past 50 years, the standard modeling paradigm for excitable cardiac tissue has seen increasingly detailed models of the dynamics of individual cells coupled in tissue solely by intercellular and interstitial current flow. Although very successful, this modeling regime has been unable to capture two important phenomena: 1) the slow intercellular calcium waves observed experimentally, and 2) how intercellular calcium events resulting in delayed after depolarizations at the cellular level could overcome a source-sink mismatch to initiate depolarization waves in tissue. In this paper, we introduce a mathematical model with subcellular spatial resolution, in which we allow both inter- and intracellular current flow and calcium diffusion. In simulations of coupled cells employing this model, we observe: a) slow inter-cellular calcium waves propagating at about 0.1 mm/s, b) faster Calcium-Depolarization-Calcium (CDC) waves, traveling at about 1 mm/s, and c) CDC-waves that can set off fast depolarization-waves (50 cm/s) in tissue with varying gap-junction conductivity.

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."

Combined computational and experimental approaches to understanding the Ca(2+) regulatory network in neurons

Ca(2+) is a ubiquitous signaling ion that regulates a variety of neuronal functions by binding to and altering the state of effector proteins. Spatial relationships and temporal dynamics of Ca(2+) elevations determine many cellular responses of neurons to chemical and electrical stimulation. There is a wealth of information regarding the properties and distribution of Ca(2+) channels, pumps, exchangers, and buffers that participate in Ca(2+) regulation. At the same time, new imaging techniques permit characterization of evoked Ca(2+) signals with increasing spatial and temporal resolution. However, understanding the mechanistic link between functional properties of Ca(2+) handling proteins and the stimulus-evoked Ca(2+) signals they orchestrate requires consideration of the way Ca(2+) handling mechanisms operate together as a system in native cells. A wide array of biophysical modeling approaches is available for studying this problem and can be used in a variety of ways. Models can be useful to explain the behavior of complex systems, to evaluate the role of individual Ca(2+) handling mechanisms, to extract valuable parameters, and to generate predictions that can be validated experimentally. In this review, we discuss recent advances in understanding the underlying mechanisms of Ca(2+) signaling in neurons via mathematical modeling. We emphasize the value of developing realistic models based on experimentally validated descriptions of Ca(2+) transport and buffering that can be tested and refined through new experiments to develop increasingly accurate biophysical descriptions of Ca(2+) signaling in neurons.