Interplay of ryanodine receptor distribution and calcium dynamics

SERCA2a gene transfer decreases sarcoplasmic reticulum calcium leak and reduces ventricular arrhythmias in a model of chronic heart failure

BACKGROUND

Sarcoplasmic reticulum calcium ATPase 2a (SERCA2a) gene therapy improves mechanical function in heart failure and is under evaluation in a clinical trial. A critical question is whether SERCA2a gene therapy predisposes to increased sarcoplasmic reticulum calcium (SR Ca(2+)) leak, cellular triggered activity, and ventricular arrhythmias in the failing heart.

METHODS AND RESULTS

We studied the influence of SERCA2a gene therapy on ventricular arrhythmogenesis in a rat chronic heart failure model. ECG telemetry studies revealed a significant antiarrhythmic effect of SERCA2a gene therapy with reduction of both spontaneous and catecholamine-induced arrhythmias in vivo. SERCA2a gene therapy also reduced susceptibility to reentry arrhythmias in ex vivo programmed electrical stimulation studies. Subcellular Ca(2+) homeostasis and spontaneous SR Ca(2+) leak characteristics were measured in failing cardiomyocytes transfected in vivo with a novel AAV9.SERCA2a vector. SR Ca(2+) leak was reduced after SERCA2a gene therapy, with reversal of the greater spark mass observed in the failing myocytes, despite normalization of SR Ca(2+) load. SERCA2a reduced ryanodine receptor phosphorylation, thereby resetting SR Ca(2+) leak threshold, leading to reduced triggered activity in vitro. Both indirect effects of reverse remodeling and direct SERCA2a effects appear to underlie the antiarrhythmic action.

CONCLUSIONS

SERCA2a gene therapy stabilizes SR Ca(2+) load, reduces ryanodine receptor phosphorylation and decreases SR Ca(2+) leak, and reduces cellular triggered activity in vitro and spontaneous and catecholamine-induced ventricular arrhythmias in vivo in failing hearts. SERCA2a gene therapy did not therefore predispose to arrhythmias and may represent a novel antiarrhythmic strategy in heart failure.

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.

Differential sensitivity of Ca²+ wave and Ca²+ spark events to ruthenium red in isolated permeabilised rabbit cardiomyocytes

Spontaneous Ca²(+) waves in cardiac muscle cells are thought to arise from the sequential firing of local Ca²(+) sparks via a fire-diffuse-fire mechanism. This study compares the ability of the ryanodine receptor (RyR) blocker ruthenium red (RuR) to inhibit these two types of Ca²(+) release in permeabilised rabbit ventricular cardiomyocytes. Perfusing with 600 nm Ca²(+) (50 μm EGTA) caused regular spontaneous Ca²(+) waves that were imaged with the fluorescence from Fluo-5F using a laser-scanning confocal microscope. Addition of 4 μm RuR caused complete inhibition of Ca²(+) waves in 50% of cardiomyocytes by 2 min and in 100% by 4 min. Separate experiments used 350 μm EGTA (600 nm Ca²(+)) to limit Ca²(+) diffusion but allow the underlying Ca(2+) sparks to be imaged. The time course of RuR-induced inhibition did not match that of waves. After 2 min of RuR, none of the characteristics of the Ca²(+) sparks were altered, and after 4 min Ca²(+) spark frequency was reduced ∼40%; no sparks could be detected after 10 min. Measurements of Ca(2+) within the SR lumen using Fluo-5N showed an increase in intra-SR Ca²(+) during the initial 2-4 min of perfusion with RuR in both wave and spark conditions. Computational modelling suggests that the sensitivity of Ca²(+) waves to RuR block depends on the number of RyRs per cluster. Therefore inhibition of Ca²(+) waves without affecting Ca²(+) sparks may be explained by block of small, non-spark producing clusters of RyRs that are important to the process of Ca²(+) wave propagation.

Simulation of the effect of rogue ryanodine receptors on a calcium wave in ventricular myocytes with heart failure

Calcium homeostasis is considered to be one of the most important factors for the contraction and relaxation of the heart muscle. However, under some pathological conditions, such as heart failure (HF), calcium homeostasis is disordered, and spontaneous waves may occur. In this study, we developed a mathematical model of formation and propagation of a calcium wave based upon a governing system of diffusion-reaction equations presented by Izu et al (2001 Biophys. J. 80 103-20) and integrated non-clustered or 'rogue' ryanodine receptors (rogue RyRs) into a two-dimensional (2D) model of ventricular myocytes isolated from failing hearts in which sarcoplasmic reticulum (SR) Ca(2+) pools are partially unloaded. The model was then used to simulate the effect of rogue RyRs on initiation and propagation of the calcium wave in ventricular myocytes with HF. Our simulation results show that rogue RyRs can amplify the diastolic SR Ca(2+) leak in the form of Ca(2+) quarks, increase the probability of occurrence of spontaneous Ca(2+) waves even with smaller SR Ca(2+) stores, accelerate Ca(2+) wave propagation, and hence lead to delayed afterdepolarizations (DADs) and cardiac arrhythmia in the diseased heart. This investigation suggests that incorporating rogue RyRs in the Ca(2+) wave model under HF conditions provides a new view of Ca(2+) dynamics that could not be mimicked by adjusting traditional parameters involved in Ca(2+) release units and other ion channels, and contributes to understanding the underlying mechanism of HF.

Cardiac cell modelling: observations from the heart of the cardiac physiome project

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field.

Organization of ryanodine receptors, transverse tubules, and sodium-calcium exchanger in rat myocytes

Confocal and total internal reflection fluorescence imaging was used to examine the distribution of caveolin-3, sodium-calcium exchange (NCX) and ryanodine receptors (RyRs) in rat ventricular myocytes. Transverse and longitudinal optical sectioning shows that NCX is distributed widely along the transverse and longitudinal tubular system (t-system). The NCX labeling consisted of both punctate and distributed components, which partially colocalize with RyRs (27%). Surface membrane labeling showed a similar pattern but the fraction of RyR clusters containing NCX label was decreased and no nonpunctate labeling was observed. Sixteen percent of RyRs were not colocalized with the t-system and 1.6% of RyRs were found on longitudinal elements of the t-system. The surface distribution of RyR labeling was not generally consistent with circular patches of RyRs. This suggests that previous estimates for the number of RyRs in a junction (based on circular close-packed arrays) need to be revised. The observed distribution of caveolin-3 labeling was consistent with its exclusion from RyR clusters. Distance maps for all colocalization pairs were calculated to give the distance between centroids of punctate labeling and edges for distributed components. The possible roles for punctate NCX labeling are discussed.

Multiscale modeling in rodent ventricular myocytes

There is a growing body of experimental evidence suggesting that the Ca(2+) signaling in ventricular myocytes is characterized by a high gradient near the cell membrane and a more uniform Ca(2+) distribution in the cell interior [1]--[7]. An important reason for this phenomenon might be that in these cells the t-tubular system forms a network of extracellular space, extending deep into the cell interior. This allows the electrical signal, that propagates rapidly along the cell membrane, to reach the vicinity of the sarcoplasmic reticulum (SR), where intracellular Ca(2+) required for myofilament activation is stored [1], [8]--[11]. Early studies of cardiac muscle showed that the t-tubules are found at intervals of about 2 lm along the longitudinal cell axis in close proximity to the Z-disks of the sarcomeres [12]. Subsequent studies have demonstrated that the t-tubular system has also longitudinal extensions [9]--[11], [13].

Three-dimensional electron microscopy reveals new details of membrane systems for Ca2+ signaling in the heart

In the current study, the three-dimensional (3D) topologies of dyadic clefts and associated membrane organelles were mapped in mouse ventricular myocardium using electron tomography. The morphological details and the distribution of membrane systems, including transverse tubules (T-tubules), junctional sarcoplasmic reticulum (SR) and vicinal mitochondria, were determined and presumed to be crucial for controlling cardiac Ca(2+) dynamics. The geometric complexity of T-tubules that varied in diameter with frequent branching was clarified. Dyadic clefts were intricately shaped and remarkably small (average 4.39x10(5) nm(3), median 2.81x10(5) nm(3)). Although a dyadic cleft of average size could hold maximum 43 ryanodine receptor (RyR) tetramers, more than one-third of clefts were smaller than the size that is able to package as many as 15 RyR tetramers. The dyadic clefts were also adjacent to one another (average end-to-end distance to the nearest dyadic cleft, 19.9 nm) and were distributed irregularly along T-tubule branches. Electron-dense structures that linked membrane organelles were frequently observed between mitochondrial outer membranes and SR or T-tubules. We, thus, propose that the topology of dyadic clefts and the neighboring cellular micro-architecture are the major determinants of the local control of Ca(2+) in the heart, including the establishment of the quantal nature of SR Ca(2+) releases (e.g. Ca(2+) sparks).

Ryanodine receptor-mediated arrhythmias and sudden cardiac death

The cardiac ryanodine receptor-Ca²⁺ release channel (RyR2) is an essential sarcoplasmic reticulum (SR) transmembrane protein that plays a central role in excitation–contraction coupling (ECC) in cardiomyocytes. Aberrant spontaneous, diastolic Ca²⁺ leak from the SR due to dysfunctional RyR2 contributes to the formation of delayed after-depolarisations, which are thought to underlie the fatal arrhythmia that occurs in both heart failure (HF) and in catecholaminergic polymorphic ventricular tachycardia (CPVT). CPVT is an inherited disorder associated with mutations in either the RyR2 or a SR luminal protein, calsequestrin. RyR2 shows normal function at rest in CPVT but the RyR2 dysfunction is unmasked by physical exercise or emotional stress, suggesting abnormal RyR2 activation as an underlying mechanism. Several potential mechanisms have been advanced to explain the dysfunctional RyR2 observed in HF and CPVT, including enhanced RyR2 phosphorylation status, altered RyR2 regulation at luminal/cytoplasmic sites and perturbed RyR2 intra/inter-molecular interactions. This review considers RyR2 dysfunction in the context of the structural and functional modulation of the channel, and potential therapeutic strategies to stabilise RyR2 function in cardiac pathology.

Three-dimensional high-resolution imaging of cardiac proteins to construct models of intracellular Ca2+ signalling in rat ventricular myocytes

Quantitative understanding of the Ca(2+) handling in cardiac ventricular myocytes requires accurate knowledge of cardiac ultrastructure and protein distribution. We have therefore developed high-resolution imaging and analysis approaches to measure the three-dimensional distribution of immunolabelled proteins with confocal microscopy. Labelling of single rat cardiac myocytes with an antibody to the Z-line marker alpha-actinin revealed a complex architecture of sarcomere misalignment across single cells. Double immunolabelling was used to relate the Z-line structure to the distribution of ryanodine receptors (RyRs, the intracellular Ca(2+) release channels) and the transverse tubular system. Both RyR and transverse tubular system distributions exhibited frequent dislocations from the simple planar geometry generally assumed in existing mathematical models. To investigate potential effects of these irregularities on Ca(2+) dynamics, we determined the three-dimensional distribution of RyR clusters within an extended section of a single rat ventricular myocyte to construct a model of stochastic Ca(2+) dynamics with a measured Ca(2+) release unit (CRU) distribution. Calculations with this model were compared with a second model in which all CRUs were placed on flat planes. The model with a realistic CRU distribution supported Ca(2+) waves that spread axially along the cell at velocities of approximately 50 mum s(-1). By contrast, in the model with planar CRU distribution the axial wave spread was slowed roughly twofold and wave propagation often nearly faltered. These results demonstrate that spatial features of the CRU distribution on multiple length scales may significantly affect intracellular Ca(2+) dynamics and must be captured in detailed mechanistic models to achieve quantitative as well as qualitative insight.

Calcium sparks

The calcium ion (Ca(2+)) is the simplest and most versatile intracellular messenger known. The discovery of Ca(2+) sparks and a related family of elementary Ca(2+) signaling events has revealed fundamental principles of the Ca(2+) signaling system. A newly appreciated "digital" subsystem consisting of brief, high Ca(2+) concentration over short distances (nanometers to microns) comingles with an "analog" global Ca(2+) signaling subsystem. Over the past 15 years, much has been learned about the theoretical and practical aspects of spark formation and detection. The quest for the spark mechanisms [the activation, coordination, and termination of Ca(2+) release units (CRUs)] has met unexpected challenges, however, and raised vexing questions about CRU operation in situ. Ample evidence shows that Ca(2+) sparks catalyze many high-threshold Ca(2+) processes involved in cardiac and skeletal muscle excitation-contraction coupling, vascular tone regulation, membrane excitability, and neuronal secretion. Investigation of Ca(2+) sparks in diseases has also begun to provide novel insights into hypertension, cardiac arrhythmias, heart failure, and muscular dystrophy. An emerging view is that spatially and temporally patterned activation of the digital subsystem confers on intracellular Ca(2+) signaling an exquisite architecture in space, time, and intensity, which underpins signaling efficiency, stability, specificity, and diversity. These recent advances in "sparkology" thus promise to unify the simplicity and complexity of Ca(2+) signaling in biology.

Simplified model of cytosolic Ca2+ dynamics in the presence of one or several clusters of Ca2+ -release channels

Calcium release from intracellular stores plays a key role in the regulation of a variety of cellular activities. In various cell types this release occurs through inositol-triphosphate (IP3) receptors which are Ca2+ channels whose open probability is modulated by the cytosolic Ca2+ concentration itself. Thus, the combination of Ca2+ release and Ca2+ diffusion evokes a variety of Ca2+ signals depending on the number and relative location of the channels that participate of them. In fact, a hierarchy of Ca2+ signals has been observed in Xenopus laevis oocytes, ranging from very localized events (puffs and blips) to waves that propagate throughout the cell. In this cell type channels are organized in clusters. The behavior of individual channels within a cluster cannot be resolved with current optical techniques. Therefore, a combination of experiments and mathematical modeling is unavoidable to understand these signals. However, the numerical simulation of a detailed mathematical model of the problem is very hard given the large range of spatial and temporal scales that must be covered. In this paper we present an alternative model in which the cluster region is modeled using a relatively fine grid but where several approximations are made to compute the cytosolic Ca2+ concentration ([Ca;{2+}]) distribution. The inner-cluster [Ca;{2+}] distribution is used to determine the openings and closings of the channels of the cluster. The spatiotemporal [Ca;{2+}] distribution outside the cluster is determined using a coarser grid in which each (active) cluster is represented by a point source whose current is proportional to the number of open channels determined before. A full reaction-diffusion system is solved on this coarser grid.

Three-dimensional geometric modeling of membrane-bound organelles in ventricular myocytes: bridging the gap between microscopic imaging and mathematical simulation

A general framework of image-based geometric processing is presented to bridge the gap between three-dimensional (3D) imaging that provides structural details of a biological system and mathematical simulation where high-quality surface or volumetric meshes are required. A 3D density map is processed in the order of image pre-processing (contrast enhancement and anisotropic filtering), feature extraction (boundary segmentation and skeletonization), and high-quality and realistic surface (triangular) and volumetric (tetrahedral) mesh generation. While the tool-chain described is applicable to general types of 3D imaging data, the performance is demonstrated specifically on membrane-bound organelles in ventricular myocytes that are imaged and reconstructed with electron microscopic (EM) tomography and two-photon microscopy (T-PM). Of particular interest in this study are two types of membrane-bound Ca(2+)-handling organelles, namely, transverse tubules (T-tubules) and junctional sarcoplasmic reticulum (jSR), both of which play an important role in regulating the excitation-contraction (E-C) coupling through dynamic Ca(2+) mobilization in cardiomyocytes.

Calsequestrin-mediated mechanism for cellular calcium transient alternans

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

Calcium handling in human embryonic stem cell-derived cardiomyocytes

The objective of the current study was to characterize calcium handling in developing human embryonic stem cell-derived cardiomyocytes (hESC-CMs). To this end, real-time polymerase chain reaction (PCR), immunocytochemistry, whole-cell voltage-clamp, and simultaneous patch-clamp/laser scanning confocal calcium imaging and surface membrane labeling with di-8-aminonaphthylethenylpridinium were used. Immunostaining studies in the hESC-CMs demonstrated the presence of the sarcoplasmic reticulum (SR) calcium release channels, ryanodine receptor-2, and inositol-1,4,5-trisphosphate (IP3) receptors. Store calcium function was manifested as action-potential-induced calcium transients. Time-to-target plots showed that these action-potential-initiated calcium transients traverse the width of the cell via a propagated wave of intracellular store calcium release. The hESC-CMs also exhibited local calcium events ("sparks") that were localized to the surface membrane. The presence of caffeine-sensitive intracellular calcium stores was manifested following application of focal, temporally limited puffs of caffeine in three different age groups: early-stage (with the initiation of beating), intermediate-stage (10 days post-beating [dpb]), and late-stage (30-40 dpb) hESC-CMs. Calcium store load gradually increased during in vitro maturation. Similarly, ryanodine application decreased the amplitude of the spontaneous calcium transients. Interestingly, the expression and function of an IP3-releasable calcium pool was also demonstrated in the hESC-CMs in experiments using caged-IP3 photolysis and antagonist application (2 microM 2-Aminoethoxydiphenyl borate). In summary, our study establishes the presence of a functional SR calcium store in early-stage hESC-CMs and shows a unique pattern of calcium handling in these cells. This study also stresses the importance of the functional characterization of hESC-CMs both for developmental studies and for the development of future myocardial cell replacement strategies. Disclosure of potential conflicts of interest is found at the end of this article.

Three-dimensional distribution of cardiac Na+-Ca2+ exchanger and ryanodine receptor during development

Mechanisms of cardiac excitation-contraction coupling in neonates are still not clearly defined. Previous work in neonates shows reverse-mode Na(+)-Ca(2+) exchange to be the primary route of Ca(2+) entry during systole and the neonatal sarcoplasmic reticulum to have similar capability as that of adult in storing and releasing Ca(2+). We investigated Na(+)-Ca(2+) exchanger (NCX) and ryanodine receptor (RyR) distribution in developing ventricular myocytes using immunofluorescence, confocal microscopy, and digital image analysis. In neonates, both NCX and RyR clusters on the surface of the cell displayed a short longitudinal periodicity of approximately 0.7 microm. However, by adulthood, both proteins were also found in the interior. In the adult, clusters of NCX on the surface of the cell retained the approximately 0.7-microm periodicity whereas clusters of RyR adopted a longer longitudinal periodicity of approximately 2.0 microm. This suggests that neonatal myocytes also have a peri-M-line RyR distribution that is absent in adult myocytes. NCX and RyR colocalized voxel density was maximal in neonates and declined significantly with ontogeny. We conclude in newborns, Ca(2+) influx via NCX could potentially activate the dense network of peripheral Ca(2+) stores via peripheral couplings, evoking Ca(2+)-induced Ca(2+) release.

Analysis of ryanodine receptor clusters in rat and human cardiac myocytes

Single rat ventricular myocytes and human ventricle tissue sections were labeled with antibodies against the ryanodine receptor (RyR) and alpha-actinin to examine the 3D distribution of RyRs with confocal microscopy. Image contrast was maximized by refractive index matching and deconvolution. The RyR label formed discrete puncta representing clusters of RyRs or "couplons" around the edges of the myofilaments with a nearest-neighbor spacing of 0.66 +/- 0.06 microm in rat and 0.78 +/- 0.07 microm in human. Each bundle of myofibrils was served by approximately six couplons, which supplied a cross-sectional area of approximately 0.6 microm(2) in rat and approximately 0.8 microm(2) in human. Although the couplons were in reasonable registration with z-lines, there were discontinuities in the longitudinal position of sarcomeres so that dislocations in the order of RyR clusters occurred. There was approximately 53% longitudinal registration of RyR clusters, suggesting a nonrandom placement of couplons around the sarcomere. These data can explain the spherical propagation of Ca(2+) waves and provide quantitative 3D data sets needed for accurate modeling of cardiac Ca(2+)-induced Ca(2+) release. By quantifying labeling intensity in rat ventricular myocytes, a lower limit of 78 RyRs per cluster (on average) was obtained. By modeling the couplon as a disk wrapping around a t-tubule and fitting cluster images, 95% of couplons contained between 120 and 260 RyRs (assuming that RyRs are tight packed with a spacing of 29 nm). Assuming similar labeling efficiency in human, from the fluorescence intensity alone we estimate that human ventricular myocytes contain approximately 30% fewer RyRs per couplon than rat.

Eavesdropping on the social lives of Ca(2+) sparks

Ca(2+) sparks arise from the stochastic opening of spatially discrete clusters of ryanodine receptors called a Ca(2+) release unit (CRU). If the RyR clusters were not spatially separated, then Ca(2+) released from one RyR would immediately diffuse to its neighbor and lead to uncontrolled, runaway Ca(2+) release throughout the cell. While physical separation provides some isolation from neighbors, CRUs are not incommunicado. When inter-neighbor interactions become large enough, Ca(2+) waves spontaneously emerge. A more circumscribed interaction shows up in high-speed two-dimensional confocal images as jumping Ca(2+) sparks that seem to be sequentially activated along the Z-line and across Z-lines. However, since Ca(2+) sparks are stochastic events how can we tell whether two sparks occurring close together in space and time are causally related or appeared simply by coincidence? Here we develop a mathematical method to disentangle cause and coincidence in a statistical sense. From our analysis we derive three fundamental properties of Ca(2+) spark generation: 1), the "intrinsic" spark frequency, the spark frequency one would observe if the CRUs were incommunicado; 2), the coupling strength, which measures how strongly one CRU affects another; and 3), the range over which the communication occurs. These parameters allow us to measure the effect RyR regulators have on the intrinsic activity of CRUs and on the coupling between them.

Phosphorylation of RyR2 and shortening of RyR2 cluster spacing in spontaneously hypertensive rat with heart failure

As a critical step toward understanding the role of abnormal intracellular Ca(2+) release via the ryanodine receptor (RyR(2)) during the development of hypertension-induced cardiac hypertrophy and heart failure, this study examines two questions: 1) At what stage, if ever, in the development of hypertrophy and heart failure is RyR(2) hyperphosphorylated at Ser(2808)? 2) Does the spatial distribution of RyR(2) clusters change in failing hearts? Using a newly developed semiquantitative immunohistochemistry method and Western blotting, we measured phosphorylation of RyR(2) at Ser(2808) in the spontaneously hypertensive rat (SHR) at four distinct disease stages. A major finding is that hyperphosphorylation of RyR(2) at Ser(2808) occurred only at late-stage heart failure in SHR, but not in age-matched controls. Furthermore, the spacing between RyR(2) clusters was shortened in failing hearts, as predicted by quantitative model simulation to increase spontaneous Ca(2+) wave generation and arrhythmias.

Hybrid stochastic and deterministic simulations of calcium blips

Intracellular calcium release is a prime example for the role of stochastic effects in cellular systems. Recent models consist of deterministic reaction-diffusion equations coupled to stochastic transitions of calcium channels. The resulting dynamics is of multiple time and spatial scales, which complicates far-reaching computer simulations. In this article, we introduce a novel hybrid scheme that is especially tailored to accurately trace events with essential stochastic variations, while deterministic concentration variables are efficiently and accurately traced at the same time. We use finite elements to efficiently resolve the extreme spatial gradients of concentration variables close to a channel. We describe the algorithmic approach and we demonstrate its efficiency compared to conventional methods. Our single-channel model matches experimental data and results in intriguing dynamics if calcium is used as charge carrier. Random openings of the channel accumulate in bursts of calcium blips that may be central for the understanding of cellular calcium dynamics.

A new approach to the detection and statistical classification of Ca2+ sparks

The availability of high-speed, two-dimensional (2-D) confocal microscopes and the expanding armamentarium of fluorescent probes presents unprecedented opportunities and new challenges for studying the spatial and temporal dynamics of cellular processes. The need to remove subjectivity from the detection process, the difficulty of the human eye to detect subtle changes in fluorescence in these 2-D images, and the large volume of data produced by these confocal microscopes call for the need to develop algorithms to automatically mark the changes in fluorescence. These fluorescence signal changes are often subtle, so the statistical estimate of the likelihood that the detected signal is not noise is an integral part of the detection algorithm. This statistical estimation is fundamental to our new approach to detection; in earlier Ca(2+) spark detectors, this statistical assessment was incidental to detection. Importantly, the use of the statistical properties of the signal local to the spark, instead of over the whole image, reduces the false positive and false negative rates. We developed an automatic spark detection algorithm based on these principles and used it to detect sparks on an inhomogeneous background of transverse tubule-labeled rat ventricular cells. Because of the large region of the cell surveyed by the confocal microscope, we can detect a large enough number of sparks to measure the dynamic changes in spark frequency in individual cells. We also found, in contrast to earlier results, that cardiac sparks are spatially symmetric. This new approach puts the detection of fluorescent signals on a firm statistical foundation.

Calcium signalling during excitation-contraction coupling in mammalian atrial myocytes

Atrial cardiomyocytes make an important contribution to the refilling of ventricles with blood, which enhances the subsequent ejection of blood from the heart. The dependence of cardiac function on the contribution of atria becomes increasingly important with age and exercise. We know much less about the calcium signals that link electrical depolarisation to contraction within atrial myocytes in comparison with ventricular myocytes. Nevertheless, recent work has shed new light on calcium signalling in atrial cells. At an ultrastructural level, atrial and ventricular myocytes have many similarities. However, a few key structural differences, in particular the lack of transverse tubules (;T-tubules') in atrial myocytes, make these two cell types display vastly different calcium patterns in response to depolarisation. The lack of T-tubules in atrial myocytes means that depolarisation provokes calcium signals that largely originate around the periphery of the cells. To engage the contractile machinery, the calcium signal must propagate centripetally deeper into the cells. This inward movement of calcium is ultimately controlled by hormones that can promote or decrease calcium release within the myocytes. Enhanced centripetal movement of calcium in atrial myocytes leads to increased contraction and a more substantial contribution to blood pumping. The calcium signalling paradigm within atrial cells applies to other cardiac cell types that also do not express T-tubules, such as neonatal ventricular myocytes, and Purkinje cells that aid in the spread of electrical depolarisation. Furthermore, during heart failure ventricular myocytes progressively lose their regular T-tubule expression, and their pattern of response resembles that of atrial cells.

Three-dimensional distribution of ryanodine receptor clusters in cardiac myocytes

The clustering of ryanodine receptors (RyR2) into functional Ca2+ release units is central to current models for cardiac excitation-contraction (E-C) coupling. Using immunolabeling and confocal microscopy, we have analyzed the distribution of RyR2 clusters in rat and ventricular atrial myocytes. The resolution of the three-dimensional structure was improved by a novel transverse sectioning method as well as digital deconvolution. In contrast to earlier reports, the mean RyR2 cluster transverse spacing was measured 1.05 microm in ventricular myocytes and estimated 0.97 microm in atrial myocytes. Intercalated RyR2 clusters were found interspersed between the Z-disks on the cell periphery but absent in the interior, forming double rows flanking the local Z-disks on the surface. The longitudinal spacing between the adjacent rows of RyR2 clusters on the Z-disks was measured to have a mean value of 1.87 microm in ventricular and 1.69 microm in atrial myocytes. The measured RyR2 cluster distribution is compatible with models of Ca2+ wave generation. The size of the typical RyR2 cluster was close to 250 nm, and this suggests that approximately 100 RyR2s might be present in a cluster. The importance of cluster size and three-dimensional spacing for current E-C coupling models is discussed.