Evolution of cardiac calcium waves from stochastic calcium sparks

We present a model that provides a unified framework for studying Ca2+ sparks and Ca2+ waves in cardiac cells. The model is novel in combining 1) use of large currents (approximately 20 pA) through the Ca2+ release units (CRUs) of the sarcoplasmic reticulum (SR); 2) stochastic Ca2+ release (or firing) of CRUs; 3) discrete, asymmetric distribution of CRUs along the longitudinal (separation distance of 2 microm) and transverse (separated by 0.4-0.8 microm) directions of the cell; and 4) anisotropic diffusion of Ca2+ and fluorescent indicator to study the evolution of Ca2+ waves from Ca2+ sparks. The model mimics the important features of Ca2+ sparks and Ca2+ waves in terms of the spontaneous spark rate, the Ca2+ wave velocity, and the pattern of wave propagation. Importantly, these features are reproduced when using experimentally measured values for the CRU Ca2+ sensitivity (approximately 15 microM). Stochastic control of CRU firing is important because it imposes constraints on the Ca2+ sensitivity of the CRU. Even with moderate (approximately 5 microM) Ca2+ sensitivity the very high spontaneous spark rate triggers numerous Ca2+ waves. In contrast, a single Ca2+ wave with arbitrarily large velocity can exist in a deterministic model when the CRU Ca2+ sensitivity is sufficiently high. The combination of low CRU Ca2+ sensitivity (approximately 15 microM), high cytosolic Ca2+ buffering capacity, and the spatial separation of CRUs help control the inherent instability of SR Ca2+ release. This allows Ca2+ waves to form and propagate given a sufficiently large initiation region, but prevents a single spark or a small group of sparks from triggering a wave.     

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

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

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

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

Superresolution Modeling of Calcium Release in the Heart

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

Life and death of a cardiac calcium spark

Calcium sparks in cardiac myocytes are brief, localized calcium releases from the sarcoplasmic reticulum (SR) believed to be caused by locally regenerative calcium-induced calcium release (CICR) via couplons, clusters of ryanodine receptors (RyRs). How such regeneration is terminated is uncertain. We performed numerical simulations of an idealized stochastic model of spark production, assuming a RyR gating scheme with only two states (open and closed). Local depletion of calcium in the SR was inevitable during a spark, and this could terminate sparks by interrupting CICR, with or without assumed modulation of RyR gating by SR lumenal calcium. Spark termination by local SR depletion was not robust: under some conditions, sparks could be greatly and variably prolonged, terminating by stochastic attrition–a phenomenon we dub “spark metastability.” Spark fluorescence rise time was not a good surrogate for the duration of calcium release. Using a highly simplified, deterministic model of the dynamics of a couplon, we show that spark metastability depends on the kinetic relationship of RyR gating and junctional SR refilling rates. The conditions for spark metastability resemble those produced by known mutations of RyR2 and CASQ2 that cause life-threatening triggered arrhythmias, and spark metastability may be mitigated by altering the kinetics of the RyR in a manner similar to the effects of drugs known to prevent those arrhythmias. The model was unable to explain the distributions of spark amplitudes and rise times seen in chemically skinned cat atrial myocytes, suggesting that such sparks may be more complex events involving heterogeneity of couplons or local propagation among sub-clusters of RyRs.     

Inhibition of Ca(2+) sparks by ruthenium red in permeabilized rat ventricular myocytes

We have compared the effects of the sarcoplasmic reticulum (SR) Ca(2+) release inhibitor, ruthenium red (RR), on single ryanodine receptor (RyR) channels in lipid bilayers, and on Ca(2+) sparks in permeabilized rat ventricular myocytes. Ruthenium red at 5 microM inhibited the open probability (P(o)) of RyRs approximately 20-50-fold, without significantly affecting the conductance or mean open time of the channel. At the same concentration, RR inhibited the frequency of Ca(2+) sparks in permeabilized myocytes by approximately 10-fold, and reduced the amplitude of large amplitude events (with most probable localization on the line scan) by approximately 3-fold. According to our theoretical simulations, performed with a numerical model of Ca(2+) spark formation, this reduction in Ca(2+) spark amplitude corresponds to an approximately 4-fold decrease in Ca(2+) release flux underlying Ca(2+) sparks. Ruthenium red (5 microM) increased the SR Ca(2+) content by approximately 2-fold (from 151 to 312 micromol/l cytosol). Considering the degree of inhibition of local Ca(2+) release events, the increase in SR Ca(2+) load by RR, and the lack of effects of RR on single RyR open time and conductance, we have estimated that Ca(2+) sparks under normal conditions are generated by openings of at least 10 single RyRs.     

Regulation of Ca2+ Sparks by Ca2+ and Mg2+ in Mammalian and Amphibian Muscle. An RyR Isoform-specific Role in Excitation–Contraction Coupling?

Ca2+ and Mg2+ are important mediators and regulators of intracellular Ca2+ signaling in muscle. The effects of changes of cytosolic [Ca2+] or [Mg2+] on elementary Ca2+ release events were determined, as functions of concentration and time, in single fast-twitch permeabilized fibers of rat and frog. Ca2+ sparks were identified and their parameters measured in confocal images of fluo-4 fluorescence. Solutions with different [Ca2+] or [Mg2+] were rapidly exchanged while imaging. Faster and spatially homogeneous changes of [Ca2+] (reaching peaks >100 microM) were achieved by photolysing Ca NP-EGTA with laser flashes. In both species, incrementing cytosolic [Ca2+] caused a steady, nearly proportional increase in spark frequency, reversible upon [Ca2+] reduction. A greater change in spark frequency, usually transient, followed sudden increases in [Ca2+] after a lag of 100 ms or more. The nonlinearity, lag, and other features of this delayed effect suggest that it requires increase of [Ca2+] inside the SR. In the frog only, increases in cytosolic [Ca2+] often resulted, after a lag, in sparks that propagated transversally. An increase in [Mg2+] caused a fall of spark frequency, but with striking species differences. In the rat, but not the frog, sparks were observed at 4-40 mM [Mg2+]. Reducing [Mg2+] below 2 mM, which should enable the RyR channel's activation (CICR) site to bind Ca2+, caused progressive increase in spark frequency in the frog, but had no effect in the rat. Spark propagation and enhancement by sub-mM Mg2+ are hallmarks of CICR. Their absence in the rat suggests that CICR requires RyR3 para-junctional clusters, present only in the frog. The observed frequency of sparks corresponds to a channel open probability of 10(-7) in the frog or 10(-8) in the rat. Together with the failure of photorelease to induce activation directly, this indicates a basal inhibition of channels in situ. It is proposed that relief of this inhibition could be the mechanism by which increased SR load increases spark frequency.     

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

Ca²⁺ sparks arise from the stochastic opening of spatially discrete clusters of ryanodine receptors called a Ca²⁺ release unit (CRU). If the RyR clusters were not spatially separated, then Ca²⁺ released from one RyR would immediately diffuse to its neighbor and lead to uncontrolled, runaway Ca²⁺ release throughout the cell. While physical separation provides some isolation from neighbors, CRUs are not incommunicado. When inter-neighbor interactions become large enough, Ca²⁺ waves spontaneously emerge. A more circumscribed interaction shows up in high-speed two-dimensional confocal images as jumping Ca²⁺ sparks that seem to be sequentially activated along the Z-line and across Z-lines. However, since Ca²⁺ 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 Ca²⁺ 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.     

Interdomain interactions within ryanodine receptors regulate Ca2+ spark frequency in skeletal muscle.

DP4 is a 36-residue synthetic peptide that corresponds to the Leu(2442)-Pro(2477) region of RyR1 that contains the reported malignant hyperthermia (MH) mutation site. It has been proposed that DP4 disrupts the normal interdomain interactions that stabilize the closed state of the Ca(2)+ release channel (Yamamoto, T., R. El-Hayek, and N. Ikemoto. 2000. J. Biol. Chem. 275:11618-11625). We have investigated the effects of DP4 on local SR Ca(2)+ release events (Ca(2)+ sparks) in saponin-permeabilized frog skeletal muscle fibers using laser scanning confocal microscopy (line-scan mode, 2 ms/line), as well as the effects of DP4 on frog SR vesicles and frog single RyR Ca(2)+ release channels reconstituted in planar lipid bilayers. DP4 caused a significant increase in Ca(2)+ spark frequency in muscle fibers. However, the mean values of the amplitude, rise time, spatial half width, and temporal half duration of the Ca(2)+ sparks, as well as the distribution of these parameters, remained essentially unchanged in the presence of DP4. Thus, DP4 increased the opening rate, but not the open time of the RyR Ca(2)+ release channel(s) generating the sparks. DP4 also increased [(3)H]ryanodine binding to SR vesicles isolated from frog and mammalian skeletal muscle, and increased the open probability of frog RyR Ca(2)+ release channels reconstituted in bilayers, without changing the amplitude of the current through those channels. However, unlike in Ca(2)+ spark experiments, DP4 produced a pronounced increase in the open time of channels in bilayers. The same peptide with an Arg(17) to Cys(17) replacement (DP4mut), which corresponds to the Arg(2458)-to-Cys(2458) mutation in MH, did not produce a significant effect on RyR activation in muscle fibers, bilayers, or SR vesicles. Mg(2)+ dependence experiments conducted with permeabilized muscle fibers indicate that DP4 preferentially binds to partially Mg(2)+-free RyR(s), thus promoting channel opening and production of Ca(2)+ sparks.     

Modeling Calcium Wave Based on Anomalous Subdiffusion of Calcium Sparks in Cardiac Myocytes

sparks and waves play important roles in calcium release and calcium propagation during the excitation-contraction (EC) coupling process in cardiac myocytes. Although the classical Fick’s law is widely used to model sparks and waves in cardiac myocytes, it fails to reasonably explain the full-width at half maximum(FWHM) paradox. However, the anomalous subdiffusion model successfully reproduces sparks of experimental results. In this paper, in the light of anomalous subdiffusion of sparks, we develop a mathematical model of calcium wave in cardiac myocytes by using stochastic release of release units (CRUs). Our model successfully reproduces calcium waves with physiological parameters. The results reveal how concentration waves propagate from an initial firing of one CRU at a corner or in the middle of considered region, answer how large in magnitude of an anomalous spark can induce a wave. With physiological currents (2pA) through CRUs, it is shown that an initial firing of four adjacent CRUs can form a wave. Furthermore, the phenomenon of calcium waves collision is also investigated.     

Physiological and pathological modulation of ryanodine receptor function in cardiac muscle

Calcium release from the sarcoplasmic reticulum (SR) in cardiac muscle occurs through a specialised release channel, the ryanodine receptor, RyR, via the process of Ca-induced Ca release (CICR). The open probability of the RyR is increased by elevation of cytoplasmic Ca concentration ([Ca(2+)](i)). However, in addition to Ca, other modulators affect the RyR open probability. Agents which increase the RyR opening during systole produce a transient increase of systolic [Ca(2+)](i) followed by a return to the initial level due to a compensating decrease of SR Ca content. Increasing RyR opening during diastole decreases SR Ca content and thereby decreases systolic [Ca(2+)](i). We therefore conclude that potentiation of RyR opening will, if anything, decrease systolic [Ca(2+)](i). The effects of specific examples of modulators of the RyR, such as phosphorylation, metabolic changes, heart failure and polyunsaturated fatty acids, are discussed.     

Control of Sarcoplasmic Reticulum Ca2+ Release by Stochastic RyR Gating within a 3D Model of the Cardiac Dyad and Importance of Induction Decay for CICR Termination

The factors responsible for the regulation of regenerative calcium-induced calcium release (CICR) during Ca²⁺ spark evolution remain unclear. Cardiac ryanodine receptor (RyR) gating in rats and sheep was recorded at physiological Ca²⁺, Mg²⁺, and ATP levels and incorporated into a 3D model of the cardiac dyad, which reproduced the time course of Ca²⁺ sparks, Ca²⁺ blinks, and Ca²⁺ spark restitution. The termination of CICR by induction decay in the model principally arose from the steep Ca²⁺ dependence of RyR closed time, with the measured sarcoplasmic reticulum (SR) lumen Ca²⁺ dependence of RyR gating making almost no contribution. The start of CICR termination was strongly dependent on the extent of local depletion of junctional SR Ca²⁺, as well as the time course of local Ca²⁺ gradients within the junctional space. Reducing the dimensions of the dyad junction reduced Ca²⁺ spark amplitude by reducing the strength of regenerative feedback within CICR. A refractory period for Ca²⁺ spark initiation and subsequent Ca²⁺ spark amplitude restitution arose from 1), the extent to which the regenerative phase of CICR can be supported by the partially depleted junctional SR, and 2), the availability of releasable Ca²⁺ in the junctional SR. The physical organization of RyRs within the junctional space had minimal effects on Ca²⁺ spark amplitude when more than nine RyRs were present. Spark amplitude had a nonlinear dependence on RyR single-channel Ca²⁺ flux, and was approximately halved by reducing the flux from 0.6 to 0.2 pA. Although rat and sheep RyRs had quite different Ca²⁺ sensitivities, Ca²⁺ spark amplitude was hardly affected. This suggests that moderate changes in RyR gating by second-messenger systems will principally alter the spatiotemporal properties of SR release, with smaller effects on the amount released.     

Oxidative Stress and Ca2+ Release Events in Mouse Cardiomyocytes

Cellular oxidative stress, associated with a variety of common cardiac diseases, is well recognized to affect the function of several key proteins involved in Ca²⁺ signaling and excitation-contraction coupling, which are known to be exquisitely sensitive to reactive oxygen species. These include the Ca²⁺ release channels of the sarcoplasmic reticulum (ryanodine receptors or RyR2s) and the Ca²⁺/calmodulin-dependent protein kinase II (CaMKII). Oxidation of RyR2s was found to increase the open probability of the channel, whereas CaMKII can be activated independent of Ca²⁺ through oxidation. Here, we investigated how oxidative stress affects RyR2 function and SR Ca²⁺ signaling in situ, by analyzing Ca²⁺ sparks in permeabilized mouse cardiomyocytes under a broad range of oxidative conditions. The results show that with increasing oxidative stress Ca²⁺ spark duration is prolonged. In addition, long and very long-lasting (up to hundreds of milliseconds) localized Ca²⁺ release events started to appear, eventually leading to sarcoplasmic reticulum (SR) Ca²⁺ depletion. These changes of release duration could be prevented by the CaMKII inhibitor KN93 and did not occur in mice lacking the CaMKII-specific S2814 phosphorylation site on RyR2. The appearance of long-lasting Ca²⁺ release events was paralleled by an increase of RyR2 oxidation, but also by RyR-S2814 phosphorylation, and by CaMKII oxidation. Our results suggest that in a strongly oxidative environment oxidation-dependent activation of CaMKII leads to RyR2 phosphorylation and thereby contributes to the massive prolongation of SR Ca²⁺ release events.     

Dantrolene prevents arrhythmogenic Ca2+ release in heart failure

In heart failure (HF), arrhythmogenic Ca(2+) release and chronic Ca(2+) depletion of the sarcoplasmic reticulum (SR) arise due to altered function of the ryanodine receptor (RyR) SR Ca(2+)-release channel. Dantrolene, a therapeutic agent used to treat malignant hyperthermia associated with mutations of the skeletal muscle type 1 RyR (RyR1), has recently been suggested to have effects on the cardiac type 2 RyR (RyR2). In this investigation, we tested the hypothesis that dantrolene exerts antiarrhythmic and inotropic effects on HF ventricular myocytes by examining multiple aspects of intracellular Ca(2+) handling. In normal rabbit myocytes, dantrolene (1 μM) had no effect on SR Ca(2+) load, postrest decay of SR Ca(2+) content, the threshold for spontaneous Ca(2+) wave initiation (i.e., the SR Ca(2+) content at which spontaneous waves initiate) and Ca(2+) spark frequency. In cardiomyocytes from failing rabbit hearts, SR Ca(2+) load and the wave initiation threshold were decreased compared with normal myocytes, Ca(2+) spark frequency was increased, and the postrest decay was potentiated. Using a novel approach of measuring cytosolic and intra-SR Ca(2+) concentration (using the low-affinity Ca(2+) indicator fluo-5N entrapped within the SR), we showed that treatment of HF cardiomyocytes with dantrolene rescued postrest decay and increased the wave initiation threshold. Additionally, dantrolene decreased Ca(2+) spark frequency while increasing the SR Ca(2+) content in HF myocytes. These data suggest that dantrolene exerts antiarrhythmic effects and preserves inotropy in HF cardiomyocytes by decreasing the incidence of diastolic Ca(2+) sparks, increasing the intra-SR Ca(2+) threshold at which spontaneous Ca(2+) waves occur, and decreasing the loss of Ca(2+) from the SR. Furthermore, the observation that dantrolene reduces arrhythmogenicity while at the same time preserves inotropy suggests that dantrolene is a potentially useful drug in the treatment of arrhythmia associated with HF.     

Synchronization of stochastic Ca²(+) release units creates a rhythmic Ca²(+) clock in cardiac pacemaker cells

In sinoatrial node cells of the heart, beating rate is controlled, in part, by local Ca2(+) releases (LCRs) from the sarcoplasmic reticulum, which couple to the action potential via electrogenic Na(+)/Ca2(+) exchange. We observed persisting, roughly periodic LCRs in depolarized rabbit sinoatrial node cells (SANCs). The features of these LCRs were reproduced by a numerical model consisting of a two-dimensional array of stochastic, diffusively coupled Ca2(+) release units (CRUs) with fixed refractory period. Because previous experimental studies showed that β-adrenergic receptor stimulation increases the rate of Ca2(+) release through each CRU (dubbed I(spark)), we explored the link between LCRs and I(spark) in our model. Increasing the CRU release current I(spark) facilitated Ca2(+)-induced-Ca2(+) release and local recruitment of neighboring CRUs to fire more synchronously. This resulted in a progression in simulated LCR size (from sparks to wavelets to global waves), LCR rhythmicity, and decrease of LCR period that parallels the changes observed experimentally with β-adrenergic receptor stimulation. The transition in LCR characteristics was steeply nonlinear over a narrow range of I(spark), resembling a phase transition. We conclude that the (partial) periodicity and rate regulation of the "Calcium clock" in SANCs are emergent properties of the diffusive coupling of an ensemble of interacting stochastic CRUs. The variation in LCR period and size with I(spark) is sufficient to account for β-adrenergic regulation of SANC beating rate.     

Ca(2+)-induced Ca(2+) release in sensory neurons: low gain amplification confers intrinsic stability

Ca(2+)-induced Ca(2+) release (CICR) is a ubiquitous mechanism by which Ca(2+) release from the endoplasmic reticulum amplifies the trigger Ca(2+) entry and generates propagating Ca(2+) waves. To elucidate the mechanisms that control this positive feedback, we investigated the spatial and temporal kinetics and measured the gain function of CICR in small sensory neurons from mammalian dorsal root ganglions (DRGs). We found that subsurface Ca(2+) release units (CRUs) are under tight local control by Ca(2+) entry, whereas medullar CRUs as a "common pool" system are recruited by inwardly propagating CICR. Active CRUs often displayed repetitive Ca(2+) sparks, conferring the ability to encode a "memory" of neuronal activity well beyond the duration of an action potential. Store Ca(2+) reserve was able to support all CRUs each to fire approximately 15 sparks, excluding use-dependent inactivation or store depletion as the major CICR termination mechanism. Importantly, CICR in DRG neurons operated in a low gain, linear regime (gain = 0.54), which conferred intrinsic stability to CICR. Combined with high Ca(2+) current density (-156 pA/pF at -10 mV), such a low gain CICR system generated large intracellular Ca(2+) transients without jeopardizing the stability. These findings provide the first demonstration that CICR operating in a low gain regime can be harnessed to provide a robust and graded amplification of Ca(2+) signal in the absence of counteracting inhibitory mechanism.     

Differential Ca2+ and Sr2+ regulation of intracellular divalent cations release in ventricular myocytes

The regulation of the Ca2+ -induced Ca2+ release (CICR) from intracellular stores is a critical step in the cardiac cycle. The inherent positive feedback of CICR should make it a self-regenerating process. It is accepted that CICR must be governed by some negative control, but its nature is still debated. We explore here the importance of the Ca2+ released from sarcoplasmic reticulum (SR) on the mechanisms that may control CICR. Specifically, we compared the effect of replacing Ca2+ with Sr2+ on intracellular Ca2+ signaling in intact cardiac myocytes as well as on the function of single ryanodine receptor (RyR) Ca2+ release channels in panar bilayers. In cells, both CICR and Sr2+ -induced Sr2+ release (SISR) were observed. Action potential induced Ca2+ -transients and spontaneous Ca2+ waves were considerably faster than their Sr2+ -mediated counterparts. However, the kinetics of Ca2+ and Sr2+ sparks was similar. At the single RyR channel level, the affinities of Ca2+ and Sr2+ activation were different but the affinities of Ca2+ and Sr2+ inactivation were similar. Fast Ca2+ and Sr2+ stimuli activated RyR channels equally fast but adaptation (a spontaneous slow transition back to steady-state activity levels) was not observed in the Sr2+ case. Together, these results suggest that regulation of the RyR channel by cytosolic Ca2+ is not involved in turning off the Ca2+ spark. In contrast, cytosolic Ca2+ is important in the propagation global Ca2+ release events and in this regard single RyR channel sensitivity to cytosolic Ca2+ activation, not low-affinity cytosolic Ca2+ inactivation, is a key factor. This suggests that the kinetics of local and global RyR-mediated Ca2+ release signals are affected in a distinct way by different divalent cations in cardiac muscle cells.     

Modeling gain and gradedness of Ca2+ release in the functional unit of the cardiac diadic space.

A model of the functional release unit (FRU) in rat cardiac muscle consisting of one dihydropyridine receptor (DHPR) and eight ryanodine receptor (RyR) channels, and the volume surrounding them, is formulated. It is assumed that no spatial [Ca2+] gradients exist in this volume, and that each FRU acts independently. The model is amenable to systematic parameter studies in which FRU dynamics are simulated at the channel level using Monte Carlo methods with Ca2+ concentrations simulated by numerical integration of a coupled system of differential equations. Using stochastic methods, Ca(2+)-induced Ca2+ release (CICR) shows both high gain and graded Ca2+ release that is robust when parameters are varied. For a single DHPR opening, the resulting RyR Ca2+ release flux is insensitive to the DHPR open duration, and is determined principally by local sarcoplasmic reticulum (SR) Ca2+ load, consistent with experimental data on Ca2+ sparks. In addition, single RyR openings are effective in triggering Ca2+ release from adjacent RyRs only when open duration is long and SR Ca2+ load is high. This indicates relatively low coupling between RyRs, and suggests a mechanism that limits the regenerative spread of RyR openings. The results also suggest that adaptation plays an important modulatory role in shaping Ca2+ release duration and magnitude, but is not solely responsible for terminating Ca2+ release. Results obtained with the stochastic model suggest that high gain and gradedness can occur by the recruitment of independent FRUs without requiring spatial [Ca2+] gradients within a functional unit or cross-coupling between adjacent functional units.     

Termination of cardiac Ca(2+) sparks: an investigative mathematical model of calcium-induced calcium release

A Ca(2+) spark arises when a cluster of sarcoplasmic reticulum (SR) channels (ryanodine receptors or RyRs) opens to release calcium in a locally regenerative manner. Normally triggered by Ca(2+) influx across the sarcolemmal or transverse tubule membrane neighboring the cluster, the Ca(2+) spark has been shown to be the elementary Ca(2+) signaling event of excitation-contraction coupling in heart muscle. However, the question of how the Ca(2+) spark terminates remains a central, unresolved issue. Here we present a new model, "sticky cluster," of SR Ca(2+) release that simulates Ca(2+) spark behavior and enables robust Ca(2+) spark termination. Two newly documented features of RyR behavior have been incorporated in this otherwise simple model: "coupled gating" and an opening rate that depends on SR lumenal [Ca(2+)]. Using a Monte Carlo method, local Ca(2+)-induced Ca(2+) release from clusters containing between 10 and 100 RyRs is modeled. After release is triggered, Ca(2+) flux from RyRs diffuses into the cytosol and binds to intracellular buffers and the fluorescent Ca(2+) indicator fluo-3 to produce the model Ca(2+) spark. Ca(2+) sparks generated by the sticky cluster model resemble those observed experimentally, and Ca(2+) spark duration and amplitude are largely insensitive to the number of RyRs in a cluster. As expected from heart cell investigation, the spontaneous Ca(2+) spark rate in the model increases with elevated cytosolic or SR lumenal [Ca(2+)]. Furthermore, reduction of RyR coupling leads to prolonged model Ca(2+) sparks just as treatment with FK506 lengthens Ca(2+) sparks in heart cells. This new model of Ca(2+) spark behavior provides a "proof of principle" test of a new hypothesis for Ca(2+) spark termination and reproduces critical features of Ca(2+) sparks observed experimentally.     

Size Matters: Ryanodine Receptor Cluster Size Heterogeneity Potentiates Calcium Waves

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