Number Of RyRs Research Articles

Live-cell photoactivated 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 photoactivated label on RyR2. This allowed correlative imaging of RyR localization, by super-resolution photoactivated localization microscopy, and Ca2+ sparks, by high-speed imaging. Two populations of Ca2+ sparks were observed: stationary events and ‘traveling’ events that spread between neighboring RyR clusters. Traveling sparks exhibited up to eight 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 intracluster RyR recruitment to generate larger events. In contrast, RyR ‘dispersion’ during heart failure facilitates the generation of traveling sparks. Thus, RyRs cooperatively generate Ca2+ sparks in a complex, malleable fashion, and channel organization regulates the propensity for local propagation of Ca2+ release.

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.

Reduced Ca Flux via Ryanodine Receptor Cluster Size or Unitary Current can both Promote Long-Lasting Ca Sparks

Calcium (Ca) sparks are fundamental E-C coupling events with typical duration of 10-50 ms. Long-lasting Ca release events, lasting >10 times longer than typical Ca sparks, have been observed experimentally when ryanodine receptors (RyRs) are partially blocked by tetracaine or ruthenium red (Zima et al., 2008 BJ & Circ Res). However, the mechanism of these events is not fully understood. Here, we use a physiologically detailed mathematical model of subcellular Ca cycling, and show how RyR cluster size (or ‘effective’ cluster size when RyRs are partially blocked) can affect long-lasting Ca release events. The single cluster contains a few to several hundred RyRs, and we use a 4-state Markov model of the RyR. Each RyR opens stochastically and is regulated by cytosolic and luminal Ca. The number of RyR channels in the cluster, diffusion within the SR network, diffusion between network and junctional SR, SERCA uptake rate and RyR open probability were varied. In order for long-lasting release events, opening events within the cluster must occur continuously since the typical open time of the RyR is only a few milliseconds. We found (1) if the number of RyRs is too small, it is difficult to keep 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) the involvement of moderate sized RyR clusters (∼8; or reduced flux/RyR) allows stable release flux lasting >500 ms, wherein local [Ca]SR can be maintained by intra-SR diffusion.

Calcium homeostasis in a local/global whole cell model of permeabilized ventricular myocytes with a Langevin description of stochastic calcium release.

Population density approaches to modeling local control of Ca(2+)-induced Ca(2+) release in cardiac myocytes can be used to construct minimal whole cell models that accurately represent heterogeneous local Ca(2+) signals. Unfortunately, the computational complexity of such "local/global" whole cell models scales with the number of Ca(2+) release unit (CaRU) states, which is a rapidly increasing function of the number of ryanodine receptors (RyRs) per CaRU. Here we present an alternative approach based on a Langevin description of the collective gating of RyRs coupled by local Ca(2+) concentration ([Ca(2+)]). The computational efficiency of this approach no longer depends on the number of RyRs per CaRU. When the RyR model is minimal, Langevin equations may be replaced by a single Fokker-Planck equation, yielding an extremely compact and efficient local/global whole cell model that reproduces and helps interpret recent experiments that investigate Ca(2+) homeostasis in permeabilized ventricular myocytes. Our calculations show that elevated myoplasmic [Ca(2+)] promotes elevated network sarcoplasmic reticulum (SR) [Ca(2+)] via SR Ca(2+)-ATPase-mediated Ca(2+) uptake. However, elevated myoplasmic [Ca(2+)] may also activate RyRs and promote stochastic SR Ca(2+) release, which can in turn decrease SR [Ca(2+)]. Increasing myoplasmic [Ca(2+)] results in an exponential increase in spark-mediated release and a linear increase in nonspark-mediated release, consistent with recent experiments. The model exhibits two steady-state release fluxes for the same network SR [Ca(2+)] depending on whether myoplasmic [Ca(2+)] is low or high. In the later case, spontaneous release decreases SR [Ca(2+)] in a manner that maintains robust Ca(2+) sparks.

Construction of Calcium Release Sites in Cardiac Myocytes

Local character of calcium release in cardiac myocytes, as defined by confocal recordings of calcium sparks, implies independent activation of individual calcium release sites based on ryanodine receptor (RyR) channel recruitment. We constructed virtual calcium release sites (vCRSs) composed of a variable number of RyR channels distributed in clusters in accordance with the experimentally observed cluster size distribution. The vCRSs consisted either of a single virtual calcium release unit (vCRU), in which all clusters shared a common dyadic space, or of multiple virtual calcium release units (CRUs) containing one cluster each and having separate dyadic spaces. We explored the stochastic behavior of vCRSs to understand the activation and recruitment of RyRs during calcium sparks. RyRs were represented by the published allosteric gating model that included regulation by cytosolic Ca2+ and Mg2+. The interaction of Mg2+ with the RyR Ca2+-binding sites and the refractory period of vCRSs were optimized to accord with the experimentally observed calcium dependence of calcium spark frequency. The Mg2+-binding parameters of RyRs that provided the best description of spark frequency depended on the number of RyRs assembled in the vCRSs. Adequate inhibitory effect of Mg2+ on the calcium dependence of RyR open probability was achieved if the vCRSs contained at least three clusters. For the distribution of the number of open RyRs in evoked calcium sparks to correspond to the experimentally observed distribution of spark calcium release fluxes, at least three clusters had to share a common virtual CRU, in which ∼3 RyRs open to form an average spark. These results reconcile the small cluster size and stochastic placement of RyRs in the release sites with the estimates of the amount of RyR protein, volume density of calcium release sites, and the size of calcium release sites in rat cardiac myocytes.

Parameter Sensitivity Analysis of a Stochastic Ca2+ Spark Model using Novel Computational Methods

Parameter sensitivity analysis is useful for identifying how changes in model parameters affect measurable model outputs. Stochastic models, however, require multiple simulations with each parameter change, which can make a comprehensive analysis extremely time-consuming. We developed a novel parameter sensitivity analysis method for stochastic models that involves randomly varying all parameters, running a single simulation with each set of parameters, and then statistically relating the random parameters to the simulation results using regression methods. We tested this method using an established stochastic Ca2+ spark model with 18 parameters. Results show that standard linear regression can successfully relate parameters to continuous model outputs such as spark amplitude and duration, and logistic regression can provide insight into how parameters affect Ca2+ spark triggering (a probabilistic process that is all-or-none in a single simulation). Benchmark studies demonstrate that the new method is less computationally intensive than standard methods by a factor of 6.6. Importantly, we tested model predictions with measurements of Ca2+ sparks in mice with knockout of the sarcoplasmic reticulum (SR) protein triadin. These mice exhibit a decrease in the number of RyRs per Ca2+ release unit, a decrease in junctional SR volume, and an increase in diastolic SR [Ca2+]. The regression model predicts that these changes cause a 30% decrease in Ca2+ spark amplitude, almost exactly matching the 29% decrease observed experimentally. Additionally, this analysis provides an intuitive and quantitative understanding of how much each alteration in the triadin knockout mouse contributes to the observed change in spark amplitude. This approach is therefore an effective, efficient and predictive method for analyzing stochastic mathematical models to gain biological insight.

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.

Relative effectiveness of two mathematical models of interpersonal contingency for the prediction of conventional measures of infant development

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.