In silico simulations reveal that RYR distribution affects the dynamics of calcium release in cardiac myocytes

The dyads of cardiac myocytes contain ryanodine receptors (RYRs) that generate calcium sparks upon activation. To test how geometric factors of RYR distribution contribute to the formation of calcium sparks, which cannot be addressed experimentally, we performed in silico simulations on a large set of models of calcium release sites (CRSs). Our models covered the observed range of RYR number, density, and spatial arrangement. The calcium release function of CRSs was modeled by RYR openings, with an open probability dependent on concentrations of free Ca²⁺ and Mg²⁺ ions, in a rapidly buffered system, with a constant open RYR calcium current. We found that simulations of spontaneous sparks by repeatedly opening one of the RYRs in a CRS produced three different types of calcium release events (CREs) in any of the models. Transformation of simulated CREs into fluorescence signals yielded calcium sparks with characteristics close to the observed ones. CRE occurrence varied broadly with the spatial distribution of RYRs in the CRS but did not consistently correlate with RYR number, surface density, or calcium current. However, it correlated with RYR coupling strength, defined as the weighted product of RYR vicinity and calcium current, so that CRE characteristics of all models followed the same state-response function. This finding revealed the synergy between structure and function of CRSs in shaping dyad function. Lastly, rearrangements of RYRs simulating hypothetical experiments on splitting and compaction of a dyad revealed an increased propensity to generate spontaneous sparks and an overall increase in calcium release in smaller and more compact dyads, thus underlying the importance and physiological role of RYR arrangement in cardiac myocytes.     

心肌细胞的钙致钙释放

心肌细胞兴奋－收缩偶联由胞内钙变中介和调控。去极化进进入细胞的少量钙通过钙下释放（ＣＩＣＲ）过程发肌质多（ＳＲ）释放更多的钙,使胞浆钙浓度升高,导致收缩近年来证明,ＳＲ钙放呈梯级特征,提出了局部控制模型,以解释这种现象。钙火花的发现,直观地证硒钙释放单位的存在,进一步支持了局部控制模型。此外,钙释放通道的适应现象,可能是ＣＩＣＲ这一正反馈过程的负调节机制。     

Activation of calcium release assessed by calcium release-induced inactivation of calcium current in rat cardiac myocytes

In mammalian cardiac myocytes, calcium released into the dyadic space rapidly inactivates calcium current (I_Ca). We used this Ca²⁺ release-dependent inactivation (RDI) of I_Ca as a local probe of sarcoplasmic reticulum Ca²⁺ release activation. In whole cell patch-clamped rat ventricular myocytes, Ca²⁺ entry induced by short prepulses from —50 mV to positive voltages caused suppression of peak I_Ca during a test pulse. The negative correlation between peak I_Ca suppression and I_Ca inactivation during the test pulse indicated that RDI evoked by the prepulse affected only calcium channels in those dyads in which calcium release was activated. Ca²⁺ ions injected during the prepulse and during the subsequent tail current suppressed peak I_Ca in the test pulse to a different extent. Quantitative analysis indicated that equal Ca²⁺ charge was 3.5 times less effective in inducing release when entering during the prepulse than when entering during the tail. Tail Ca²⁺ charge injected by the first voltage-dependent calcium channel (DHPR) openings was three times less effective than that injected by DHPR reopenings. These findings suggest that calcium release activation can be profoundly influenced by the recent history of L-type Ca²⁺ channel activity due to potentiation of ryanodine receptors (RyRs) by previous calcium influx. This conclusion was confirmed at the level of single RyRs in planar lipid bilayers: using flash photolysis of the calcium cage NP-EGTA to generate two sequential calcium stimuli, we showed that RyR activation in response to the second stimulus was four times higher than that in response to the first stimulus. excitation-contraction coupling     

A mathematical model of spontaneous calcium release in cardiac myocytes

In cardiac myocytes, calcium (Ca) can be released from the sarcoplasmic reticulum independently of Ca influx from voltage-dependent membrane channels. This efflux of Ca, referred to as spontaneous Ca release (SCR), is due to Ryanodine receptor fluctuations, which can induce spontaneous Ca sparks, which propagate to form Ca waves. This release of Ca can then induce delayed after-depolarizations (DADs), which can lead to arrhythmogenic-triggered activity in the heart. However, despite its importance, to date there is no mathematical model of SCR that accounts for experimentally observed features of subcellular Ca. In this article, we present an experimentally based model of SCR that reproduces the timing distribution of spontaneous Ca sparks and key features of the propagation of Ca waves emanating from these spontaneous sparks. We have coupled this model to an ionic model for the rabbit ventricular action potential to simulate SCR within several thousand cells in cardiac tissue. We implement this model to study the formation of an ectopic beat on a cable of cells that exhibit SCR-induced DADs.     

Polyunsaturated dietary fats change the properties of calcium sparks in adult rat atrial myocytes

This study investigated the effects of dietary omega-3 polyunsaturated fatty acids on calcium handling mechanisms in cardiac myocytes, with the hypothesis that this effect underlies some of the antiarrhythmic properties of these compounds. Adult male Sprague Dawley rats had their standard chow supplemented with either lard (57% saturated and 40% monounsaturated fat), canola oil (60% monounsaturated, 33% polyunsaturated) or fish oil (78% polyunsaturated). Isolated cardiac atrial myocytes from these animals were loaded with fluo-3AM and examined with laser scanning confocal microscopy. The dietary interventions resulted in considerable changes in the membrane phospholipid composition of cardiac cell membranes, particularly the ratio of n-6 to n-3 (2.17 with lard supplement and 1.28 with fish oil supplement). Calcium sparks in myocytes from rats which received saturated fat were significantly more prolonged than those from rats which received fish oil. (Lard = 105.4 +/- 18.9 ms; Fish oil = 43.5 +/- 4.7 ms: mean +/- s.e.m). The results for canola oil were intermediate (56.4 +/- 9.0 ms). The prolongation of the sparks in rats fed lard was primarily due to a higher proportion of sparks with long plateaus and/or slowed kinetics in this group. The frequency of sparks was not significantly different in cells from any group. We conclude that calcium handling mechanisms in rat atrial myocytes are affected by inclusion of different fats in the diet, correlated with changes in the cell membrane phospholipid composition, and speculate that this may underlie some of the antiarrhythmic properties of these dietary compounds.     

Modification of cardiac RYR2 gating by a peptide from the central domain of the RYR2

The effect of a domain peptide DP_CPVTc from the central region of the RYR2 on ryanodine receptors from rat heart has been examined in planar lipid bilayers. At a zero holding potential and at 8 mmol L^?1 luminal Ca²⁺ concentration, DP_CPVTc induced concentrationdependent activation of the ryanodine receptor that led up to 20-fold increase of P_O at saturating DP_CPVTc concentrations. DP_CPVTc prolonged RyR2 openings and increased RyR2 opening frequency. At all peptide concentrations the channels displayed large variability in open probability, open time and frequency of openings. With increasing peptide concentration, the fraction of high open probability records increased together with their open time. The closed times of neither low- nor high-open probability records depended on peptide concentration. The concentration dependence of all gating parameters had EC₅₀ of 20 μmol L^?1 and a Hill slope of 2. Comparison of the effects of DP_CPVTc with the effects of ATP and cytosolic Ca²⁺ suggests that activation does not involve luminal feed-through and is not caused by modulation of the cytosolic activation A-site. The data suggest that although “domain unzipping” by DP_CPVTc occurs in both modes of RyR activity, it affects RyR gating only when the channel resides in the H-mode of activity.     

Effect of platelet release products on cytosolic calcium in cardiac myocytes

The effect of platelet release products on cytosolic calcium [( Ca++]i) was examined by monitoring the fluorescence of chick embryonic heart cells loaded with the fluorescent calcium indicator indo-1 AM. Cell free filtrate of platelet release products was obtained from rabbit platelets activated with thrombin or collagen. This filtrate caused a rapid increase in both systolic and diastolic [Ca++]i in a dose-dependent manner. The effect was not blocked by pretreating the platelets with aspirin or a thromboxane synthetase inhibitor. It was not mimicked by a thromboxane analog, or by several substances known to be released from platelets including ADP, serotonin, or platelet activating factor. Apyrase or ATP-gamma S had no effect on the activity. The responsible product was heat-sensitive, trypsin-sensitive, and partitioned into the aqueous phase of a chloroform suspension. It has a low molecular weight (less than 3kD) and is sensitive to 2-mercaptoethanol. Protease inhibitor appears to prolong the activity. These results suggest that trypsin-sensitive peptide(s) released from activated platelets can increase [Ca++]i in cardiac cells.     

Modulation of sarcoplasmic reticulum calcium release by calsequestrin in cardiac myocytes

Calsequestrin (CASQ2) is a high capacity Ca-binding protein expressed inside the sarcoplasmic reticulum (SR). Mutations in the cardiac calsequestrin gene (CASQ2) have been linked to arrhythmias and sudden death induced by exercise and emotional stress. We have studied the function of CASQ2 and the consequences of arrhythmogenic CASQ2 mutations on intracellular Ca signalling using a combination of approaches of reverse genetics and cellular physiology in adult cardiac myocytes. We have found that CASQ2 is an essential determinant of the ability of the SR to store and release Ca2+ in cardiac muscle. CASQ2 serves as a reservoir for Ca2+ that is readily accessible for Ca(2+)-induced Ca2+ release (CICR) and also as an active Ca2+ buffer that modulates the local luminal Ca-dependent closure of the SR Ca2+ release channels. At the same time, CASQ2 stabilizes the CICR process by slowing the functional recharging of SR Ca2+ stores. Abnormal restitution of the Ca2+ release channels from a luminal Ca-dependent refractory state could account for ventricular arrhythmias associated with mutations in the CASQ2 gene.     

Multidimensional detection and analysis of Ca2+ sparks in cardiac myocytes

Examining calcium spark morphology and its relationship to the structure of the cardiac myocyte offers a direct means of understanding excitation-contraction coupling mechanisms. Traditional confocal line scanning achieves excellent temporal spark resolution but at the cost of spatial information in the perpendicular dimension. To address this, we developed a methodology to identify and analyze sparks obtained via two-dimensional confocal or charge-coupled device microscopy. The technique consists of nonlinearly subtracting the background fluorescence, thresholding the data on the basis of noise level, and then localizing the spark peaks via a generalized extrema test, while taking care to detect and separate adjacent peaks. In this article, we describe the algorithm, compare its performance to a previously validated spark detection algorithm, and demonstrate it by applying it to both a synthetic replica and an experimental preparation of a two-dimensional isotropic myocyte monolayer exhibiting sparks during a calcium transient. We find that our multidimensional algorithm provides better sensitivity than the conventional method under conditions of temporally heterogeneous background fluorescence, and the inclusion of peak segmentation reduces false negative rates when spark density is high. Our algorithm is robust and can be effectively used with different imaging modalities and allows spark identification and quantification in subcellular, cellular, and tissue preparations.     

A probability density approach to modeling local control of calcium-induced calcium release in cardiac myocytes

We present a probability density approach to modeling localized Ca2+ influx via L-type Ca2+ channels and Ca2+-induced Ca2+ release mediated by clusters of ryanodine receptors during excitation-contraction coupling in cardiac myocytes. Coupled advection-reaction equations are derived relating the time-dependent probability density of subsarcolemmal subspace and junctional sarcoplasmic reticulum [Ca2+] conditioned on "Ca2+ release unit" state. When these equations are solved numerically using a high-resolution finite difference scheme and the resulting probability densities are coupled to ordinary differential equations for the bulk myoplasmic and sarcoplasmic reticulum [Ca2+], a realistic but minimal model of cardiac excitation-contraction coupling is produced. Modeling Ca2+ release unit activity using this probability density approach avoids the computationally demanding task of resolving spatial aspects of global Ca2+ signaling, while accurately representing heterogeneous local Ca2+ signals in a population of diadic subspaces and junctional sarcoplasmic reticulum depletion domains. The probability density approach is validated for a physiologically realistic number of Ca2+ release units and benchmarked for computational efficiency by comparison to traditional Monte Carlo simulations. In simulated voltage-clamp protocols, both the probability density and Monte Carlo approaches to modeling local control of excitation-contraction coupling produce high-gain Ca2+ release that is graded with changes in membrane potential, a phenomenon not exhibited by so-called "common pool" models. However, a probability density calculation can be significantly faster than the corresponding Monte Carlo simulation, especially when cellular parameters are such that diadic subspace [Ca2+] is in quasistatic equilibrium with junctional sarcoplasmic reticulum [Ca2+] and, consequently, univariate rather than multivariate probability densities may be employed.     

Nonlinear propagation of spherical calcium waves in rat cardiac myocytes.

Spontaneous calcium waves in enzymatically isolated rat cardiac myocytes were investigated by confocal laser scanning microscopy (CLSM) using the fluorescent Ca2+-indicator fluo-3 AM. As recently shown, a spreading wave of enhanced cytosolic calcium appears, most probably during Ca2+ overload, and is initiated by an elementary event called a "calcium spark." When measured by conventional fluorescence microscopy the propagation velocity of spontaneous calcium waves determined at several points along the cardiac myocyte was previously found to be constant. More precise measurements with a CLSM showed a nonlinear propagation. The wave velocity was low, close to the focus, and increased with increasing time and propagation length, approaching a maximum of 113 microns/s. This result was surprising, inasmuch as for geometrical reasons a decrease of the propagation velocity might be expected if the confocal plane is not identical with that plane where the focus of the wave was localized. It is suggested that the propagation velocity is essentially dependent on the curvature of the spreading wave. From the linear relationship of velocity versus curvature, a critical radius of 2.7 +/- 1.4 microns (mean +/- SD) was worked out, below which an outward propagation of the wave will not take place. Once released from a sufficiently extended cluster of sarcoplasmic reticulum release channels, calcium diffuses and will activate its neighbors. While traveling away, the volume into which calcium diffuses becomes effectively smaller than at low radii. This effect is the consequence of the summation of elementary events (Ca2+ sparks) and leads to a steeper increase of the cytosolic calcium concentration after a certain diffusion path length. Thus the time taken to reach a critical threshold of [Ca2+]i at the neighboring calcium release sites decreases with decreasing curvature and the wave will propagate faster.     

Cyclic ADP-ribose and the regulation of calcium-induced calcium release in eggs and cardiac myocytes

Cyclic ADP-ribose (cADPR) is a cyclic metabolite of NAD⁺ synthesised in cells and tissues expressing ADP-ribosyl cyclases. Although it was first discovered in sea-urchin egg extracts as a potent calcium mobilizing agent, subsequent studies have indicated that it may have a widespread action in the activation of calcium-release channels in such diverse systems as mammalian neurones, myocytes, blood cells, eggs, and plant microsomes. In this review we focus on recent work suggesting that cADPR enhances the sensitivity of ryanodine-sensitive calcium-release channels (RyRs) to activation by calcium, a phenomenon termed calcium-induced calcium release (CICR). Two roles for cADPR in calcium signaling are discussed. The first is as a classical second messenger where its levels are controlled by extracellular stimuli, and the second mode of cellular regulation is that the levels of intracellular cADPR may set the sensitivity of RyRs to activation by an influx of calcium in excitable cells. These two possible actions of cADPR are illustrated by considering the signal transduction events during the fertilization of the sea-urchin egg and the modulation of CICR during excitation-coupling in isolated guinea-pig ventricular myocytes, respectively.     

Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release

Calcium ions are an important second messenger in living cells. Indeed calcium signals in the form of waves have been the subject of much recent experimental interest. It is now well established that these waves are composed of elementary stochastic release events (calcium puffs or sparks) from spatially localised calcium stores. The aim of this paper is to analyse how the stochastic nature of individual receptors within these stores combines to create stochastic behaviour on long time-scales that may ultimately lead to waves of activity in a spatially extended cell model. Techniques from asymptotic analysis and stochastic phase–plane analysis are used to show that a large cluster of receptor channels leads to a release probability with a sigmoidal dependence on calcium density. This release probability is incorporated into a computationally inexpensive model of calcium release based upon a stochastic generalisation of the fire-diffuse-fire (FDF) threshold model. Numerical simulations of the model in one and two dimensions (with stores arranged on both regular and disordered lattices) illustrate that stochastic calcium release leads to the spontaneous production of calcium sparks that may merge to form saltatory waves. Illustrations of spreading circular waves, spirals and more irregular waves are presented. Furthermore, receptor noise is shown to generate a form of array enhanced coherence resonance whereby all calcium stores release periodically and simultaneously.     

Moment closure for local control models of calcium-induced calcium release in cardiac myocytes

In prior work, we introduced a probability density approach to modeling local control of Ca²⁺-induced Ca²⁺ release in cardiac myocytes, where we derived coupled advection-reaction equations for the time-dependent bivariate probability density of subsarcolemmal subspace and junctional sarcoplasmic reticulum (SR) [Ca²⁺] conditioned on Ca²⁺ release unit (CaRU) state. When coupled to ordinary differential equations (ODEs) for the bulk myoplasmic and network SR [Ca²⁺], a realistic but minimal model of cardiac excitation-contraction coupling was produced that avoids the computationally demanding task of resolving spatial aspects of global Ca²⁺ signaling, while accurately representing heterogeneous local Ca²⁺ signals in a population of diadic subspaces and junctional SR depletion domains. Here we introduce a computationally efficient method for simulating such whole cell models when the dynamics of subspace [Ca²⁺] are much faster than those of junctional SR [Ca²⁺]. The method begins with the derivation of a system of ODEs describing the time-evolution of the moments of the univariate probability density functions for junctional SR [Ca²⁺] jointly distributed with CaRU state. This open system of ODEs is then closed using an algebraic relationship that expresses the third moment of junctional SR [Ca²⁺] in terms of the first and second moments. In simulated voltage-clamp protocols using 12-state CaRUs that respond to the dynamics of both subspace and junctional SR [Ca²⁺], this moment-closure approach to simulating local control of excitation-contraction coupling produces high-gain Ca²⁺ release that is graded with changes in membrane potential, a phenomenon not exhibited by common pool models. Benchmark simulations indicate that the moment-closure approach is nearly 10,000-times more computationally efficient than corresponding Monte Carlo simulations while leading to nearly identical results. We conclude by applying the moment-closure approach to study the restitution of Ca²⁺-induced Ca²⁺ release during simulated two-pulse voltage-clamp protocols.     

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.     

A simplified local control model of calcium-induced calcium release in cardiac ventricular myocytes

Calcium (Ca2+)-induced Ca2+ release (CICR) in cardiac myocytes exhibits high gain and is graded. These properties result from local control of Ca2+ release. Existing local control models of Ca2+ release in which interactions between L-Type Ca2+ channels (LCCs) and ryanodine-sensitive Ca2+ release channels (RyRs) are simulated stochastically are able to reconstruct these properties, but only at high computational cost. Here we present a general analytical approach for deriving simplified models of local control of CICR, consisting of low-dimensional systems of coupled ordinary differential equations, from these more complex local control models in which LCC-RyR interactions are simulated stochastically. The resulting model, referred to as the coupled LCC-RyR gating model, successfully reproduces a range of experimental data, including L-Type Ca2+ current in response to voltage-clamp stimuli, inactivation of LCC current with and without Ca2+ release from the sarcoplasmic reticulum, voltage-dependence of excitation-contraction coupling gain, graded release, and the force-frequency relationship. The model does so with low computational cost.     

牛磺酸对大鼠心肌细胞内钙浓度的影响

牛磺酸 (Ｔａｕｒｉｎｅ ,Ｔａｕ)是可兴奋组织中含量最为丰富的游离氨基酸 ,是细胞自稳态的重要调节物质。在多种心血管疾病的临床与实验研究中具有明显的细胞保护作用。其作用机制与调节心肌细胞的钙浓度有关。用同位素示踪技术已证实Ｔａｕ在细胞内“高钙”状态下能抑制钙的跨膜内流。本文采用Ｆｕｒａ 2荧光技术测定Ｔａｕ对成年大鼠分离心肌细胞在静息、高钾去极化以及缺氧 /复氧条件下游离 [Ｃａ ]ｉ,旨在进一步探讨Ｔａｕ的作用机制。1　材料与方法(1)动物实验　雄性Ｗｉｓｔａｒ大鼠 (军事医学科学院四所提供 )。 2 0 %乌拉坦ｉｐ…     

Velocity-curvature relationship of colliding spherical calcium waves in rat cardiac myocytes.

Colliding spherical calcium waves in enzymatically isolated rat cardiac myocytes develop new wavefronts propagating perpendicular to the original direction. When investigated by confocal laser scanning microscopy (CLSM), using the fluorescent Ca2+ indicator fluo-3 AM, "cusp"-like structures become visible that are favorably approximated by double parabolae. The time-dependent position of the vertices is used to determine propagation velocity and negative curvature of the wavefront in the region of collision. It is evident that negatively curved waves propagate faster than positively curved, single waves. Considering two perfectly equal expanding circular waves, we demonstrated that the collision of calcium waves is due to an autocatalytic process (calcium-induced calcium release), and not to a simple phenomenon of interference. Following the spatiotemporal organization in simpler chemical systems maintained under conditions far from the thermodynamic equilibrium (Belousov-Zhabotinskii reaction), the dependence of the normal velocity on the curvature of the spreading wavefront is given by a linear relation. The so-called velocity-curvature relationship makes clear that the velocity is enhanced by curvature toward the direction of forward propagation and decreased by curvature away from the direction of forward propagation (with an influence of the diffusion coefficient). Experimentally obtained velocity data of both negatively and positively curved calcium waves were approximated by orthogonal weighted regression. The negative slope of the straight line resulted in an effective diffusion coefficient of 1.2 x 10(-4) mm2/s. From the so-called critical radius, which must be exceeded to initiate a traveling calcium wave, a critical volume (with enhanced [Ca2+]i) of approximately 12 microm3 was calculated. This is almost identical to the volume that is occupied by a single calcium spark.