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.     

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.     

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.     

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。     

Model of calcium-induced calcium release mechanism in cardiac cells

A model with which to elucidate the mechanism of Ca²⁺ release from, and Ca²⁺ loading in the sarcoplasmic reticulum (SR) by Ca²⁺ current (I _Ca) in cardiac cells is proposed. The SR is assumed to be comprised of three functional subcompartments: (1) the main calcium store (MCS), which contains most of the calcium (both free and bound); (2) the releasable terminal (RT), which contains the calcium readily available for release; and (3) the longitudinal network of the SR (LSR), which sequesters and the transfers the sarcoplasmic calcium to the RT. A rapid increase of the Ca²⁺ concentration at the outer surface of the SR (Ca_e) due to the fast component ofI _Ca activates and inactivates this surface, inducing the release of Ca²⁺ from the RT to the sarcoplasmic space. The RT in turn is further activated and inactivated by a increase in the concentration of sarcoplasmic Ca²⁺. The Ca²⁺ in the sarcoplasmic space is then sequestered by the LSR, leading to the reactivation of the RT. Further increase of Ca_e due to the slow component ofI _Ca enhances the entry of Ca²⁺ into the MCS to be bound by the binding substance. The free Ca²⁺ released from the Ca-binding substance complex is transferred to the RT for subsequent release. The activation, inactivation and reactivation are Ca²⁺-mediated and time-dependent. The proposed model yields simulation of the many events qualitatively similar to those observed experimentally in skinned cardiac cells.     

Multi-scale models of local control of calcium induced calcium release

Calcium-induced-calcium-release in cardiac myocytes is the release of Ca(2+) from the sarcoplasmic reticulum (SR) triggered by Ca(2+) entering the cell through L-type Ca(2+) channels. The Ca(2+) is released through ryanodine receptors which 'sense' local [Ca(2+)] in the small region (the diadic space) positioned between the t-tubules and the SR. The length-scale of a single diad is of the order of 10nm and the diffusion time-scale is of order of 1 micros with each cell containing approximately 10,000 diadic spaces which act independently. However, typically one is interested in Ca(2+) currents at the whole cell level and higher. This is a multi-scale problem and cannot be solved by direct computation. In this paper we develop a general framework for deriving approximate solutions of these models.     

Kinetic studies of calcium-induced calcium release in cardiac sarcoplasmic reticulum vesicles

Fast Ca(2+) release kinetics were measured in cardiac sarcoplasmic reticulum vesicles actively loaded with Ca(2+). Release was induced in solutions containing 1.2 mM free ATP and variable free [Ca(2+)] and [Mg(2+)]. Release rate constants (k) were 10-fold higher at pCa 6 than at pCa 5 whereas Ryanodine binding was highest at pCa < or =5. These results suggest that channels respond differently when exposed to sudden [Ca(2+)] changes than when exposed to Ca(2+) for longer periods. Vesicles with severalfold different luminal calcium contents exhibited double exponential release kinetics at pCa 6, suggesting that channels undergo time-dependent activity changes. Addition of Mg(2+) produced a marked inhibition of release kinetics at pCa 6 (K(0.5) = 63 microM) but not at pCa 5. Coexistence of calcium activation and inhibition sites with equally fast binding kinetics is proposed to explain this behavior. Thimerosal activated release kinetics at pCa 5 at all [Mg(2+)] tested and increased at pCa 6 the K(0.5) for Mg(2+) inhibition, from 63 microM to 136 microM. We discuss the possible relevance of these results, which suggest release through RyR2 channels is subject to fast regulation by Ca(2+) and Mg(2+) followed by time-dependent regulation, to the physiological mechanisms of cardiac channel opening and closing.     

Decreased expression of ryanodine receptors alters calcium-induced calcium release mechanism in mdx duodenal myocytes

It is generally believed that alterations of calcium homeostasis play a key role in skeletal muscle atrophy and degeneration observed in Duchenne's muscular dystrophy and mdx mice. Mechanical activity is also impaired in gastrointestinal muscles, but the cellular and molecular mechanisms of this pathological state have not yet been investigated. We showed, in mdx duodenal myocytes, that both caffeine- and depolarization-induced calcium responses were inhibited, whereas acetylcholine- and thapsigargin-induced calcium responses were not significantly affected compared with control mice. Calcium-induced calcium release efficiency was impaired in mdx duodenal myocytes depending only on inhibition of ryanodine receptor expression. Duodenal myocytes expressed both type 2 and type 3 ryanodine receptors and were unable to produce calcium sparks. In control and mdx duodenal myocytes, both caffeine- and depolarization-induced calcium responses were dose-dependently and specifically inhibited with the anti-type 2 ryanodine receptor antibody. A strong inhibition of type 2 ryanodine receptor in mdx duodenal myocytes was observed on the mRNA as well as on the protein level. Taken together, our results suggest that inhibition of type 2 ryanodine receptor expression in mdx duodenal myocytes may account for the decreased calcium release from the sarcoplasmic reticulum and reduced mechanical activity.     

Analysis of calcium-induced calcium release in cardiac sarcoplasmic reticulum vesicles using models derived from single-channel data.

The planar lipid bilayer and vesicle release experiments are two alternative approaches used to study the function of the ryanodine receptor (RyR) channel at the subcellular level. In this work, we combine models of gating (Zahradníková and Zahradník, Biophys. J. 71 (1996) 2996-3012) and permeation (Tinker et al., J. Gen. Physiol. 100 (1992) 495-517) of the cardiac RyR channel to simulate calcium release experiments on sarcoplasmic reticulum vesicles. The resulting model and real experimental data agreed well within the experimental scatter, confirming indistinguishable properties of the RyRC in the vesicle preparation and in the planar lipid bilayer. The previously observed differences in calcium dependencies of the release and the gating processes can be explained by binding of calcium within the RyRC conducting pore. A novel method of analysis of calcium dependence of calcium release was developed and tested. Three gating models of the RyRC, showing, respectively, an increase, no change, and a decrease in calcium sensitivity over time, were compared. The described method of analysis enabled determination of temporal changes in calcium sensitivity, giving potential for detection of the adaptation/inactivation phenomena of the RyRC in both vesicle and in situ release experiments.     

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.     

Fura-2 antagonises calcium-induced calcium release

Calcium-induced calcium release (CICR) from the endoplasmic reticulum (ER) takes place through ryanodine receptors (RyRs) and it is often revealed by an increase of the cytosolic Ca(2+) concentration ([Ca(2+)](c)) induced by caffeine. Using fura-2-loaded cells, we find such an effect in bovine adrenal chromaffin cells, but not in cerebellar granule neurones or in HEK-293 cells. In contrast, a caffeine-induced [Ca(2+)](c) increase was clearly visible with either fluo-3 or cytosolic aequorin. Simultaneous loading with fura-2 prevented the [Ca(2+)](c) increase reported by the other Ca(2+) probes. Caffeine-induced Ca(2+) release was also measured by following changes of [Ca(2+)] inside the ER ([Ca(2+)](ER)) with ER-targeted aequorin in HEK-293 cells. Fura-2 loading did not modify Ca(2+) release from the ER. Thus, fura-2, but not fluo-3, antagonises the generation of the cytosolic Ca(2+) signal induced by activation of RyRs. Cytosolic Ca(2+) buffering and/or acceleration of Ca(2+) diffusion through the cytosol may contribute to these actions. Both effects may interfere with the generation of microdomains of high [Ca(2+)](c) near the ER release channels, which are essential for the propagation of the Ca(2+) wave through the cytosol. In any case, our results caution the use of fura-2 to study CICR.     

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.     

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.     

Elevation of mitochondrial calcium by ryanodine-sensitive calcium-induced calcium release

Calcium is an important regulator of mitochondrial function. Since there can be tight coupling between inositol 1,4, 5-trisphosphate-sensitive Ca(2+) release and elevation of mitochondrial calcium concentration, we have investigated whether a similar relationship exists between the release of Ca(2+) from the ryanodine receptor and the elevation of mitochondrial Ca(2+). Perfusion of permeabilized A10 cells with inositol 1,4, 5-trisphosphate resulted in a large transient elevation of mitochondrial Ca(2+) to about 8 microm. The response was inhibited by heparin but not ryanodine. Perfusion of the cells with Ca(2+) buffers in excess of 1 microm leads to large increases in mitochondrial Ca(2+) that are much greater than the perfused Ca(2+). These increases, which average around 10 microm, are enhanced by caffeine and inhibited by ryanodine and depletion of the intracellular stores with either orthovanadate or thapsigargin. We conclude that Ca(2+)-induced Ca(2+) release at the ryanodine receptor generates microdomains of elevated Ca(2+) that are sensed by adjacent mitochondria. In addition to ryanodine-sensitive stores acting as a source of Ca(2+), Ca(2+)-induced Ca(2+) release is required to generate efficient elevation of mitochondrial Ca(2+).     

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     

Protein geometry and placement in the cardiac dyad influence macroscopic properties of calcium-induced calcium release

In cardiac ventricular myocytes, events crucial to excitation-contraction coupling take place in spatially restricted microdomains known as dyads. The movement and dynamics of calcium (Ca2+) ions in the dyad have often been described by assigning continuously valued Ca2+ concentrations to one or more dyadic compartments. However, even at its peak, the estimated number of free Ca2+ ions present in a single dyad is small (approximately 10-100 ions). This in turn suggests that modeling dyadic calcium dynamics using laws of mass action may be inappropriate. In this study, we develop a model of stochastic molecular signaling between L-type Ca2+ channels (LCCs) and ryanodine receptors (RyR2s) that describes: a), known features of dyad geometry, including the space-filling properties of key dyadic proteins; and b), movement of individual Ca2+ ions within the dyad, as driven by electrodiffusion. The model enables investigation of how local Ca2+ signaling is influenced by dyad structure, including the configuration of key proteins within the dyad, the location of Ca2+ binding sites, and membrane surface charges. Using this model, we demonstrate that LCC-RyR2 signaling is influenced by both the stochastic dynamics of Ca2+ ions in the dyad as well as the shape and relative positioning of dyad proteins. Results suggest the hypothesis that the relative placement and shape of the RyR2 proteins helps to "funnel" Ca2+ ions to RyR2 binding sites, thus increasing excitation-contraction coupling gain.     

The voltage-sensitive release mechanism of excitation contraction coupling in rabbit cardiac muscle is explained by calcium-induced calcium release

The putative voltage-sensitive release mechanism (VSRM) was investigated in rabbit cardiac myocytes at 37 degrees C with high resistance microelectrodes to minimize intracellular dialysis. When the holding potential was adjusted from -40 to -60 mV, the putative VSRM was expected to operate alongside CICR. Under these conditions however, we did not observe a plateau at positive potentials of the cell shortening versus voltage relationship. The threshold for cell shortening changed by -10 mV, but this resulted from a similar change of the threshold for activation of inward current. Cell shortening under conditions where the putative VSRM was expected to operate was blocked in a dose dependent way by nifedipine and CdCl2 and blocked completely by NiCl2. "Tail contractions" persisted in the presence of nifedipine and CdCl2 but were blocked completely by NiCl2. Block of early outward current by 4-aminopyridine and 4-acetoamido-4'-isothiocyanato-stilbene-2,2'-disulfonic acid (SITS) demonstrated persisting inward current during test depolarizations despite the presence of nifedipine and CdCl2. Inward current did not persist in the presence of NiCl2. A tonic component of cell shortening that was prominent during depolarizations to positive potentials under conditions selective for the putative VSRM was sensitive to rapidly applied changes in superfusate [Na+] and to the outward Na+/Ca2+ exchange current blocking drug KB-R7943. This component of cell shortening was thought to be the result of Na+/Ca2+ exchange-mediated excitation contraction coupling. Cell shortening recorded under conditions selective for the putative VSRM was increased by the enhanced state of phosphorylation induced by isoprenaline (1 microM) and by enhancing sarcoplasmic reticulum Ca2+ content by manipulation of the conditioning steps. Under these conditions, cell shortening at positive test depolarizations was converted from tonic to phasic. We conclude that the putative VSRM is explained by CICR with the Ca2+ "trigger" supplied by unblocked L-type Ca2+ channels and Na+/Ca2+ exchange.     

A calcium-induced calcium release mechanism mediated by calsequestrin

Calcium (Ca²⁺)-induced Ca²⁺ release (CICR) is widely accepted as the principal mechanism linking electrical excitation and mechanical contraction in cardiac cells. The CICR mechanism has been understood mainly based on binding of cytosolic Ca²⁺ with ryanodine receptors (RyRs) and inducing Ca²⁺ release from the sarcoplasmic reticulum (SR). However, recent experiments suggest that SR lumenal Ca²⁺ may also participate in regulating RyR gating through calsequestrin (CSQ), the SR lumenal Ca²⁺ buffer. We investigate how SR Ca²⁺ release via RyR is regulated by Ca²⁺ and calsequestrin (CSQ). First, a mathematical model of RyR kinetics is derived based on experimental evidence. We assume that the RyR has three binding sites, two cytosolic sites for Ca²⁺ activation and inactivation, and one SR lumenal site for CSQ binding. The open probability (P_o) of the RyR is found by simulation under controlled cytosolic and SR lumenal Ca²⁺. Both peak and steady-state P_o effectively increase as SR lumenal Ca²⁺ increases. Second, we incorporate the RyR model into a CICR model that has both a diadic space and the junctional SR (jSR). At low jSR Ca²⁺ loads, CSQs are more likely to bind with the RyR and act to inhibit jSR Ca²⁺ release, while at high SR loads CSQs are more likely to detach from the RyR, thereby increasing jSR Ca²⁺ release. Furthermore, this CICR model produces a nonlinear relationship between fractional jSR Ca²⁺ release and jSR load. These findings agree with experimental observations in lipid bilayers and cardiac myocytes.     

A model of propagating calcium-induced calcium release mediated by calcium diffusion

The effect of sudden local fluctuations of the free sarcoplasmic [Ca++]i in cardiac cells on calcium release and calcium uptake by the sarcoplasmic reticulum (SR) was calculated with the aid of a simplified model of SR calcium handling. The model was used to evaluate whether propagation of calcium transients and the range of propagation velocities observed experimentally (0.05-15 mm s(-1)) could be predicted. Calcium fluctuations propagate by virtue of focal calcium release from the SR, diffusion through the cytosol (which is modulated by binding to troponin and calmodulin and sequestration by the SR), and subsequently induce calcium release from adjacent release sites of the SR. The minimal and maximal velocities derived from the simulation were 0.09 and 15 mm s(-1) respectively. The method of solution involved writing the diffusion equation as a difference equation in the spatial coordinates. Thus, coupled ordinary differential equations in time with banded coefficients were generated. The coupled equations were solved using Gear's sixth order predictor-corrector algorithm for stiff equations with reflective boundaries. The most important determinants of the velocity of propagation of the calcium waves were the diastolic [Ca++]i, the rate of rise of the release, and the amount of calcium released from the SR. The results are consistent with the assumptions that calcium loading causes an increase in intracellular calcium and calcium in the SR, and an increase in the amount and rate of calcium released. These two effects combine to increase the propagation velocity at higher levels of calcium loading.