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.     

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。     

Spontaneous channel activity of the inositol 1,4,5-trisphosphate (InsP3) receptor (InsP3R). Application of allosteric modeling to calcium and InsP3 regulation of InsP3R single-channel gating

The InsP3R Ca2+ release channel has a biphasic dependence on cytoplasmic free Ca2+ concentration ([Ca2+]i). InsP3 activates gating primarily by reducing the sensitivity of the channel to inhibition by high [Ca2+]i. To determine if relieving Ca2+ inhibition is sufficient for channel activation, we examined single-channel activities in low [Ca2+]i in the absence of InsP3, by patch clamping isolated Xenopus oocyte nuclei. For both endogenous Xenopus type 1 and recombinant rat type 3 InsP3R channels, spontaneous InsP3-independent channel activities with low open probability Po ( approximately 0.03) were observed in [Ca2+]i < 5 nM with the same frequency as in the presence of InsP3, whereas no activities were observed in 25 nM Ca2+. These results establish the half-maximal inhibitory [Ca2+]i of the channel to be 1.2-4.0 nM in the absence of InsP3, and demonstrate that the channel can be active when all of its ligand-binding sites (including InsP3) are unoccupied. In the simplest allosteric model that fits all observations in nuclear patch-clamp studies of [Ca2+]i and InsP3 regulation of steady-state channel gating behavior of types 1 and 3 InsP3R isoforms, including spontaneous InsP3-independent channel activities, the tetrameric channel can adopt six different conformations, the equilibria among which are controlled by two inhibitory and one activating Ca2+-binding and one InsP3-binding sites in a manner outlined in the Monod-Wyman-Changeux model. InsP3 binding activates gating by affecting the Ca2+ affinities of the high-affinity inhibitory sites in different conformations, transforming it into an activating site. Ca2+ inhibition of InsP3-liganded channels is mediated by an InsP3-independent low-affinity inhibitory site. The model also suggests that besides the ligand-regulated gating mechanism, the channel has a ligand-independent gating mechanism responsible for maximum channel Po being less than unity. The validity of this model was established by its successful quantitative prediction of channel behavior after it had been exposed to ultra-low bath [Ca2+].     

Altered elementary calcium release events and enhanced calcium release by thymol in rat skeletal muscle

The effects of thymol on steps of excitation-contraction coupling were studied on fast-twitch muscles of rodents. Thymol was found to increase the depolarization-induced release of calcium from the sarcoplasmic reticulum, which could not be attributed to a decreased calcium-dependent inactivation of calcium release channels/ryanodine receptors or altered intramembrane charge movement, but rather to a more efficient coupling of depolarization to channel opening. Thymol increased ryanodine binding to heavy sarcoplasmic reticulum vesicles, with a half-activating concentration of 144 micro M and a Hill coefficient of 1.89, and the open probability of the isolated and reconstituted ryanodine receptors, from 0.09 +/- 0.03 to 0.22 +/- 0.04 at 30 micro M. At higher concentrations the drug induced long-lasting open events on a full conducting state. Elementary calcium release events imaged using laser scanning confocal microscopy in the line-scan mode were reduced in size, 0.92 +/- 0.01 vs. 0.70 +/- 0.01, but increased in duration, 56 +/- 1 vs. 79 +/- 1 ms, by 30 micro M thymol, with an increase in the relative proportion of lone embers. Higher concentrations favored long events, resembling embers in control, with duration often exceeding 500 ms. These findings provide direct experimental evidence that the opening of a single release channel will generate an ember, rather than a spark, in mammalian skeletal muscle.     

InsP(3)-mediated calcium release induced by heterologous expression of total chicory Leaf RNA

A calcium dependent-chloride current (I(ni)) was recorded in Xenopus oocytes injected with total RNA from chicory leaf tissues, following depolarization from -35 to +60 mV. However, the signal transduction mechanism mediating I(ni) is unknown. The development of this current was mimicked by intracellular injection of the second messenger InsP(3) in control (non-injected) oocytes. Moreover, InsP(3) injection after I(ni) rundown did not reinitiate the current. The same phenomenon was observed following a second injection into control oocytes. Measurement of InsP(3) production in injected oocytes showed a net increase in the InsP(3) level on depolarization. Moreover, extracellular application of caffeine (5 mM) significantly reduced the number of oocytes displaying I(ni). Also, extracellular application of U-73122, a potent PLC inhibitor, clearly reduced the occurrence of I(ni). These data provide the first evidence that the calcium homeostasis mechanism induced by heterologous expression of total RNA from chicory leaves involves the InsP(3) signaling pathway.     

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.     

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     

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.     

Effects of ryanoids on spontaneous and depolarization-evoked calcium release events in frog muscle

The effects of ryanoids on calcium sparks and transients were studied in voltage-clamped cut frog muscle fibers with a laser scanning confocal microscope. For each ryanoid employed, several sequential effects were observed, including: a), transient increases in spontaneous spark frequency; b), conversions of sparks to long-lasting steady glows; and c), occasional interruptions of the glows. The ratio of the amplitude of the glow induced by a ryanoid to that of the precursory spark followed the order: ryanodol > ryanodine > C(10)-O(eq)-glycyl-ryanodine > C(10)-O(eq)-beta-alanyl-ryanodol. This sequence of glow amplitudes parallels that of the subconductances induced by these ryanoids in single-channel studies, suggesting that the glows reflect Ca(2+) fluxes through semiopen calcium release channels. Ryanoids also abolished depolarization-evoked sparks elicited with small pulses, and transformed the calcium release during depolarization to a uniform nonsparking fluorescence signal. The ratio of this signal, averaged spatially, to that of the control followed the order: ryanodol < ryanodine < C(10)-O(eq)-glycyl-ryanodine < C(10)-O(eq)-beta-alanyl-ryanodol, implying an inverse relationship with the amplitudes of ryanoid-induced glows. The observation that depolarization-evoked calcium release can occur after ryanoid suppression of calcium sparks suggests the possibility of a new strategic approach for treating skeletal muscle diseases resulting from leaky calcium release channels.     

Acetylcholine evokes an InsP3R1-dependent transient Ca2+ signal in rat duodenum myocytes

In smooth muscle myocytes, agonist-activated release of calcium ions (Ca2+) stored in the sarcoplasmic reticulum (SR) occurs via different but overlapping transduction pathways. Hence, to fully study how SR Ca2+ channels are activated, the simultaneous activation of different Ca2+ signals should be separated. In rat duodenum myocytes, we have previously characterized that acetylcholine (ACh) induces Ca2+ oscillations by binding to its M2 muscarinic receptor and activating the ryanodine receptor subtype 2. Here, we show that ACh simultaneously evokes a Ca2+ signal dependent on activation of inositol 1,4,5-trisphosphate (InsP3) receptor subtype 1. A pharmacologic approach, the use of antisense oligonucleotides directed against InsP3R1, and the expression of a specific biosensor derived from green-fluorescent protein coupled to the pleckstrin homology domain of phospholipase C, suggested that the InsP3R1-dependent Ca2+ signal is transient and due to a transient synthesis of InsP3 via M3 muscarinic receptor. Moreover, we suggest that both M2 and M3 signalling pathways are modulating phosphatidylinositol 4,5-bisphosphate and InsP3 concentration, thus describing closely interacting pathways activated by ACh in duodenum myocytes.     

Temperature-dependent calcium-induced calcium release via InsP3 receptors in mouse olfactory ensheathing glial cells

Cooling can induce Ca(2+) signaling via activation of temperature-sensitive ion channels such as TRPM8, TRPA1 and ryanodine receptor channels. Here we have studied the mechanism of cooling-evoked Ca(2+) signaling in mouse olfactory ensheathing cells (OECs), a specialized type of glial cells in the olfactory nerve layer of the olfactory bulb. Reducing the temperature from above 30°C to 28°C and below triggered Ca(2+) transients that persisted in the absence of external Ca(2+), but were suppressed after Ca(2+) store depletion by cyclopiazonic acid. Cooling-evoked Ca(2+) transients were present in mice deficient of TRPM8 and TRPA1, and were not inhibited by ryanodine receptor antagonists. Inhibition of InsP(3) receptors with 2-APB and caffeine entirely blocked cooling-evoked Ca(2+) transients. Moderate Ca(2+) increases, as evoked by flash photolysis of NP-EGTA (caged Ca(2+)) and cyclopiazonic acid, triggered InsP(3) receptor-mediated Ca(2+) release at 22°C, but not at 31°C. The results suggest that InsP(3) receptors mediate Ca(2+)-induced Ca(2+) release in OECs, and that this Ca(2+) release is temperature-sensitive and can be suppressed at temperatures above 28°C.     

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.     

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.     

Mini-dystrophin expression down-regulates IP3-mediated calcium release events in resting dystrophin-deficient muscle cells

We present here evidence for the enhancement, at rest, of an inositol 1,4,5-trisphosphate (IP3)-mediated calcium signaling pathway in myotubes from dystrophin-deficient cell lines (SolC1(-)) as compared to a cell line from the same origin but transfected with mini-dystrophin (SolD(+)). With confocal microscopy, the number of sites discharging calcium (release site density [RSD]) was quantified and found more elevated in SolC1(-) than in SolD(+) myotubes. Variations of membrane potential had no significant effect on this difference, and higher resting [Ca2+]i in SolC1(-) (Marchand, E., B. Constantin, H. Balghi, M.C. Claudepierre, A. Cantereau, C. Magaud, A. Mouzou, G. Raymond, S. Braun, and C. Cognard. 2004. Exp. Cell Res. 297:363-379) cannot explain alone higher RSD. The exposure with SR Ca(2+) channel inhibitors (ryanodine and 2-APB) and phospholipase C inhibitor (U73122) significantly reduced RSD in both cell types but with a stronger effect in dystrophin-deficient SolC1(-) myotubes. Immunocytochemistry allowed us to localize ryanodine receptors (RyRs) as well as IP3 receptors (IP3Rs), IP3R-1 and IP3R-2 isoforms, indicating the presence of both RyRs-dependent and IP3-dependent release systems in both cells. We previously reported evidence for the enhancement, through a Gi protein, of the IP3-mediated calcium signaling pathway in SolC1(-) as compared to SolD(+) myotubes during a high K(+) stimulation (Balghi, H., S. Sebille, B. Constantin, S. Patri, V. Thoreau, L. Mondin, E. Mok, A. Kitzis, G. Raymond, and C. Cognard. 2006. J. Gen. Physiol. 127:171-182). Here we show that, at rest, these regulation mechanisms are also involved in the modulation of calcium release activities. The enhancement of resting release activity may participate in the calcium overload observed in dystrophin-deficient myotubes, and our findings support the hypothesis of the regulatory role of mini-dystrophin on intracellular signaling.     

Simulations of inositol phosphate metabolism and its interaction with InsP(3)-mediated calcium release

Inositol phosphates function as second messengers for a variety of extracellular signals. Ins(1,4,5)P(3) generated by phospholipase C-mediated hydrolysis of phosphatidylinositol bisphosphate, triggers numerous cellular processes by regulating calcium release from internal stores. The Ins(1,4,5)P(3) signal is coupled to a complex metabolic cascade involving a series of phosphatases and kinases. These enzymes generate a range of inositol phosphate derivatives, many of which have signaling roles of their own. We have integrated published biochemical data to build a mass action model for InsP(3) metabolism. The model includes most inositol phosphates that are currently known to interact with each other. We have used this model to study the effects of a G-protein coupled receptor stimulus that activates phospholipase C on the inositol phosphates. We have also monitored how the metabolic cascade interacts with Ins(1,4,5)P(3)-mediated calcium release. We find temporal dynamics of most inositol phosphates to be strongly influenced by the elaborate networking. We also show that Ins(1,3,4,5)P(4) plays a key role in InsP(3) dynamics and allows for paired pulse facilitation of calcium release. Calcium oscillations produce oscillatory responses in parts of the metabolic network and are in turn temporally modulated by the metabolism of InsP(3).     

Phosphate release and force generation in cardiac myocytes investigated with caged phosphate and caged calcium.

The phosphate (P(i)) dissociation step of the cross-bridge cycle was investigated in skinned rat ventricular myocytes to examine its role in force generation and Ca(2+) regulation in cardiac muscle. Pulse photolysis of caged P(i) (alpha-carboxyl-2-nitrobenzyl phosphate) produced up to 3 mM P(i) within the filament lattice, resulting in an approximately exponential decline in steady-state tension. The apparent rate constant, k (rho i), increased linearly with total P(i) concentration (initial plus photoreleased), giving an apparent second-order rate constant for P(i) binding of 3100 M(-1) s(-1), which is intermediate in value between fast and slow skeletal muscles. A decrease in the level of Ca(2+) activation to 20% of maximum tension reduced k (rho i) by twofold and increased the relative amplitude by threefold, consistent with modulation of P(i) release by Ca2+. A three-state model, with separate but coupled transitions for force generation and P(i) dissociation, and a Ca(2+)-sensitive forward rate constant for force generation, was compatible with the data. There was no evidence for a slow phase of tension decline observed previously in fast skeletal fibers at low Ca(2+), suggesting differences in cooperative mechanisms in cardiac and skeletal muscle. In separate experiments, tension development was initiated from a relaxed state by photolysis of caged Ca(2+). The apparent rate constant, k(Ca), was accelerated in the presence of high P(i) consistent with close coupling between force generation and P(i) dissociation, even when force development was initiated from a relaxed state. k(Ca) was also dependent on the level of Ca(2+) activation. However, significant quantitative differences between k (rho i) and k(Ca), including different sensitivities to Ca(2+) and P(i) indicate that caged Ca(2+) tension transients are influenced by additional Ca(2+)-dependent but P i-independent steps that occur before P(i) release. Data from both types of measurements suggest that kinetic transitions associated with P(i) dissociation are modulated by the Ca(2+) regulatory system and partially limit the physiological rate of tension development in cardiac muscle.     

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.