Ca Sparks Research Articles

Calcium alternans in a couplon network model of ventricular myocytes: role of sarcoplasmic reticulum load

Intracellular calcium (Ca) alternans in cardiac myocytes have been shown in many experimental studies, and the mechanisms remain incompletely understood. We recently developed a "3R theory" that links Ca sparks to whole cell Ca alternans through three critical properties: randomness of Ca sparks; recruitment of a Ca spark by neighboring Ca sparks; and refractoriness of Ca release units. In this study, we used computer simulation of a physiologically detailed mathematical model of a ventricular myocyte couplon network to study how sarcoplasmic reticulum (SR) Ca load and other physiological parameters, such as ryanodine receptor sensitivity, SR uptake rate, Na-Ca exchange strength, and Ca buffer levels affect Ca alternans in the context of 3R theory. We developed a method to calculate the parameters used in the 3R theory (i.e., the primary spark rate and the recruitment rate) from the physiologically detailed Ca cycling model and paced the model periodically to elicit Ca alternans. We show that alternans only occurs for an intermediate range of the SR Ca load, and the underlying mechanism can be explained via its effects on the 3Rs. Furthermore, we show that altering the physiological parameters not only directly changes the 3Rs but also alters the SR Ca load, having an indirect effect on the 3Rs as well. Therefore, our present study links the SR Ca load and other physiological parameters to whole cell Ca alternans through the framework of the 3R theory, providing a general mechanistic understanding of Ca alternans in ventricular myocytes.

Criticality in Intracellular Calcium Signaling in Cardiac Myocytes

Calcium (Ca) is a ubiquitous second messenger that regulates many biological functions. The elementary events of local Ca signaling are Ca sparks, which occur randomly in time and space, and integrate to produce global signaling events such as intra- and intercellular Ca waves and whole-cell Ca oscillations. Despite extensive experimental characterization in many systems, the transition from local random to global synchronous events is still poorly understood. Here we show that criticality, a ubiquitous dynamical phenomenon in nature, is responsible for the transition from local to global Ca signaling. We demonstrate this first in a computational model of Ca signaling in a cardiac myocyte and then experimentally in mouse ventricular myocytes, complemented by a theoretical agent-based model to delineate the underlying dynamics. We show that the interaction between the Ca release units via Ca-induced Ca release causes self-organization of Ca spark clusters. When the coupling between Ca release units is weak, the cluster-size distribution is exponential. As the interactions become strong, the cluster-size distribution changes to a power-law distribution, which is characteristic of criticality in thermodynamic and complex nonlinear systems, and facilitates the formation and propagation of Ca waves and whole-cell Ca oscillations. Our findings illustrate how criticality is harnessed by a biological cell to regulate Ca signaling via self-organization of random subcellular events into cellular-scale oscillations, and provide a general theoretical framework for the transition from local Ca signaling to global Ca signaling in biological cells.

Mechanical unloading reverses transverse tubule remodelling and normalizes local Ca2+‐induced Ca2+release in a rodent model of heart failure

AimsCa2+-induced Ca2+ release (CICR) is critical for contraction in cardiomyocytes. The transverse (t)-tubule system guarantees the proximity of the triggers for Ca2+ release [L-type Ca2+ channel, dihydropyridine receptors (DHPRs)] and the sarcoplasmic reticulum Ca2+ release channels [ryanodine receptors (RyRs)]. Transverse tubule disruption occurs early in heart failure (HF). Clinical studies of left ventricular assist devices in HF indicate that mechanical unloading induces reverse remodelling. We hypothesize that unloading of failing hearts normalizes t-tubule structure and improves CICR.Methods and resultsHeart failure was induced in Lewis rats by left coronary artery ligation for 12 weeks; sham-operated animals were used as controls. Failing hearts were mechanically unloaded for 4 weeks by heterotopic abdominal heart transplantation (HF-UN). HF reduced the t-tubule density measured by di-8-ANEPPS staining in isolated left ventricular myocytes, and this was reversed by unloading. The deterioration in the regularity of the t-tubule system in HF was also reversed in HF-UN. Scanning ion conductance microscopy showed the reappearance of normal surface striations in HF-UN. Electron microscopy revealed recovery of normal t-tubule microarchitecture in HF-UN. L-type Ca2+ current density, measured using whole-cell patch clamping, was reduced in HF but unaffected by unloading. The variance of the time-to-peak of the Ca2+ transient, an index of CICR dyssynchrony, was increased in HF and normalized by unloading. The increased Ca2+ spark frequency observed in HF was reduced in HF-UN. These results could be explained by the recoupling of orphaned RyRs in HF, as indicated by immunofluorescence.ConclusionsOur data show that mechanical unloading of the failing heart reverses the pathological remodelling of the t-tubule system and improves CICR.

Cardiac arrhythmia mechanisms in rats with heart failure induced by pulmonary hypertension.

Pulmonary hypertension provokes right heart failure and arrhythmias. Better understanding of the mechanisms underlying these arrhythmias is needed to facilitate new therapeutic approaches for the hypertensive, failing right ventricle (RV). The aim of our study was to identify the mechanisms generating arrhythmias in a model of RV failure induced by pulmonary hypertension. Rats were injected with monocrotaline to induce either RV hypertrophy or failure or with saline (control). ECGs were measured in conscious, unrestrained animals by telemetry. In isolated hearts, electrical activity was measured by optical mapping and myofiber orientation by diffusion tensor-MRI. Sarcoplasmic reticular Ca(2+) handling was studied in single myocytes. Compared with control animals, the T-wave of the ECG was prolonged and in three of seven heart failure animals, prominent T-wave alternans occurred. Discordant action potential (AP) alternans occurred in isolated failing hearts and Ca(2+) transient alternans in failing myocytes. In failing hearts, AP duration and dispersion were increased; conduction velocity and AP restitution were steeper. The latter was intrinsic to failing single myocytes. Failing hearts had greater fiber angle disarray; this correlated with AP duration. Failing myocytes had reduced sarco(endo)plasmic reticular Ca(2+)-ATPase activity, increased sarcoplasmic reticular Ca(2+)-release fraction, and increased Ca(2+) spark leak. In hypertrophied hearts and myocytes, dysfunctional adaptation had begun, but alternans did not develop. We conclude that increased electrical and structural heterogeneity and dysfunctional sarcoplasmic reticular Ca(2+) handling increased the probability of alternans, a proarrhythmic predictor of sudden cardiac death. These mechanisms are potential therapeutic targets for the correction of arrhythmias in hypertensive, failing RVs.

Functional evidence for an active role of B-type natriuretic peptide in cardiac remodelling and pro-arrhythmogenicity

During heart failure (HF), the left ventricle (LV) releases B-type natriuretic peptide (BNP), possibly contributing to adverse cardiovascular events including ventricular arrhythmias (VAs) and LV remodelling. We investigated the cardiac effects of chronic BNP elevation in healthy mice and compared the results with a model of HF after myocardial infarction (PMI mice). Healthy mice were exposed to circulating BNP levels (BNP-Sham) similar to those measured in PMI mice. Telemetric surface electrocardiograms showed that in contrast with fibrotic PMI mice, electrical conduction was not affected in BNP-Sham mice. VAs were observed in both BNP-Sham and PMI but not in Sham mice. Analysis of heart rate variability indicated that chronic BNP infusion increased cardiac sympathetic tone. At the cellular level, BNP reduced Ca(2+) transients and impaired Ca(2+) reuptake in the sarcoplasmic reticulum, in line with blunted SR Ca(2+) ATPase 2a and S100A1 expression. BNP increased Ca(2+) spark frequency, reflecting Ca(2+) leak through ryanodine receptors, elevated diastolic Ca(2+), and promoted spontaneous Ca(2+) waves. Similar effects were observed in PMI mice. Most of these effects were reduced in BNP-Sham and PMI mice by the selective β1-adrenergic blocker metoprolol. Elevated BNP levels, by inducing sympathetic overdrive and altering Ca(2+) handling, promote adverse cardiac remodelling and VAs, which could account in part for the progression of HF after MI. The early use of β-blockers to prevent the deleterious effects of chronic BNP exposure may be beneficial in HF.

Regulatory Effect of Connexin 43 on Basal Ca2+ Signaling in Rat Ventricular Myocytes

BackgroundIt has been found that gap junction-associated intracellular Ca2+ [Ca2+]i disturbance contributes to the arrhythmogenesis and hyperconstriction in diseased heart. However, whether functional gaps are also involved in the regulation of normal Ca2+ signaling, in particular the basal [Ca2+]i activities, is unclear.Methods and ResultsGlobal and local Ca2+ signaling and gap permeability were monitored in cultured neonatal rat ventricular myocytes (NRVMs) and freshly isolated mouse ventricular myocytes by Fluo4/AM and Lucifer yellow (LY), respectively. The results showed that inhibition of gap communication by heptanol, Gap 27 and flufenamic acid or interference of connexin 43 (Cx43) with siRNA led to a significant suppression of LY uptake and, importantly, attenuations of global Ca2+ transients and local Ca2+ sparks in monolayer NRVMs and Ca2+ sparks in adult ventricular myocytes. In contrast, overexpression of rat-Cx43 in NRVMs induced enhancements in the above measurements, and so did in HEK293 cells expressing rat Cx43. Additionally, membrane-permeable inositol 1,4,5-trisphosphate (IP3 butyryloxymethyl ester) and phenylephrine, an agonist of adrenergic receptor, could relieve the inhibited Ca2+ signal and LY uptake by gap uncouplers, whereas blockade of IP3 receptor with xestospongin C or 2-aminoethoxydiphenylborate mimicked the effects of gap inhibitors. More importantly, all these gap-associated effects on Ca2+ signaling were also found in single NRVMs that only have hemichannels instead of gap junctions. Further immunostaining/immunoblotting single myocytes with antibody against Cx43 demonstrated apparent increases in membrane labeling of Cx43 and non-junctional Cx43 in overexpressed cells, suggesting functional hemichannels exist and also contribute to the Ca2+ signaling regulation in cardiomyocytes.ConclusionsThese data demonstrate that Cx43-associated gap coupling plays a role in the regulation of resting Ca2+ signaling in normal ventricular myocytes, in which IP3/IP3 receptor coupling is involved. This finding may provide a novel regulatory pathway for mediation of spontaneous global and local Ca2+ activities in cardiomyocytes.

Function and expression of ryanodine receptors and inositol 1,4,5‐trisphosphate receptors in smooth muscle cells of murine feed arteries and arterioles

We tested the hypothesis that vasomotor control is differentially regulated between feed arteries and downstream arterioles from the cremaster muscle of C57BL/6 mice. In isolated pressurized arteries, confocal Ca(2+) imaging of smooth muscle cells (SMCs) revealed Ca(2+) sparks and Ca(2+) waves. Ryanodine receptor (RyR) antagonists (ryanodine and tetracaine) inhibited both sparks and waves but increased global Ca(2+) and myogenic tone. In arterioles, SMCs exhibited only Ca(2+) waves that were insensitive to ryanodine or tetracaine. Pharmacological interventions indicated that RyRs are functionally coupled to large-conductance, Ca(2+)-activated K(+) channels (BK(Ca)) in SMCs of arteries, whereas BK(Ca) appear functionally coupled to voltage-gated Ca2+ channels in SMCs of arterioles. Inositol 1,4,5-trisphosphate receptor (IP3R) antagonists (xestospongin D or 2-aminoethoxydiphenyl borate) or a phospholipase C inhibitor (U73122) attenuated Ca(2+) waves, global Ca(2+) and myogenic tone in arteries and arterioles but had no effect on arterial sparks. Real-time PCR of isolated SMCs revealed RyR2 as the most abundant isoform transcript; arteries expressed twice the RyR2 but only 65% the RyR3 of arterioles and neither vessel expressed RyR1. Immunofluorescent localisation of RyR protein indicated bright, clustered staining of arterial SMCs in contrast to diffuse staining in arteriolar SMCs. Expression of IP(3)R transcripts and protein immunofluorescence were similar in SMCs of both vessels with IP(3)R1>>IP(3)R2>IP(3)R3. Despite similar expression of IP(3)Rs and dependence of Ca(2+) waves on IP(3)Rs, these data illustrate pronounced regional heterogeneity in function and expression of RyRs between SMCs of the same vascular resistance network. We conclude that vasomotor control is differentially regulated in feed arteries vs. downstream arterioles.

Can the Sodium-Calcium Exchanger Initiate or Suppress Calcium Sparks in Cardiac Myocytes?

Positive feedback of Calcium (Ca)-induced Ca release is the mechanism of Ca spark formation in cardiac myocytes. To initiate this process, a certain amount of Ca in the cleft space is necessary. When the membrane potential becomes higher during excitation-contraction coupling, Ca can enter through both Ca current (ICaL) and sodium-calcium exchanger (NCX) and may activate ryanodine receptors to initiate a Ca spark. On the other hand, at the resting membrane potential (Vm ∼–80 mV), NCX removes Ca from the cell (forward mode). If Ca released from the sarcoplasmic reticulum is quickly removed via forward mode NCX before Ca-induced Ca release starts, the Ca release becomes nonspark Ca leak. This would also be influenced by the cleft/noncleft distribution of NCX, which is unknown. Using a physiologically detailed mathematical model of subcellular Ca cycling, we analyze how NCX strength and distribution alter Ca spark formation. During excitation-contraction coupling, most Ca sparks are induced by ICaL with very few due to NCX current. At the resting membrane potential if most NCX is localized to the cleft, spontaneous Ca sparks are significantly reduced.

Refractoriness of sarcoplasmic reticulum Ca2+ release determines Ca2+ alternans in atrial myocytes.

Cardiac alternans is a recognized risk factor for cardiac arrhythmia and sudden cardiac death. At the cellular level, Ca(2+) alternans appears as cytosolic Ca(2+) transients of alternating amplitude at regular beating frequency. Cardiac alternans is a multifactorial process but has been linked to disturbances in intracellular Ca(2+) regulation. In atrial myocytes, we tested the role of voltage-gated Ca(2+) current, sarcoplasmic reticulum (SR) Ca(2+) load, and restitution properties of SR Ca(2+) release for the occurrence of pacing-induced Ca(2+) alternans. Voltage-clamp experiments revealed that peak Ca(2+) current was not affected during alternans, and alternans of end-diastolic SR Ca(2+) load, evaluated by application of caffeine or measured directly with an intra-SR fluorescent Ca(2+) indicator (fluo-5N), were not a requirement for cytosolic Ca(2+) alternans. Restitution properties and kinetics of refractoriness of Ca(2+) release after activation during alternans were evaluated by four different approaches: measurements of 1) the delay (latency) of occurrence of spontaneous global Ca(2+) releases and 2) Ca(2+) spark frequency, both during rest after a large and small alternans Ca(2+) transient; 3) the magnitude of premature action potential-induced Ca(2+) transients after a large and small beat; and 4) the efficacy of a photolytically induced Ca(2+) signal (Ca(2+) uncaging from DM-nitrophen) to trigger additional Ca(2+) release during alternans. The results showed that the latency of global spontaneous Ca(2+) release was prolonged and Ca(2+) spark frequency was decreased after the large Ca(2+) transient during alternans. Furthermore, the restitution curve of the Ca(2+) transient elicited by premature action potentials or by photolysis-induced Ca(2+) release from the SR lagged behind after a large-amplitude transient during alternans compared with the small-amplitude transient. The data demonstrate that beat-to-beat alternation of the time-dependent restitution properties and refractory kinetics of the SR Ca(2+) release mechanism represents a key mechanism underlying cardiac alternans.

Ankyrin-B reduction enhances Ca spark-mediated SR Ca release promoting cardiac myocyte arrhythmic activity

Ankyrin-B (AnkB) loss-of-function may cause ventricular arrhythmias and sudden cardiac death in humans. Cardiac myocytes from AnkB heterozygous mice (AnkB(+/-)) show reduced expression and altered localization of Na/Ca exchanger (NCX) and Na/K-ATPase (NKA), key players in regulating [Na](i) and [Ca](i). Here we investigate how AnkB reduction affects cardiac [Na](i), [Ca](i) and SR Ca release. We found reduced NCX and NKA transport function but unaltered [Na](i) and diastolic [Ca](i) in myocytes from AnkB(+/-) vs. wild-type (WT) mice. Ca transients, SR Ca content and fractional SR Ca release were larger in AnkB(+/-) myocytes. The frequency of spontaneous, diastolic Ca sparks (CaSpF) was significantly higher in intact myocytes from AnkB(+/-) vs. WT myocytes (with and without isoproterenol), even when normalized for SR Ca load. However, total ryanodine receptor (RyR)-mediated SR Ca leak (tetracaine-sensitive) was not different between groups. Thus, in AnkB(+/-) mice SR Ca leak is biased towards more Ca sparks (vs. smaller release events), suggesting more coordinated openings of RyRs in a cluster. This is due to local cytosolic RyR regulation, rather than intrinsic RyR differences, since CaSpF was similar in saponin-permeabilized myocytes from WT and AnkB(+/-) mice. The more coordinated RyRs openings resulted in an increased propensity of pro-arrhythmic Ca waves in AnkB(+/-) myocytes. In conclusion, AnkB reduction alters cardiac Na and Ca transport and enhances the coupled RyR openings, resulting in more frequent Ca sparks and waves although the total SR Ca leak is unaffected. This could enhance the propensity for triggered arrhythmias in AnkB(+/-) mice.

Cardiac FKBP12.6 overexpression protects against triggered ventricular tachycardia in pressure overloaded mouse hearts

Alterations in RyR2 function have been proposed as a major pathophysiological mechanism of arrhythmias and heart failure (HF). Cardiac FKBP12.6 overexpression protects against myocardial infarction-induced HF and catecholamine-promoted ventricular arrhythmias. We tested the hypothesis that FKBP12.6 overexpression protects against maladaptive LVH and triggered ventricular arrhythmias following transverse aorta constriction (TAC) in the mouse. The TAC-associated mortality rate was significantly lower in male transgenic (DT) than in Ctr mice (p<0.05). TAC-associated maladaptive hypertrophy was blunted in DT mice especially 1month post-TAC and their SERCA2a/PLB ratio remained unchanged 1 and 2months post-TAC. Two months after TAC, trains of 30 stimuli (burst pacing) performed following isoproterenol injection (0.2mg/kg, ip), induced VT in 50% of the TAC-Ctr and in none of the TAC-DT mice (p=0.022). The increase in myocyte shortening and Ca(2+) spark frequency observed in sham-operated Ctr mice in response to 50 nM isoproterenol was reduced in DT mice, and abolished in TAC-DT mice. NCX1 function was reduced in Sham-DT and TAC-DT compared with Sham-Ctr and TAC-Ctr mice, respectively (p<0.05 for the 2 comparisons). In mice killed after isoproterenol injection and burst pacing, RyR2 S2814 phosphorylation was decreased by 50% in TAC-DT versus TAC-Ctr mice (p<0.05), with no change in RyR2 S2808 and PLB S16 and T17 phosphorylation. Cardiac FKBP12.6 overexpression in the mouse blunts pressure overload-induced maladaptive LV remodelling and protects against catecholamine-promoted burst pacing-induced ventricular tachycardia by decreasing cardiac sensitivity to adrenergic stress and RyR2 S2814 phosphorylation, and decreasing NCX1 activity.

Dantrolene rescues arrhythmogenic RYR2 defect in a patient‐specific stem cell model of catecholaminergic polymorphic ventricular tachycardia

Coordinated release of calcium (Ca2+) from the sarcoplasmic reticulum (SR) through cardiac ryanodine receptor (RYR2) channels is essential for cardiomyocyte function. In catecholaminergic polymorphic ventricular tachycardia (CPVT), an inherited disease characterized by stress-induced ventricular arrhythmias in young patients with structurally normal hearts, autosomal dominant mutations in RYR2 or recessive mutations in calsequestrin lead to aberrant diastolic Ca2+ release from the SR causing arrhythmogenic delayed after depolarizations (DADs). Here, we report the generation of induced pluripotent stem cells (iPSCs) from a CPVT patient carrying a novel RYR2 S406L mutation. In patient iPSC-derived cardiomyocytes, catecholaminergic stress led to elevated diastolic Ca2+ concentrations, a reduced SR Ca2+ content and an increased susceptibility to DADs and arrhythmia as compared to control myocytes. This was due to increased frequency and duration of elementary Ca2+ release events (Ca2+ sparks). Dantrolene, a drug effective on malignant hyperthermia, restored normal Ca2+ spark properties and rescued the arrhythmogenic phenotype. This suggests defective inter-domain interactions within the RYR2 channel as the pathomechanism of the S406L mutation. Our work provides a new in vitro model to study the pathogenesis of human cardiac arrhythmias and develop novel therapies for CPVT.

Can the Sodium-Calcium Exchanger Initiate or Supress Calcium Sparks in Cardiac Myocytes?

Calcium (Ca) sparks in cardiac myocyte are formed by positive feedback (Ca induced Ca release). At the resting membrane potential (Vm ∼-80 mV), the sodium-calcium exchanger (NCX) removes Ca from the cell (forward mode). If Ca released from the sarcoplasmic reticulum (SR) is quickly removed via forward mode NCX before the positive feedback process starts, the Ca release becomes non-spark Ca leak. However, at higher Vm, Ca enters through the NCX (reverse mode) and Ca entry through reverse mode NCX may activate ryanodine receptors (RyRs) and initiate Ca sparks. These are also influenced by the cleft/non-cleft distribution of NCX, which is still unknown. In this study, using physiologically detailed mathematical model of the subcellular Ca cycling, we investigate how the magnitude of NCX current and the distribution of NCXs alter Ca spark formation. We find that at the resting membrane potential if all NCXs are localized to the cleft, Ca sparks are significantly reduced (at [Ca]SR=700 μM, there is a 40% reduction vs. the case where all NCXs locate outside of the cleft). During excitation-contraction coupling, most Ca sparks are induced by L-type Ca current (ICaL) and only a small fraction of Ca sparks are due to NCX current at Vm = 0mV. If Vm is higher (+40 mV), since ICaL becomes smaller and NCX becomes larger, more sparks are induced by NCX. But the absolute number of Ca sparks is limited. These results also strongly depend on the distribution of NCXs. If many NCXs locate close to RyRs, NCX currents initiate Ca sparks much more efficiently. This underscores the criticality of NCX localization regarding functional impact on SR Ca release.

Effects of Cytosolic Ca Buffering on Sarcoplasmic Reticulum Ca Leak in Permeabilized Rabbit Ventricular Myocytes

In this study we tested the hypothesis that local Ca-induced Ca release (CICR) within ryanodine receptor (RyR2) release clusters plays an important role in defining spark-mediated sarcoplasmic reticulum (SR) Ca leak. We studied to what degree changes of cytosolic Ca buffer capacity affect single RyR activity in lipid bilayers, Ca spark properties, and SR Ca leak in permeabilized ventricular myocytes. No substantial changes in single RyR2 function were observed if BAPTA (a fast Ca buffer) was added (holding free Ca constant) to the EGTA-buffered cytosolic solution. However, the same cytosolic BAPTA addition almost completely eliminated Ca sparks in cells. The elimination of Ca sparks by BAPTA was not due to a decrease in SR Ca load. The addition of the fast cytosolic Ca buffer significantly decreased SR Ca leak, particularly at high [Ca]SR (>400 μM) where Ca sparks significantly contribute to SR Ca leak. In contrast, lowering cytosolic Ca buffer capacity (by decreasing EGTA from 0.36 to 0.1 mM; keeping free Ca constant) drastically increased Ca spark frequency and width, leading to generation of multifocal (or propagating) Ca sparks. This decrease in cytosolic Ca buffer capacity also significantly accelerated SR Ca leak as a result of augmentation of Ca spark-mediated component of SR Ca leak. In conclusion, by changing cytosolic Ca buffering (capacity or affinity) we were able to experimentally separate Ca spark- and non-spark- mediated component of the overall SR Ca leak in ventricular myocytes. These data also suggest that changes in the dynamics of local cytosolic Ca handling (buffering, extrusion, etc.) are physiologically important in determining the degree of spark and non-spark mediated SR Ca leak.

Self-Organized Criticality Underlies Arrhythmogenic Calcium Waves in Cardiac Myocytes

In cardiac myocytes, calcium (Ca)-induced Ca release can give rise to propagating Ca waves that promote cardiac arrhythmias. To understand the mechanism underlying the transition from localized Ca sparks to global Ca waves, we developed a mathematical model of a spatially-distributed network of diffusively coupled Ca release units (CRUs) comprised of junctional/longitudinal sarcoplasmic reticulum and dyadic/cytoplasmic spaces with physiologically realistic dimensions. As total Ca was increased in the model, Ca spark cluster sizes initially exhibited an exponential distribution, which transitioned to a scale-free power-law (f-β) distribution near the threshold at which random Ca sparks transitioned to Ca waves. The power-law relationship indicates that Ca release patterns in the CRU network are governed by a dynamical mechanism called self-organized criticality, the same process underlying many natural world phenomena such as avalanches and earthquakes. We tested this prediction experimentally in saponin-permeabilized cardiac myocytes. As free Ca, buffered with 0.5 mM EGTA, was increased, Ca spark cluster size transitioned from an exponential distribution to a power-law distribution at a free Ca concentration of 400 nM. Consistent with self-organized criticality, this Ca concentration was near the threshold for spark-to-wave transition since fully propagating waves were observed above 400 nM Ca. Below this concentration, Ca was released mostly as individual sparks, and spark cluster sizes followed an exponential rather than power-law distribution. In conclusion, our findings provide both theoretical and experimental evidence that the transition from Ca sparks to arrhythmogenic Ca waves in cardiac myocytes is mediated by the dynamical process of self-organized criticality, common to many natural phenomena. This provides a theoretical framework for developing interventions which modulate the Ca spark-to-wave transition threshold as a potential therapeutic strategy for preventing arrhythmias.

Computational Modeling and Numerical Methods for Spatiotemporal Calcium Cycling in Ventricular Myocytes

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain and the myoplasm domain in each CRU are modeled by 5 × 5 × 5 voxels to maintain proper Ca diffusion. Advanced numerical algorithms implemented on graphical processing units were used for fast computational simulations. For a myocyte containing 100 × 20 × 10 CRUs, a 1-s heart time simulation takes about 10 min of machine time on a single NVIDIA Tesla C2050. Examples of simulated Ca cycling dynamics, such as Ca sparks, Ca waves, and Ca alternans, are shown.

Requirement for Functional BK Channels in Maintaining Oscillation in Venomotor Tone Revealed by Species Differences in Expression of the β1 Accessory Subunits

We determined the possible role of large-conductance Ca2+-activated K (BK) channels in regulation of venous tone in small capacitance veins and blood pressure. In rat mesenteric venous smooth muscle cells (MV SMC), BK channel α- and β1-subunits were coexpressed, unitary BK currents were detected, and single-channel currents were sensitive to voltage and [Ca2+]i. Rat MV SMCs displayed Ca sparks and iberiotoxin-sensitive spontaneous transient outward currents. Under resting conditions in vitro, rat MV exhibited nifedipine-sensitive spontaneous oscillatory constrictions. Blockade of BK channels by paxilline and Ca2+ sparks by ryanodine constricted rat MV. Nifedipine caused venodilation and blocked paxilline-induced, KCl-induced (20 mM), and BayK8644-induced contraction. Acute inhibition of BK channels with iberiotoxin in vivo increased blood pressure and reduced venous capacitance, measured as an increase in mean circulatory filling pressure in conscious rats. BK channel α-subunits and L-type Ca2+ channel α1-C subunits are expressed in murine MV. However, these channels are not functional because murine MV lack nifedipine-sensitive basal tone and rhythmic constrictions. Murine MV were also insensitive to paxilline, ryanodine, KCl, and BayK8644, consistent with our previous studies showing that murine MV do not have BK β1-subunits. These data show that not only there are species-dependent properties in ion channel control of venomotor tone but also BK channels are required for rhythmic oscillations in venous tone.

Quantification of the CICR Response to Artificial Ca Sparks in Striated Muscle

In cardiac muscle physiologic Ca2+ release is CICR, but in skeletal muscle the role of CICR remains unsettled. “Artificial Ca2+ sparks” of up to 8 μM were produced by 2-photon irradiation of Ca2+ cages, applied in the near vicinity of membrane-permeabilized skeletal fibers from frogs and mice, and rabbit atrial and ventricular myocytes, while confocally imaging their Ca2+ response with Fluo-4FF. In response to transients as low as 0.28 μM, frog fibers produced waves (n=16) that satisfied the definition of CICR (Endo, PhRev 2009), including inhibition by Mg2+. Cardiomyocytes responded similarly, with waves that could propagate fully or partially through the cells. Responses were absent in mouse skeletal fibers (n=51) unless RyR opening was promoted pharmacologically (n=24). The underlying Ca2+ flux was calculated from fluorescence images by generalizing the “backward” method (Rios et al, JGP 1999). In frog fibers, fluxes were found to reach 55 mM/s, which is close to values measured under voltage clamp depolarization. A positive three-way correlation was found among flux, speed and extent of propagation. Accordingly, the responses of cardiomyocytes and pharmacologically conditioned mammalian fibers, both of which had smaller flux, were of lower velocity and sometimes limited propagation range. The quantitative properties of the propagating wave, in all cases, were well described by a simple continuum model of sources and sinks, with a common threshold [Ca2+] for channel opening (Kupferman et al, BJ 1997). This description suggests a fundamental commonality of mechanisms. The lower flux and higher threshold [Ca2+] in mice are consistent with the notion that CICR is supported by isoform 3 or beta (in the frog), and that isoform 1 in situ is less susceptible to CICR. Supported by NIAMS and NHLBI (NIH).

Calcium Alternans in a Couplon Network Model of Ventricular Myocytes: Roles of Sarcoplasmic Reticulum Load

Intracellular calcium (Ca) alternans of cardiac myocytes has been shown in many experimental studies, and the mechanisms remain incompletely understood. We recently developed a “3R theory” in which alternans arises as a result of the interactions of three critical properties: Randomness of Ca sparks; Recruitment of a Ca spark to its neighboring Ca release units (CRUs); and Refractoriness of the CRU. On the other hand, experimental studies have shown that sarcoplasmic reticulum (SR) Ca load plays important roles in the genesis of Ca alternans. In this study, we use computer simulation to study how SR Ca load and other physiological parameters, such as RyR sensitivity, SERCA pump, CRU spacing, Na-Ca exchange strength, L-type Ca conductance, etc., affect Ca alternans. Our model consists of 100 x 20 x 10 CRUs coupled via Ca diffusion in the cytoplasmic and SR space. Each CRU contains 100 RyRs with individual RyRs simulated stochastically. We developed a method to calculate the primary spark rate and the recruitment rate, and paced the model to periodically to elicit Ca alternans. We show that altering the physiological parameters not only directly change the 3 R's but also alters the SR Ca load (or the total Ca of the cell), and thus Ca alternans properties. However, higher SR Ca load causes more Ca leak which in turn causes RyRs to be more sensitive to cytosolic Ca, affecting primary spark rate and recruitment. Therefore, our present study shows that although the 3R theory does not include the SR load per se, the SR Ca load affects Ca alternans via its effects on the 3 R's.

Regulation of sarcoplasmic reticulum Ca²⁺ leak by cytosolic Ca²⁺ in rabbit ventricular myocytes.

Sarcoplasmic reticulum (SR) Ca(2+) leak determines SR Ca(2+) content and, therefore, the amplitude of global Ca(2+) transients in ventricular myocytes. However, it remains unresolved to what extent Ca(2+) leak can be modulated by cytosolic [Ca(2+)] ([Ca(2+)](i)). Here, we studied the effects of [Ca(2+)](i) on SR Ca(2+) leak in permeabilized rabbit ventricular myocytes. Using confocal microscopy we monitored SR Ca(2+) leak as the change in [Ca(2+)](SR) (with Fluo-5N) after complete SERCA inhibition with thapsigargin (10 μm). Increasing [Ca(2+)](i) from 150 to 250 nM significantly increased SR Ca(2+) leak over the entire range of [Ca(2+)](SR). This increase was associated with an augmentation of both Ca(2+) spark- and non-spark-mediated Ca(2+) leak. Further increasing [Ca(2+)](i) to 350 nM led to rapid [Ca](2+)](SR) depletion due to the occurrence of Ca(2+) waves. The augmentation of SR Ca(2+) leak by high [Ca(2+)](i) was insensitive to inhibition of Ca(2+)-calmodulin-dependent protein kinase II. In contrast, lowering [Ca(2+)](i) to 50 nM markedly decreased SR Ca(2+) leak rate and nearly abolished Ca(2+) sparks. When the ryanodine receptor (RyR) was completely inhibited with ruthenium red (50 μM), changes in [Ca(2+)](i) between 50 and 350 nM did not produce any significant effect on SR Ca(2+) leak, indicating that [Ca(2+)](i) alters SR Ca(2+) leak solely by regulating RyR activity. In summary, [Ca(2+)](i) in the range of 50-350 nM has a significant effect on SR Ca(2+) leak rate mainly via direct regulation of RyR activity. As RyR activity depends highly on [Ca(2+)](i) and [Ca(2+)](SR), SR Ca(2+) leak remains relatively constant during the declining phase of the Ca(2+) transient when [Ca(2+)](SR) and [Ca(2+)](i) change in opposite directions.