Model of calcium movements in the mammalian myocardium: interval-strength relationship

A model is proposed to describe the interval-strength relationship in mammalian cardiac muscle in terms of "discrete" calcium movements associated with each cycle. The sarcoplasmic reticulum is assumed to be comprised of three functional sub-compartments: (1) The "main calcium store" which contains most of the calcium (predominantly bound) and is considered, due to its large buffering capacity, to account for the "long-term memory" lasting 7-10 beats. (2) The "releasable terminal" which contains the calcium readily available for release (all or most of it free) and accounts for the "short-term memory" which affects the subsequent beat. (3) The longitudinal network of the SR recirculating the myofibrillar calcium to the "main calcium store". The total content of calcium in the main store is determined by the transsarcolemmal influx and efflux. While influx occurs only during depolarization, efflux occurs during the whole cardiac cycle. The amount of free calcium in the main store is determined by an equilibrium equation. The release of calcium from the "releasable terminal" is governed by a "concentration-dependent" mechanism. This implies that when the concentration in the "releasable terminal" increases, the fraction released increases and the residual calcium left for the subsequent contraction decreases. The model predicts the following interval-strength relationships: steady state peak tension; changes from one steady rate to another; restitution curves; post-stimulation potentiation; paired stimulation; premature beats; post-extrasystolic potentiation following interpolated, basal or complimentary interval.     

Mechanisms of calcium transient and action potential alternans in cardiac cells and tissues

Alternation of cardiac action potential duration (APD) from beat to beat and concurrent alternation of the amplitude of the calcium transient are regarded as important arrhythmia mechanisms. These phenomena are causally interrelated and can be reliably evoked by an increase in beat frequency or by ischemia. The first part of this historical review deals with the physiology of APD alternans. Sections recounting the evolution of knowledge about calcium-activated ion currents and calcium transient alternans are interspersed among sections describing the growth of the so-called "restitution hypothesis," which involves time-dependent recovery of potassium channels (including their passage through pre-open states) as a function of diastolic interval. Major developments are generally in chronological order, but it is necessary to move back and forth between the two theories to respect the overall time line, which runs from about l965 to the present. The concluding two sections deal with the pathophysiology of calcium transient and APD alternans during ischemia, which may be the basis for out-of-hospital cardiac arrest during the initial stages of acute myocardial infarction.     

Model of intracellular calcium cycling in ventricular myocytes

We present a mathematical model of calcium cycling that takes into account the spatially localized nature of release events that correspond to experimentally observed calcium sparks. This model naturally incorporates graded release by making the rate at which calcium sparks are recruited proportional to the whole cell L-type calcium current, with the total release of calcium from the sarcoplasmic reticulum (SR) being just the sum of local releases. The dynamics of calcium cycling is studied by pacing the model with a clamped action potential waveform. Experimentally observed calcium alternans are obtained at high pacing rates. The results show that the underlying mechanism for this phenomenon is a steep nonlinear dependence of the calcium released from the SR on the diastolic SR calcium concentration (SR load) and/or the diastolic calcium level in the cytosol, where the dependence on diastolic calcium is due to calcium-induced inactivation of the L-type calcium current. In addition, the results reveal that the calcium dynamics can become chaotic even though the voltage pacing is periodic. We reduce the equations of the model to a two-dimensional discrete map that relates the SR and cytosolic concentrations at one beat and the previous beat. From this map, we obtain a condition for the onset of calcium alternans in terms of the slopes of the release-versus-SR load and release-versus-diastolic-calcium curves. From an analysis of this map, we also obtain an understanding of the origin of chaotic dynamics.     

Regulation of Ca2+ and electrical alternans in cardiac myocytes: role of CAMKII and repolarizing currents

Alternans of cardiac repolarization is associated with arrhythmias and sudden death. At the cellular level, alternans involves beat-to-beat oscillation of the action potential (AP) and possibly Ca(2+) transient (CaT). Because of experimental difficulty in independently controlling the Ca(2+) and electrical subsystems, mathematical modeling provides additional insights into mechanisms and causality. Pacing protocols were conducted in a canine ventricular myocyte model with the following results: 1) CaT alternans results from refractoriness of the sarcoplasmic reticulum Ca(2+) release system; alternation of the L-type calcium current has a negligible effect; 2) CaT-AP coupling during late AP occurs through the sodium-calcium exchanger and underlies AP duration (APD) alternans; 3) increased Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) activity extends the range of CaT and APD alternans to slower frequencies and increases alternans magnitude; its decrease suppresses CaT and APD alternans, exerting an antiarrhythmic effect; and 4) increase of the rapid delayed rectifier current (I(Kr)) also suppresses APD alternans but without suppressing CaT alternans. Thus CaMKII inhibition eliminates APD alternans by eliminating its cause (CaT alternans) while I(Kr) enhancement does so by weakening CaT-APD coupling. The simulations identify combined CaMKII inhibition and I(Kr) enhancement as a possible antiarrhythmic intervention.     

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.     

Dependency of Calcium Alternans on Ryanodine Receptor Refractoriness

Background

Rapid pacing rates induce alternations in the cytosolic calcium concentration caused by fluctuations in calcium released from the sarcoplasmic reticulum (SR). However, the relationship between calcium alternans and refractoriness of the SR calcium release channel (RyR2) remains elusive.

Methodology/Principal Findings

To investigate how ryanodine receptor (RyR2) refractoriness modulates calcium handling on a beat-to-beat basis using a numerical rabbit cardiomyocyte model. We used a mathematical rabbit cardiomyocyte model to study the beat-to-beat calcium response as a function of RyR2 activation and inactivation. Bi-dimensional maps were constructed depicting the beat-to-beat response. When alternans was observed, a novel numerical clamping protocol was used to determine whether alternans was caused by oscillations in SR calcium loading or by RyR2 refractoriness. Using this protocol, we identified regions of RyR2 gating parameters where SR calcium loading or RyR2 refractoriness underlie the induction of calcium alternans, and we found that at the onset of alternans both mechanisms contribute. At low inactivation rates of the RyR2, calcium alternans was caused by alternation in SR calcium loading, while at low activation rates it was caused by alternation in the level of available RyR2s.

Conclusions/Significance

We have mapped cardiomyocyte beat-to-beat responses as a function of RyR2 activation and inactivation, identifying domains where SR calcium load or RyR2 refractoriness underlie the induction of calcium alternans. A corollary of this work is that RyR2 refractoriness due to slow recovery from inactivation can be the cause of calcium alternans even when alternation in SR calcium load is present.     

The decrease in the presynaptic calcium current is a major cause of short-term depression at a calyx-type synapse

Repetitive nerve firings cause short-term depression (STD) of release at many synapses. Its underlying mechanism is largely attributed to depletion of a readily releasable vesicle pool (RRP) and a decreased probability of releasing a readily releasable vesicle during an action potential. Which of these two mechanisms is dominant and the mechanism that decreases the release probability remain debated. Here, we report that a decreased release probability is caused by a calcium-induced inhibition of presynaptic calcium channels, particularly P/Q-type channels at the calyx of Held in rat brainstem. This mechanism was the dominant cause of STD in a wide range of stimulation conditions, such as during 2 to 20 action potential-equivalent stimuli (AP-e) at 0.2-30 Hz and after 2 to 20 AP-e at 0.2-100 Hz. Only during > or = 100 Hz AP-e was depletion the dominant mechanism.     

A novel presynaptic inhibitory mechanism underlies paired pulse depression at a fast central synapse.

Several distinct mechanisms may cause synaptic depression, a common form of short-term synaptic plasticity. These include postsynaptic receptor desensitization, presynaptic depletion of releasable vesicles, or other presynaptic mechanisms depressing vesicle release. At the endbulb of Held, a fast central calyceal synapse in the auditory pathway, cyclothiazide (CTZ) abolished marked paired pulse depression (PPD) by acting presynaptically to enhance transmitter release, rather than by blocking postsynaptic receptor desensitization. PPD and its response to CTZ were not altered by prior depletion of the releasable vesicle pool but were blocked by lowering external calcium concentration, while raising external calcium enhanced PPD. We conclude that a major component of PPD at the endbulb is due to a novel, transient depression of release, which is dependent on the level of presynaptic calcium entry and is CTZ sensitive.     

Calsequestrin-mediated mechanism for cellular calcium transient alternans

Intracellular calcium transient alternans (CTA) has a recognized role in arrhythmogenesis, but its origin is not yet fully understood. Recent models of CTA are based on a steep relationship between calcium release from the sarcoplasmic reticulum (SR) and its calcium load before release. This mechanism alone, however, does not explain recent observations of CTA without diastolic SR calcium content alternations. In addition, nanoscopic imaging of calcium dynamics has revealed that the elementary calcium release units of the SR can become refractory independently of their local calcium content. Here we show using a new physiologically detailed mathematical model of calcium cycling that luminal gating of the calcium release channels (RyRs) mediated by the luminal buffer calsequestrin (CSQN) can cause CTA independently of the steepness of the release-load relationship. In this complementary mechanism, CTA is caused by a beat-to-beat alternation in the number of refractory RyR channels and can occur with or without diastolic SR calcium content alternans depending on pacing conditions and uptake dynamics. The model has unique features, in that it treats a realistic number of spatially distributed and diffusively coupled dyads, each one with a realistic number of RyR channels, and that luminal CSQN buffering and gating is incorporated based on experimental data that characterizes the effect of the conformational state of CSQN on its buffering properties. In addition to reproducing observed features of CTA, this multiscale model is able to describe recent experiments in which CSQN expression levels were genetically altered as well as to reproduce nanoscopic measurements of spark restitution properties. The ability to link microscopic properties of the calcium release units to whole cell behavior makes this model a powerful tool to investigate the arrhythmogenic role of abnormal calcium handling in many pathological settings.     

Arrhythmogenic Transient Dynamics in Cardiac Myocytes

Cardiac action potential alternans and early afterdepolarizations (EADs) are linked to cardiac arrhythmias. Periodic action potentials (period 1) in healthy conditions bifurcate to other states such as period 2 or chaos when alternans or EADs occur in pathological conditions. The mechanisms of alternans and EADs have been extensively studied under steady-state conditions, but lethal arrhythmias often occur during the transition between steady states. Why arrhythmias tend to develop during the transition is unclear. We used low-dimensional mathematical models to analyze dynamical mechanisms of transient alternans and EADs. We show that depending on the route from one state to another, action potential alternans and EADs may occur during the transition between two periodic steady states. The route taken depends on the time course of external perturbations or intrinsic signaling, such as β-adrenergic stimulation, which regulate cardiac calcium and potassium currents with differential kinetics.     

Voltage and Calcium Dynamics Both Underlie Cellular Alternans in Cardiac Myocytes

Cardiac alternans, a putative trigger event for cardiac reentry, is a beat-to-beat alternation in membrane potential and calcium transient. Alternans was originally attributed to instabilities in transmembrane ion channel dynamics (i.e., the voltage mechanism). As of this writing, the predominant view is that instabilities in subcellular calcium handling are the main underlying mechanism. That being said, because the voltage and calcium systems are bidirectionally coupled, theoretical studies have suggested that both mechanisms can contribute. To date, to our knowledge, no experimental evidence of such a dual role within the same cell has been reported. Here, a combined electrophysiological and calcium imaging approach was developed and used to illuminate the contributions of voltage and calcium dynamics to alternans. An experimentally feasible protocol, quantification of subcellular calcium alternans and restitution slope during cycle-length ramping alternans control, was designed and validated. This approach allows simultaneous illumination of the contributions of voltage and calcium-driven instability to total cellular instability as a function of cycle-length. Application of this protocol in in vitro guinea-pig left-ventricular myocytes demonstrated that both voltage- and calcium-driven instabilities underlie alternans, and that the relative contributions of the two systems change as a function of pacing rate.     

Voltage and Calcium Dynamics Both Underlie Cellular Alternans in Cardiac Myocytes

Cardiac alternans, a putative trigger event for cardiac reentry, is a beat-to-beat alternation in membrane potential and calcium transient. Alternans was originally attributed to instabilities in transmembrane ion channel dynamics (i.e., the voltage mechanism). As of this writing, the predominant view is that instabilities in subcellular calcium handling are the main underlying mechanism. That being said, because the voltage and calcium systems are bidirectionally coupled, theoretical studies have suggested that both mechanisms can contribute. To date, to our knowledge, no experimental evidence of such a dual role within the same cell has been reported. Here, a combined electrophysiological and calcium imaging approach was developed and used to illuminate the contributions of voltage and calcium dynamics to alternans. An experimentally feasible protocol, quantification of subcellular calcium alternans and restitution slope during cycle-length ramping alternans control, was designed and validated. This approach allows simultaneous illumination of the contributions of voltage and calcium-driven instability to total cellular instability as a function of cycle-length. Application of this protocol in in vitro guinea-pig left-ventricular myocytes demonstrated that both voltage- and calcium-driven instabilities underlie alternans, and that the relative contributions of the two systems change as a function of pacing rate.     

Intracellular Calcium Pools in Neuroblastoma × Glioma Hybrid NG108–15 Cells

The intracellular nonmitochondrial calcium pools of saponin-permeabilized NG108-15 cells were characterized using inositol 1,4,5-trisphosphate (IP3) and GTP. IP3 or GTP alone induced release of 47 and 68%, respectively, of the calcium that was releasable by A23187. GTP induced release of a further 24% of the calcium after IP3 treatment, whereas IP3 induced release of a further 11% of the calcium after GTP treatment. Guanosine 5'-O-(3-thio)triphosphate had little effect on IP3-induced calcium release but completely inhibited GTP-induced calcium release. In contrast, heparin inhibited the action of IP3 but not that of GTP. The results imply the existence of at least three nonmitochondrial pools: (a) 31% is releasable by IP3 and GTP, (b) 11% is releasable by IP3 alone, and (c) 24% is releasable by GTP alone. GTP enhanced calcium uptake in the presence of oxalate with an EC50 of 0.6 microM and stimulated calcium release in the absence of oxalate with an EC50 of 0.32 microM. The similar EC50 values for these dual effects of GTP on calcium movement suggest that GTP exerts its dual action by the same mechanism.     

Formation of Spatially Discordant Alternans Due to Fluctuations and Diffusion of Calcium

Spatially discordant alternans (SDA) of action potential duration (APD) is a phenomenon where different regions of cardiac tissue exhibit an alternating sequence of APD that are out-of-phase. SDA is arrhythmogenic since it can induce spatial heterogeneity of refractoriness, which can cause wavebreak and reentry. However, the underlying mechanisms for the formation of SDA are not completely understood. In this paper, we present a novel mechanism for the formation of SDA in the case where the cellular instability leading to alternans is caused by intracellular calcium (Ca) cycling, and where Ca transient and APD alternans are electromechanically concordant. In particular, we show that SDA is formed when rapidly paced cardiac tissue develops alternans over many beats due to Ca accumulation in the sarcoplasmic reticulum (SR). The mechanism presented here relies on the observation that Ca cycling fluctuations dictate Ca alternans phase since the amplitude of Ca alternans is small during the early stages of pacing. Thus, different regions of a cardiac myocyte will typically develop Ca alternans which are opposite in phase at the early stages of pacing. These subcellular patterns then gradually coarsen due to interactions with membrane voltage to form steady state SDA of voltage and Ca on the tissue scale. This mechanism for SDA is distinct from well-known mechanisms that rely on conduction velocity restitution, and a Turing-like mechanism known to apply only in the case where APD and Ca alternans are electromechanically discordant. Furthermore, we argue that this mechanism is robust, and is likely to underlie a wide range of experimentally observed patterns of SDA.     

Effect of caffeine on kinetics of accumulation and release of Ca2+ by vesicles of the sarcoplasmic reticulum of skeletal muscle

The action of caffeine was studied on the heavy sarcoplasmic reticulum fraction enriched by vesicles derived from terminal cisterns. Caffeine lowers the ATP-dependent accumulation of Ca2+ by vesicles and enhances the first rapid phase of the Ci2+ release from vesicles. The action of caffeine was transient, reversed, Ca2+-dependent. The data obtained suggest that the reduction of ATP-dependent calcium accumulation and enhancement of calcium release by caffeine are mediated by the mechanism of Ca2+-induced Ca2+ release and support the view that caffeine may regulate the equilibrium between open and closed states of Ca2+-channel by increasing the affinity of Ca2+-receptor site of the channel.     

Calcium oxalate and calcium phosphate capacities of cardiac sarcoplasmic reticulum

Both oxalate-supported and phosphate-supported calcium uptake by canine cardiac sarcoplasmic reticulum initially increase linearly with time but fall to a steady-state level within 20 min. The departure from linearity could be due to a decrease in influx or to an increase in efflux of calcium. Because Ca2+-ATPase activity is linear, a decrease in the influx of calcium is an unlikely cause of the non-linear calcium uptake curves. A possible cause of an increase in calcium efflux is rupture of the vesicles. This hypothesis was tested by investigating the amount of calcium which could be released upon addition of 5 mM EGTA. The amount of rapidly releasable calcium was zero until a threshold calcium uptake of about 4-6 mumol calcium oxalate or calcium phosphate per mg was reached. After that point the rapidly releasable calcium continued to increase with calcium oxalate to reach more than 23 mumol/mg, but stayed constant at about 0.7 mumol/mg for calcium phosphate. The rapidly releasable calcium was attributed to calcium oxalate or calcium phosphate crystals externalized by vesicle rupture. The differences in the amounts of rapidly releasable calcium were attributed to different kinetics of calcium phosphate and calcium oxalate dissolution. Addition of ryanodine caused a marked increase in the threshold for rapidly releasable calcium oxalate. Transmission electron micrographs showed that vesicles can become filled with calcium oxalate crystals, but the vesicles were heterogeneous with respect to their size and their sensitivity to ryanodine. These observations support the hypothesis that calcium oxalate and calcium phosphate capacities are limited by vesicle rupture and that ryanodine increases the capacity by closing a calcium channel in a subpopulation of vesicles that otherwise would not accumulate calcium.     

Oscillation in cycle length induces transient discordant and steady-state concordant alternans in the heart

Alternans is a beat-to-beat alternation of the cardiac action potential duration (APD) or intracellular calcium (Ca(i)) transient. In cardiac tissue, alternans can be spatially concordant or discordant, of which the latter has been shown to increase dispersion of repolarization and promote a substrate for initiation of ventricular fibrillation. Alternans has been studied almost exclusively under constant cycle length pacing conditions. However, heart rate varies greatly on a beat-by-beat basis in normal and pathological conditions. The purpose of this study was to determine if applying a repetitive but non-constant pacing pattern, specifically cycle length oscillation (CLO), promotes or suppresses a proarrhythmic substrate. We performed computational simulations and optical mapping experiments to investigate the potential consequences of CLO. In a single cell computational model, CLO induced APD and Ca(i) alternans, which became "phase-matched" with the applied oscillation. As a consequence of the phase-matching, in one-dimensional cable simulations, neonatal rat ventricular myocyte monolayers, and isolated adult guinea pig hearts CLO could transiently induce spatial and electromechanical discordant alternans followed by a steady-state of concordance. Our results demonstrated that under certain conditions, CLO can initiate ventricular fibrillation in the isolated hearts. On the other hand, CLO can also exert an antiarrhythmic effect by converting an existing state of discordant alternans to concordant alternans.     

Characteristics of functioning of electromechanical coupling in striated muscles of higher and lower vertebrates

A comparative pharmacological analysis of relative contributions of different signal transduction pathways in the activation of contraction (excitation-contraction coupling, ECC) in intact fast striated muscles of frog and lamprey was performed. It was found that the major mechanism responsible for the ECC in muscles of both animals is Ca2+ release from the sarcoplasmic reticulum through the ryanodine-sensitive channels. However, the ECC in lamprey muscle displays some important differences in the units of electromechanical coupling, which precede the calcium release from sarcoplasmic reticulum. The maximum contraction force in frog muscle develops during caffeine-induced contracture, which indicates that all Ca2+ stored in sarcoplasmic reticulum is released through ryanodine-sensitive channels. In contrast, in lamprey muscle, the maximum force develops not in response to high caffeine concentration, but in response to repetitive electrical stimulation. Hence, in addition to stores liberated by ryanodine-sensitive channels, some other sources of calcium ions should exist, which contribute to the contraction activation. A source of this additional Ca2+ ions can be external medium, because acetylcholine contracture is abolished in a calcium-free medium. In frog muscle, the acetylcholine contracture was abolished in a Na(+)-free solution. It was concluded that in frog muscle ECC can be triggered by changes in the transmembrane potential (depolarization-induced calcium release), while in lamprey muscle the entry of calcium ions into myoplasm as the trigger in ECC (calcium-induced calcium release). The lamprey muscle was found to be more resistant to tetrodotoxin and tetracaine, which is indicative of a role in the activation of contraction of tetrodotoxin-resistant Na+ and/or Ca2+ channels. It was concluded, that ECC mechanism in striated muscles of low vertebrates is not limited by the generally accepted scheme of depolarization-induced calcium release but can include some other schemes, which require the Ca2+ influx into the cell.     

心肌细胞兴奋-收缩偶联的微观机制

心肌细胞的兴奋 收缩偶联 (ECC)本质上是胞膜上的电压门控L 型钙通道 (LCCs)和胞内ryanodine受体 (RyRs)之间通过钙诱导钙释放 (CICR)机制进行沟通进而引发肌细胞收缩的过程。最近的研究进一步揭示了微观水平上LCCs和RyRs之间的信息联系。在钙偶联位点 (couplons)上 ,LCCs因膜去极化而随机开放 ,在局部产生高强度的钙脉冲 (即钙小星 ,Ca2 sparklet) ,作用于邻近肌质网终末池上的RyRs。钙偶联位点通过由钙小星随机激活的RyRs(即钙释放通道 )以钙火花 (Ca2 spark)的形式释放钙。这些钙在全细胞水平上总和即形成钙瞬变 (Ca2 transient)。因此 ,钙小星触发钙火花就构成了ECC中的基本事件。本文重点阐述LCCs和RyRs分子间的信号转导机制 ,也即从微观水平上探讨CICR及ECC的形成机制。