Numerical simulation of Ca2+ "sparks" in skeletal muscle

A 3D diffusional-compartmental model of the calcium dynamics in cytosol, sarcoplasmic reticulum and mitochondria of murine skeletal muscle fibers

Variations of free calcium concentration ([Ca2+]) are powerful intracellular signals, controlling contraction as well as metabolism in muscle cells. To fully understand the role of calcium redistribution upon excitation and contraction in skeletal muscle cells, the local [Ca2+] in different compartments needs to be taken into consideration. Fluorescent probes allow the determination of [Ca2+] in the cytosol where myofibrils are embedded, the lumen of the sarcoplasmic reticulum (SR) and the mitochondrial matrix. Previously, models have been developed describing intracellular calcium handling in skeletal and cardiac muscle cells. However, a comprehensive model describing the kinetics of the changes in free calcium concentration in these three compartments is lacking. We designed a new 3D compartmental model of the half sarcomere with radial symmetry, which accounts for diffusion of Ca2+ into the three compartments and simulates its dynamics at rest and at various rates of stimulation in mice skeletal muscle fibers. This model satisfactorily reproduces both the amplitude and time course of the variations of [Ca2+] in the three compartments in mouse fast fibers. As an illustration of the applicability of the model, we investigated the effects of Calsequestrin (CSQ) ablation. CSQ is the main Ca2+ buffer in the SR, localized in close proximity of its calcium release sites and near to the mitochondria. CSQ knock-out mice muscles still preserve a near-normal contractile behavior, but it is unclear whether this is caused by additional SR calcium buffering or a significant contribution of calcium entry from extracellular space, via stored-operated calcium entry (SOCE). The model enabled quantitative assessment of these two scenarios by comparison to measurements of local calcium in the cytosol, the SR and the mitochondria. In conclusion, the model represents a useful tool to investigate the impact of protein ablation and of pharmacological interventions on intracellular calcium dynamics in mice skeletal muscle.

Voltage sensing mechanism in skeletal muscle excitation-contraction coupling: coming of age or midlife crisis?

The process by which muscle fiber electrical depolarization is linked to activation of muscle contraction is known as excitation-contraction coupling (ECC). Our understanding of ECC has increased enormously since the early scientific descriptions of the phenomenon of electrical activation of muscle contraction by Galvani that date back to the end of the eighteenth century. Major advances in electrical and optical measurements, including muscle fiber voltage clamp to reveal membrane electrical properties, in conjunction with the development of electron microscopy to unveil structural details provided an elegant view of ECC in skeletal muscle during the last century. This surge of knowledge on structural and biophysical aspects of the skeletal muscle was followed by breakthroughs in biochemistry and molecular biology, which allowed for the isolation, purification, and DNA sequencing of the muscle fiber membrane calcium channel/transverse tubule (TT) membrane voltage sensor (Cav1.1) for ECC and of the muscle ryanodine receptor/sarcoplasmic reticulum Ca2+ release channel (RyR1), two essential players of ECC in skeletal muscle. In regard to the process of voltage sensing for controlling calcium release, numerous studies support the concept that the TT Cav1.1 channel is the voltage sensor for ECC, as well as also being a Ca2+ channel in the TT membrane. In this review, we present early and recent findings that support and define the role of Cav1.1 as a voltage sensor for ECC.

Calcium-induced release of calcium in muscle: 50 years of work and the emerging consensus

Ryanodine-sensitive intracellular Ca2+ channels (RyRs) open upon binding Ca2+ at cytosolic-facing sites. This results in concerted, self-reinforcing opening of RyRs clustered in specialized regions on the membranes of Ca2+ storage organelles (endoplasmic reticulum and sarcoplasmic reticulum), a process that produces Ca2+-induced Ca2+ release (CICR). The process is optimized to achieve large but brief and localized increases in cytosolic Ca2+ concentration, a feature now believed to be critical for encoding the multiplicity of signals conveyed by this ion. In this paper, I trace the path of research that led to a consensus on the physiological significance of CICR in skeletal muscle, beginning with its discovery. I focus on the approaches that were developed to quantify the contribution of CICR to the Ca2+ increase that results in contraction, as opposed to the flux activated directly by membrane depolarization (depolarization-induced Ca2+ release [DICR]). Although the emerging consensus is that CICR plays an important role alongside DICR in most taxa, its contribution in most mammalian muscles appears to be limited to embryogenesis. Finally, I survey the relevance of CICR, confirmed or plausible, to pathogenesis as well as the multiple questions about activation of release channels that remain unanswered after 50 years.

Microdomain calcium fluctuations as a colored noise process

Calcium ions play a key role in subcellular signaling as localized transients of the intracellular calcium concentration modify the activity of ion channels, enzymes and transcription factors, among others. The intracellular calcium concentration is inherently noisy, as diffusion, the transient binding to and dissociation from buffer molecules and stochastically gating calcium channels contribute to the fluctuations of the local copy number of Ca²⁺ ions. We study the properties of the fluctuating calcium concentration in sub-femtoliter volumes using an exact stochastic simulation algorithm and approximations to the exact stochastic solution. It is shown that the time course of the local calcium concentration represents a colored noise process whose autocorrelation time is a function of buffer kinetics and diffusion constants. Using the chemical Langevin description and the excess buffer approximation of the process, fast approximative algorithms and theoretical connections to the Ornstein-Uhlenbeck process are obtained. In a generic example, we show how calcium noise can couple to the dynamics of a single variable moving in a double-well potential, leading to a colored noise induced transition. Our work shows how a multitude of intracellular signaling pathways may be influenced by the inherent stochasticity of calcium signals, a key messenger in virtually any cell type, and how the calcium signal can be implemented efficiently in cellular signaling models.

Calcium waves initiating from the anomalous subdiffusive calcium sparks

The objective of the study is to investigate the propagation of Ca(2+) waves in full-width cardiac myocytes and carry out sensitivity analysis to study the effects of various physiological parameters on global Ca(2+) waves. Based on the anomalous subdiffusion of Ca(2+) sparks, a mathematical model was proposed to characterize the Ca(2+) waves. The computed results were in agreement with the experimental measurements using confocal microscopy. This model includes variables of current through the Ca(2+) release unit (CRU; ICRU), duration of current flow through CRU (Topen), Ca(2+) sensitivity parameter (K), the longitudinal and transverse spatial separation of CRUs (lx and ly, where x denotes longitudinal direction (x-axis) and y denotes transverse direction (y-axis)) and Ca(2+) diffusion coefficients (Dx, Dy). The spatio-temporal mechanism of the anomalous Ca(2+) sparks led to results that were different from those based on Fick's law. The major findings were reported as: ICRU affected the dynamic properties of Ca(2+) waves more significantly than Topen; the effect of K on the properties of Ca(2+) waves was negligible; ly affected the amplitude significantly, but lx affected the longitudinal velocity significantly; in turn, the limitation and significance of the study are discussed.

Evoked centripetal Ca(2+) mobilization in cardiac Purkinje cells: insight from a model of three Ca(2+) release regions

Despite strong suspicion that abnormal Ca(2+) handling in Purkinje cells (P-cells) is implicated in life-threatening forms of ventricular tachycardias, the mechanism underlying the Ca(2+) cycling of these cells under normal conditions is still unclear. There is mounting evidence that P-cells have a unique Ca(2+) handling system. Notably complex spontaneous Ca(2+) activity was previously recorded in canine P-cells and was explained by a mechanistic hypothesis involving a triple layered system of Ca(2+) release channels. Here we examined the validity of this hypothesis for the electrically evoked Ca(2+) transient which was shown, in the dog and rabbit, to occur progressively from the periphery to the interior of the cell. To do so, the hypothesis was incorporated in a model of intracellular Ca(2+) dynamics which was then used to reproduce numerically the Ca(2+) activity of P-cells under stimulated conditions. The modelling was thus performed through a 2D computational array that encompassed three distinct Ca(2+) release nodes arranged, respectively, into three consecutive adjacent regions. A system of partial differential equations (PDEs) expressed numerically the principal cellular functions that modulate the local cytosolic Ca(2+) concentration (Cai). The apparent node-to-node progression of elevated Cai was obtained by combining Ca(2+) diffusion and 'Ca(2+)-induced Ca(2+) release'. To provide the modelling with a reliable experimental reference, we first re-examined the Ca(2+) mobilization in swine stimulated P-cells by 2D confocal microscopy. As reported earlier for the dog and rabbit, a centripetal Ca(2+) transient was readily visible in 22 stimulated P-cells from six adult Yucatan swine hearts (pacing rate: 0.1 Hz; pulse duration: 25 ms, pulse amplitude: 10% above threshold; 1 mm Ca(2+); 35°C; pH 7.3). An accurate replication of the observed centripetal Ca(2+) propagation was generated by the model for four representative cell examples and confirmed by statistical comparisons of simulations against cell data. Selective inactivation of Ca(2+) release regions of the computational array showed that an intermediate layer of Ca(2+) release nodes with an ~30-40% lower Ca(2+) activation threshold was required to reproduce the phenomenon. Our computational analysis was therefore fully consistent with the activation of a triple layered system of Ca(2+) release channels as a mechanism of centripetal Ca(2+) signalling in P-cells. Moreover, the model clearly indicated that the intermediate Ca(2+) release layer with increased sensitivity for Ca(2+) plays an important role in the specific intracellular Ca(2+) mobilization of Purkinje fibres and could therefore be a relevant determinant of cardiac conduction.

Intracellular calcium movements during excitation-contraction coupling in mammalian slow-twitch and fast-twitch muscle fibers

In skeletal muscle fibers, action potentials elicit contractions by releasing calcium ions (Ca²⁺) from the sarcoplasmic reticulum. Experiments on individual mouse muscle fibers micro-injected with a rapidly responding fluorescent Ca²⁺ indicator dye reveal that the amount of Ca²⁺ released is three- to fourfold larger in fast-twitch fibers than in slow-twitch fibers, and the proportion of the released Ca²⁺ that binds to troponin to activate contraction is substantially smaller.

Properties of Ca2+ sparks revealed by four-dimensional confocal imaging of cardiac muscle

Parameters (amplitude, width, kinetics) of Ca²⁺ sparks imaged confocally are affected by errors when the spark source is not in focus. To identify sparks that were in focus, we used fast scanning (LSM 5 LIVE; Carl Zeiss) combined with fast piezoelectric focusing to acquire x–y images in three planes at 1-µm separation (x-y-z-t mode). In 3,000 x–y scans in each of 34 membrane-permeabilized cat atrial cardiomyocytes, 6,906 sparks were detected. 767 sparks were in focus. They had greater amplitude, but their spatial width and rise time were similar compared with all sparks recorded. Their distribution of amplitudes had a mode at ΔF/F₀ = 0.7. The Ca²⁺ release current underlying in-focus sparks was 11 pA, requiring 20 to 30 open channels, a number at the high end of earlier estimates. Spark frequency was greater than in earlier imaging studies of permeabilized ventricular cells, suggesting a greater susceptibility to excitation, which could have functional relevance for atrial cells. Ca²⁺ release flux peaked earlier than the time of peak fluorescence and then decayed, consistent with significant sarcoplasmic reticulum (SR) depletion. The evolution of fluorescence and release flux were strikingly similar for in-focus sparks of different rise time (T). Spark termination involves both depletion of Ca²⁺ in the SR and channel closure, which may be synchronized by depletion. The observation of similar flux in sparks of different T requires either that channel closure and other termination processes be independent of the determinants of flux (including [Ca²⁺]_SR) or that different channel clusters respond to [Ca²⁺]_SR with different sensitivity.

Simulation strategies for calcium microdomains and calcium-regulated calcium channels

In this article, we present an overview of simulation strategies in the context of subcellular domains where calcium-dependent signaling plays an important role. The presentation follows the spatial and temporal scales involved and represented by each algorithm. As an exemplary cell type, we will mainly cite work done on striated muscle cells, i.e. skeletal and cardiac muscle. For these cells, a wealth of ultrastructural, biophysical and electrophysiological data is at hand. Moreover, these cells also express ubiquitous signaling pathways as they are found in many other cell types and thus, the generalization of the methods and results presented here is straightforward.The models considered comprise the basic calcium signaling machinery as found in most excitable cell types including Ca(2+) ions, diffusible and stationary buffer systems, and calcium regulated calcium release channels. Simulation strategies can be differentiated in stochastic and deterministic algorithms. Historically, deterministic approaches based on the macroscopic reaction rate equations were the first models considered. As experimental methods elucidated highly localized Ca(2+) signaling events occurring in femtoliter volumes, stochastic methods were increasingly considered. However, detailed simulations of single molecule trajectories are rarely performed as the computational cost implied is too large. On the mesoscopic level, Gillespie's algorithm is extensively used in the systems biology community and with increasing frequency also in models of microdomain calcium signaling. To increase computational speed, fast approximations were derived from Gillespie's exact algorithm, most notably the chemical Langevin equation and the τ-leap algorithm. Finally, in order to integrate deterministic and stochastic effects in multiscale simulations, hybrid algorithms are increasingly used. These include stochastic models of ion channels combined with deterministic descriptions of the calcium buffering and diffusion system on the one hand, and algorithms that switch between deterministic and stochastic simulation steps in a context-dependent manner on the other. The basic assumptions of the listed methods as well as implementation schemes are given in the text. We conclude with a perspective on possible future developments of the field.

Age-related regulation of excitation-contraction coupling in rat heart

Hearts from subjects with different ages have different Ca(2+) signaling. Release of Ca(2+) from intracellular stores in response to an action potential initiates cardiac contraction. Both depolarization-stimulated and spontaneous Ca(2+) releases, Ca(2+) transients and Ca(2+) sparks, demonstrate the main events of excitation-contraction coupling (ECC). Global increase in free Ca(2+) concentration ([Ca(2+)]( i )) consists of summation of Ca(2+) release events in cardiomyocytes. Since the Ca(2+) flux induced by Ca(2+) sparks reports a summation of ryanodine-sensitive Ca(2+) release channels (RyR2s)'s behavior in a spark cluster, evaluation of the properties of Ca(2+) sparks and Ca(2+) transients may provide insight into the role of RyR2s on altered heart function between 3-month-old (young adult) and 6-month-old (mature adult) rats. Basal [Ca(2+)]( i ) and Ca(2+) sparks frequency were significantly higher in mature adult rats compared to those of young adults. Moreover, amplitudes of Ca(2+) sparks and Ca(2+) transients were significantly smaller in mature adults than those of young adults with longer time courses. A smaller L-type Ca(2+) current density and decreased SR Ca(2+) load was observed in mature adult rats. In addition, RyR2s were markedly hyperphosphorylated, and phosphorylation levels of PKA and CaMKII were higher in heart from mature adults compared to those of young adults, whereas their SERCA protein levels were similar. Our data demonstrate that hearts from rats with different ages have different Ca(2+) signaling including hyperphosphorylation of RyR2s and higher basal [Ca(2+)]( i ) together with increased oxidized protein-thiols in mature adult rats compared to those of young adults, which play important roles in ECC. Finally, we report that ECC efficiency changes with age during maturation, partially related with an increased cellular oxidation level leading to reduced free protein-thiols in cardiomyocytes.

Model Convolution: A Computational Approach to Digital Image Interpretation

Digital fluorescence microscopy is commonly used to track individual proteins and their dynamics in living cells. However, extracting molecule-specific information from fluorescence images is often limited by the noise and blur intrinsic to the cell and the imaging system. Here we discuss a method called “model-convolution,” which uses experimentally measured noise and blur to simulate the process of imaging fluorescent proteins whose spatial distribution cannot be resolved. We then compare model-convolution to the more standard approach of experimental deconvolution. In some circumstances, standard experimental deconvolution approaches fail to yield the correct underlying fluorophore distribution. In these situations, model-convolution removes the uncertainty associated with deconvolution and therefore allows direct statistical comparison of experimental and theoretical data. Thus, if there are structural constraints on molecular organization, the model-convolution method better utilizes information gathered via fluorescence microscopy, and naturally integrates experiment and theory.

Low-affinity Ca2+ indicators compared in measurements of skeletal muscle Ca2+ transients

The low-affinity fluorescent Ca(2+) indicators OGB-5N, Fluo-5N, fura-5N, Rhod-5N, and Mag-fluo-4 were evaluated for their ability to accurately track the kinetics of the spatially averaged free Ca(2+) transient (Delta[Ca(2+)]) in skeletal muscle. Frog single fibers were injected with one of the above indicators and, usually, furaptra (previously shown to rapidly track Delta[Ca(2+)]). In response to an action potential, the full duration at half-maximum of the indicator's fluorescence change (DeltaF) was found to be larger with OGB-5N, Fluo-5N, fura-5N, and Rhod-5N than with furaptra; thus, these indicators do not track Delta[Ca(2+)] with kinetic fidelity. In contrast, the DeltaF time course of Mag-fluo-4 was identical to furaptra's; thus, Mag-fluo-4 also yields reliable kinetic information about Delta[Ca(2+)]. Mag-fluo-4's DeltaF has a larger signal/noise ratio than furaptra's (for similar indicator concentrations), and should thus be more useful for tracking Delta[Ca(2+)] in small cell volumes. However, because the resting fluorescence of Mag-fluo-4 probably arises largely from indicator that is bound with Mg(2+), the amplitude of the Mag-fluo-4 signal, and its calibration in Delta[Ca(2+)] units, is likely to be more sensitive to variations in [Mg(2+)] than furaptra's.

Calcium-Induced Calcium Release in Skeletal Muscle

Calcium-induced calcium release (CICR) was first discovered in skeletal muscle. CICR is defined as Ca2+ release by the action of Ca2+ alone without the simultaneous action of other activating processes. CICR is biphasically dependent on Ca2+ concentration; is inhibited by Mg2+, procaine, and tetracaine; and is potentiated by ATP, other adenine compounds, and caffeine. With depolarization of the sarcoplasmic reticulum (SR), a potential change of the SR membrane in which the luminal side becomes more negative, CICR is activated for several seconds and is then inactivated. All three types of ryanodine receptors (RyRs) show CICR activity. At least one RyR, RyR1, also shows non-CICR Ca2+ release, such as that triggered by the t-tubule voltage sensor, by clofibric acid, and by SR depolarization. Maximum rates of CICR, at the optimal Ca2+ concentration in the presence of physiological levels of ATP and Mg2+ determined in skinned fibers and fragmented SR, are much lower than the rate of physiological Ca2+ release. The primary event of physiological Ca2+ release, the Ca2+ spark, is the simultaneous opening of multiple channels, the coordinating mechanism of which does not appear to be CICR because of the low probability of CICR opening under physiological conditions. The coordination may require Ca2+, but in that case, some other stimulus or stimuli must be provided simultaneously, which is not CICR by definition. Thus CICR does not appear to contribute significantly to physiological Ca2+ release. On the other hand, CICR appears to play a key role in caffeine contracture and malignant hyperthermia. The potentiation of voltage-activated Ca2+ release by caffeine, however, does not seem to occur through secondary CICR, although the site where caffeine potentiates voltage-activated Ca2+ release might be the same site where caffeine potentiates CICR.

Stochastic simulation of calcium microdomains in the vicinity of an L-type calcium channel

We study numerically the local dynamics of the intracellular calcium concentration in the vicinity of a voltage- and calcium-dependent plasma membrane L-type calcium channel. To account for the low number of Ca(2+) ions and buffer molecules present in sub-femtoliter volumes, we use an exact stochastic simulation algorithm including diffusion. We present a novel, unified simulation method that implements reaction-diffusion events of Ca(2+) ions and buffer molecules, stochastic ion channel gating and channel conductance as a multivariate Markov process. For fixed-voltage dynamics, e.g. under voltage-clamp conditions, it is shown that voltage-sensitive channel-gating steps can be incorporated exactly. We compare multi- and single-voxel geometries and show that the single-voxel approach leads to almost identical first- and second-order moments, at much lower computation time. Numerical examples illustrate the variability in local Ca(2+) fluctuations as induced by bursts of channel openings in response to membrane depolarisations. Finally, by introducing calmodulin as a link, it is shown how this variability is passed on to downstream signalling pathways. The method may prove useful to study calcium microdomains and calcium-regulated processes triggered by membrane depolarisations as evoked by, e.g., viral channel-forming proteins during virus-host cell interactions.

Calcium sparks

The calcium ion (Ca(2+)) is the simplest and most versatile intracellular messenger known. The discovery of Ca(2+) sparks and a related family of elementary Ca(2+) signaling events has revealed fundamental principles of the Ca(2+) signaling system. A newly appreciated "digital" subsystem consisting of brief, high Ca(2+) concentration over short distances (nanometers to microns) comingles with an "analog" global Ca(2+) signaling subsystem. Over the past 15 years, much has been learned about the theoretical and practical aspects of spark formation and detection. The quest for the spark mechanisms [the activation, coordination, and termination of Ca(2+) release units (CRUs)] has met unexpected challenges, however, and raised vexing questions about CRU operation in situ. Ample evidence shows that Ca(2+) sparks catalyze many high-threshold Ca(2+) processes involved in cardiac and skeletal muscle excitation-contraction coupling, vascular tone regulation, membrane excitability, and neuronal secretion. Investigation of Ca(2+) sparks in diseases has also begun to provide novel insights into hypertension, cardiac arrhythmias, heart failure, and muscular dystrophy. An emerging view is that spatially and temporally patterned activation of the digital subsystem confers on intracellular Ca(2+) signaling an exquisite architecture in space, time, and intensity, which underpins signaling efficiency, stability, specificity, and diversity. These recent advances in "sparkology" thus promise to unify the simplicity and complexity of Ca(2+) signaling in biology.

Calcium-dependent inactivation terminates calcium release in skeletal muscle of amphibians

In skeletal muscle of amphibians, the cell-wide cytosolic release of calcium that enables contraction in response to an action potential appears to be built of Ca²⁺ sparks. The mechanism that rapidly terminates this release was investigated by studying the termination of Ca²⁺ release underlying sparks. In groups of thousands of sparks occurring spontaneously in membrane-permeabilized frog muscle cells a complex relationship was found between amplitude a and rise time T, which in sparks corresponds to the active time of the underlying Ca²⁺ release. This relationship included a range of T where a paradoxically decreased with increasing T. Three different methods were used to estimate Ca²⁺ release flux in groups of sparks of different T. Using every method, it was found that T and flux were inversely correlated, roughly inversely proportional. A simple model in which release sources were inactivated by cytosolic Ca²⁺ was able to explain the relationship. The predictive value of the model, evaluated by analyzing the variance of spark amplitude, was found to be high when allowance was made for the out-of-focus error contribution to the total variance. This contribution was estimated using a theory of confocal scanning (Ríos, E., N. Shirokova, W.G. Kirsch, G. Pizarro, M.D. Stern, H. Cheng, and A. González. Biophys. J. 2001. 80:169–183), which was confirmed in the present work by simulated line scanning of simulated sparks. Considering these results and other available evidence it is concluded that Ca²⁺-dependent inactivation, or CDI, provides the crucial mechanism for termination of sparks and cell-wide Ca²⁺ release in amphibians. Given the similarities in kinetics of release termination observed in cell-averaged records of amphibian and mammalian muscle, and in spite of differences in activation mechanisms, CDI is likely to play a central role in mammals as well. Trivially, an inverse proportionality between release flux and duration, in sparks or in global release of skeletal muscle, maintains constancy of the amount of released Ca²⁺.

Transport-dependent calcium signaling in spatially segregated cellular caveolar domains

We developed a two-dimensional model of transport-dependent intracellular calcium signaling in endothelial cells (ECs). Our purpose was to evaluate the effects of spatial colocalization of endothelial nitric oxide synthase (eNOS) and capacitative calcium entry (CCE) channels in caveolae on eNOS activation in response to ATP. Caveolae are specialized microdomains of the plasma membrane that contain a variety of signaling molecules to optimize their interactions and regulate their activity. In ECs, these molecules include CCE channels and eNOS. To achieve a quantitative understanding of the mechanisms of microdomain calcium signaling and the preferential sensitivity of eNOS to calcium entering the cell through CCE channels, we constructed a mathematical model incorporating the cell morphology and cellular physiological processes. The model predicts that the spatial segregation of calcium channels in ECs can create transport-dependent sharp gradients in calcium concentration within the cell. The calcium concentration gradient is affected by channel density and cell geometry. This transport-dependent calcium signaling specificity effect is enhanced in ECs by increasing the spatial segregation of the caveolar signaling domains. Our simulation significantly advances the understanding of how Ca2+, despite its many potential actions, can mediate selective activation of signaling pathways. We show that diffusion-limited calcium transport allows functional compartmentalization of signaling pathways based on the spatial arrangements of Ca2+ sources and targets.

Fast XYT imaging of elementary calcium release events in muscle with multifocal multiphoton microscopy and wavelet denoising and detection

We used multifocal multiphoton microscopy to image fast, localized elevations of the cytosolic Ca2+ concentration in two spatial dimensions plus time (XYT). This technique extends the common spatially 1-D XT imaging and allows the acquisition of more than ten times longer time series (>500 images) and ten times larger areas of interest than for previously used confocal XYT imaging techniques due to lower phototoxicity and fast multifocal scanning. We recorded spontaneously occurring elementary Ca2+ release events in chemically permeabilized adult mammalian skeletal muscle fibers using two-photon excitation of the fluorescent dye Fluo-4. The resulting time series were analyzed with an automated denoising and detection algorithm based on the à trous implementation of the discrete wavelet transform. Wavelet coefficient hard-thresholding is used for denoising and event detection is performed across several wavelet scales. The spatiotemporal characteristics of the detected Ca2+ release events are followed throughout the XYT stack and are parametrized using a biophysically valid anisotropic Gaussian event model. The proposed method allows a detailed spatiotemporal analysis of elementary Ca2+ release events underlying the excitation-contraction coupling process in muscle.

Ca2+ sparks in skeletal muscle

The study of Ca2+ sparks has led to extensive new information regarding the gating of the Ca2+ release channels underlying these events in skeletal, cardiac and smooth muscle cells, as well as the possible roles of these local Ca2+ release events in muscle function. Here we review basic procedures for studying Ca2+ sparks in skeletal muscle, primarily from frog, as well as the basic results concerning the properties of these events, their pattern and frequency of occurrence during fiber depolarization and the mechanisms underlying their termination. Finally, we also consider the contribution of different ryanodine receptor (RyR) isoforms to Ca2+ sparks and the number of RyR Ca2+ release channels that may contribute to the generation of a Ca2+ spark. Over the decade since their discovery, Ca2+ sparks have provided a wealth of information concerning the function of Ca2+ release channels within their intracellular environment.

Elementary Ca2+ release events in mammalian skeletal muscle: effects of the anaesthetic drug thiopental

We examined the effect of clinically relevant doses of thiopental (10-100 microM) on Ca2+ release from the sarcoplasmic reticulum of chemically skinned skeletal muscle fibres of the mouse. Elementary Ca2+ release events (ECRE) were recorded with confocal microscopy and were detected and analysed by an automated algorithm. Thiopental at 25 microM evoked a marked increase in ECRE frequency (events/100 microm/s) from 0.64 +/- 0.32 to 1.56 +/- 0.38 (P < 0.001). Incubation with 5 microM ryanodine significantly reduced spontaneous and evoked ECRE frequencies to 0.08 +/- 0.08 (P < 0.001) and 0.39 +/- 0.25 (25 microM thiopental, P < 0.001) respectively. Thiopental-evoked ECRE show different morphological characteristics compared to spontaneous events. Maximum relative amplitudes (DeltaF/F0)max and spatial width (full width at half maximum) of the events were substantially increased. Full duration at half maximum was increased and some very long events (200 ms compared to approximately 30 ms standard) were produced. The rise times as an indicator of the channel open time were slightly increased. Furthermore, the occurrence of repetitive ECRE was observed. These events, in contrast to previous observations in amphibian skeletal muscle fibres, displayed a multitude of different release patterns. In particular, a repetitive ECRE mode with successively decaying amplitudes was identified and the inter-event intervals were analysed. Estimation of the underlying Ca2+ release current suggests that during repetitive events with a decaying amplitude a decreasing amount of Ca2+ was released within the individual release event. Possible underlying mechanisms are discussed. In summary, thiopental seems to be a potent RyR1 agonist and substantially alters the gating mechanisms of RyR Ca2+ release channel clusters already in clinically relevant doses, i.e. doses administered during general anaesthesia.

Effects of diabetes on ryanodine receptor Ca release channel (RyR2) and Ca2+ homeostasis in rat heart

The defects identified in the mechanical activity of the hearts from type 1 diabetic animals include alteration of Ca2+ signaling via changes in critical processes that regulate intracellular Ca2+ concentration. These defects result partially from a dysfunction of cardiac ryanodine receptor calcium release channel (RyR2). The present study was designed to determine whether the properties of the Ca2+ sparks might provide insight into the role of RyR2 in the altered Ca2+ signaling in cardiomyocytes from diabetic animals when they were analyzed together with Ca2+ transients. Basal Ca2+ level as well as Ca2+-spark frequency of cardiomyoctes isolated from 5-week streptozotocin (STZ)-induced diabetic rats significantly increased with respect to aged-matched control rats. Ca2+ transients exhibited significantly reduced amplitude and prolonged time courses as well as depressed Ca2+ loading of sarcoplasmic reticulum in diabetic rats. Spatio-temporal properties of the Ca2+ sparks in cardiomyocytes isolated from diabetic rats were also significantly altered to being almost parallel to the changes of Ca2+ transients. In addition, RyR2 from diabetic rat hearts were hyperphosphorylated and protein levels of both RyR2 and FKBP12.6 depleted. These data show that STZ-induced diabetic rat hearts exhibit altered local Ca2+ signaling with increased basal Ca2+ level.

Calcium sparks in skeletal muscle fibers

Ca(2+) sparks monitor transient local releases of Ca(2+) from the sarcoplasmic reticulum (SR) into the myoplasm. The release takes place through ryanodine receptors (RYRs), the Ca(2+)-release channels of the SR. In intact fibers from frog skeletal muscle, the temporal and spatial properties of voltage-activated Ca(2+) sparks are well simulated by a model that assumes that the Ca(2+) flux underlying a spark is 2.5 pA (units of Ca(2+) current) for 4.6 ms (18 degrees C). This flux amplitude suggests that 1-5 active RYRs participate in the generation of a typical voltage-activated spark under physiological conditions. A major goal of future experiments is to estimate this number more precisely and, if it is two or more, to investigate the communication mechanism that allows multiple RYRs to be co-activated in a rapid but self-limited fashion.

Calcium sparks in muscle cells: interactive procedures for automatic detection and measurements on line-scan confocal images series

In muscle cells, force development is controlled by Ca2+ ions, which are rapidly released from the sarcoplasmic reticulum (SR) during sarcolemmal depolarization. In addition to this synchronized spatially homogeneous calcium signal, localized quantal Ca2+ release events (sparks) have been recorded using laser scanning confocal fluorescence microscopy. Previously, algorithms without user intervention have been developed to automatically detect and analyse sparks on confocal line-scan (space-time: 512 x 512 pixels) single images. Here we present a computer program that we called "HARVest of Elementary Events" (HARVELE) developed to both analyse events on series of confocal images and follow sparks morphology from one site during several seconds. HARVELE, coded in the image-processing language IDL 5.3., can be applied on series of n images (512 x 512 x n) obtained from the same scanning line. Computing simultaneously entire series of images allows to measure, for each release site, the frequency and the morphology of release with the conventional amplitude, size, time and duration parameters defined for sparks analysis. The use of these procedures rapidly provides much information about the properties of calcium release sites in muscle cells population and can be applied on any elementary calcium events whatever the type of cell.

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.

Imaging microdomain Ca2+ in muscle cells

Ca2+ ions passing through a single or a cluster of Ca2+-permeable channels create microscopic, short-lived Ca2+ gradients that constitute the building blocks of cellular Ca2+ signaling. Over the last decade, imaging microdomain Ca2+ in muscle cells has unveiled the exquisite spatial and temporal architecture of intracellular Ca2+ dynamics and has reshaped our understanding of Ca2+ signaling mechanisms. Major advances include the visualization of "Ca2+ sparks" as the elementary events of Ca2+ release from the sarcoplasmic reticulum (SR), "Ca2+ sparklets" produced by openings of single Ca2+-permeable channels, miniature Ca2+ transients in single mitochondria ("marks"), and SR luminal Ca2+ depletion transients ("scraps"). As a model system, a cardiac myocyte contains a 3-dimensional grid of 104 spark ignition sites, stochastic activation of which summates into global Ca2+ transients. Tracking intermolecular coupling between single L-type Ca2+ channels and Ca2+ sparks has provided direct evidence validating the local control theory of Ca2+-induced Ca2+ release in the heart. In vascular smooth muscle myocytes, Ca2+ can paradoxically signal both vessel constriction (by global Ca2+ transients) and relaxation (by subsurface Ca2+ sparks). These findings shed new light on the origin of Ca2+ signaling efficiency, specificity, and versatility. In addition, microdomain Ca2+ imaging offers a novel modality that complements electrophysiological approaches in characterizing Ca2+ channels in intact cells.

Imaging single cardiac ryanodine receptor Ca2+ fluxes in lipid bilayers

In this and an accompanying report we describe two steps, single-channel imaging and channel immobilization, necessary for using optical imaging to analyze the function of ryanodine receptor (RyR) channels reconstituted in lipid bilayers. An optical bilayer system capable of laser scanning confocal imaging of fluo-3 fluorescence due to Ca2+ flux through single RyR2 channels and simultaneous recording of single channel currents was developed. A voltage command protocol was devised in which the amplitude, time course, shape, and hence the quantity of Ca2+ flux through a single RyR2 channel is controlled solely by the voltage imposed across the bilayer. Using this system, the voltage command protocol, and concentrations of Ca2+ (25-50 mM) that result in saturating RyR2 Ca2+ currents, proportional fluo-3 fluorescence was recorded simultaneously with Ca2+ currents having amplitudes of 0.25-14 pA. Ca2+ sparks, similar to those obtained with conventional microscope-based laser scanning confocal systems, were imaged in mouse ventricular cardiomyocytes using the optical bilayer system. The utility of the optical bilayer for systematic investigation of how cellular factors extrinsic to the RyR2 channel, such as Ca2+ buffers and diffusion, alter fluo-3 fluorescent responses to RyR2 Ca2+ currents, and for addressing other current research questions is discussed.

Effect of phosphatidylinositol and inside-out erythrocyte vesicles on autolysis of μ- and m-calpain from bovine skeletal muscle

The finding that phospholipid micelles lowered the Ca2+ concentration required for autolysis of the calpains led to a hypothesis suggesting that the calpains are translocated to the plasma membrane where they interact with phospholipids to initiate their autolysis. However, the effect of plasma membranes themselves on the Ca2+ concentration required for calpain autolysis has never been reported. Also, if interaction with a membrane lowers the Ca2+ required for autolysis, the membrane-bound-calpain must autolyze itself, because it would be the only calpain having the reduced Ca2+ requirement. This implies that the autolysis is an intramolecular process, although several studies have shown that autolysis of the calpains in an in vitro assay and in the absence of phospholipid is an intermolecular process. Inside-out vesicles prepared from erythrocytes had no effect on the Ca2+ concentration required for autolysis of either mu- or m-calpain, although phosphatidylinositol (PI) decreased the Ca2+ concentration required for autolysis of the same calpains. The presence of a substrate for the calpains, beta-casein, reduced the rate of autolysis of both mu- and m-calpain both in the presence and in the absence of PI, suggesting that mu- and m-calpain autolysis is an intermolecular process in the presence of PI just as it is in its absence. Because IOV have no effect on the Ca2+ concentration required for calpain autolysis, association with the plasma membrane, at least with erythrocyte plasma membranes, does not initiate calpain autolysis by reducing the Ca2+ concentration required for autolysis as suggested by the membrane-activation hypothesis. Interaction with a membrane may serve to bind calpains to their substrates rather than promoting autolysis.

Voltage-dependent Ca2+ fluxes in skeletal myotubes determined using a removal model analysis

The purpose of this study was to quantify the Ca2+ fluxes underlying Ca2+ transients and their voltage dependence in myotubes by using the "removal model fit" approach. Myotubes obtained from the mouse C2C12 muscle cell line were voltage-clamped and loaded with a solution containing the fluorescent indicator dye fura-2 (200 microM) and a high concentration of EGTA (15 mM). Ca2+ inward currents and intracellular ratiometric fluorescence transients were recorded in parallel. The decaying phases of Ca2+-dependent fluorescence signals after repolarization were fitted by theoretical curves obtained from a model that included the indicator dye, a slow Ca2+ buffer (to represent EGTA), and a sequestration mechanism as Ca2+ removal components. For each cell, the rate constants of slow buffer and transport and the off rate constant of fura-2 were determined in the fit. The resulting characterization of the removal properties was used to extract the Ca2+ input fluxes from the measured Ca2+ transients during depolarizing pulses. In most experiments, intracellular Ca2+ release dominated the Ca2+ input flux. In these experiments, the Ca2+ flux was characterized by an initial peak followed by a lower tonic phase. The voltage dependence of peak and tonic phase could be described by sigmoidal curves that reached half-maximal activation at -16 and -20 mV, respectively, compared with -2 mV for the activation of Ca2+ conductance. The ratio of the peak to tonic phase (flux ratio) showed a gradual increase with voltage as in rat muscle fibers indicating the similarity to EC coupling in mature mammalian muscle. In a subgroup of myotubes exhibiting small fluorescence signals and in cells treated with 30 microM of the SERCA pump inhibitor cyclopiazonic acid (CPA) and 10 mM caffeine, the calculated Ca2+ input flux closely resembled the L-type Ca2+ current, consistent with the absence of SR Ca2+ release under these conditions and in support of a valid determination of the time course of myoplasmic Ca2+ input flux based on the optical indicator measurements.

Defects in ryanodine receptor calcium release in skeletal muscle from post-myocardial infarct rats

Defective calcium (Ca2+) signaling and impaired contractile function have been observed in skeletal muscle secondary to impaired myocardial function. However, the molecular basis for these muscle defects have not been identified. In this study, we evaluated the alterations of the ryanodine-sensitive Ca2+ release channels (RyR1) by analyzing global and local Ca2+ signaling in a rat postmyocardial infarction (PMI) model of myocardial overload. Ca2+ transients, measured with multiphoton imaging in individual fibers within a whole extensor digitorum longus (EDL) muscle, exhibited significantly reduced amplitude and a prolonged time course in PMI. Spatio-temporal properties of spontaneous Ca2+ sparks in fibers isolated from PMI EDL muscles were also significantly altered. In addition, RyR1 from PMI skeletal muscles were PKA-hyperphosphorylated and depleted of the FK506 binding protein (FKBP12). These data show that PMI skeletal muscles exhibit altered local Ca2+ signaling, associated with hyperphosphorylation of RyR1. The observed changes in Ca2+ signaling may contribute to defective excitation-contraction coupling in muscle that can contribute to the reduced exercise capacity in PMI, out of proportion to the degree of cardiac dysfunction.

Ca2+ sparks and embers of mammalian muscle. Properties of the sources

Ca2+ sparks of membrane-permeabilized rat muscle cells were analyzed to derive properties of their sources. Most events identified in longitudinal confocal line scans looked like sparks, but 23% (1,000 out of 4,300) were followed by long-lasting embers. Some were preceded by embers, and 48 were "lone embers." Average spatial width was approximately 2 microm in the rat and 1.5 microm in frog events in analogous solutions. Amplitudes were 33% smaller and rise times 50% greater in the rat. Differences were highly significant. The greater spatial width was not a consequence of greater open time of the rat source, and was greatest at the shortest rise times, suggesting a wider Ca2+ source. In the rat, but not the frog, spark width was greater in scans transversal to the fiber axis. These features suggested that rat spark sources were elongated transversally. Ca2+ release was calculated in averages of sparks with long embers. Release current during the averaged ember started at 3 or 7 pA (depending on assumptions), whereas in lone embers it was 0.7 or 1.3 pA, which suggests that embers that trail sparks start with five open channels. Analysis of a spark with leading ember yielded a current ratio ranging from 37 to 160 in spark and ember, as if 37-160 channels opened in the spark. In simulations, 25-60 pA of Ca2+ current exiting a point source was required to reproduce frog sparks. 130 pA, exiting a cylindric source of 3 microm, qualitatively reproduced rat sparks. In conclusion, sparks of rat muscle require a greater current than frog sparks, exiting a source elongated transversally to the fiber axis, constituted by 35-260 channels. Not infrequently, a few of those remain open and produce the trailing ember.

Mechanisms of microtubule-based kinetochore positioning in the yeast metaphase spindle

It has been hypothesized that spatial gradients in kMT dynamic instability facilitate mitotic spindle formation and chromosome movement. To test this hypothesis requires the analysis of kMT dynamics, which have not been resolved at the single kMT level in living cells. The budding yeast spindle offers an attractive system in which to study kMT dynamics because, in contrast to animal cells, there is only one kMT per kinetochore. To visualize metaphase kMT plus-end dynamics in yeast, a strain containing a green fluorescent protein fusion to the kinetochore protein, Cse4, was imaged by fluorescence microscopy. Although individual kinetochores were not resolvable, we found that models of kMT dynamics could be evaluated by simulating the stochastic kMT dynamics and then simulating the fluorescence imaging of kMT plus-end-associated kinetochores. Statistical comparison of model-predicted images to experimentally observed images demonstrated that a pure dynamic instability model for kMT dynamics in the yeast metaphase spindle was unacceptable. However, when a temporally stable spatial gradient in the catastrophe or rescue frequency was added to the model, there was reasonable agreement between the model and the experiment. These results provide the first evidence of temporally stable spatial gradients of kMT catastrophe and/or rescue frequency in living cells.

Simulation of calcium sparks in cut skeletal muscle fibers of the frog

Spark mass, the volume integral of Delta F/F, was investigated theoretically and with simulations. These studies show that the amount of Ca2+ bound to fluo-3 is proportional to mass times the total concentration of fluo-3 ([fluo-3T]); the proportionality constant depends on resting Ca2+ concentration ([Ca2+]R). In the simulation of a Ca2+ spark in an intact frog fiber with [fluo-3T] = 100 microM, fluo-3 captures approximately one-fourth of the Ca2+ released from the sarcoplasmic reticulum (SR). Since mass in cut fibers is several times that in intact fibers, both with similar values of [fluo-3T] and [Ca2+]R, it seems likely that SR Ca2+ release is larger in cut fiber sparks or that fluo-3 is able to capture a larger fraction of the released Ca2+ in cut fibers, perhaps because of reduced intrinsic Ca2+ buffering. Computer simulations were used to identify these and other factors that may underlie the differences in mass and other properties of sparks in intact and cut fibers. Our spark model, which successfully simulates calcium sparks in intact fibers, was modified to reflect the conditions of cut fiber measurements. The results show that, if the protein Ca2+-buffering power of myoplasm is the same as that in intact fibers, the Ca2+ source flux underlying a spark in cut fibers is 5-10 times that in intact fibers. Smaller source fluxes are required for less buffer. In the extreme case in which Ca2+ binding to troponin is zero, the source flux needs to be 3-5 times that in intact fibers. An increased Ca2+ source flux could arise from an increase in Ca2+ flux through one ryanodine receptor (RYR) or an increase in the number of active RYRs per spark, or both. These results indicate that the gating of RYRs, or their apparent single channel Ca2+ flux, is different in frog cut fibers--and, perhaps, in other disrupted preparations--than in intact fibers.

Spatiotemporal features of Ca2+ buffering and diffusion in atrial cardiac myocytes with inhibited sarcoplasmic reticulum

Ca(2+) signaling in cells is largely governed by Ca(2+) diffusion and Ca(2+) binding to mobile and stationary Ca(2+) buffers, including organelles. To examine Ca(2+) signaling in cardiac atrial myocytes, a mathematical model of Ca(2+) diffusion was developed which represents several subcellular compartments, including a subsarcolemmal space with restricted diffusion, a myofilament space, and the cytosol. The model was used to quantitatively simulate experimental Ca(2+) signals in terms of amplitude, time course, and spatial features. For experimental reference data, L-type Ca(2+) currents were recorded from atrial cells with the whole-cell voltage-clamp technique. Ca(2+) signals were simultaneously imaged with the fluorescent Ca(2+) indicator Fluo-3 and a laser-scanning confocal microscope. The simulations indicate that in atrial myocytes lacking T-tubules, Ca(2+) movement from the cell membrane to the center of the cells relies strongly on the presence of mobile Ca(2+) buffers, particularly when the sarcoplasmic reticulum is inhibited pharmacologically. Furthermore, during the influx of Ca(2+) large and steep concentration gradients are predicted between the cytosol and the submicroscopically narrow subsarcolemmal space. In addition, the computations revealed that, despite its low Ca(2+) affinity, ATP acts as a significant buffer and carrier for Ca(2+), even at the modest elevations of [Ca(2+)](i) reached during influx of Ca(2+).

Comparison of simulated and measured calcium sparks in intact skeletal muscle fibers of the frog

Calcium sparks in frog intact skeletal muscle fibers were modeled as stereotypical events that arise from a constant efflux of Ca(2+) from a point source for a fixed period of time (e.g., 2.5 pA of Ca(2+) current for 4.6 ms; 18 degrees C). The model calculates the local changes in the concentrations of free Ca(2+) and of Ca(2+) bound to the major intrinsic myoplasmic Ca(2+) buffers (troponin, ATP, parvalbumin, and the SR Ca(2+) pump) and to the Ca(2+) indicator (fluo-3). A distinctive feature of the model is the inclusion of a binding reaction between fluo-3 and myoplasmic proteins, a process that strongly affects fluo-3's Ca(2+)-reaction kinetics, its apparent diffusion constant, and hence the morphology of sparks. DeltaF/F (the change in fluo-3's fluorescence divided by its resting fluorescence) was estimated from the calculated changes in fluo-3 convolved with the microscope point-spread function. To facilitate comparisons with measured sparks, noise and other sources of variability were included in a random repetitive fashion to generate a large number of simulated sparks that could be analyzed in the same way as the measured sparks. In the initial simulations, the binding of Ca(2+) to the two regulatory sites on troponin was assumed to follow identical and independent binding reactions. These simulations failed to accurately predict the falling phase of the measured sparks. A second set of simulations, which incorporated the idea of positive cooperativity in the binding of Ca(2+) to troponin, produced reasonable agreement with the measurements. Under the assumption that the single channel Ca(2+) current of a ryanodine receptor (RYR) is 0.5-2 pA, the results suggest that 1-5 active RYRs generate an average Ca(2+) spark in a frog intact muscle fiber.

Stochastic properties of Ca(2+) release of inositol 1,4,5-trisphosphate receptor clusters

Intracellular Ca(2+) release is controlled by inositol 1,4,5-trisphosphate (IP(3)) receptors or ryanodine receptors. These receptors are typically distributed in clusters with several or tens of channels. The random opening and closing of these channels introduces stochasticity into the elementary calcium release mechanism. Stochastic release events have been experimentally observed in a variety of cell types and have been termed sparks and puffs. We put forward a stochastic version of the Li-Rinzel model (the deactivation binding process is described by a Markovian scheme) and a computationally more efficient Langevin approach to model the stochastic Ca(2+) oscillation of single clusters. Statistical properties such as Ca(2+) puff amplitudes, lifetimes, and interpuff intervals are studied with both models and compared with experimental observations. For clusters with tens of channels, a simply decaying amplitude distribution is typically observed at low IP(3) concentration, while a single peak distribution appears at high IP(3) concentration.

Termination of cardiac Ca(2+) sparks: an investigative mathematical model of calcium-induced calcium release

A Ca(2+) spark arises when a cluster of sarcoplasmic reticulum (SR) channels (ryanodine receptors or RyRs) opens to release calcium in a locally regenerative manner. Normally triggered by Ca(2+) influx across the sarcolemmal or transverse tubule membrane neighboring the cluster, the Ca(2+) spark has been shown to be the elementary Ca(2+) signaling event of excitation-contraction coupling in heart muscle. However, the question of how the Ca(2+) spark terminates remains a central, unresolved issue. Here we present a new model, "sticky cluster," of SR Ca(2+) release that simulates Ca(2+) spark behavior and enables robust Ca(2+) spark termination. Two newly documented features of RyR behavior have been incorporated in this otherwise simple model: "coupled gating" and an opening rate that depends on SR lumenal [Ca(2+)]. Using a Monte Carlo method, local Ca(2+)-induced Ca(2+) release from clusters containing between 10 and 100 RyRs is modeled. After release is triggered, Ca(2+) flux from RyRs diffuses into the cytosol and binds to intracellular buffers and the fluorescent Ca(2+) indicator fluo-3 to produce the model Ca(2+) spark. Ca(2+) sparks generated by the sticky cluster model resemble those observed experimentally, and Ca(2+) spark duration and amplitude are largely insensitive to the number of RyRs in a cluster. As expected from heart cell investigation, the spontaneous Ca(2+) spark rate in the model increases with elevated cytosolic or SR lumenal [Ca(2+)]. Furthermore, reduction of RyR coupling leads to prolonged model Ca(2+) sparks just as treatment with FK506 lengthens Ca(2+) sparks in heart cells. This new model of Ca(2+) spark behavior provides a "proof of principle" test of a new hypothesis for Ca(2+) spark termination and reproduces critical features of Ca(2+) sparks observed experimentally.

Calcium sparks in intact skeletal muscle fibers of the frog

Calcium sparks were studied in frog intact skeletal muscle fibers using a home-built confocal scanner whose point-spread function was estimated to be approximately 0.21 microm in x and y and approximately 0.51 microm in z. Observations were made at 17-20 degrees C on fibers from Rana pipiens and Rana temporaria. Fibers were studied in two external solutions: normal Ringer's ([K(+)] = 2.5 mM; estimated membrane potential, -80 to -90 mV) and elevated [K(+)] Ringer's (most frequently, [K(+)] = 13 mM; estimated membrane potential, -60 to -65 mV). The frequency of sparks was 0.04-0.05 sarcomere(-1) s(-1) in normal Ringer's; the frequency increased approximately tenfold in 13 mM [K(+)] Ringer's. Spark properties in each solution were similar for the two species; they were also similar when scanned in the x and the y directions. From fits of standard functional forms to the temporal and spatial profiles of the sparks, the following mean values were estimated for the morphological parameters: rise time, approximately 4 ms; peak amplitude, approximately 1 DeltaF/F (change in fluorescence divided by resting fluorescence); decay time constant, approximately 5 ms; full duration at half maximum (FDHM), approximately 6 ms; late offset, approximately 0.01 DeltaF/F; full width at half maximum (FWHM), approximately 1.0 microm; mass (calculated as amplitude x 1.206 x FWHM(3)), 1.3-1.9 microm(3). Although the rise time is similar to that measured previously in frog cut fibers (5-6 ms; 17-23 degrees C), cut fiber sparks have a longer duration (FDHM, 9-15 ms), a wider extent (FWHM, 1.3-2.3 microm), and a strikingly larger mass (by 3-10-fold). Possible explanations for the increase in mass in cut fibers are a reduction in the Ca(2+) buffering power of myoplasm in cut fibers and an increase in the flux of Ca(2+) during release.

Large currents generate cardiac Ca2+ sparks

Previous models of cardiac Ca2+ sparks have assumed that Ca2+ currents through the Ca2+ release units (CRUs) were approximately 1-2 pA, producing sparks with peak fluorescence ratio (F/F(0)) of approximately 2.0 and a full-width at half maximum (FWHM) of approximately 1 microm. Here, we present actual Ca2+ sparks with peak F/F(0) of >6 and a FWHM of approximately 2 microm, and a mathematical model of such sparks, the main feature of which is a much larger underlying Ca2+ current. Assuming infinite reaction rates and no endogenous buffers, we obtain a lower bound of approximately 11 pA needed to generate a Ca2+ spark with FWHM of 2 microm. Under realistic conditions, the CRU current must be approximately 20 pA to generate a 2- microm Ca2+)spark. For currents > or =5 pA, the computed spark amplitudes (F/F(0)) are large (approximately 6-12 depending on buffer model). We considered several factors that might produce sparks with FWHM approximately 2 microm without using large currents. Possible protein-dye interactions increased the FWHM slightly. Hypothetical Ca2+ "quarks" had little effect, as did blurring of sparks by the confocal microscope. A clusters of CRUs, each producing 10 pA simultaneously, can produce sparks with FWHM approximately 2 microm. We conclude that cardiac Ca2+ sparks are significantly larger in peak amplitude than previously thought, that such large Ca2+ sparks are consistent with the measured FWHM of approximately 2 microm, and that the underlying Ca2+ current is in the range of 10-20 pA.

A preferred amplitude of calcium sparks in skeletal muscle

In skeletal and cardiac muscle, calcium release from the sarcoplasmic reticulum, leading to contraction, often results in calcium sparks. Because sparks are recorded by confocal microscopy in line-scanning mode, their measured amplitude depends on their true amplitude and the position of the spark relative to the scanned line. We present a method to derive from measured amplitude histograms the actual distribution of spark amplitudes. The method worked well when tested on simulated distributions of experimental sparks. Applied to massive numbers of sparks imaged in frog skeletal muscle under voltage clamp in reference conditions, the method yielded either a decaying amplitude distribution (6 cells) or one with a central mode (5 cells). Caffeine at 0.5 or 1 mM reversibly enhanced this mode (5 cells) or induced its appearance (4 cells). The occurrence of a mode in the amplitude distribution was highly correlated with the presence of a mode in the distribution of spark rise times or in the joint distribution of rise times and spatial widths. If sparks were produced by individual Markovian release channels evolving reversibly, they should not have a preferred rise time or amplitude. Channel groups, instead, could cooperate allosterically or through their calcium sensitivity, and give rise to a stereotyped amplitude in their collective spark.

Evolution of cardiac calcium waves from stochastic calcium sparks

We present a model that provides a unified framework for studying Ca2+ sparks and Ca2+ waves in cardiac cells. The model is novel in combining 1) use of large currents (approximately 20 pA) through the Ca2+ release units (CRUs) of the sarcoplasmic reticulum (SR); 2) stochastic Ca2+ release (or firing) of CRUs; 3) discrete, asymmetric distribution of CRUs along the longitudinal (separation distance of 2 microm) and transverse (separated by 0.4-0.8 microm) directions of the cell; and 4) anisotropic diffusion of Ca2+ and fluorescent indicator to study the evolution of Ca2+ waves from Ca2+ sparks. The model mimics the important features of Ca2+ sparks and Ca2+ waves in terms of the spontaneous spark rate, the Ca2+ wave velocity, and the pattern of wave propagation. Importantly, these features are reproduced when using experimentally measured values for the CRU Ca2+ sensitivity (approximately 15 microM). Stochastic control of CRU firing is important because it imposes constraints on the Ca2+ sensitivity of the CRU. Even with moderate (approximately 5 microM) Ca2+ sensitivity the very high spontaneous spark rate triggers numerous Ca2+ waves. In contrast, a single Ca2+ wave with arbitrarily large velocity can exist in a deterministic model when the CRU Ca2+ sensitivity is sufficiently high. The combination of low CRU Ca2+ sensitivity (approximately 15 microM), high cytosolic Ca2+ buffering capacity, and the spatial separation of CRUs help control the inherent instability of SR Ca2+ release. This allows Ca2+ waves to form and propagate given a sufficiently large initiation region, but prevents a single spark or a small group of sparks from triggering a wave.

Effects of imperatoxin A on local sarcoplasmic reticulum Ca(2+) release in frog skeletal muscle

We have investigated the effects of imperatoxin A (IpTx(a)) on local calcium release events in permeabilized frog skeletal muscle fibers, using laser scanning confocal microscopy in linescan mode. IpTx(a) induced the appearance of Ca(2+) release events from the sarcoplasmic reticulum that are approximately 2 s and have a smaller amplitude (31 +/- 2%) than the "Ca(2+) sparks" normally seen in the absence of toxin. The frequency of occurrence of long-duration imperatoxin-induced Ca(2+) release events increased in proportion to IpTx(a) concentrations ranging from 10 nM to 50 nM. The mean duration of imperatoxin-induced events in muscle fibers was independent of toxin concentration and agreed closely with the channel open time in experiments on isolated frog ryanodine receptors (RyRs) reconstituted in planar lipid bilayer, where IpTx(a) induced opening of single Ca(2+) release channels to prolonged subconductance states. These results suggest involvement of a single molecule of IpTx(a) in the activation of a single Ca(2+) release channel to produce a long-duration event. Assuming the ratio of full conductance to subconductance to be the same in the fibers as in bilayer, the amplitude of a spark relative to the long event indicates involvement of at most four RyR Ca(2+) release channels in the production of short-duration Ca(2+) sparks.

Two mechanisms for termination of individual Ca2+ sparks in skeletal muscle

Ca(2+) sparks are brief, localized elevations of myoplasmic [Ca(2+)] caused by release of increments of Ca(2+) via sarcoplasmic reticulum Ca(2+) release channels in muscle. The properties of individual sparks provide information regarding the opening of sarcoplasmic reticulum Ca(2+) channels within functioning cells. Here we use high-speed confocal microscopy to show that individual Ca(2+) sparks activated by membrane depolarization in single frog skeletal muscle fibers can be terminated prematurely by repolarization. Thus, either voltage sensor deactivation on repolarization or release channel inactivation during continued depolarization can terminate the Ca(2+) release channel activity underlying voltage-activated Ca(2+) sparks in skeletal muscle.

Expression of ryanodine receptor RyR3 produces Ca2+ sparks in dyspedic myotubes

Discrete, localized elevations of myoplasmic [Ca2+], Ca2+ 'sparks', were readily detected using the fluorescent Ca2+ indicator fluo-3 and laser scanning confocal microscopy in 'dyspedic' 1B5 myotubes, i.e. myotubes which do not express ryanodine receptors (RyRs), transduced with virions containing cDNA for RyR type 3 that were saponin permeabilized to allow dye entry. Ca2+ sparks were never observed in non-transduced RyR null myotubes. The spatial locations of sparks observed in permeabilized myotubes roughly corresponded to regions of RyR protein expression in the same myotube as detected after subsequent fixation and antibody staining. Permeabilized RyR3-transduced myotubes exhibited similar punctate peripheral RyR3 protein immunohistochemical patterns as myotubes fixed before permeabilization indicating that permeabilization did not affect the structural organization of the triad. Ca2+ sparks, recorded in line scan mode, in permeabilized myotubes expressing RyR3 exhibited mean amplitudes (change in fluorescence/mean fluorescence, DeltaF/F: 1.20 +/- 0.04) and temporal rise times (10-90%; 6.31 +/- 0.12 ms) similar to those of sparks recorded in permeabilized frog skeletal muscle fibres (0.98 +/- 0.01; 6.11 +/- 0.07, respectively) using the same confocal system. Spatial extent and temporal duration of the Ca2+ sparks were approximately 40% larger in the RyR3-expressing myotube cultures than in frog fibres. Ca2+ sparks recorded in line scan mode often occurred repetitively at the same spatial location in RyR3-expressing myotubes. Such repetitive events were highly reproducible in amplitude and spatio-temporal properties, as previously observed for repetitive mode sparks in frog skeletal muscle. Ca2+ sparks recorded in xy mode were frequently compressed in the y (slower scan) direction compared to the x direction. This asymmetry was reproduced assuming spatially symmetric events having the time course of Ca2+ sparks recorded in line scan (xt) mode. These expression studies demonstrate that the presence of RyR3 is sufficient for the production of Ca2+ sparks in a skeletal muscle system lacking the expression of any other RyR isoform.

Involvement of multiple intracellular release channels in calcium sparks of skeletal muscle

In many types of muscle, intracellular Ca(2+) release for contraction consists of brief Ca(2+) sparks. Whether these result from the opening of one or many channels in the sarcoplasmic reticulum is not known. Examining massive numbers of sparks from frog skeletal muscle and evaluating their Ca(2+) release current, we provide evidence that they are generated by multiple channels. A mode is demonstrated in the distribution of spark rise times in the presence of the channel activator caffeine. This finding contradicts expectations for single channels evolving reversibly, but not for channels in a group, which collectively could give rise to a stereotyped spark. The release channel agonists imperatoxin A, ryanodine, and bastadin 10 elicit fluorescence events that start with a spark, then decay to steady levels roughly proportional to the unitary conductances of 35%, 50%, and 100% that the agonists, respectively, promote in bilayer experiments. This correspondence indicates that the steady phase is produced by one open channel. Calculated Ca(2+) release current decays 10- to 20-fold from spark to steady phase, which requires that six or more channels be open during the spark.

The spark and its ember: separately gated local components of Ca(2+) release in skeletal muscle

Amplitude, spatial width, and rise time of Ca(2+) sparks were compared in frog fast-twitch muscle, in three conditions that alter activation of release channels by [Ca(2+)]. A total of approximately 17,000 sparks from 30 cells were evaluated. In cells under voltage clamp, caffeine (0.5 or 1 mM) increased average spark width by 28%, rise time by 18%, and amplitude by 7%. Increases in width were significant even among events of the same rise time. Spontaneous events recorded in permeabilized fibers with low internal [Mg(2+)] (0.4 mM), had width and rise times greater than in reference, and not significantly different than those in caffeine. The spark average in reference rides on a continuous fluorescence "ridge" and is continued by an "ember," a prolongation of width approximately 1 microm and amplitude <0.2, vanishing in approximately 100 ms. Ridge and ember were absent in caffeine and in permeabilized cells. Exposure of voltage-clamped cells to high internal [Mg(2+)] (7 mM) had effects opposite to caffeine, reducing spark width by 26% and amplitude by 27%. In high [Mg(2+)], the ember was visible in individual sparks as a prolongation of variable duration and amplitude up to 1.2. Based on simulations and calculation of Ca(2+) release flux from averaged sparks, the increase in spark width caused by caffeine was interpreted as evidence of an increase in radius of the release source-presumably by recruitment of additional channels. Conversely, spark narrowing suggests loss of contributing channels in high Mg(2+). Therefore, these changes in spark width at constant rise times are evidence of a multichannel origin of sparks. Because ridge and ember were reduced by promoters of Ca(2+)-dependent activation (caffeine, low [Mg(2+)]) and became more visible in the presence of its inhibitors, they are probably manifestations of Ca(2+) release directly operated by voltage sensors.

A repetitive mode of activation of discrete Ca2+ release events (Ca2+ sparks) in frog skeletal muscle fibres

1. Ca2+ release events (Ca2+ 'sparks'), which are believed to arise from the opening of a sarcoplasmic reticulum (SR) Ca2+ release channel or a small cluster of such channels that act as a release unit, have been measured in single, frog (Rana pipiens) skeletal muscle fibres. 2. Under conditions of extremely low rates of occurrence of Ca2+ sparks we observed, within individual identified triads, repetitive Ca2+ release events which occurred at a frequency more than 100-fold greater than the prevailing average event rate. Repetitive sparks were recorded during voltage-clamp test depolarizations after a brief (0.3-2 s) repriming interval in fibres held at 0 mV and in chronically depolarized, 'notched' fibres. 3. These repetitive events are likely to arise from the re-opening of the same SR Ca2+ release channel or release unit operating in a repetitive gating mode ('rep-mode'), rather than from the random activation of multiple, independent channels or release units within a triad. A train of rep-mode events thus represents a series of Ca2+ sparks arising from a single location within the fibre. Rep-mode events are activated among different triads in a random manner after brief repriming. The frequency of repetitive events among all identified events during voltage-clamp depolarization to 0 mV after brief repriming was 3.9 +/- 1.3 %. The occurrence of repetitive events was not related to exposure of the fibre to laser illumination. 4. The events observed within a rep-mode train exhibited a relatively uniform amplitude. Analysis of intervals between identified events in triads exhibiting rep-mode trains indicated similar variations of fluorescence as in neighbouring, quiescent triads, suggesting there was not a significant number of small, unidentified events at the triads exhibiting rep-mode activity. 5. The distribution of rep-mode interspark intervals exhibited a paucity of events at short intervals, consistent with the need for recovery from inactivation before activation of the next event in a repetitive train. The mean interspark interval of repetitive sparks during voltage-clamp depolarizations was 88 +/- 5 ms, and was independent of membrane potential. 6. The individual Ca2+ sparks within a rep-mode train were similar in average amplitude and spatiotemporal extent to singly occurring sparks, suggesting a common mechanism for termination of the channel opening(s) underlying both types of events. The average properties of the sparks did not vary during a train. The relative amplitude of a spark within a rep-mode was not correlated with its rise time. 7. Repetitive Ca2+ release events represent a mode of gating of SR Ca2+ release channels which may be significant during long depolarizations and which may be influenced by the biochemical state of the SR ryanodine receptor Ca2+ release channels.