Linking flickering to waves and whole-cell oscillations in a mitochondrial network model

It has been shown that transient single mitochondrial depolarizations, known as flickers, tend to occur randomly in space and time. On the other hand, many studies have shown that mitochondrial depolarization waves and whole-cell oscillations occur under oxidative stress. How single mitochondrial flickering events and whole-cell oscillations are mechanistically linked remains unclear. In this study, we developed a Markov model of the inner membrane anion channel in which reactive-oxidative-species (ROS)-induced opening of the inner membrane anion channel causes transient mitochondrial depolarizations in a single mitochondrion that occur in a nonperiodic manner, simulating flickering. We then coupled the individual mitochondria into a network, in which flickers occur randomly and sparsely when a small number of mitochondria are in the state of high superoxide production. As the number of mitochondria in the high-superoxide-production state increases, short-lived or abortive waves due to ROS-induced ROS release coexist with flickers. When the number of mitochondria in the high-superoxide-production state reaches a critical number, recurring propagating waves are observed. The origins of the waves occur randomly in space and are self-organized as a consequence of random flickering and local synchronization. We show that at this critical state, the depolarization clusters exhibit a power-law distribution, a signature of self-organized criticality. In addition, the whole-cell mitochondrial membrane potential changes from exhibiting small random fluctuations to more periodic oscillations as the superoxide production rate increases. These simulation results may provide mechanistic insight into the transition from random mitochondrial flickering to the waves and whole-cell oscillations observed in many experimental studies.     

Ca2+-sensing transgenic mice: postsynaptic signaling in smooth muscle

Genetically encoded signaling proteins provide remarkable opportunities to design and target the expression of molecules that can be used to report critical cellular events in vivo, thereby markedly extending the scope and physiological relevance of studies of cell function. Here we report the development of a transgenic mouse expressing such a reporter and its use to examine postsynaptic signaling in smooth muscle. The circularly permutated, Ca2+-sensing molecule G-CaMP (Nakai, J., Ohkura, M., and Imoto, K. (2001) Nat. Biotechnol. 19, 137-141) was expressed in vascular and non-vascular smooth muscle and functioned as a lineage-specific intracellular Ca2+ reporter. Detrusor tissue from these mice was used to identify two separate types of postsynaptic Ca2+ signals, mediated by distinct neurotransmitters. Intrinsic nerve stimulation evoked rapid, whole-cell Ca2+ transients, or "Ca2+ flashes," and slowly propagating Ca2+ waves. We show that Ca2+ flashes occur through P2X receptor stimulation and ryanodine receptor-mediated Ca2+ release, whereas Ca2+ waves arise from muscarinic receptor stimulation and inositol trisphosphate-mediated Ca2+ release. The distinct ionotropic and metabotropic postsynaptic Ca2+ signals are related at the level of Ca2+ release. Importantly, individual myocytes are capable of both postsynaptic responses, and a transition between Ca2+ -induced Ca2+ release and inositol trisphosphate waves occurs at higher synaptic inputs. Ca2+ signaling mice should provide significant advantages in the study of processive biological signaling.     

Initiation of IP(3)-mediated Ca(2+) waves in Xenopus oocytes.

Inositol (1,4,5)-trisphosphate (IP(3)) evokes Ca(2+) liberation in Xenopus oocytes as elementary events (Ca(2+) puffs) that become coupled to propagate Ca(2+) waves with increasing [IP(3)]. To investigate this transition between local and global Ca(2+) signaling, we developed an optical method for evoking rapid subcellular Ca(2+) elevations, while independently photoreleasing IP(3) and simultaneously recording confocal Ca(2+) images. Focal Ca(2+) elevations triggered waves within 100 ms of photoreleasing IP(3), compared with latencies of seconds following photorelease of IP(3) alone. Wave velocity varied with [IP(3)] but was independent of time after photorelease of IP(3), indicating that delayed wave initiation did not involve slow binding of IP(3) to its receptors. The amount of Ca(2+) required to trigger a wave was approximately 10-fold greater than the average size of puffs, and puffs showed no progressive increase in magnitude before waves initiated. Instead, Ca(2+) puffs contributed to a slow rise in basal free [Ca(2+)], which further increased puff frequency and sensitized IP(3) receptors so that individual events then triggered waves. Because the wave threshold is much greater than the size of the elementary puff, cells can employ both local and global signaling mechanisms, and the summation of stochastic behavior of elementary events allows generation of reproducible periodic waves.     

Multiscale modeling of calcium cycling in cardiac ventricular myocyte: macroscopic consequences of microscopic dyadic function

In cardiac ventricular myocytes, calcium (Ca) release occurs at distinct structures (dyads) along t-tubules, where L-type Ca channels (LCCs) appose sarcoplasmic reticulum (SR) Ca release channels (RyR2s). We developed a model of the cardiac ventricular myocyte that simulates local stochastic Ca release processes. At the local Ca release level, the model reproduces Ca spark properties. At the whole-cell level, the model reproduces the action potential, Ca currents, and Ca transients. Changes in microscopic dyadic properties (e.g., during detubulation in heart failure) affect whole-cell behavior in complex ways, which we investigated by simulating changes in the dyadic volume and number of LCCs/RyR2s in the dyad, and effects of calsequestrin (CSQN) as a Ca buffer (CSQN buffer) or a luminal Ca sensor (CSQN regulator). We obtained the following results: 1), Increased dyadic volume and reduced LCCs/RyR2s decrease excitation-contraction coupling gain and cause asynchrony of SR Ca release, and interdyad coupling partially compensates for the reduced synchrony. 2), Impaired CSQN buffer depresses Ca transients without affecting the synchrony of SR Ca release. 3), When CSQN regulator function is impaired, interdyad coupling augments diastolic Ca release activity to form Ca waves and long-lasting Ca release events.     

Activation and propagation of Ca(2+) release during excitation-contraction coupling in atrial myocytes

Fast two-dimensional confocal microscopy and the Ca(2+) indicator fluo-4 were used to study excitation-contraction (E-C) coupling in cat atrial myocytes which lack transverse tubules and contain both subsarcolemmal junctional (j-SR) and central nonjunctional (nj-SR) sarcoplasmic reticulum. Action potentials elicited by field stimulation induced transient increases of intracellular Ca(2+) concentration ([Ca(2+)](i)) that were highly inhomogeneous. Increases started at distinct subsarcolemmal release sites spaced approximately 2 microm apart. The amplitude and the latency of Ca(2+) release from these sites varied from beat to beat. Subsarcolemmal release fused to build a peripheral ring of elevated [Ca(2+)](i), which actively propagated to the center of the cells via Ca(2+)-induced Ca(2+) release. Resting myocytes exhibited spontaneous Ca(2+) release events, including Ca(2+) sparks and local (microscopic) or global (macroscopic) [Ca(2+)](i) waves. The microscopic [Ca(2+)](i) waves propagated in a saltatory fashion along the sarcolemma ("coupled" Ca(2+) sparks) revealing the sequential activation of Ca(2+) release sites of the j-SR. Moreover, during global [Ca(2+)](i) waves, Ca(2+) release was evident from individual nj-SR sites. Ca(2+) release sites were arranged in a regular three-dimensional grid as deduced from the functional data and shown by immunostaining of ryanodine receptor Ca(2+) release channels. The longitudinal and transverse distances between individual Ca(2+) release sites were both approximately 2 microm. Furthermore, electron microscopy revealed a continuous sarcotubular network and one peripheral coupling of j-SR with the sarcolemma per sarcomere. The results demonstrate directly that, in cat atrial myocytes, the action potential-induced whole-cell [Ca(2+)](i) transient is the spatio-temporal summation of Ca(2+) release from subsarcolemmal and central sites. First, j-SR sites are activated in a stochastic fashion by the opening of voltage-dependent sarcolemmal Ca(2+) channels. Subsequently, nj-SR sites are activated by Ca(2+)-induced Ca(2+) release propagating from the periphery.     

Differential Ca2+ and Sr2+ regulation of intracellular divalent cations release in ventricular myocytes

The regulation of the Ca2+ -induced Ca2+ release (CICR) from intracellular stores is a critical step in the cardiac cycle. The inherent positive feedback of CICR should make it a self-regenerating process. It is accepted that CICR must be governed by some negative control, but its nature is still debated. We explore here the importance of the Ca2+ released from sarcoplasmic reticulum (SR) on the mechanisms that may control CICR. Specifically, we compared the effect of replacing Ca2+ with Sr2+ on intracellular Ca2+ signaling in intact cardiac myocytes as well as on the function of single ryanodine receptor (RyR) Ca2+ release channels in panar bilayers. In cells, both CICR and Sr2+ -induced Sr2+ release (SISR) were observed. Action potential induced Ca2+ -transients and spontaneous Ca2+ waves were considerably faster than their Sr2+ -mediated counterparts. However, the kinetics of Ca2+ and Sr2+ sparks was similar. At the single RyR channel level, the affinities of Ca2+ and Sr2+ activation were different but the affinities of Ca2+ and Sr2+ inactivation were similar. Fast Ca2+ and Sr2+ stimuli activated RyR channels equally fast but adaptation (a spontaneous slow transition back to steady-state activity levels) was not observed in the Sr2+ case. Together, these results suggest that regulation of the RyR channel by cytosolic Ca2+ is not involved in turning off the Ca2+ spark. In contrast, cytosolic Ca2+ is important in the propagation global Ca2+ release events and in this regard single RyR channel sensitivity to cytosolic Ca2+ activation, not low-affinity cytosolic Ca2+ inactivation, is a key factor. This suggests that the kinetics of local and global RyR-mediated Ca2+ release signals are affected in a distinct way by different divalent cations in cardiac muscle cells.     

Long-Lasting Sparks: Multi-Metastability and Release Competition in the Calcium Release Unit Network

Calcium (Ca) sparks are elementary events of biological Ca signaling. A normal Ca spark has a brief duration in the range of 10 to 100 ms, but long-lasting sparks with durations of several hundred milliseconds to seconds are also widely observed. Experiments have shown that the transition from normal to long-lasting sparks can occur when ryanodine receptor (RyR) open probability is either increased or decreased. Here, we demonstrate theoretically and computationally that long-lasting sparks emerge as a collective dynamical behavior of the network of diffusively coupled Ca release units (CRUs). We show that normal sparks occur when the CRU network is monostable and excitable, while long-lasting sparks occur when the network dynamics possesses multiple metastable attractors, each attractor corresponding to a different spatial firing pattern of sparks. We further highlight the mechanisms and conditions that produce long-lasting sparks, demonstrating the existence of an optimal range of RyR open probability favoring long-lasting sparks. We find that when CRU firings are sparse and sarcoplasmic reticulum (SR) Ca load is high, increasing RyR open probability promotes long-lasting sparks by potentiating Ca-induced Ca release (CICR). In contrast, when CICR is already strong enough to produce frequent firings, decreasing RyR open probability counter-intuitively promotes long-lasting sparks by decreasing spark frequency. The decrease in spark frequency promotes intra-SR Ca diffusion from neighboring non-firing CRUs to the firing CRUs, which helps to maintain the local SR Ca concentration of the firing CRUs above a critical level to sustain firing. In this setting, decreasing RyR open probability further suppresses long-lasting sparks by weakening CICR. Since a long-lasting spark terminates via the Kramers’ escape process over a potential barrier, its duration exhibits an exponential distribution determined by the barrier height and noise strength, which is modulated differently by different ways of altering the Ca release flux strength.     

Calcium wave propagation in pancreatic acinar cells: functional interaction of inositol 1,4,5-trisphosphate receptors, ryanodine receptors, and mitochondria

In pancreatic acinar cells, inositol 1,4,5-trisphosphate (InsP(3))-dependent cytosolic calcium ([Ca(2+)](i)) increases resulting from agonist stimulation are initiated in an apical "trigger zone," where the vast majority of InsP(3) receptors (InsP(3)R) are localized. At threshold stimulation, [Ca(2+)](i) signals are confined to this region, whereas at concentrations of agonists that optimally evoke secretion, a global Ca(2+) wave results. Simple diffusion of Ca(2+) from the trigger zone is unlikely to account for a global [Ca(2+)](i) elevation. Furthermore, mitochondrial import has been reported to limit Ca(2+) diffusion from the trigger zone. As such, there is no consensus as to how local [Ca(2+)](i) signals become global responses. This study therefore investigated the mechanism responsible for these events. Agonist-evoked [Ca(2+)](i) oscillations were converted to sustained [Ca(2+)](i) increases after inhibition of mitochondrial Ca(2+) import. These [Ca(2+)](i) increases were dependent on Ca(2+) release from the endoplasmic reticulum and were blocked by 100 microM ryanodine. Similarly, "uncaging" of physiological [Ca(2+)](i) levels in whole-cell patch-clamped cells resulted in rapid activation of a Ca(2+)-activated current, the recovery of which was prolonged by inhibition of mitochondrial import. This effect was also abolished by ryanodine receptor (RyR) blockade. Photolysis of d-myo InsP(3) P(4(5))-1-(2-nitrophenyl)-ethyl ester (caged InsP(3)) produced either apically localized or global [Ca(2+)](i) increases in a dose-dependent manner, as visualized by digital imaging. Mitochondrial inhibition permitted apically localized increases to propagate throughout the cell as a wave, but this propagation was inhibited by ryanodine and was not seen for minimal control responses resembling [Ca(2+)](i) puffs. Global [Ca(2+)](i) rises initiated by InsP(3) were also reduced by ryanodine, limiting the increase to a region slightly larger than the trigger zone. These data suggest that, while Ca(2+) release is initially triggered through InsP(3)R, release by RyRs is the dominant mechanism for propagating global waves. In addition, mitochondrial Ca(2+) import controls the spread of Ca(2+) throughout acinar cells by modulating RyR activation.     

Invited review: significance of spatial and temporal heterogeneity of calcium transients in smooth muscle.

The multiplicity of mechanisms involved in regulation of intracellular Ca(2+) concentration ([Ca(2+)](i)) in smooth muscle results in both intra- and intercellular heterogeneities in [Ca(2+)](i). Heterogeneity in [Ca(2+)](i) regulation is reflected by the presence of spontaneous, localized [Ca(2+)](i) transients (Ca(2+) sparks) representing Ca(2+) release through ryanodine receptor (RyR) channels. Ca(2+) sparks display variable spatial Ca(2+) distributions with every occurrence within and across cellular regions. Individual sparks are often grouped, and fusion of sparks produces large local elevations in [Ca(2+)](i) that occasionally trigger propagating [Ca(2+)](i) waves. Ca(2+) sparks may modulate membrane potential and thus smooth muscle contractility. Sparks may also be the target of other regulatory factors in smooth muscle. Agonists induce propagating [Ca(2+)](i) oscillations that originate from foci with high spark incidence and also represent Ca(2+) release through RyR channels. With increasing agonist concentration, the peak of regional [Ca(2+)](i) oscillations remains relatively constant, whereas both frequency and propagation velocity increase. In contrast, the global cellular response appears as a concentration-dependent increase in peak as well as mean cellular [Ca(2+)](i), representing a spatial and temporal integration of the oscillations. The significance of agonist-induced [Ca(2+)](i) oscillations lies in the establishment of a global [Ca(2+)](i) level for slower Ca(2+)-dependent physiological processes.     

Control of astrocyte Ca(2+) oscillations and waves by oscillating translocation and activation of protein kinase C

BACKGROUND: Glutamate-induced Ca2+ oscillations and waves coordinate astrocyte signaling responses, which in turn regulate neuronal excitability. Recent studies have suggested that the generation of these Ca2+ oscillations requires a negative feedback that involves the activation of conventional protein kinase C (cPKC). Here, we use total internal reflection fluorescence (TIRF) microscopy to investigate if and how periodic plasma membrane translocation of cPKC is used to generate Ca2+ oscillations and waves. RESULTS: Glutamate stimulation of astrocytes triggered highly localized GFP-PKCgamma plasma membrane translocation events, induced rapid oscillations in GFP-PKCgamma translocation, and generated GFP-PKCgamma translocation waves that propagated across and between cells. These translocation responses were primarily mediated by the Ca2+-sensitive C2 domains of PKCgamma and were driven by localized Ca2+ spikes, by oscillations in Ca2+ concentration, and by propagating Ca(2+) waves, respectively. Interestingly, GFP-conjugated C1 domains from PKCgamma or PKCdelta that have been shown to bind diacylglycerol (DAG) also oscillated between the cytosol and the plasma membrane after glutamate stimulation, suggesting that PKC is repetitively activated by combined oscillating increases in Ca(2+) and DAG concentrations. The expression of C1 domains, which increases the DAG buffering capacity and thereby delays changes in DAG concentrations, led to a marked prolongation of Ca(2+) spikes, suggesting that PKC activation is involved in terminating individual Ca(2+) spikes and waves and in defining the time period between Ca(2+) spikes. CONCLUSIONS: Our study suggests that cPKCs have a negative feedback role on Ca(2+) oscillations and waves that is mediated by their repetitive activation by oscillating DAG and Ca(2+) concentrations. Periodic translocation and activation of cPKC can be a rapid and markedly localized signaling event that can limit the duration of individual Ca(2+) spikes and waves and can define the Ca(2+) spike and wave frequencies.     

Disposition of calcium release units in agarose gel for an optimal propagation of Ca2+ signals

Clusters of calcium-loaded sarcoplasmic reticulum (SR) vesicles in agarose gel were previously shown to behave as an excitable medium that propagates calcium waves. In a 3D-hexagonal disposition, the distance between neighboring spheres (which may stand for SR vesicles) is constant and the relationship between distance and vesicular protein concentration is expected to be nonlinear. To obtain a distribution of SR vesicles at different protein concentrations as homogeneous as possible, liquid agarose gels were carefully stirred. Electron micrographs, however, did not confirm the expected relationship between inter-SR vesicle distance and vesicular protein concentration. Light micrographs, to the contrary, resulted in a protein concentration-dependent disposition of clusters of SR vesicles, which is described by a linear function. Stable calcium waves in agarose gel occurred at SR vesicle protein concentrations between 7 and 16 g/l. At lower protein concentrations, local calcium oscillations or abortive waves were observed. The velocities of calcium waves were optimum at approximately 12 g/l and amounted to nearly 60 microm/s. The corresponding distance of neighboring calcium release units was calculated to be approximately 4 microm. The results further show that calcium signaling in the described reaction-diffusion system is optimal in a relatively small range of diffusion lengths. A change by +/-2 microm resulted in a reduction of the propagation velocity by 40%. It would appear that 1), the distance between calcium release units (clusters of ryanodine receptors in cells) is a sensitive parameter concerning propagation of Ca2+ signals; and 2), a dysfunction of the reaction-diffusion system in living cells, however, might have a negative effect on the spreading of intracellular calcium signals, thus on the cell's function.     

Localized Ca2+ uncaging reveals polarized distribution of Ca2+-sensitive Ca2+ release sites: mechanism of unidirectional Ca2+ waves

Ca2+-induced Ca2+ release (CICR) plays an important role in the generation of cytosolic Ca2+ signals in many cell types. However, it is inherently difficult to distinguish experimentally between the contributions of messenger-induced Ca2+ release and CICR. We have directly tested the CICR sensitivity of different regions of intact pancreatic acinar cells using local uncaging of caged Ca2+. In the apical region, local uncaging of Ca2+ was able to trigger a CICR wave, which propagated toward the base. CICR could not be triggered in the basal region, despite the known presence of ryanodine receptors. The triggering of CICR from the apical region was inhibited by a pharmacological block of ryanodine or inositol trisphosphate receptors, indicating that global signals require coordinated Ca2+ release. Subthreshold agonist stimulation increased the probability of triggering CICR by apical uncaging, and uncaging-induced CICR could activate long-lasting Ca2+ oscillations. However, with subthreshold stimulation, CICR could still not be initiated in the basal region. CICR is the major process responsible for global Ca2+ transients, and intracellular variations in sensitivity to CICR predetermine the activation pattern of Ca2+ waves.     

Intercellular calcium signaling in astrocytes via ATP release through connexin hemichannels.

Astrocytes are capable of widespread intercellular communication via propagated increases in intracellular Ca(2+) concentration. We have used patch clamp, dye flux, ATP assay, and Ca(2+) imaging techniques to show that one mechanism for this intercellular Ca(2+) signaling in astrocytes is the release of ATP through connexin channels ("hemichannels") in individual cells. Astrocytes showed low Ca(2+)-activated whole-cell currents consistent with connexin hemichannel currents that were inhibited by the connexin channel inhibitor flufenamic acid (FFA). Astrocytes also showed molecular weight-specific influx and release of dyes, consistent with flux through connexin hemichannels. Transmembrane dye flux evoked by mechanical stimulation was potentiated by low Ca(2+) and was inhibited by FFA and Gd(3+). Mechanical stimulation also evoked release of ATP that was potentiated by low Ca(2+) and inhibited by FFA and Gd(3+). Similar whole-cell currents, transmembrane dye flux, and ATP release were observed in C6 glioma cells expressing connexin43 but were not observed in parent C6 cells. The connexin hemichannel activator quinine evoked ATP release and Ca(2+) signaling in astrocytes and in C6 cells expressing connexin43. The propagation of intercellular Ca(2+) waves in astrocytes was also potentiated by quinine and inhibited by FFA and Gd(3+). Release of ATP through connexin hemichannels represents a novel signaling pathway for intercellular communication in astrocytes and other non-excitable cells.     

Functional Modeling of the Shift in Cellular Calcium Dynamics at the Onset of Synchronization in Smooth Muscle Cells

In the present paper we address the nature of synchronization properties found in populations of mesenteric artery smooth muscle cells. We present a minimal model of the onset of synchronization in the individual smooth muscle cell that is manifested as a transition from calcium waves to whole-cell calcium oscillations. We discuss how different types of ion currents may influence both amplitude and frequency in the regime of whole-cell oscillations. The model may also explain the occurrence of mixed-mode oscillations and chaotic oscillations frequently observed in the experimental system.     

Asynchronous calcium waves in smooth muscle cells

Asynchronous Ca2+ waves or wave-like [Ca2+]i oscillations constitute a specialized form of agonist-induced Ca2+ signaling that is observed in a variety of smooth muscle cell types. Functionally, it is involved in the contractile regulation of the smooth muscle cells as it signals for tonic contraction in certain smooth muscle cells while causing relaxation in others. Mechanistically, repetitive Ca2+ waves are produced by repetitive cycles of sarcoplasmic reticulum Ca2+ release followed by Ca2+ uptake. Plasmalemmal Ca2+ entry mechanisms are important for providing the additional Ca2+ necessary to maintain proper refilling of the sarcoplasmic reticulum Ca2+ store and support ongoing Ca2+ waves. In this paper, we will review the phenomenon of asynchronous Ca2+ waves in smooth muscle and discuss the scientific and clinical significance of this new understanding.     

Long distance communication between muscarinic receptors and Ca2+ release channels revealed by carbachol uncaging in cell-attached patch pipette

We have investigated the characteristics of cytosolic Ca2+ signals induced by muscarinic receptor activation of pancreatic acinar cells that reside within intact pancreatic tissue. We show that these cells exhibit global Ca2+ waves and local apical Ca2+ spikes. This is the first evidence for local Ca2+ signaling in undissociated pancreatic tissue. The mechanism of formation of localized Ca2+ signals was examined using a novel approach involving photolysis of caged carbachol inside a patch pipette attached to the basal surface of an acinar unit. This local activation of basal muscarinic receptors elicited local cytosolic Ca2+ spikes in the apical pole more than 15 microm away from the site of stimulation. In some experiments, local basal receptor activation elicited a Ca2+ wave that started in the apical pole and then spread toward the base. Currently, there are two competing hypotheses for preferential apical Ca2+ signaling. One invokes the need for structural proximity of the cholinergic receptors and the Ca2+ release channels in the apical pole, whereas the other postulates long distance communication between basal receptors and the channels. Our intrapipette uncaging experiments provide definitive evidence for long distance communication between basal muscarinic receptors and apical Ca2+ release channels.     

Synchronization of stochastic Ca²(+) release units creates a rhythmic Ca²(+) clock in cardiac pacemaker cells

In sinoatrial node cells of the heart, beating rate is controlled, in part, by local Ca2(+) releases (LCRs) from the sarcoplasmic reticulum, which couple to the action potential via electrogenic Na(+)/Ca2(+) exchange. We observed persisting, roughly periodic LCRs in depolarized rabbit sinoatrial node cells (SANCs). The features of these LCRs were reproduced by a numerical model consisting of a two-dimensional array of stochastic, diffusively coupled Ca2(+) release units (CRUs) with fixed refractory period. Because previous experimental studies showed that β-adrenergic receptor stimulation increases the rate of Ca2(+) release through each CRU (dubbed I(spark)), we explored the link between LCRs and I(spark) in our model. Increasing the CRU release current I(spark) facilitated Ca2(+)-induced-Ca2(+) release and local recruitment of neighboring CRUs to fire more synchronously. This resulted in a progression in simulated LCR size (from sparks to wavelets to global waves), LCR rhythmicity, and decrease of LCR period that parallels the changes observed experimentally with β-adrenergic receptor stimulation. The transition in LCR characteristics was steeply nonlinear over a narrow range of I(spark), resembling a phase transition. We conclude that the (partial) periodicity and rate regulation of the "Calcium clock" in SANCs are emergent properties of the diffusive coupling of an ensemble of interacting stochastic CRUs. The variation in LCR period and size with I(spark) is sufficient to account for β-adrenergic regulation of SANC beating rate.