Mean-field coupling of calcium oscillations in a multicellular system of rat hepatocytes

In a multicellular system of rat hepatocytes and even in an intact liver, cytoplasmic calcium oscillations are synchronized and highly coordinated. In this paper, the mean-field coupling term has been introduced to describe the coupling flux, which is more efficient than gap junctional coupling terms. An optimal coupling strength and an optimal stimulation level for the synchronization of the coupled system have been observed in this paper. Moreover, it has been proved that these results are independent of the cells number. Interestingly, it has been observed that the intracellular noise and the extracellular noise have different effects on the synchronization of the coupled system.     

Effects of gap junction to Ca(2+) and to IP(3) on the synchronization of intercellular calcium oscillations in hepatocytes

The frequency of free cytosolic calcium concentration ([Ca(2+)]) oscillations elicited by a given agonist concentration differs between individual hepatocytes. However, in multicellular systems of rat hepatocytes and even in the intact liver, [Ca(2+)] oscillations are synchronized and highly coordinated. In this paper, we have investigated theoretically the gap junction permeable to calcium and to IP(3) on intercellular synchronization by means of a mathematical model, respectively. It is shown that gap junction permeable to calcium and to IP(3) are effective on synchronizing calcium oscillations in coupled hepatocytes. Our theoretical results are similar either for the case of Ca(2+) acting as coordinating messenger or for the case of IP(3) as coordinating messenger. There exists an optimal coupling strength for a pair of connected hepatocytes. Appropriate coupling strength and IP(3) level can induce various harmonic locking of intercellular [Ca(2+)] oscillations. Furthermore, a phase diagram in two-dimensional parameter space of the coupling strength and IP(3) level (or the velocity of IP(3) synthesis) has been predicted, in which the synchronization region is similar to Arnol'd tongue.     

Phase synchronization and coherence resonance of stochastic calcium oscillations in coupled hepatocytes

The frequency of free cytosolic calcium concentration ([Ca(2+)]) oscillations elicited by a given agonist concentration differs between individual hepatocytes. However, in multicellular systems of rat hepatocytes and even in the intact liver, [Ca(2+)] oscillations are synchronized and highly coordinated. In this paper, we have investigated theoretically the effects of gap junction permeable to calcium and of the total Ca(2+) channel number located on endoplasmic reticulum on intercellular synchronization. Figures of ratio between mean oscillating frequency of coupled cells describe visually the process of phase-locking. By virtue of a set of phase analysis, we can observe a gradual transition from synchronous behavior to nonsynchronous behavior. Furthermore, a signal-to-noise ratio in two dimensional parameter space (coupling strength-total Ca(2+) channel number) has suggested that, coherence resonance will occur for appropriate noise and coupling.     

Mechanism of receptor-oriented intercellular calcium wave propagation in hepatocytes.

Intercellular calcium signals are propagated in multicellular hepatocyte systems as well as in the intact liver. The stimulation of connected hepatocytes by glycogenolytic agonists induces reproducible sequences of intracellular calcium concentration increases, resulting in unidirectional intercellular calcium waves. Hepatocytes are characterized by a gradient of vasopressin binding sites from the periportal to perivenous areas of the cell plate in hepatic lobules. Also, coordination of calcium signals between neighboring cells requires the presence of the agonist at each cell surface as well as gap junction permeability. We present a model based on the junctional coupling of several hepatocytes differing in sensitivity to the agonist and thus in the intrinsic period of calcium oscillations. In this model, each hepatocyte displays repetitive calcium spikes with a slight phase shift with respect to neighboring cells, giving rise to a phase wave. The orientation of the apparent calcium wave is imposed by the direction of the gradient of hormonal sensitivity. Calcium spikes are coordinated by the diffusion across junctions of small amounts of inositol 1,4, 5-trisphosphate (InsP(3)). Theoretical predictions from this model are confirmed experimentally. Thus, major physiological insights may be gained from this model for coordination and spatial orientation of intercellular signals.-Dupont, G., Tordjmann, T., Clair, C., Swillens, S., Claret, M., Combettes, L. Mechanism of receptor-oriented intercellular calcium wave propagation in hepatocytes.     

Ca2+ dynamics in a population of smooth muscle cells: modeling the recruitment and synchronization

Many experimental studies have shown that arterial smooth muscle cells respond with cytosolic calcium rises to vasoconstrictor stimulation. A low vasoconstrictor concentration gives rise to asynchronous spikes in the calcium concentration in a few cells (asynchronous flashing). With a greater vasoconstrictor concentration, the number of smooth muscle cells responding in this way increases (recruitment) and calcium oscillations may appear. These oscillations may eventually synchronize and generate arterial contraction and vasomotion. We show that these phenomena of recruitment and synchronization naturally emerge from a model of a population of smooth muscle cells coupled through their gap junctions. The effects of electrical, calcium, and inositol 1,4,5-trisphosphate coupling are studied. A weak calcium coupling is crucial to obtain a synchronization of calcium oscillations and the minimal required calcium permeability is deduced. Moreover, we note that an electrical coupling can generate oscillations, but also has a desynchronizing effect. Inositol 1,4,5-trisphosphate diffusion does not play an important role to achieve synchronization. Our model is validated by published in vitro experiments obtained on rat mesenteric arterial segments.     

Emergent properties of electrically coupled smooth muscle cells

Asynchronous and synchronous calcium oscillations occur in a variety of cells. A well-established pathway for intercellular communication is provided by gap junctions which connect adjacent cells and can mediate electrical and chemical coupling. Several experimental studies report that cells presenting only a transient increase when freshly dispersed may oscillate when they are coupled. Such observations suggest that the role of gap junctions is not only to coordinate calcium oscillations of adjacent cells. Gap junctions may also be important to generate oscillations. Here we illustrate the emergent properties of electrically coupled smooth muscle cells using a model that we recently proposed. A bifurcation analysis in the case of two cells reveals that synchronous and asynchronous calcium oscillations can be induced by electrical coupling. In a larger population of smooth muscle cells, electrical coupling may result in the creation of groups of cells presenting synchronous calcium oscillations. The elements of one group may be distant from each other. Moreover, our results highlight a general mechanism by which gap junctional electrical coupling can give rise to out of phase calcium oscillations in smooth muscle cells that are non-oscillating when uncoupled. All these observations remain true in the case of non-identical cells, except that the solution corresponding to synchronous calcium oscillations disappears and that the formation of groups is sensitive to the degree of heterogeneity. The first two authors contributed equally to this work.     

Photoliberating inositol-1,4,5-trisphosphate triggers ATP release that is blocked by the connexin mimetic peptide gap 26

Calcium signals can be communicated between cells by the diffusion of a second messenger through gap junction channels or by the release of an extracellular purinergic messenger. We investigated the contribution of these two pathways in endothelial cell lines by photoliberating InsP(3) or calcium from intracellular caged precursors, and recording either the resulting intercellular calcium wave or else the released ATP with a luciferin/luciferase assay. Photoliberating InsP(3) in a single cell within a confluent culture triggered an intercellular calcium wave, which was inhibited by the gap junction blocker alpha-glycyrrhetinic acid (alpha-GA), the connexin mimetic peptide gap 26, the purinergic inhibitors suramin, PPADS and apyrase and by purinergic receptor desensitisation. InsP(3)-triggered calcium waves were able to cross 20 microm wide cell-free zones. Photoliberating InsP(3) triggered ATP release that was blocked by buffering intracellular calcium with BAPTA and by applying gap 26. Gap 26, however, did not inhibit the gap junctional coupling between the cells as measured by fluorescence recovery after photobleaching. Photoliberating calcium did not trigger intercellular calcium waves or ATP release. We conclude that InsP(3)-triggered ATP release through connexin hemichannels contributes to the intercellular propagation of calcium signals.     

The dynamics of calcium oscillations that activate mammalian eggs

It has been known for some time that mammalian eggs are activated by a series of intracellular calcium oscillations that occur shortly after sperm egg membrane fusion. Recent work has identified a novel sperm specific phospholipase C zeta as the likely agent that stimulates the calcium oscillations in eggs after sperm-egg membrane fusion. PLCzeta is stimulated by low intracellular calcium levels in a manner which suggests that there is a regenerative feedback of calcium release and PLCzeta induced inositol 1,4,5-trisphophate (InsP(3)) production in eggs. This implies calcium oscillations in fertilizing mammalian eggs are driven by underlying oscillations of InsP(3). This model of oscillations is supported by the response of mouse eggs to sudden increases in InsP(3). The cellular targets of calcium oscillations include calmodulin-dependent protein kinases, protein kinase C and mitochondria. There is evidence that eggs might be best activated by multiple calcium increases rather than a single calcium rise. As yet we do not fully understand how the target of calcium in a mammalian egg might decode the patterns of calcium changes that can occur during egg activation.     

Fast calcium wave propagation mediated by electrically conducted excitation and boosted by CICR

We have investigated synchronization and propagation of calcium oscillations, mediated by gap junctional excitation transmission. For that purpose we used an experimentally based model of normal rat kidney (NRK) cells, electrically coupled in a one-dimensional configuration (linear strand). Fibroblasts such as NRK cells can form an excitable syncytium and generate spontaneous inositol 1,4,5-trisphosphate (IP(3))-mediated intracellular calcium waves, which may spread over a monolayer culture in a coordinated fashion. An intracellular calcium oscillation in a pacemaker cell causes a membrane depolarization from within that cell via calcium-activated chloride channels, leading to an L-type calcium channel-based action potential (AP) in that cell. This AP is then transmitted to the electrically connected neighbor cell, and the calcium inflow during that transmitted AP triggers a calcium wave in that neighbor cell by opening of IP(3) receptor channels, causing calcium-induced calcium release (CICR). In this way the calcium wave of the pacemaker cell is rapidly propagated by the electrically transmitted AP. Propagation of APs in a strand of cells depends on the number of terminal pacemaker cells, the L-type calcium conductance of the cells, and the electrical coupling between the cells. Our results show that the coupling between IP(3)-mediated calcium oscillations and AP firing provides a robust mechanism for fast propagation of activity across a network of cells, which is representative for many other cell types such as gastrointestinal cells, urethral cells, and pacemaker cells in the heart.     

Tumour necrosis factor alpha inhibits purinergic calcium signalling in blood-brain barrier endothelial cells

The breaching of the blood-brain barrier is an essential aspect in the pathogenesis of neuroinflammatory diseases, in which tumour necrosis factor alpha (TNF-alpha) as well as endothelial calcium ions play a key role. We investigated whether TNF-alpha could influence the communication of calcium signals between brain endothelial cells (GP8 and RBE4). Intercellular calcium waves triggered by mechanical stimulation or photoliberation of InsP3 in single cells were significantly reduced in size after TNF-alpha exposure (1000 U/mL, 2 and 24 h). Calcium signals are communicated between cells by means of gap junctional and paracrine purinergic signalling. TNF-alpha significantly inhibited gap junctional coupling, stimulated the basal release of ATP, and dose-dependently blocked the triggered component of ATP release. The cytokine displayed similar effects on the uptake of a fluorescent reporter dye into the cells. Previous work with connexin mimetic peptides demonstrated that the triggered ATP release in these cells is connexin-related; these peptides did, however, not influence the elevated basal ATP release caused by TNF-alpha. We conclude that TNF-alpha depresses calcium signal communication in blood-brain barrier endothelial cells, by reducing gap junctional coupling and by inhibiting triggered ATP release. The cytokine thus inhibits connexin-related communication pathways like gap junctions and connexin hemichannels.     

Diffusion of calcium and metabolites in pancreatic islets: killing oscillations with a pitchfork

Cell coupling is important for the normal function of the beta-cells of the pancreatic islet of Langerhans, which secrete insulin in response to elevated plasma glucose. In the islets, electrical and metabolic communications are mediated by gap junctions. Although electrical coupling is believed to account for synchronization of the islets, the role and significance of diffusion of calcium and metabolites are not clear. To address these questions we analyze two different mathematical models of islet calcium and electrical dynamics. To study diffusion of calcium, we use a modified Morris-Lecar model. Based on our analysis, we conclude that intercellular diffusion of calcium is not necessary for islet synchronization, at most supplementing electrical coupling. Metabolic coupling is investigated with a recent mathematical model incorporating glycolytic oscillations. Bifurcation analysis of the coupled system reveals several modes of behavior, depending on the relative strength of electrical and metabolic coupling. We find that whereas electrical coupling always produces synchrony, metabolic coupling can abolish both oscillations and synchrony, explaining some puzzling experimental observations. We suggest that these modes are generic features of square-wave bursters and relaxation oscillators coupled through either the activation or recovery variable.     

Spatial phase pattern in one-dimensional arrays of limit cycle oscillators with discrete coupling

We present a model of limit cycle oscillators for collective oscillations in intracellular calcium concentration in cell communities. A phase-dependent discrete coupling between nearest neighbors is introduced into the model on the basis of the experimental observation that intercellular transmission of calcium or calcium mobilizing messenger is effected by gap junction and gap junctional permeability is affected by intracellular calcium concentration. The spatial phase pattern of several clusters in which oscillations are in phase is found with the phase-dependent discrete coupling.     

Inositol 1,4,5-trisphosphate receptors in the heart

Inositol 1,4,5-trisphosphate (InsP3) is an established calcium-mobilizing messenger, which is well-known to activate Ca2+ signaling in many cell types. Contractile cardiomyocytes express hormone receptors that are coupled to the production of InsP3. Such cardioactive hormones, including endothelin, may have profound inotropic and arrhythmogenic actions, but it is unclear whether InsP3 underlies any of these effects. We have examined the expression and localization of InsP3 receptors (InsP3Rs), and the potential role of InsP3 in modulating cardiac excitation-contraction coupling (EC coupling). Stimulation of electrically-paced atrial and ventricular myocytes with a membrane-permeant InsP3 ester was found to evoke an increase in the amplitudes of action potential-evoked Ca2+ transients and to cause pro-arrhythmic diastolic Ca2+ transients. All the effects of the InsP3 ester could be blocked using a membrane-permeant antagonist of InsP3Rs (2-aminoethoxydiphenyl borate; 2-APB). Furthermore, 2-APB blocked arrhythmias evoked by endothelin and delayed the onset of positive inotropic responses. Our data indicate that atrial and ventricular cardiomyocytes express functional InsP3Rs, and these channels have the potential to influence EC coupling.     

Pharmacological sensitivity of ATP release triggered by photoliberation of inositol-1,4,5-trisphosphate and zero extracellular calcium in brain endothelial cells

Recently, ATP has gained much interest as an extracellular messenger involved in the communication of calcium signals between cells. The mechanism of ATP release is, however, still a matter of debate. In the present study we investigated the possible contribution of connexin hemichannels or ion channels in the release of ATP in GP8, a rat brain endothelial cell line. Release of ATP was triggered by photoactivation of InsP(3) or by reducing the extracellular calcium concentration. Both trigger protocols induced ATP release significantly above baseline. InsP(3)-triggered ATP release was completely blocked by alpha-glycyrrhetinic acid (alpha-GA), the connexin mimetic peptides gap 26 and 27, and the trivalent ions gadolinium and lanthanum. ATP release triggered by zero calcium was, in addition to these substances, also blocked by flufenamic acid (FFA), niflumic acid, and NPPB. Gap 27 selectively blocked zero calcium-triggered ATP release in connexin-43 transfected HeLa cells, while having no effect in wild-type and connexin-32 transfected cells. Of all the agents used, only alpha-GA, FFA and NPPB significantly reduced gap junctional coupling. In conclusion, InsP(3) and zero calcium-triggered ATP release show major similarities but also some differences in their sensitivity to the agents applied. It is suggested that both stimuli trigger ATP release through the same mechanism, which is connexin-dependent, permeable in both directions, potently blocked by connexin mimetic peptides, and consistent with the opening of connexin hemichannels.     

Multiple factors influence calcium synchronization in arterial vasomotion

The intercellular synchronization of spontaneous calcium (Ca(2+)) oscillations in individual smooth muscle cells is a prerequisite for vasomotion. A detailed mathematical model of Ca(2+) dynamics in rat mesenteric arteries shows that a number of synchronizing and desynchronizing pathways may be involved. In particular, Ca(2+)-dependent phospholipase C, the intercellular diffusion of inositol trisphosphate (IP(3), and to a lesser extent Ca(2+)), IP(3) receptors, diacylglycerol-activated nonselective cation channels, and Ca(2+)-activated chloride channels can contribute to synchronization, whereas large-conductance Ca(2+)-activated potassium channels have a desynchronizing effect. Depending on the contractile state and agonist concentrations, different pathways become predominant, and can be revealed by carefully inhibiting the oscillatory component of their total activity. The phase shift between the Ca(2+) and membrane potential oscillations can change, and thus electrical coupling through gap junctions can mediate either synchronization or desynchronization. The effect of the endothelium is highly variable because it can simultaneously enhance the intercellular coupling and affect multiple smooth muscle cell components. Here, we outline a system of increased complexity and propose potential synchronization mechanisms that need to be experimentally tested.     

Calcium oscillations: phenomena, mechanisms and significance

Many hormones that mobilise intracellular calcium via inositol 1,4,5 trisphosphate induce oscillations in cytoplasmic free Ca. Two basic oscillatory patterns occur: quasi-sinusoidal oscillations and repetitive free Ca transients. The mechanisms responsible for generating these oscillations are not clear; calcium-induced calcium release, interplay between two intracellular calcium pools and repetitive generation of InsP3 are discussed. The significance of different oscillatory patterns induced by different agonists in the same cell is emphasised, and mechanisms by which the oscillators may retain-receptor specific information are proposed, such as negative feedback onto receptors or G-proteins by protein kinase C. Reasons why cells generate free Ca oscillations and possible consequences such as oscillations in downstream pathways are explored. The possibility that pathological conditions such as aluminium toxicity are exerted through distortion of oscillatory free Ca signalling is raised.     

Gap junction coupling and calcium waves in the pancreatic islet

The pancreatic islet is a highly coupled, multicellular system that exhibits complex spatiotemporal electrical activity in response to elevated glucose levels. The emergent properties of islets, which differ from those arising in isolated islet cells, are believed to arise in part by gap junctional coupling, but the mechanisms through which this coupling occurs are poorly understood. To uncover these mechanisms, we have used both high-speed imaging and theoretical modeling of the electrical activity in pancreatic islets under a reduction in the gap junction mediated electrical coupling. Utilizing islets from a gap junction protein connexin 36 knockout mouse model together with chemical inhibitors, we can modulate the electrical coupling in the islet in a precise manner and quantify this modulation by electrophysiology measurements. We find that after a reduction in electrical coupling, calcium waves are slowed as well as disrupted, and the number of cells showing synchronous calcium oscillations is reduced. This behavior can be reproduced by computational modeling of a heterogeneous population of β-cells with heterogeneous levels of electrical coupling. The resulting quantitative agreement between the data and analytical models of islet connectivity, using only a single free parameter, reveals the mechanistic underpinnings of the multicellular behavior of the islet.     

Model for synchronization of pancreatic beta-cells by gap junction coupling.

Pancreatic beta-cells coupled by gap junctions in sufficiently large clusters exhibit regular electrical bursting activity, which is described by the Chay-Keizer model and its variants. According to most reports, however, isolated cells exhibit disorganized spiking. We have previously (Sherman, A. J. Rinzel, and J. Keizer, 1988. Biophys. J. 54:411-425) modeled these behaviors by hypothesizing that stochastic channel fluctuations disrupt the bursts. We showed that when cells are coupled by infinite conductance gap junctions, so that the cluster is isopotential and may be viewed as a single "supercell," the fluctuations are shared over a larger membrane area and hence dampened. Bursting emerges when there are more than approximately 50 cells in the cluster. In the model the temporal organization of spikes into bursts increases the amplitude of intracellular calcium oscillations, which may be relevant for insulin secretion. We now extend the previous work by considering the case of a true "multicell" model with finite gap junctional conductance. Whereas the previous study assumed that the cells were synchronized, we can now study the process of synchronization itself. We show that, for sufficiently large clusters, the cells both synchronize and begin to burst with moderate, physiologically reasonable gap junctional conductance. An unexpected finding is that the burst period is longer, and calcium amplitude greater, than when coupling is infinitely strong, with an optimum in the range of 150-250 pS. Our model is in good agreement with recent experimental data of Perez-Armendariz, M., D. C. Spray, and M. V. L. Bennett. (1991. Biophys. J. 59:76-92) showing extensive gap junctions in beta-cell pairs with mean interfacial conductance of 213 +/- 113 pS. The optimality property of our model is noteworthy because simple slow-wave models without spikes do not show the same behavior.     

Functional InsP3 receptors that may modulate excitation-contraction coupling in the heart

The roles of the Ca2+-mobilising messenger inositol 1,4,5-trisphosphate (InsP3) in heart are unclear, although many hormones activate InsP3 production in cardiomyocytes and some of their inotropic, chronotropic and arrhythmogenic effects may be due to Ca2+ release mediated by InsP3 receptors (InsP3Rs) [1-3]. In the present study, we examined the expression and subcellular localisation of InsP3R isoforms, and investigated their potential role in modulating excitation-contraction coupling (EC coupling). Western, PCR and InsP3-binding analysis indicated that both atrial and ventricular myocytes expressed mainly type II InsP3Rs, with approximately sixfold higher levels of InsP3Rs in atrial cells. Co-immunostaining of atrial myocytes with antibodies against type II ryanodine receptors (RyRs) and type II InsP3Rs revealed that the latter were arranged in the subsarcolemmal space where they largely co-localised with the junctional RyRs. Stimulation of quiescent or electrically paced atrial myocytes with a membrane-permeant InsP3 ester, which enters cells and directly activates InsP3Rs, caused the appearance of spontaneous Ca2+-release events. In addition, in paced cells, the InsP3 ester evoked an increase in the amplitudes of action potential-evoked Ca2+ transients. These data indicate that atrial cardiomyocytes express functional InsP3Rs, and that these channels could modulate EC coupling.