Activation of a cGMP-sensitive calcium-dependent chloride channel may cause transition from calcium waves to whole cell oscillations in smooth muscle cells

In vitro, alpha-adrenoreceptor stimulation of rat mesenteric small arteries often leads to a rhythmic change in wall tension, i.e., vasomotion. Within the individual smooth muscle cells of the vascular wall, vasomotion is often preceded by a period of asynchronous calcium waves. Abruptly, these low-frequency waves may transform into high-frequency whole cell calcium oscillations. Simultaneously, multiple cells synchronize, leading to rhythmic generation of tension. We present a mathematical model of vascular smooth muscle cells that aims at characterizing this sudden transition. Simulations show calcium waves sweeping through the cytoplasm when the sarcoplasmic reticulum (SR) is stimulated to release calcium. A rise in cGMP leads to the experimentally observed transition from waves to whole cell calcium oscillations. At the same time, membrane potential starts to oscillate and the frequency approximately doubles. In this transition, the simulated results point to a key role for a recently discovered cGMP-sensitive calcium-dependent chloride channel. This channel depolarizes the membrane in response to calcium released from the SR. In turn, depolarization causes a uniform opening of L-type calcium channels on the cell surface, stimulating a synchronized release of SR calcium and inducing the shift from waves to whole cell oscillations. The effect of the channel is therefore to couple the processes of the SR with those of the membrane. We hypothesize that the shift in oscillatory mode and the associated onset of oscillations in membrane potential within the individual cell may underlie sudden intercellular synchronization and the appearance of vasomotion.     

Endothelial coordination of cerebral vasomotion via myoendothelial gap junctions containing connexins 37 and 40

Control of cerebral vasculature differs from that of systemic vessels outside the blood-brain barrier. The hypothesis that the endothelium modulates vasomotion via direct myoendothelial coupling was investigated in a small vessel of the cerebral circulation. In the primary branch of the rat basilar artery, membrane potential, diameter, and calcium dynamics associated with vasomotion were examined using selective inhibitors of endothelial function in intact and endothelium-denuded arteries. Vessel anatomy, protein, and mRNA expression were studied using conventional electron microscopy high-resolution ultrastructural and confocal immunohistochemistry and quantitative PCR. Membrane potential oscillations were present in both endothelial cells and smooth muscle cells (SMCs), and these preceded rhythmical contractions during which adjacent SMC intracellular calcium concentration ([Ca(2+)](i)) waves were synchronized. Endothelium removal abolished vasomotion and desynchronized adjacent smooth muscle cell [Ca(2+)](i) waves. N(G)-nitro-l-arginine methyl ester (10 microM) did not mimic this effect, and dibutyryl cGMP (300 muM) failed to resynchronize [Ca(2+)](i) waves in endothelium-denuded arteries. Combined charybdotoxin and apamin abolished vasomotion and depolarized and constricted vessels, even in absence of endothelium. Separately, (37,43)Gap27 and (40)Gap27 abolished vasomotion. Extensive myoendothelial gap junctions (3 per endothelial cell) composed of connexins 37 and 40 connected the endothelial cell and SMC layers. Synchronized vasomotion in rat basilar artery is endothelium dependent, with [Ca(2+)](i) waves generated within SMCs being coordinated by electrical coupling via myoendothelial gap junctions.     

Antiphase oscillations of endothelium and smooth muscle [Ca2+]i in vasomotion of rat mesenteric small arteries

The mechanisms leading to vasomotion in the presence of noradrenaline and inhibitors of the sarcoplasmic/endoplasmic reticulum calcium ATPase were investigated in isolated rat mesenteric small arteries. Isobaric diameter and isometric force were measured together with membrane potential in endothelial cells and smooth muscle cells (SMC). Calcium in the endothelial cells and SMC was imaged with confocal microscopy. In the presence of noradrenaline and cyclopiazonic acid, ryanodine-insensitive oscillations in tone were produced. The frequency was about 1 min(-1) and amplitude about 70% of the maximal tone. The amplitude was reduced by indomethacin and increased with L-NAME. Vasomotion was inhibited by nifedipine and by 40 mM potassium. The frequency was increased and amplitude decreased by removal of the endothelium and by application of charybdotoxin and apamin. The vasomotion was associated with in-phase oscillations of membrane potential in endothelial cells and SMC and oscillations of [Ca2+]i that were in near anti-phase. We suggest a working model for the generation of oscillation based on a membrane oscillator where ion channels in both endothelial cells and SMC interact via a current running between the two cell types through myoendothelial gap junctions, which sets up a near anti-phase oscillation of [Ca2+]i in the two cell types.     

Role of voltage-dependent modulation of store Ca2+ release in synchronization of Ca2+ oscillations

Slow waves are rhythmic depolarizations that underlie mechanical activity of many smooth muscles. Slow waves result through rhythmic Ca(2+) release from intracellular Ca(2+) stores through inositol 1,4,5-trisphosphate (IP(3)) sensitive receptors and Ca(2+)-induced Ca(2+) release. Ca(2+) oscillations are transformed into membrane depolarizations by generation of a Ca(2+)-activated inward current. Importantly, the store Ca(2+) oscillations that underlie slow waves are entrained across many cells over large distances. It has been shown that IP(3) receptor-mediated Ca(2+) release is enhanced by membrane depolarization. Previous studies have implicated diffusion of Ca(2+) or the second messenger IP(3) across gap junctions in synchronization of Ca(2+) oscillations. In this study, a novel mechanism of Ca(2+) store entrainment through depolarization-induced IP(3) receptor-mediated Ca(2+) release is investigated. This mechanism is significantly different from chemical coupling-based mechanisms, as membrane potential has a coupling effect over distances several orders of magnitude greater than either diffusion of Ca(2+) or IP(3) through gap junctions. It is shown that electrical coupling acting through voltage-dependent modulation of store Ca(2+) release is able to synchronize oscillations of cells even when cells are widely separated and have different intrinsic frequencies of oscillation.     

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.     

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.     

Model of intercellular calcium oscillations in hepatocytes: synchronization of heterogeneous cells.

Hepatocytes respond with repetitive cytosolic calcium spikes to stimulation by vasopressin and noradrenalin. In the intact liver, calcium oscillations occur in a synchronized fashion as periodic waves across whole liver lobules, but the mechanism of intercellular coupling remains unclear. Recently, it has been shown that individual hepatocytes can have very different intrinsic oscillation frequencies but become phase-locked when coupled by gap junctions. We investigate the gap junction hypothesis for intercellular synchronization by means of a mathematical model. It is shown that junctional calcium fluxes are effective in synchronizing calcium oscillations in coupled hepatocytes. An experimentally testable estimate is given for the junctional coupling coefficient required; it mainly depends on the degree of heterogeneity between cells. Intercellular synchronization by junctional calcium diffusion may occur also in other cell types exhibiting calcium-activated calcium release through InsP(3) receptors, if the gap junctional coupling is strong enough and the InsP(3) receptors are sufficiently sensitized by InsP(3).     

Role of membrane potential in vasomotion of isolated pressurized rat arteries

Vasomotion, the phenomenon of vessel diameter oscillation, regulates blood flow and resistance. The main parameters implicated in vasomotion are particularly the membrane potential and the cytosolic free calcium in smooth muscle cells. In this study, these parameters were measured in rat perfused-pressurized mesenteric artery segments. The application of norepinephrine (NE) caused rhythmic diameter contractions and membrane potential oscillations (amplitude; 5.3 +/- 0.3 mV, frequency; 0.09 +/- 0.01 Hz). Verapamil (1 microM) abolished this vasomotion. During vasomotion, 10(-5) M ouabain (Na(+)-K(+) ATPase inhibitor) decreased the amplitude of the electrical oscillations but not their frequency (amplitude; 3.7 +/- 0.3 mV, frequency; 0.08 +/- 0.002 Hz). Although a high concentration of ouabain (10(-3) M) (which exhibits non-specific effects) abolished both electrical membrane potential oscillations and vasomotion, we conclude that the Na+-K+ ATPase could not be implicated in the generation of the membrane potential oscillations. We conclude that in rat perfused-pressurized mesenteric artery, the slow wave membrane type of potential oscillation by rhythmically gating voltage-dependent calcium channels, is responsible for the oscillation of intracellular calcium and thus vasomotion.     

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.     

Sarcoplasmic reticulum vesicles embedded in agarose gel exhibit propagating calcium waves

In different cell types, activation of signal transduction pathways leads to the generation of calcium oscillations and/or waves. Due to this important impact for cellular function, calcium waves are the subject of intensive investigations. To study interactions of cell organelles with no influence of the cell membrane, sarcoplasmic reticulum (SR) vesicles and well-coupled mitochondria were reconstituted. For the first time, we demonstrate the generation and propagation of calcium waves in a suspension of sarcoplasmic reticulum vesicles, embedded in an agarose gel. The propagation dynamics resemble those of calcium waves in living cells. Moreover, the addition of well-coupled mitochondria leads to more pronounced and significantly faster propagating waves, demonstrating the importance of the mitochondrial Ca(2+) transport. The experimental and simulation results indicate the resemblance of the in vitro system to an excitable medium.     

Role of the endothelium on arterial vasomotion

It is well-known that cyclic variations of the vascular diameter, a phenomenon called vasomotion, are induced by synchronous calcium oscillations of smooth muscle cells (SMCs). However, the role of the endothelium on vasomotion is unclear. Some experimental studies claim that the endothelium is necessary for synchronization and vasomotion, whereas others report rhythmic contractions in the absence of an intact endothelium. Moreover, endothelium-derived factors have been shown to abolish vasomotion by desynchronizing the calcium signals in SMCs. By modeling the calcium dynamics of a population of SMCs coupled to a population of endothelial cells, we analyze the effects of an SMC vasoconstrictor stimulation on endothelial cells and the feedback of endothelium-derived factors. Our results show that the endothelium essentially decreases the SMCs calcium level and may move the SMCs from a steady state to an oscillatory domain, and vice versa. In the oscillatory domain, a population of coupled SMCs exhibits synchronous calcium oscillations. Outside the oscillatory domain, the coupled SMCs present only irregular calcium flashings arising from noise modeling stochastic opening of channels. Our findings provide explanations for the published contradictory experimental observations.     

Spontaneous calcium oscillations during diastole in the whole heart: the influence of ryanodine reception function and gap junction coupling

Triggered arrhythmias due to spontaneous cytoplasmic calcium oscillations occur in a variety of disease conditions; however, their cellular mechanisms in tissue are not clear. We hypothesize that spontaneous calcium oscillations in the whole heart are due to calcium release from the sarcoplasmic reticulum and are facilitated by calcium diffusion through gap junctions. Optical mapping of cytoplasmic calcium from Langendorff perfused guinea pig hearts (n = 10) was performed using oxygenated Tyrode's solution (in mM): 140 NaCl, 0.7 MgCl, 4.5 KCl, 5.5 dextrose, 5 HEPES, and 5.5 CaCl? (pH 7.45, 34°C). Rapid pacing was used to induce diastolic calcium oscillations. In all preparations, pacing-induced multicellular diastolic calcium oscillations (m-SCR) occurred across most of the mapping field, at all pacing rates tested. Ryanodine (1 μM) eliminated all m-SCR activity. Low-dose caffeine (1 mM) increased m-SCR amplitude (+10.4 ± 4.4%, P < 0.05) and decreased m-SCR time-to-peak (-17.4 ± 6.7%, P < 0.05) and its temporal synchronization (i.e., range) across the mapping field (-26.9 ± 17.1%, P < 0.05). Surprisingly, carbenoxolone increased the amplitude of m-SCR activity (+14.8 ± 4.1%, P < 0.05) and decreased m-SCR time-to-peak (-11.3 ± 9.6%, P < 0.01) and its synchronization (-37.0 ± 19.1%, P < 0.05), similar to caffeine. In isolated myocytes, carbenoxolone (50 μM) had no effect on the frequency of aftercontractions, suggesting the effect of cell-to-cell uncoupling on m-SCR activity is tissue specific. Therefore, in the whole heart, overt m-SCR activity caused by calcium release from the SR can be induced over a broad range of pacing rates. Enhanced ryanodine receptor open probability and, surprisingly, decreased cell-to-cell coupling increased the amplitude and temporal synchronization of spontaneous calcium release in tissue.     

Diffusion of extracellular K+ can synchronize bursting oscillations in a model islet of Langerhans.

Electrical bursting oscillations of mammalian pancreatic beta-cells are synchronous among cells within an islet. While electrical coupling among cells via gap junctions has been demonstrated, its extent and topology are unclear. The beta-cells also share an extracellular compartment in which oscillations of K+ concentration have been measured (Perez-Armendariz and Atwater, 1985). These oscillations (1-2 mM) are synchronous with the burst pattern, and apparently are caused by the oscillating voltage-dependent membrane currents: Extracellular K+ concentration (Ke) rises during the depolarized active (spiking) phase and falls during the hyperpolarized silent phase. Because raising Ke depolarizes the cell membrane by increasing the potassium reversal potential (VK), any cell in the active phase should recruit nonspiking cells into the active phase. The opposite is predicted for the silent phase. This positive feedback system might couple the cells' electrical activity and synchronize bursting. We have explored this possibility using a theoretical model for bursting of beta-cells (Sherman et al., 1988) and K+ diffusion in the extracellular space of an islet. Computer simulations demonstrate that the bursts synchronize very quickly (within one burst) without gap junctional coupling among the cells. The shape and amplitude of computed Ke oscillations resemble those seen in experiments for certain parameter ranges. The model cells synchronize with exterior cells leading, though incorporating heterogeneous cell properties can allow interior cells to lead. The model islet can also be forced to oscillate at both faster and slower frequencies using periodic pulses of higher K+ in the medium surrounding the islet. Phase plane analysis was used to understand the synchronization mechanism. The results of our model suggest that diffusion of extracellular K+ may contribute to coupling and synchronization of electrical oscillations in beta-cells within an islet.     

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.     

Morphology and molecular composition of sarcoplasmic reticulum surface junctions in the absence of DHPR and RyR in mouse skeletal muscle

Calcium release during excitation-contraction coupling of skeletal muscle cells is initiated by the functional interaction of the exterior membrane and the sarcoplasmic reticulum (SR), mediated by the "mechanical" coupling of ryanodine receptors (RyR) and dihydropyridine receptors (DHPR). RyR is the sarcoplasmic reticulum Ca(2+) release channel and DHPR is an L-type calcium channel of exterior membranes (surface membrane and T tubules), which acts as the voltage sensor of excitation-contraction coupling. The two proteins communicate with each other at junctions between SR and exterior membranes called calcium release units and are associated with several proteins of which triadin and calsequestrin are the best characterized. Calcium release units are present in diaphragm muscles and hind limb derived primary cultures of double knock out mice lacking both DHPR and RyR. The junctions show coupling between exterior membranes and SR, and an apparently normal content and disposition of triadin and calsequestrin. Therefore SR-surface docking, targeting of triadin and calsequestrin to the junctional SR domains and the structural organization of the two latter proteins are not affected by lack of DHPR and RyR. Interestingly, simultaneous lack of the two major excitation-contraction coupling proteins results in decrease of calcium release units frequency in the diaphragm, compared with either single knockout mutation.     

Effect of syncytium structure of receptor systems on stochastic resonance induced by chaotic potential fluctuation.

To study a role of syncytium structure of sensory receptor systems in the detection of weak signals through stochastic resonance, we present a model of a receptor system with syncytium structure in which receptor cells are interconnected by gap junctions. The apical membrane of each cell includes two kinds of ion channels whose gating processes are described by the deterministic model. The membrane potential of each cell fluctuates chaotically or periodically, depending on the dynamical state of collective channel gating. The chaotic fluctuation of membrane potential acts as internal noise for the stochastic resonance. The detection ability of the system increases as the electric conductance between adjacent cells generated by the gap junction increases. This effect of gap junctions arises mainly from the fact that the synchronization of chaotic fluctuation of membrane potential between the receptor cells is strengthened as the density of gap junctions is increased.     

Anti-phase calcium oscillations in astrocytes via inositol (1, 4, 5)-trisphosphate regeneration

Observations in cultured mouse astrocytes suggest anti-phase synchronization of cytosolic calcium concentrations in nearest neighbor cells that are coupled through gap junctions. A mathematical model is used to investigate physiologic conditions under which diffusion of the second messenger inositol (1, 4, 5)-trisphosphate (IP(3)) through gap junctions can facilitate synchronized anti-phase Ca(2+) oscillations. Our model predicts anti-phase oscillations in both cytosolic calcium and IP(3) concentrations if (a) the gap junction permeability is within a window of values and (b) IP(3) is regenerated in the astrocytes via, e.g. phospholipase C(delta). This result sheds new light on the current dispute on the mechanism of intercellular calcium signaling. It provides indirect evidence for a partially regenerative mechanism as the model excludes anti-phase synchrony in the absence of IP(3) regeneration.     

A quantitative model for linking Na+/Ca2+ exchanger to SERCA during refilling of the sarcoplasmic reticulum to sustain [Ca2+] oscillations in vascular smooth muscle

We have developed a quantitative model for the creation of cytoplasmic Ca²⁺ gradients near the inner surface of the plasma membrane (PM). In particular we simulated the refilling of the sarcoplasmic reticulum (SR) via PM–SR junctions during asynchronous [Ca²⁺]_i oscillations in smooth muscle cells of the rabbit inferior vena cava. We have combined confocal microscopy data on the [Ca²⁺]_i oscillations, force transduction data from cell contraction studies and electron microscopic images to build a basis for computational simulations that model the transport of calcium ions from Na⁺/Ca²⁺ exchangers (NCX) on the PM to sarcoplasmic/endoplasmic reticulum Ca²⁺ ATPase (SERCA) pumps on the SR as a three-dimensional random walk through the PM–SR junctional cytoplasmic spaces. Electron microscopic ultrastructural images of the smooth muscle cells were elaborated with software algorithms to produce a very clear and dimensionally accurate picture of the PM–SR junctions. From this study, we conclude that it is plausible and possible for enough Ca²⁺ to pass through the PM–SR junctions to replete the SR during the regenerative Ca²⁺ release, which underlies agonist induced asynchronous Ca²⁺ oscillations in vascular smooth muscle.     

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.