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.     

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.     

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 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.     

Down-regulation of the inositol 1,4,5-trisphosphate receptor in mouse eggs following fertilization or parthenogenetic activation

Fertilization in mammalian eggs is characterized by the presence of intracellular calcium ([Ca(2+)]i) oscillations. In mouse eggs, these oscillations cease after a variable period of time and this is accompanied by a decrease in inositol 1,4,5-trisphosphate receptor (IP3R) responsiveness and down-regulation of the IP3R type 1 (IP3R-1). To investigate the signaling pathway responsible for inducing IP3R-1 down-regulation during fertilization, mouse eggs were exposed to or injected with several Ca(2+)-releasing agonists and the amounts of IP3R-1 immunoreactivity evaluated by Western blotting. Exposure to ethanol or ionomycin, which induce a single [Ca(2+)]i rise, failed to signal down-regulation of IP3R-1. However, [Ca(2+)]i oscillations induced by injection of boar sperm fractions (SF), which presumably stimulate production of IP3, or adenophostin A, an IP3R agonist, both induced down-regulation of IP3R-1 of a magnitude similar to or greater than that observed after fertilization. Exposure to thimerosal, an oxidizing agent that modifies the IP3R without stimulating production of IP3, also initiated down-regulation of IP3R-1, although oscillations initiated by SrCl(2) failed to evoke down-regulation of IP3R-1. The degradation of IP3R-1 in mouse eggs appears to be mediated by the proteasome pathway because it was inhibited by preincubation with lactacystin, a very specific proteasome inhibitor. We therefore suggest that persistent stimulation of the phosphoinositide pathway in mouse eggs by the sperm during fertilization or by injection of SF leads to down-regulation of the IP3R-1.     

Hemichannel-mediated inositol 1,4,5-trisphosphate (IP3) release in the cochlea: a novel mechanism of IP3 intercellular signaling

Inositol 1,4,5-trisphosphate (IP(3)) is an important second messenger that can trigger a Ca(2+) wave prolongated between cells. This intercellular signaling was found defective in some gap junction connexin deafness mutants. In this study, the mechanism underlying IP(3) intercellular signaling in the cochlea was investigated. A gap junction channel is composed of two hemichannels. By using a fluorescence polarization technique to measure IP(3) concentration, the authors found that IP(3) could be released by gap junction hemichannels in the cochlea. The IP(3) release was increased about three- to fivefold by the reduction of extracellular Ca(2+) concentration or by mechanical stress. This incremental release could be blocked by gap junction blockers but not eliminated by a purinergic P2x receptor antagonist and verapamil, which is a selective P-glycoprotein inhibitor inhibiting the ATP-binding cassette transporters. The authors also found that IP(3) receptors were extensively expressed in the cochlear sensory epithelium, including on the cell surface. Extracellular application of IP(3) could trigger cellular Ca(2+) elevation. This Ca(2+) elevation was eliminated by the gap junction hemichannel blocker. These data reveal that IP(3) can pass through hemichannels acting as an extracellular mediator to participate in intercellular signaling. This hemichannel-mediated extracellular pathway may play an important role in long-distance intercellular communication in the cochlea, given that IP(3) only has a short lifetime in the cytoplasm.     

The intercellular synchronization of ca(2+) oscillations evaluates cx36-dependent coupling

Connexin36 (Cx36) plays an important role in insulin secretion by controlling the intercellular synchronization of Ca(2+) transients induced during stimulation. The lack of drugs acting on Cx36 channels is a major limitation in further unraveling the molecular mechanism underlying this effect. To screen for such drugs, we have developed an assay allowing for a semi-automatic, fluorimetric quantification of Ca(2+) transients in large populations of MIN6 cells. Here, we show that (1) compared to control cells, MIN6 cells with reduced Cx36 expression or function showed decreased synchrony of glucose-induced Ca(2+) oscillations; (2) glibenclamide, a sulphonylurea which promotes Cx36 junctions and coupling, increased the number of synchronous MIN6 cells, whereas quinine, an antimalarial drug which inhibits Cx36-dependent coupling, decreased this proportion; (3) several drugs were identified that altered the intercellular Ca(2+) synchronization, cell coupling and distribution of Cx36; (4) some of them also affected insulin content. The data indicate that the intercellular synchronization of Ca(2+) oscillations provides a reliable and non-invasive measurement of Cx36-dependent coupling, which is useful to identify novel drugs affecting the function of β-cells, neurons, and neuron-related cells that express Cx36.     

Strongly decreased gap junctional permeability to inositol 1,4, 5-trisphosphate in connexin32 deficient hepatocytes

Livers from connexin32 (Cx32) deficient mice have been shown to be defective in hormonally induced glucose mobilization. In order to determine whether this effect is due to decreased diffusion of the second messenger inositol 1,4,5-trisphosphate (IP(3)) between hepatocytes, we injected iontophoretically different amounts of IP(3) in Fura-2 loaded hepatocyte doublets (i.e. cell pairs) from wild type or Cx32 deficient mice. Whereas 84% of wild type hepatocytes showed an intercellular Ca(2+) wave spreading from the injected cell to the neighboring cell, only 25% of Cx32 deficient hepatocyte doublets did so. The amount of IP(3) necessary to induce an intercellular Ca(2+) wave in Cx32 deficient hepatocyte doublets was estimated to be about 25-fold higher than in wild type doublets. This confirms the notion that the low hormonally or electrically induced glucose mobilization found in Cx32 deficient livers relative to wild type livers is due to largely hindered diffusion of IP(3) between Cx32 deficient hepatocytes.     

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.     

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.     

Coordinated intercellular calcium waves induced by noradrenaline in rat hepatocytes: dual control by gap junction permeability and agonist.

Calcium-mobilizing agonists induce intracellular Ca2+ concentration ([Ca2+]i) changes thought to trigger cellular responses. In connected cells, rises in [Ca2+]i can propagate from cell to cell as intercellular Ca2+ waves, the mechanisms of which are not elucidated. Using fura2-loaded rat hepatocytes, we studied the mechanisms controlling coordination and intercellular propagation of noradrenaline-induced Ca2+ signals. Gap junction blockade with 18 alpha-glycyrrhetinic acid resulted in a loss of coordination between connected cells. We found that second messengers and [Ca2+]i rises in one hepatocyte cannot trigger Ca2+ responses in connected cells, suggesting that diffusion across gap junctions, while required for coordination, is not sufficient by itself for the propagation of intercellular Ca2+ waves. In addition, our experiments revealed functional differences between noradrenaline-induced Ca2+ signals in connected hepatocytes. These results demonstrate that intercellular Ca2+ signals in multicellular systems of rat hepatocytes are propagated and highly organized through complex mechanisms involving at least three factors. First, gap junction coupling ensures coordination of [Ca2+]i oscillations between the different cells; second, the presence of hormone at each hepatocyte is required for cell-cell Ca2+ signal propagation; and third, functional differences between adjacent connected hepatocytes could allow a 'pacemaker-like' intercellular spread of Ca2+ waves.     

Models of IP3 and Ca2+ oscillations: frequency encoding and identification of underlying feedbacks

Hormones that act through the calcium-releasing messenger, inositol 1,4,5-trisphosphate (IP3), cause intracellular calcium oscillations, which have been ascribed to calcium feedbacks on the IP3 receptor. Recent studies have shown that IP3 levels oscillate together with the cytoplasmic calcium concentration. To investigate the functional significance of this phenomenon, we have developed mathematical models of the interaction of both second messengers. The models account for both positive and negative feedbacks of calcium on IP3 metabolism, mediated by calcium activation of phospholipase C and IP3 3-kinase, respectively. The coupled IP3 and calcium oscillations have a greatly expanded frequency range compared to calcium fluctuations obtained with clamped IP3. Therefore the feedbacks can be physiologically important in supporting the efficient frequency encoding of hormone concentration observed in many cell types. This action of the feedbacks depends on the turnover rate of IP3. To shape the oscillations, positive feedback requires fast IP3 turnover, whereas negative feedback requires slow IP3 turnover. The ectopic expression of an IP3 binding protein has been used to decrease the rate of IP3 turnover experimentally, resulting in a dose-dependent slowing and eventual quenching of the Ca2+ oscillations. These results are consistent with a model based on positive feedback of Ca2+ on IP3 production.     

Apoptosis driven by IP(3)-linked mitochondrial calcium signals

Increases of mitochondrial matrix [Ca(2+)] ([Ca(2+)](m)) evoked by calcium mobilizing agonists play a fundamental role in the physiological control of cellular energy metabolism. Here, we report that apoptotic stimuli induce a switch in mitochondrial calcium signalling at the beginning of the apoptotic process by facilitating Ca(2+)-induced opening of the mitochondrial permeability transition pore (PTP). Thus [Ca(2+)](m) signals evoked by addition of large Ca(2+) pulses or, unexpectedly, by IP(3)-mediated cytosolic [Ca(2+)] spikes trigger mitochondrial permeability transition and, in turn, cytochrome c release. IP(3)-induced opening of PTP is dependent on a privileged Ca(2+) signal transmission from IP(3) receptors to mitochondria. After the decay of Ca(2+) spikes, resealing of PTP occurs allowing mitochondrial metabolism to recover, whereas activation of caspases is triggered by cytochrome c released to the cytosol. This organization provides an efficient mechanism to establish caspase activation while mitochondrial metabolism is maintained to meet ATP requirements of apoptotic cell death.     

Local induction of pacemaking activity in a monolayer of electrically coupled quiescent NRK fibroblasts

Cultures of normal rat kidney (NRK) fibroblasts may display spontaneous calcium action potentials which propagate throughout the cellular monolayer. Pacemaking activity of NRK cells was studied by patch clamp electrophysiology and vital calcium imaging, using a new experimental approach in which a ring was placed on the monolayer in order to physically separate pacemakers within or under the ring and follower cells outside the ring. Stimulation of cells inside the ring with IP(3)-generating hormones such as prostaglandin F(2alpha) (PGF(2alpha)) resulted in the induction of periodic action potentials outside the ring, which were abolished when the L-type calcium channel blocker nifedipine was added outside the ring, but not inside the ring. PGF(2alpha)-treated cells displayed asynchronous IP(3)-mediated calcium oscillations of variable frequency, while follower cells outside the ring showed synchronous calcium transients which coincided with the propagating action potential. Mathematical modelling indicated that addition of PGF(2alpha) inside the ring induced both a membrane potential gradient and an intracellular IP(3) gradient, both of which are essential for the induction of pacemaking activity under the ring. These data show that intercellular coupling between PGF(2alpha)-treated and non-treated cells is essential for the generation of a functional pacemaker area whereby synchronization of calcium oscillations occurs by activation of L-type calcium channels.     

Role of Ca(2+) in the pacemaker-like property of spinal motoneurons

It is generally accepted that locomotion in vertebrate species is produced by signals coded and integrated by neurons of the spinal cord. In fact, the basic features of locomotion, including patterns and rhythms, are generated by a network of neurons called the CPG (central pattern generator) essentially localized in the lumbar segments of the spinal cord. However, the detailed mechanisms underlying the rhythmic aspect of CPG-generated locomotion are not fully understood. Here, we report data of studies that focus on the role of Ca(2+)-related mechanisms involved in the expression of the pacemaker property of lumbar motoneurons that innervate the hindlimbs. In fact, it has become increasingly clear that Ca(2+) plays a determinant function in the expression of this active and conditional rhythmic property. In addition to NMDA-mediated currents (NMDA is an agonist of the calcium permeable ionotropic glutamatergic receptor) and to a Ca(2+)-dependent K(+) current that were found twenty years ago to contribute to intrinsic voltage oscillations in motoneurons, a pivotal role for voltage-gated channels (e.g., CaV1.3) and intracellular Ca(2+) concentrations ([Ca(2+)]i) have recently been shown. Increasing evidence of a role for metabotropic receptor subtypes, calmodulin (a calcium binding protein), ryanodine and IP3-sensitive intracellular stores of Ca(2+) suggests that additional mechanisms are yet to be identified. A detailed understanding of the complex role of Ca(2+) in mediating the auto-rhythmic property of spinal neurons may contribute to the development of novel therapeutic approaches to induce locomotion after spinal cord injury.     

Sequence, cloning, expression and characterisation of the 81-kDa surface membrane protein (P80) of Mycoplasma agalactiae

In response to heat-stable enterotoxin of Vibrio cholerae non-O1, the initial rise of cytosolic Ca(2+) occurred with activation of IP(3). Chelation of extracellular Ca(2+) with EGTA and suspension of cells in Ca(2+) free buffer both demonstrated the involvement of internal stores in the rise of [Ca(2+)]i. Cells pretreated with dantrolene resulted in decrease of [Ca(2+)]i response which suggested that the rise of intracellular level of Ca(2+) was mostly due to the mobilization from IP(3) sensitive stores. When the cytosolic Ca(2+) was chelated by loading the cells with BAPTA, NAG-ST could not induce Ca(2+) entry to the cell as assessed by Mn(2+) quenching of fura-2 fluorescence which suggested that calcium influx across the plasma membrane depends upon initial rise of this bivalent cation that maintained the sustained phase of [Ca(2+)]i response. Addition of toxin to the fura-2-loaded cells, preincubated with lanthanum chloride, resulted in reduction of [Ca(2+)]i level with a short duration of irregular sustained phase further suggesting that the influx of Ca(2+) across the plasma membrane might be through the calcium channel.     

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.     

Dynamic gap junctional communication: a delimiting model for tissue responses.

Gap junctions are aqueous intercellular channels formed by a diverse class of membrane-spanning proteins, known as connexins. These aqueous pores provide partial cytoplasmic continuity between cells in most tissues, and are freely permeable to a host of physiologically relevant second messenger molecules/ionic species (e.g., Ca2+, IP3, cAMP, cGMP). Despite the fact that these second messenger molecules/ionic species have been shown to alter junctional patency, there is no clear basis for understanding how dynamic and transient changes in the intracellular concentration of second messenger molecules might modulate the extent of intercellular communication among coupled cells. Thus, we have modified the tissue monolayer model of Ramanan and Brink (1990) to account for both the up-regulatory and down-regulatory effects on junctions by second messenger molecules that diffuse through gap junctions. We have chosen the vascular wall as our morphological correlate because of its anisotropy and large investment of gap junctions. The model allows us to illustrate the putative behavior of gap junctions under a variety of physiologically relevant conditions. The modeling studies demonstrated that transient alterations in intracellular second messenger concentrations are capable of producing 50-125% changes in the number of cells recruited into a functional syncytial unit, after activation of a single cell. Moreover, the model conditions required to demonstrate such physiologically relevant changes in intercellular diffusion among coupled cells are commonly observed in intact tissues and cultured cells.