Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms

Intracellular Ca(2+) oscillations are commonly observed in a large number of cell types in response to stimulation by an extracellular agonist. In most cell types the mechanism of regular spiking is well understood and models based on Ca(2+)-induced Ca(2+) release (CICR) can account for many experimental observations. However, cells do not always exhibit simple Ca(2+) oscillations. In response to given agonists, some cells show more complex behaviour in the form of bursting, i.e. trains of Ca(2+) spikes separated by silent phases. Here we develop several theoretical models, based on physiologically plausible assumptions, that could account for complex intracellular Ca(2+) oscillations. The models are all based on one- or two-pool models based on CICR. We extend these models by (i) considering the inhibition of the Ca(2+)-release channel on a unique intracellular store at high cytosolic Ca(2+) concentrations, (ii) taking into account the Ca(2+)-activated degradation of inositol 1,4,5-trisphosphate (IP(3)), or (iii) considering explicity the evolution of the Ca(2+) concentration in two different pools, one sensitive and the other one insensitive to IP(3). Besides simple periodic oscillations, these three models can all account for more complex oscillatory behaviour in the form of bursting. Moreover, the model that takes the kinetics of IP(3) into account shows chaotic behaviour.     

Complex calcium oscillations and the role of mitochondria and cytosolic proteins

Intracellular calcium oscillations, which are oscillatory changes of cytosolic calcium concentration in response to agonist stimulation, are experimentally well observed in various living cells. Simple calcium oscillations represent the most common pattern and many mathematical models have been published to describe this type of oscillation. On the other hand, relatively few theoretical studies have been proposed to give an explanation of complex intracellular calcium oscillations, such as bursting and chaos. In this paper, we develop a new possible mechanism for complex calcium oscillations based on the interplay between three calcium stores in the cell: the endoplasmic reticulum (ER), mitochondria and cytosolic proteins. The majority ( approximately 80%) of calcium released from the ER is first very quickly sequestered by mitochondria. Afterwards, a much slower release of calcium from the mitochondria serves as the calcium supply for the intermediate calcium exchanges between the ER and the cytosolic proteins causing bursting calcium oscillations. Depending on the permeability of the ER channels and on the kinetic properties of calcium binding to the cytosolic proteins, different patterns of complex calcium oscillations appear. With our model, we are able to explain simple calcium oscillations, bursting and chaos. Chaos is also observed for calcium oscillations in the bursting mode.     

A theoretical study of effects of cytosolic Ca2+ oscillations on activation of glycogen phosphorylase

Taking into account the Ca(2+)-stimulated degradation of inositol 1,4,5-trisphosphate (IP(3)) by a 3-kinase, we have theoretically explored the effects of both simple and complex Ca(2+) oscillations on the regulation of a phosphorylation-dephosphorylation cycle process involved in glycogen degradation by glycogen phosphorylase a-form, respectively. For the case of simple Ca(2+) oscillations, the roles of cytosolic Ca(2+) oscillations in the regulation of active phosphorylase depend upon the maximum rate of IP(3) degradation by the 3-kinase, V(M5). In particular, the smaller the values of V(M5) are, the lower the effective Ca(2+) threshold for the activation of glycogen phosphorylase will be. For the case of complex Ca(2+) oscillations, the average level of fraction of active phosphorylase is nearly independent from the level of stimulation increasing in the bursting oscillatory domain. Both simple and complex Ca(2+) oscillations can contribute to increase the efficiency and specificity of cellular signalling, and some theoretical results of activation of glycogen phosphorylase regulated by Ca(2+) oscillations are close to the experimental results for gene expression in lymphocytes.     

Calcium oscillations induced by ATP in human umbilical cord smooth muscle cells

Arterial smooth muscle cells exhibit vasomotion, related to oscillations in intracellular Ca(2+) concentration, but the origin and function of these has not yet been fully determined. We measured intracellular Ca(2+) using conventional fluorescent methods in primary cultured, human umbilical cord artery smooth muscle cells (HUCASMC). Spontaneous oscillations in Ca(2+) was found in only 1% of all cells but exogenous, micromolar concentrations of ATP could induce Ca(2+) oscillations in 70% of cells with the most common pattern being one of regular amplitude and frequency with a return to basal levels between each peak. The P2Y agonist, UTP, but not the P2X agonist alphabeta-methylene ATP, could also induce Ca(2+) oscillations. Once induced, these oscillations could not be blocked by G-protein, PLC, VGCC or TRP channel antagonists applied individually, but could be prevented when antagonists were applied together. In the presence of EGTA, micromolar concentrations of ATP induced an elevation in intracellular Ca(2+) but did not induce Ca(2+) oscillations. The oscillation frequency induced by ATP was affected by bath Ca(2+) concentration. Taken together, these data suggest that external Ca(2+) entry maintains the Ca(2+) oscillation induced by activation of P2Y receptors. Once induced, multiple mechanisms are involved to maintain the oscillation and the oscillation frequency is determined by the speed of Ca(2+) refilling. Chronic hypoxia enhanced the Ca(2+) response and altered the oscillation frequency. We suggest that these oscillations may play a role in the maintenance of umbilical blood flow during situations in which GPCR are activated.     

Ca2+ shuttling between endoplasmic reticulum and mitochondria underlying Ca2+ oscillations

Although many cell functions are regulated by Ca(2+) oscillations induced by a cyclic release of Ca(2+) from intracellular Ca(2+) stores, the pacemaker mechanism of Ca(2+) oscillations remains to be explained. Using green fluorescent protein-based Ca(2+) indicators that are targeted to intracellular Ca(2+) stores, the endoplasmic reticulum (ER) and mitochondria, we found that Ca(2+) shuttles between the ER and mitochondria in phase with Ca(2+) oscillations. Following agonist stimulation, Ca(2+) release from the ER generated the first Ca(2+) oscillation and loaded mitochondria with Ca(2+). Before the second Ca(2+) oscillation, Ca(2+) release from the mitochondria by means of the Na(+)/Ca(2+) exchanger caused a gradual increase in cytoplasmic Ca(2+) concentration, inducing a regenerative ER Ca(2+) release, which generated the peak of Ca(2+) oscillation and partially reloaded the mitochondria. This sequence of events was repeated until mitochondrial Ca(2+) was depleted. Thus, Ca(2+) shuttling between the ER and mitochondria may have a pacemaker role in the generation of Ca(2+) oscillations.     

Effects of inositol 1,4,5-trisphosphate receptor-mediated intracellular stochastic calcium oscillations on activation of glycogen phosphorylase

In various cell types cytosolic calcium (Ca(2+)) is an important regulator. The possible role of Ca(2+) release from the inositol 1,4,5-trisphosphate (IP(3)) receptor channel in the regulation of the phosphorylation-dephosphorylation cycle process involved in glycogen degradation by glycogen phosphorylase have theoretically investigated by using the Li-Rinzel model for cytosolic Ca(2+) oscillations. For the case of deterministic cytosolic Ca(2+) oscillations, there exists an optimal frequency of cytosolic Ca(2+) oscillations at which the average fraction of active glycogen phosphorylase reaches a maximum value, and a mutation for the average fraction of active glycogen phosphorylase occurs at the higher bifurcation point of Ca(2+) oscillations. For the case of stochastic cytosolic Ca(2+) oscillations, the fraction of active phosphorylase is strongly affected by the number of IP(3) receptor channels and the level of IP(3) concentration. Small number of IP(3) receptor channels can potentiate the sensitivity of the activity of glycogen phosphorylase. The average frequency and amplitude of active phosphorylase stochastic oscillations are increased with the level of increasing IP(3) stimuli. The various distributions for the amplitude of active glycogen phosphorylase oscillations in parameters plane are discussed.     

Imaging of the Yellow Cameleon 3.6 indicator reveals that elevations in cytosolic Ca2+ follow oscillating increases in growth in root hairs of Arabidopsis

In tip-growing cells, the tip-high Ca(2+) gradient is thought to regulate the activity of components of the growth machinery, including the cytoskeleton, Ca(2+)-dependent regulatory proteins, and the secretory apparatus. In pollen tubes, both the Ca(2+) gradient and cell elongation show oscillatory behavior, reinforcing the link between the two. We report that in growing root hairs of Arabidopsis (Arabidopsis thaliana), an oscillating tip-focused Ca(2+) gradient can be resolved through imaging of a cytosolically expressed Yellow Cameleon 3.6 fluorescence resonance energy transfer-based Ca(2+) sensor. Both elongation of the root hairs and the associated tip-focused Ca(2+) gradient show a similar dynamic character, oscillating with a frequency of 2 to 4 min(-1). Cross-correlation analysis indicates that the Ca(2+) oscillations lag the growth oscillations by 5.3 +/- 0.3 s. However, growth never completely stops, even during the slow cycle of an oscillation, and the concomitant tip Ca(2+) level is always slightly elevated compared with the resting Ca(2+) concentration along the distal shaft, behind the growing tip. Artificially increasing Ca(2+) using the Ca(2+) ionophore A23187 leads to immediate cessation of elongation and thickening of the apical cell wall. In contrast, dissipating the Ca(2+) gradient using either the Ca(2+) channel blocker La(3+) or the Ca(2+) chelator EGTA is accompanied by an increase in the rate of cell expansion and eventual bursting of the root hair tip. These observations are consistent with a model in which the maximal oscillatory increase in cytosolic Ca(2+) is triggered by cell expansion associated with tip growth and plays a role in the subsequent restriction of growth.     

Signal-induced Ca2+ oscillations: properties of a model based on Ca(2+)-induced Ca2+ release.

We consider a simple, minimal model for signal-induced Ca2+ oscillations based on Ca(2+)-induced Ca2+ release. The model takes into account the existence of two pools of intracellular Ca2+, namely, one sensitive to inositol 1,4,5 trisphosphate (InsP3) whose synthesis is elicited by the stimulus, and one insensitive to InsP3. The discharge of the latter pool into the cytosol is activated by cytosolic Ca2+. Oscillations in cytosolic Ca2+ arise in this model either spontaneously or in an appropriate range of external stimulation; these oscillations do not require the concomitant, periodic variation of InsP3. The following properties of the model are reviewed and compared with experimental observations: (a) Control of the frequency of Ca2+ oscillations by the external stimulus or extracellular Ca2+; (b) correlation of latency with period of Ca2+ oscillations obtained at different levels of stimulation; (c) effect of a transient increase in InsP3; (d) phase shift and transient suppression of Ca2+ oscillations by Ca2+ pulses, and (e) propagation of Ca2+ waves. It is shown that on all these counts the model provides a simple, unified explanation for a number of experimental observations in a variety of cell types. The model based on Ca(2+)-induced Ca2+ release can be extended to incorporate variations in the level of InsP3 as well as desensitization of the InsP3 receptor; besides accounting for the phenomena described by the minimal model, the extended model might also account for the occurrence of complex Ca2+ oscillations.     

Signaling between intracellular Ca2+ stores and depletion-activated Ca2+ channels generates [Ca2+]i oscillations in T lymphocytes

Stimulation through the antigen receptor (TCR) of T lymphocytes triggers cytosolic calcium ([Ca2+]i) oscillations that are critically dependent on Ca2+ entry across the plasma membrane. We have investigated the roles of Ca2+ influx and depletion of intracellular Ca2+ stores in the oscillation mechanism, using single-cell Ca2+ imaging techniques and agents that deplete the stores. Thapsigargin (TG; 5-25 nM), cyclopiazonic acid (CPA; 5-20 microM), and tert- butylhydroquinone (tBHQ; 80-200 microM), inhibitors of endoplasmic reticulum Ca(2+)-ATPases, as well as the Ca2+ ionophore ionomycin (5-40 nM), elicit [Ca2+]i oscillations in human T cells. The oscillation frequency is approximately 5 mHz (for ATPase inhibitors) to approximately 10 mHz (for ionomycin) at 22-24 degrees C. The [Ca2+]i oscillations resemble those evoked by TCR ligation in terms of their shape, amplitude, and an absolute dependence on Ca2+ influx. Ca(2+)- ATPase inhibitors and ionomycin induce oscillations only within a narrow range of drug concentrations that are expected to cause partial depletion of intracellular stores. Ca(2+)-induced Ca2+ release does not appear to be significantly involved, as rapid removal of extracellular Ca2+ elicits the same rate of [Ca2+]i decline during the rising and falling phases of the oscillation cycle. Both transmembrane Ca2+ influx and the content of ionomycin-releasable Ca2+ pools fluctuate in oscillating cells. From these data, we propose a model in which [Ca2+]i oscillations in T cells result from the interaction between intracellular Ca2+ stores and depletion-activated Ca2+ channels in the plasma membrane.     

Birhythmicity, trirhythmicity and chaos in bursting calcium oscillations

We have analyzed various types of complex calcium oscillations. The oscillations are explained with a model based on calcium-induced calcium release (CICR). In addition to the endoplasmic reticulum as the main intracellular Ca2+ store, mitochondrial and cytosolic Ca2+ binding proteins are also taken into account. This model was previously proposed for the study of the physiological role of mitochondria and the cytosolic proteins in gene rating complex Ca2+ oscillations [1]. Here, we investigated the occurrence of different types of Ca2+ oscillations obtained by the model, i.e. simple oscillations, bursting, and chaos. In a bifurcation diagram, we have shown that all these various modes of oscillatory behavior are obtained by a change of only one model parameter, which corresponds to the physiological variability of an agonist. Bursting oscillations were studied in more detail because they express birhythmicity, trirhythmicity and chaotic behavior. Two different routes to chaos are observed in the model: in addition to the usual period doubling cascade, we also show intermittency. For the characterization of the chaotic behavior, we made use of return maps and Lyapunov exponents. The potential biological role of chaos in intracellular signaling is discussed.     

Ca2+ oscillations stimulate an ATP increase during fertilization of mouse eggs

Mammalian eggs and embryos rely upon mitochondrial ATP production to survive and proceed through preimplantation development. Ca(2+) oscillations at fertilization have been shown to cause a reduction of mitochondrial NAD+ and flavoproteins, suggesting they might also cause changes in cytosolic ATP levels. Here, we have monitored intracellular Ca(2+) and ATP levels in fertilizing mouse eggs by imaging the fluorescence of a Ca(2+) dye and luminescence of firefly luciferase. At fertilization an initial increase in ATP levels occurs with the first Ca(2+) transient, with a second increase occurring about 1 h later. The increase in cytosolic ATP was estimated to be from a prefertilization concentration of 1.9 mM to a peak value of 3 mM. ATP levels returned to prefertilization values as the Ca(2+) oscillations terminated. An increase in ATP also occurred with other stimuli that increase Ca(2+) and it was blocked when Ca(2+) oscillations were inhibited by BAPTA injection. Additionally, an ATP increase was not seen when eggs were activated by cycloheximide, which does not cause a Ca(2+) increase. These data suggest that mammalian fertilization is associated with a sudden but transient increase in cytosolic ATP and that Ca(2+) oscillations are both necessary and sufficient to cause this increase in ATP levels.     

Synchronous oscillation of the cytoplasmic Ca2+ concentration and membrane potential in cultured epithelial cells (Intestine 407)

Cultured epithelial Intestine 407 cells exhibit regular oscillations of the membrane potential with repeated hyperpolarizations. These hyperpolarizations were inhibited not only by K+ channel blockers (tetraethylammonium and nonyltriethylammonium) but also by inhibitors of the Ca2+-activated K+ channel (quinine and quinidine). Using Ca2+-selective microelectrodes, cyclic increases in the cytosolic free Ca2+ concentration of more than 1 X 10(-6) M were found to coincide with the cyclic membrane hyperpolarizations. Thus, it appears that the potential oscillation is brought about by the oscillation of the intracellular free Ca2+ level which induces periodic activation of the Ca2+-dependent K+ channels. Neither the deprivation of extracellular Ca2+ nor the application of Ca2+ channel blockers (Co2+ and Ni2+) abolished the potential oscillation. Mitochondrial inhibitors (KCN, NaN3, antimycin A, FCCP and dinitrophenol) inhibited the potential oscillation, whereas glycolytic inhibitors (iodoacetic acid and NaF) had no effects. Caffeine and oxalate, which affect the microsomal Ca2+ transport, failed to exert any effect upon the potential oscillation. It is concluded that the cytosolic Ca2+ oscillation results from cyclic releases of Ca2+ from the intracellular storage site, which depends upon mitochondrial activities.     

Different patterns of receptor-activated cytoplasmic Ca2+ oscillations in single pancreatic acinar cells: dependence on receptor type, agonist concentration and intracellular Ca2+ buffering.

Agonist-specific cytosolic Ca2+ oscillation patterns can be observed in individual cells and these have been explained by the co-existence of separate oscillatory mechanisms. In pancreatic acinar cells activation of muscarinic receptors typically evokes sinusoidal oscillations whereas stimulation of cholecystokinin (CCK) receptors evokes transient oscillations consisting of Ca2+ waves with long intervals between them. We have monitored changes in the cytosolic Ca2+ concentration ([Ca2+]i) by measuring Ca2(+)-activated Cl- currents in single internally perfused mouse pancreatic acinar cells. With minimal intracellular Ca2+ buffering we found that low concentrations of both ACh (50 nM) and CCK (10 pM) evoked repetitive short-lasting Ca2+ spikes of the same duration and frequency, but the probability of a spike being followed by a longer and larger Ca2+ wave was low for ACh and high for CCK. The probability that the receptor-evoked shortlasting Ca2+ spikes would initiate more substantial Ca2+ waves was dramatically increased by intracellular perfusion with solutions containing high concentrations of the mobile low affinity Ca2+ buffers citrate (10-40 mM) or ATP (10-20 mM). The different Ca2+ oscillation patterns normally induced by ACh and CCK would therefore appear not to be caused by separate mechanisms. We propose that specific receptor-controlled modulation of Ca2+ signal spreading, either by regulation of Ca2+ uptake into organelles and/or cellular Ca2+ extrusion, or by changing the sensitivity of the Ca2(+)-induced Ca2+ release mechanism, can be mimicked experimentally by different degrees of cytosolic Ca2+ buffering and can account for the various cytosolic Ca2+ spike patterns.     

RyR channels and glucose-regulated pancreatic β-cells

Ryanodine receptor channel model is introduced to a dynamical model of pancreatic beta-cells to discuss the effects of RyR channels and glucose concentration on membrane potential. The results show Ca(2+) concentration changes responding to enhance of glucose concentration is more quickly than that of activating RyR channels, and both methods can induce bursting action potential and increase free cytosolic Ca(2+) concentration. An interesting finding is that moderate stimulation to RyR channels will result in a kind of "complex bursting", which is more effective in enhancing average Ca(2+) concentration and insulin section.     

Mitochondria regulate the amplitude of simple and complex calcium oscillations.

In a mathematical model for simple calcium oscillations [Biophys. Chem. 71 (1998) 125], it has been shown that mitochondria play an important role in the maintenance of constant amplitudes of cytosolic Ca(2+) oscillations. Simple plausible rate laws for Ca(2+) fluxes across the inner mitochondrial membrane have been used in this model. Here we show that it is possible to use the same rate laws as a plug-in element in other existing mathematical models and obtain the same effect on amplitude regulation. This result appears to be universal, independent of the type of model and the type of Ca(2+) oscillations. We demonstrate this on two models for spiking Ca(2+) oscillations [J. Biol. Chem. 266 (1991) 11068; Cell Calcium 14 (1993) 311] and on two recent models for bursting Ca(2+) oscillations; one of them being a receptor-operated model [Biophys. J. 79 (2000) 1188] and the other one being a store-operated model [BioSystems 57 (2000) 75].     

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.     

PLC zeta: a sperm-specific trigger of Ca(2+) oscillations in eggs and embryo development

Upon fertilisation by sperm, mammalian eggs are activated by a series of intracellular Ca(2+) oscillations that are essential for embryo development. The mechanism by which sperm induces this complex signalling phenomenon is unknown. One proposal is that the sperm introduces an exclusive cytosolic factor into the egg that elicits serial Ca(2+) release. The 'sperm factor' hypothesis has not been ratified because a sperm-specific protein that generates repetitive Ca(2+) transients and egg activation has not been found. We identify a novel, sperm-specific phospholipase C, PLC zeta, that triggers Ca(2+) oscillations in mouse eggs indistinguishable from those at fertilisation. PLC zeta removal from sperm extracts abolishes Ca(2+) release in eggs. Moreover, the PLC zeta content of a single sperm was sufficient to produce Ca(2+) oscillations as well as normal embryo development to blastocyst. Our results are consistent with sperm PLC zeta as the molecular trigger for development of a fertilised egg into an embryo.     

A model of intracellular Ca2+ oscillations based on the activity of the intermediate-conductance Ca2+-activated K+ channels

Intracellular Ca2+ oscillations are observed in a large number of non-excitable cells. While most appear to reflect an intermittent Ca2+ release from intracellular stores, in some instances intracellular Ca2+ oscillations strongly depend on Ca2+ influx, and are coupled to oscillations of the membrane potential, suggesting that a plasma membrane-based mechanism may be involved. We have developed a theoretical model for the latter type of intracellular Ca2+ oscillations based on the Ca2+-dependent modulation of the intermediate-conductance, Ca2+-activated K+ (IKCa) channel. The functioning of this model relies on the Ca2+-dependent activation, and the much slower Ca2+-dependent rundown of this channel. We have shown that Ca2+-dependent activation of the IKCa channels, the consequent membrane hyperpolarization and the resulting increase in Ca2+ influx may confer the positive feedback mechanism required for the ascending phase of the oscillation. The much slower Ca2+-dependent rundown process will conversely halt this positive loop, and establish the descending phase of the intracellular Ca2+ oscillation. We found that this simple model gives rise to intracellular Ca2+ oscillations when using physiologically reasonable parameters, suggesting that IKCa channels could participate in the generation of intracellular Ca2+ oscillations.