Hormone-induced calcium oscillations in liver cells can be explained by a simple one pool model

Hormone-induced oscillations of the free intracellular calcium concentration are thought to be relevant for frequency encoding of hormone signals. In liver cells, such Ca2+ oscillations occur in response to stimulation by hormones acting via phosphoinositide breakdown. This observation may be explained by cooperative, positive feedback of Ca2+ on its own release from one inositol 1,4,5-trisphosphate-sensitive pool, obviating oscillations of inositol 1,4,5-trisphosphate. The kinetic rate laws of the associated model have a mathematical structure reminiscent of the Brusselator, a hypothetical chemical model involving a rather improbable trimolecular reaction step, thus giving a realistic biological interpretation to this hallmark of dissipative structures. We propose that calmodulin is involved in mediating this cooperativity and positive feedback, as suggested by the presented experiments. For one, hormone-induced calcium oscillations can be inhibited by the (nonphenothiazine) calmodulin antagonists calmidazolium or CGS 9343 B. Alternatively, in cells overstimulated by hormone, as characterized by a non-oscillatory elevated Ca2+ concentration, these antagonists could again restore sustained calcium oscillations. The experimental observations, including modulation of the oscillations by extracellular calcium, were in qualitative agreement with the predictions of our mathematical model.     

Measurement of intracellular IP3 during Ca2+ oscillations in mouse eggs with GFP-based FRET probe

Intracellular Ca2+ oscillations in fertilized mammalian eggs, the key signal that stimulates egg activation and early embryonic development, are regulated by inositol 1,4,5-trisphosphate (IP3) signaling pathway. We investigated temporal changes in intracellular IP3 concentration ([IP3]i) in mouse eggs, using a fluorescent probe based on fluorescence resonance energy transfer between two green fluorescent protein variants, during Ca2+ oscillations induced by fertilization or expression of phospholipase Czeta (PLCzeta), an egg-activating sperm factor candidate. Fluorescence measurements suggested the elevation of [IP3]i in fertilized eggs, and the enhancement of PLCzeta-mediated IP3 production by cytoplasmic Ca2+ was observed during Ca2+ oscillations or in response to CaCl2 microinjection. The results supported the view that PLCzeta is the sperm factor to stimulate IP3 pathway, and suggested that high Ca2+ sensitivity of PLCzeta activity and positive feedback from released Ca2+ are important for triggering and maintaining Ca2+ oscillations.     

Perturbation of myo-inositol-1,4,5-trisphosphate levels during agonist-induced Ca2+ oscillations.

Agonist-induced Ca2+ oscillations in rat hepatocytes involve the production of myo-inositol-1,4,5-trisphosphate (IP3), which stimulates the release of Ca2+ from intracellular stores. The oscillatory frequency is conditioned by the agonist concentration. This study investigated the role of IP3 concentration in the modulation of oscillatory frequency by using microinjected photolabile IP3 analogs. Photorelease of IP3 during hormone-induced oscillations evoked a Ca2+ spike, after which oscillations resumed with a delay corresponding to the period set by the agonists. IP3 photorelease had no influence on the frequency of oscillations. After photorelease of 1-(alpha-glycerophosphoryl)-D-myo-inositol-4,5-diphosphate (GPIP2), a slowly metabolized IP3 analog, the frequency of oscillations initially increased by 34% and declined to its original level within approximately 6 min. Both IP3 and GPIP2 effects can be explained by their rate of degradation: the half-life of IP3, which is a few seconds, can account for the lack of influence of IP3 photorelease on the frequency, whereas the slower metabolism of GPIP2 allowed a transient acceleration of the oscillations. The phase shift introduced by IP3 is likely the result of the brief elevation of Ca2+ during spiking that resets the IP3 receptor to a state of maximum inactivation. A mathematical model of Ca2+ oscillations is in satisfactory agreement with the observed results.     

Stabilizing role of calcium store-dependent plasma membrane calcium channels in action-potential firing and intracellular calcium oscillations

In many biological systems, cells display spontaneous calcium oscillations (CaOs) and repetitive action-potential firing. These phenomena have been described separately by models for intracellular inositol trisphosphate (IP3)-mediated CaOs and for plasma membrane excitability. In this study, we present an integrated model that combines an excitable membrane with an IP3-mediated intracellular calcium oscillator. The IP3 receptor is described as an endoplasmic reticulum (ER) calcium channel with open and close probabilities that depend on the cytoplasmic concentration of IP3 and Ca2+. We show that simply combining this ER model for intracellular CaOs with a model for membrane excitability of normal rat kidney (NRK) fibroblasts leads to instability of intracellular calcium dynamics. To ensure stable long-term periodic firing of action potentials and CaOs, it is essential to incorporate calcium transporters controlled by feedback of the ER store filling, for example, store-operated calcium channels in the plasma membrane. For low IP3 concentrations, our integrated NRK cell model is at rest at -70 mV. For higher IP3 concentrations, the CaOs become activated and trigger repetitive firing of action potentials. At high IP3 concentrations, the basal intracellular calcium concentration becomes elevated and the cell is depolarized near -20 mV. These predictions are in agreement with the different proliferative states of cultures of NRK fibroblasts. We postulate that the stabilizing role of calcium channels and/or other calcium transporters controlled by feedback from the ER store is essential for any cell in which calcium signaling by intracellular CaOs involves both ER and plasma membrane calcium fluxes.     

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.     

Ca(2+)-sensor region of IP(3) receptor controls intracellular Ca(2+) signaling

Many important cell functions are controlled by Ca(2+) release from intracellular stores via the inositol 1,4,5-trisphosphate receptor (IP(3)R), which requires both IP(3) and Ca(2+) for its activity. Due to the Ca(2+) requirement, the IP(3)R and the cytoplasmic Ca(2+) concentration form a positive feedback loop, which has been assumed to confer regenerativity on the IP(3)-induced Ca(2+) release and to play an important role in the generation of spatiotemporal patterns of Ca(2+) signals such as Ca(2+) waves and oscillations. Here we show that glutamate 2100 of rat type 1 IP(3)R (IP(3)R1) is a key residue for the Ca(2+) requirement. Substitution of this residue by aspartate (E2100D) results in a 10-fold decrease in the Ca(2+) sensitivity without other effects on the properties of the IP(3)R1. Agonist-induced Ca(2+) responses are greatly diminished in cells expressing the E2100D mutant IP(3)R1, particularly the rate of rise of initial Ca(2+) spike is markedly reduced and the subsequent Ca(2+) oscillations are abolished. These results demonstrate that the Ca(2+) sensitivity of the IP(3)R is functionally indispensable for the determination of Ca(2+) signaling patterns.     

Modelling receptor-controlled intracellular calcium oscillators.

This paper presents mathematical models for the hepatocyte calcium oscillator which follow the concepts in a class of informal models developed to account for the striking dependence on the receptor type of several features of the calcium oscillations, in particular the shape and duration of the free calcium transients. The essence of these models is that the transients should be timed by a build-up of activated GTP-binding proteins, which, combined with positive feedback processes and perhaps with cooperative effects, leads to a sudden activation of phospholipase C (PLC), followed by negative feedback processes which switch off the calcium rise and lead to a fall in free calcium back to resting levels. These models predict pulsatile oscillations in inositol (1,4,5)P3 as well as in free calcium. We show that receptor-controlled intracellular calcium oscillators involving an unknown positive feedback pathway onto PLC and negative feedback from protein kinase C (PKC) onto G-proteins and receptors, or negative feedback by stimulation of GTPase activity can simulate many of the features of observed intracellular calcium oscillations. These oscillators exhibit a dependence of frequency on agonist concentration and a dependence of transient duration on receptor and G-protein type. We also show that a PLC-dependent GTPase activating factor (GAF) could provide explanations for some otherwise puzzling features of intracellular calcium oscillations.     

Modeling of Ca2+ flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores

We have developed a detailed mathematical model of ionic flux in beta-cells that includes the most essential channels and pumps in the plasma membrane. This model is coupled to equations describing Ca2+, inositol 1,4,5-trisphosphate (IP3), ATP, and Na+ homeostasis, including the uptake and release of Ca2+ by the endoplasmic reticulum (ER). In our model, metabolically derived ATP activates inward Ca2+ flux by regulation of ATP-sensitive K+ channels and depolarization of the plasma membrane. Results from the simulations support the hypothesis that intracellular Na+ and Ca2+ in the ER can be the main variables driving both fast (2-7 osc/min) and slow intracellular Ca2+ concentration oscillations (0.3-0.9 osc/min) and that the effect of IP3 on Ca2+ leak from the ER contributes to the pattern of slow calcium oscillations. Simulations also show that filling the ER Ca2+ stores leads to faster electrical bursting and Ca2+ oscillations. Specific Ca2+ oscillations in isolated beta-cell lines can also be simulated.     

Modeling the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations

Calcium (Ca2+) oscillations play fundamental roles in various cell signaling processes and have been the subject of numerous modeling studies. Here we have implemented a general mathematical model to simulate the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations. In addition, we have compared two different models of the inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) and their influences on intracellular Ca2+ oscillations. Store-operated Ca2+ entry following Ca2+ depletion of endoplasmic reticulum (ER) is an important component of Ca2+ signaling. We have developed a phenomenological model of store-operated Ca2+ entry via store-operated Ca2+ (SOC) channels, which are activated upon ER Ca2+ depletion. The depletion evokes a bi-phasic Ca2+ signal, which is also produced in our mathematical model. The IP3R is an important regulator of intracellular Ca2+ signals. This IP3 sensitive Ca2+ channel is also regulated by Ca2+. We apply two IP3R models, the Mak-McBride-Foskett model and the De Young and Keizer model, with significantly different channel characteristics. Our results show that the two separate IP3R models evoke intracellular Ca2+ oscillations with different frequencies and amplitudes. Store-operated Ca2+ entry affects the oscillatory behavior of these intracellular Ca2+ oscillations. The IP3 threshold is altered when store-operated Ca2+ entry is excluded from the model. Frequencies and amplitudes of intracellular Ca2+ oscillations are also altered without store-operated Ca2+ entry. Under certain conditions, when intracellular Ca2+ oscillations are absent, excluding store-operated Ca2+ entry induces an oscillatory response. These findings increase knowledge concerning store-operated Ca2+ entry and its impact on intracellular Ca2+ oscillations.     

The variety of cytosolic calcium responses and possible roles of PLC and PKC

A model of ligand-induced intracellular calcium (Ca2+) responses incorporating phospholipase C (PLC) and protein kinase C (PKC) is developed for the purpose of understanding the mechanisms underlying the observed temporal patterns of intracellular calcium (Ca(i)2+) under sustained agonist stimulation. Some studies have suggested that inhibition of ligand receptors and PLC by PKC could generate sinusoidal Ca2+ oscillations, while PKC-independent Ca2+-induced Ca2+ release (CICR) via IP(3)-gated Ca2+ channels on the endoplasmic reticulum (ER) is believed to be responsible for baseline spiking. However, some evidence also indicates that baseline spiking can be observed under high-PKC activity, or under low-PKC activity with low agonist stimulus, as well. Insight into the basis of these observations regarding the role of PKC in Ca(i)2+ response patterns can be gained by developing and analyzing a mathematical model of Ca(i)2+ responses. We do this herein and find that (1) interaction of CICR and the sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) pump is enough to generate both types of Ca(i)2+ oscillations, (2) there exist four possible Ca(i)2+ response patterns under sustained agonist stimulus: a sub-threshold response (SR), baseline spiking, sinusoidal oscillations (SO) and transient with plateau, and (3) the IP(3) concentration, which is controlled by the strength of the interaction between PKC and PLC, can be used to predict the Ca(i)2+ response patterns. From this analysis we conclude that the different patterns of Ca(i)2+ oscillations can be understood as a generic consequence of the interactions between CICR via the IP(3)-gated Ca(2+) channels in response to changes in the level of IP(3), and re-uptake into the ER/SR via the SERCA pump. PKC, in conjunction with PLC, can act as a switch between different Ca(i)2+ response patterns by modulating the cytosolic IP(3) level, which determines the Ca(i)2+ patterns.     

Oscillations of intracellular calcium induced by vasopressin in individual fura-2-loaded mesangial cells. Frequency dependence on basal calcium concentration, agonist concentration, and temperature

Intracellular free calcium concentration ([Ca2+]i) was measured in fura-2-loaded single rat mesangial cells by dual wavelength spectrofluorometry. Stimulation with arginine vasopressin (AVP) caused an initial sharp rise of [Ca2+]i followed by repetitive spikes. The frequency of the oscillations was dependent on the concentration of AVP. At 0.1, 1.0, 10.0, and 100.0 nM AVP, the frequencies of oscillations were 0.17 +/- 0.05 (n = 6), 0.32 +/- 0.05 (n = 6), 0.49 +/- 0.05 (n = 6), and 0.48 +/- 0.05 min-1 (n = 5), respectively. Reduction in extracellular [Ca2+] reduced the frequency of AVP-induced oscillations but did not abolish the oscillations. The frequency of calcium oscillations, upon stimulation with 1.0 nM AVP, was directly correlated with the basal [Ca2+]i prior to stimulation. Oscillation frequency increased with increasing temperature. An Arrhenius plot between 24 and 37 degrees C indicated a strong temperature dependency of the oscillations with a Q10 of 3.0. Protein kinase C stimulation by active phorbol esters inhibited AVP-induced calcium oscillations but not the initial [Ca2+] response to AVP. These observations are consistent with a model incorporating a feedback loop linking [Ca2+]i to the mechanism of [Ca2+]i increase. Ca(2+)-induced Ca2+ release may be involved, whereby inositol 1,4,5-trisphosphate (inositol 1,4,5-P3) formation releases Ca2+ from an inositol 1,4,5-P3-sensitive pool, with subsequent Ca2+ uptake and release from an inositol 1,4,5-P3-insensitive pool.     

Cytosolic Ca2+ oscillations in REF52 fibroblasts: Ca(2+)-stimulated IP3 production or voltage-dependent Ca2+ channels as key positive feedback elements.

Oscillations in cytosolic free calcium concentrations ([Ca2+]i) can be elicited in REF52 fibroblasts by three different modes of stimulation. We have previously demonstrated that [Ca2+]i oscillations result when these cells are simultaneously depolarized and stimulated with a hormone linked to phosphoinositide breakdown. Further evidence is now presented that such oscillations are linked to fluctuations in the concentration of IP3 and the Ca2+ content of an IP3-sensitive Ca2+ store. [Ca2+]i oscillations can also be generated in REF52 cells either by direct stimulation of G-proteins with GTP gamma S or AlF4- or by destabilizing the membrane potential and opening voltage-dependent calcium channels. This report compares the different types of oscillations and their mechanisms.     

Minimal requirements for calcium oscillations driven by the IP3 receptor.

Hormones and neurotransmitters that act through inositol 1,4,5-trisphosphate (IP3) can induce oscillations of cytosolic Ca2+ ([Ca2+]c), which render dynamic regulation of intracellular targets. Imaging of fluorescent Ca2+ indicators located within intracellular Ca2+ stores was used to monitor IP3 receptor channel (IP3R) function and to demonstrate that IP3-dependent oscillations of Ca2+ release and re-uptake can be reproduced in single permeabilized hepatocytes. This system was used to define the minimum essential components of the oscillation mechanism. With IP3 clamped at a submaximal concentration, coordinated cycles of IP3R activation and subsequent inactivation were observed in each cell. Cycling between these states was dependent on feedback effects of released Ca2+ and the ensuing [Ca2+]c increase, but did not require Ca2+ re-accumulation. [Ca2+]c can act at distinct stimulatory and inhibitory sites on the IP3R, but whereas the Ca2+ release phase was driven by a Ca2+-induced increase in IP3 sensitivity, Ca2+ release could be terminated by intrinsic inactivation after IP3 bound to the Ca2+-sensitized IP3R without occupation of the inhibitory Ca2+-binding site. These findings were confirmed using Sr2+, which only interacts with the stimulatory site. Moreover, vasopressin induced Sr2+ oscillations in intact cells in which intracellular Ca2+ was completely replaced with Sr2+. Thus, [Ca2+]c oscillations can be driven by a coupled process of Ca2+-induced activation and obligatory intrinsic inactivation of the Ca2+-sensitized state of the IP3R, without a requirement for occupation of the inhibitory Ca2+-binding site.     

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.     

L-type Ca2+ channels and K+ channels specifically modulate the frequency and amplitude of spontaneous Ca2+ oscillations and have distinct roles in prolactin release in GH3 cells

GH3 cells showed spontaneous rhythmic oscillations in intracellular calcium concentration ([Ca2+]i) and spontaneous prolactin release. The L-type Ca2+ channel inhibitor nimodipine reduced the frequency of Ca2+ oscillations at lower concentrations (100nM-1 microM), whereas at higher concentrations (10 microM), it completely abolished them. Ca2+ oscillations persisted following exposure to thapsigargin, indicating that inositol 1,4,5-trisphosphate-sensitive intracellular Ca2+ stores were not required for spontaneous activity. The K+ channel inhibitors Ba2+, Cs+, and tetraethylammonium (TEA) had distinct effects on different K+ currents, as well as on Ca2+ oscillations and prolactin release. Cs+ inhibited the inward rectifier K+ current (KIR) and increased the frequency of Ca2+ oscillations. TEA inhibited outward K+ currents activated at voltages above -40 mV (grouped within the category of Ca2+ and voltage-activated currents, KCa,V) and increased the amplitude of Ca2+ oscillations. Ba2+ inhibited both KIR and KCa,V and increased both the amplitude and the frequency of Ca2+ oscillations. Prolactin release was increased by Ba2+ and Cs+ but not by TEA. These results indicate that L-type Ca2+ channels and KIR channels modulate the frequency of Ca2+ oscillations and prolactin release, whereas TEA-sensitive KCa,V channels modulate the amplitude of Ca2+ oscillations without altering prolactin release. Differential regulation of these channels can produce frequency or amplitude modulation of calcium signaling that stimulates specific pituitary cell functions.     

Mitochondria suppress local feedback activation of inositol 1,4, 5-trisphosphate receptors by Ca2+.

The concerted action of inositol 1,4,5-trisphosphate (IP3) and Ca2+ on the IP3 receptor Ca2+ release channel (IP3R) is a fundamental step in the generation of cytosolic Ca2+ oscillations and waves, which underlie Ca2+ signaling in many cells. Mitochondria appear in close association with regions of endoplasmic reticulum (ER) enriched in IP3R and are particularly responsive to IP3-induced increases of cytosolic Ca2+ ([Ca2+]c). To determine whether feedback regulation of the IP3R by released Ca2+ is modulated by mitochondrial Ca2+ uptake, the interactions between ER and mitochondrial Ca2+ pools were examined by fluorescence imaging of compartmentalized Ca2+ indicators in permeabilized hepatocytes. IP3 decreased luminal ER Ca2+ ([Ca2+]ER), and this was paralleled by an increase in mitochondrial matrix Ca2+ ([Ca2+]m) and activation of Ca2+-sensitive mitochondrial metabolism. Remarkably, the decrease in [Ca2+]ER evoked by submaximal IP3 was enhanced when mitochondrial Ca2+ uptake was blocked with ruthenium red or uncoupler. Moreover, subcellular regions that were relatively deficient in mitochondria demonstrated greater sensitivity to IP3 than regions of the cell with a high density of mitochondria. These data demonstrate that Ca2+ uptake by the mitochondria suppresses the local positive feedback effects of Ca2+ on the IP3R, giving rise to subcellular heterogeneity in IP3 sensitivity and IP3R excitability. Thus, mitochondria can play an important role in setting the threshold for activation and establishing the subcellular pattern of IP3-dependent [Ca2+]c signaling.     

Sensing and refilling calcium stores in an excitable cell.

Inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ mobilization leads to depletion of the endoplasmic reticulum (ER) and an increase in Ca2+ entry. We show here for the gonadotroph, an excitable endocrine cell, that sensing of ER Ca2+ content can occur without the Ca2+ release-activated Ca2+ current (Icrac), but rather through the coupling of IP3-induced Ca2+ oscillations to plasma membrane voltage spikes that gate Ca2+ entry. Thus we demonstrate that capacitative Ca2+ entry is accomplished through Ca(2+)-controlled Ca2+ entry. We develop a comprehensive model, with parameter values constrained by available experimental data, to simulate the spatiotemporal behavior of agonist-induced Ca2+ signals in both the cytosol and ER lumen of gonadotrophs. The model combines two previously developed models, one for ER-mediated Ca2+ oscillations and another for plasma membrane potential-driven Ca2+ oscillations. Simulations show agreement with existing experimental records of store content, cytosolic Ca2+ concentration ([Ca2+]i), and electrical activity, and make a variety of new, experimentally testable predictions. In particular, computations with the model suggest that [Ca2+]i in the vicinity of the plasma membrane acts as a messenger for ER content via Ca(2+)-activated K+ channels and Ca2+ pumps in the plasma membrane. We conclude that, in excitable cells that do not express Icrac, [Ca2+]i profiles provide a sensitive mechanism for regulating net calcium flux through the plasma membrane during both store depletion and refilling.     

Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling.

This review provides a comparative overview of recent developments in the modelling of cellular calcium oscillations. A large variety of mathematical models have been developed for this wide-spread phenomenon in intra- and intercellular signalling. From these, a general model is extracted that involves six types of concentration variables: inositol 1,4,5-trisphosphate (IP3), cytoplasmic, endoplasmic reticulum and mitochondrial calcium, the occupied binding sites of calcium buffers, and the fraction of active IP3 receptor calcium release channels. Using this framework, the models of calcium oscillations can be classified into 'minimal' models containing two variables and 'extended' models of three and more variables. Three types of minimal models are identified that are all based on calcium-induced calcium release (CICR), but differ with respect to the mechanisms limiting CICR. Extended models include IP3--calcium cross-coupling, calcium sequestration by mitochondria, the detailed gating kinetics of the IP3 receptor, and the dynamics of G-protein activation. In addition to generating regular oscillations, such models can describe bursting and chaotic calcium dynamics. The earlier hypothesis that information in calcium oscillations is encoded mainly by their frequency is nowadays modified in that some effect is attributed to amplitude encoding or temporal encoding. This point is discussed with reference to the analysis of the local and global bifurcations by which calcium oscillations can arise. Moreover, the question of how calcium binding proteins can sense and transform oscillatory signals is addressed. Recently, potential mechanisms leading to the coordination of oscillations in coupled cells have been investigated by mathematical modelling. For this, the general modelling framework is extended to include cytoplasmic and gap-junctional diffusion of IP3 and calcium, and specific models are compared. Various suggestions concerning the physiological significance of oscillatory behaviour in intra- and intercellular signalling are discussed. The article is concluded with a discussion of obstacles and prospects.     

A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte.

We construct a minimal model of cytosolic free Ca2+ oscillations based on Ca2+ release via the inositol 1,4,5-trisphosphate (IP3) receptor/Ca2+ channel (IP3R) of a single intracellular Ca2+ pool. The model relies on experimental evidence that the cytosolic free calcium concentration ([Ca2+]c) modulates the IP3R in a biphasic manner, with Ca2+ release inhibited by low and high [Ca2+]c and facilitated by intermediate [Ca2+]c, and that channel inactivation occurs on a slower time scale than activation. The model produces [Ca2+]c oscillations at constant [IP3] and reproduces a number of crucial experiments. The two-dimensional spatial model with IP3 dynamics, cytosolic diffusion of IP3 (Dp = 300 microns 2 s-1), and cytosolic diffusion of Ca2+ (Dc = 20 microns 2 s-1) produces circular, planar, and spiral waves of Ca2+ with speeds of 7-15 microns.s-1, which annihilate upon collision. Increasing extracellular [Ca2+] influx increases wave speed and baseline [Ca2+]c. A [Ca2+]c-dependent Ca2+ diffusion coefficient does not alter the qualitative behavior of the model. An important model prediction is that channel inactivation must occur on a slower time scale than activation in order for waves to propagate. The model serves to capture the essential macroscopic mechanisms that are involved in the production of intracellular Ca2+ oscillations and traveling waves in the Xenopus laevis oocyte.     

Role of Ca(2+)-ATPase in spontaneous oscillations of cytosolic free Ca2+ in GH3 rat pituitary cells.

The relative contribution of voltage-sensitive Ca2+ channels, Ca(2+)-ATPases, and Ca2+ release from intracellular stores to spontaneous oscillations in cytosolic free Ca2+ concentration ([Ca2+]i) observed in secretory cells is not well characterized owing to a lack of specific inhibitors for a novel thapsigargin (Tg)-insensitive Ca(2+)-ATPase expressed in these cells. We show that spontaneous [Ca2+]i oscillations in GH3 cells were unaffected by Ca2+ depletion in inositol-1,4,5-trisphosphate (IP3)-sensitive Ca2+ stores by the treatment of Tg, but could be initiated by application of caffeine. Moreover, we demonstrate for the first time that these spontaneous [Ca2+]i oscillations were highly temperature dependent. Decreasing the temperature from 22 to 17 degrees C resulted in an increase in the frequency, a reduction in the amplitude, and large inhibition of [Ca2+]i oscillations. Furthermore, the rate of ATP-dependent 45Ca2+ uptake into GH3-derived microsomes was greatly reduced at 17 degrees C. The effect of decreased temperatures on extracellular Ca2+ influx was minor because the frequency and amplitude of spontaneous action potentials, which activate L-type Ca2+ channels, was relatively unchanged at 17 degrees C. These results suggest that in GH3 secretory cells, Ca2+ influx via L-type Ca2+ channels initiates spontaneous [Ca2+]i oscillations, which are then maintained by the combined activity of Ca(2+)-ATPase and Ca(2+)-induced Ca2+ release from Tg/IP3-insensitive intracellular stores.