Effects of rapid buffers on Ca2+ diffusion and Ca2+ oscillations.

Based on realistic mechanisms of Ca2+ buffering that include both stationary and mobile buffers, we derive and investigate models of Ca2+ diffusion in the presence of rapid buffers. We obtain a single transport equation for Ca2+ that contains the effects caused by both stationary and mobile buffers. For stationary buffers alone, we obtain an expression for the effective diffusion constant of Ca2+ that depends on local Ca2+ concentrations. Mobile buffers, such as fura-2, BAPTA, or small endogenous proteins, give rise to a transport equation that is no longer strictly diffusive. Calculations are presented to show that these effects can modify greatly the manner and rate at which Ca2+ diffuses in cells, and we compare these results with recent measurements by Allbritton et al. (1992). As a prelude to work on Ca2+ waves, we use a simplified version of our model of the activation and inhibition of the IP3 receptor Ca2+ channel in the ER membrane to illustrate the way in which Ca2+ buffering can affect both the amplitude and existence of Ca2+ oscillations.     

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.     

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.     

Intercellular Ca2+ wave propagation through gap-junctional Ca2+ diffusion: a theoretical study

Intercellular regenerative calcium waves in systems such as the liver and the blowfly salivary gland have been hypothesized to spread through calcium-induced calcium release (CICR) and gap-junctional calcium diffusion. A simple mathematical model of this mechanism is developed. It includes CICR and calcium removal from the cytoplasm, cytoplasmic and gap-junctional calcium diffusion, and calcium buffering. For a piecewise linear approximation of the calcium kinetics, expressions in terms of the cellular parameters are derived for 1) the condition for the propagation of intercellular waves, and 2) the characteristic time of the delay of a wave encountered at the gap junctions. Intercellular propagation relies on the local excitation of CICR in the perijunctional space by gap-junctional calcium influx. This mechanism is compatible with low effective calcium diffusivity, and necessitates that CICR can be excited in every cell along the path of a wave. The gap-junctional calcium permeability required for intercellular waves in the model falls in the range of reported gap-junctional permeability values. The concentration of diffusive cytoplasmic calcium buffers and the maximal rate of CICR, in the case of inositol 1,4,5-trisphosphate (IP3) receptor calcium release channels set by the IP(3) concentration, are shown to be further determinants of wave behavior.     

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.     

Rapid functional assays of intracellular Ca2+ channels

Functional assays of intracellular Ca2+ channels, such as the inositol 1,4,5-trisphosphate receptor (IP3R), have generally used 45Ca2+-flux assays, fluorescent indicators loaded within either the cytosol or the endoplasmic reticulum (ER) of single cells, or electrophysiological analyses. None of these methods is readily applicable to rapid, high-throughput quantitative analyses. Here we provide a detailed protocol for high-throughput functional analysis of native and recombinant IP3Rs. A low-affinity Ca2+ indicator (mag-fluo-4) trapped within the ER of permeabilized cells is shown to report changes in luminal free Ca2+ concentration reliably. An automated fluorescence plate reader allows rapid measurement of Ca2+ release from intracellular stores mediated by IP3R. The method can be readily adapted to other cell types or to the analysis of other intracellular Ca2+ channels. This protocol can be completed in 2-3 h.     

Endoplasmic reticulum Ca2+ store: regulation of Ca2+ release and reuptake by intracellular and extracellular Ca2+ in pancreatic acinar cells

We investigated the effect of cytosolic and extracellular Ca2+ on Ca2+ signals in pancreatic acinar cells by measuring Ca2+ concentration in the cytosol([Ca2+]c) and in the lumen of the ER([Ca2+]Lu). To control buffers and dye in the cytosol, a patch-clamp microelectrode was employed. Acetylcholine released Ca2+ mainly from the basolateral ER-rich part of the cell. The rate of Ca2+ release from the ER was highly sensitive to the buffering of [Ca2+]c whereas ER Ca2+ refilling was enhanced by supplying free Ca2+ to the cytosol with [Ca2+]c clamped at resting levels with a patch pipette containing 10 mM BAPTA and 2 mM Ca2+. Elevation of extracellular Ca2+ to 10 mM from 1 mM raised resting [Ca2+]c slightly and often generated [Ca2+]c oscillations in single or clustered cells. Although pancreatic acinar cells are reported to have extracellular Ca2+-sensing receptors linked to phospholipase C that mobilize Ca2+ from the ER, exposure of cells to 10 mM Ca2+ did not decrease [Ca2+]Lu but rather raised it. From these findings we conclude that 1) ER Ca2+ release is strictly regulated by feedback inhibition of [Ca2+]c, 2) ER Ca2+ refilling is determined by the rate of Ca2+ influx and occurs mainly in the tiny subplasmalemmal spaces, 3) extracellular Ca2+-induced [Ca2+]c oscillations appear to be triggered not by activation of extracellular Ca2+-sensing receptors but by the ER sensitised by elevated [Ca2+]c and [Ca2+]Lu.     

IP3R, store-operated Ca2+ entry and neuronal Ca2+ homoeostasis in Drosophila

The IP3R (inositol 1,4,5-trisphosphate receptor) releases Ca2+ from the ER (endoplasmic reticulum) store upon binding to its ligand InsP3, which is thought to be generated by activation of certain membrane-bound G-protein-coupled receptors in Drosophila. Depletion of Ca2+ in the ER store also activates SOCE (store-operated Ca2+ entry) from the extracellular milieu across the plasma membrane, leading to a second rise in cytosolic Ca2+, which is then pumped back into the ER. The role of the IP3R and SOCE in mediating Ca2+ homoeostasis in neurons, their requirement in neuronal function and effect on neuronal physiology and as a consequence behaviour, are reviewed in the present article.     

The role of mitochondria for Ca2+ refilling of the endoplasmic reticulum

Endoplasmic reticulum (ER) Ca2+ refilling is an active process to ensure an appropriate ER Ca2+ content under basal conditions and to maintain or restore ER Ca2+ concentration during/after cell stimulation. The mechanisms to achieve successful ER Ca2+ refilling are multiple and built on a concerted action of processes that provide a suitable reservoir for Ca2+ sequestration into the ER. Despite mitochondria having been found to play an essential role in the maintenance of capacitative Ca2+ entry by buffering subplasmalemmal Ca2+, their contribution to ER Ca2+ refilling was not subjected to detailed analysis so far. Thus, this study was designed to elucidate the involvement of mitochondria in Ca2+ store refilling during and after cell stimulation. ER Ca2+ refilling was found to be accomplished even during continuous inositol 1,4,5-trisphosphate (IP3)-triggered ER Ca2+ release by an agonist. Basically, ER Ca2+ refilling depended on the presence of extracellular Ca2+ as the source and sarcoplasmic/endoplasmic reticulum Ca2+ ATPase (SERCA) activity. Interestingly, in the presence of an IP3-generating agonist, ER Ca2+ refilling was prevented by the inhibition of trans-mitochondrial Ca2+ flux by CGP 37157 (7-chloro-5-(2-chlorophenyl)-1,5-dihydro-4,1-benzothiazepin-2(3H)-one) that precludes the mitochondrial Na+/Ca2+ exchanger as well as by mitochondrial depolarization using a mixture of oligomycin and antimycin A. In contrast, after the removal of the agonist, ER refilling was found to be largely independent of trans-mitochondrial Ca2+ flux. Under these conditions, ER Ca2+ refilling took place even without an associated Ca2+ elevation in the deeper cytosol, thus, indicating that superficial ER domains mimic mitochondrial Ca2+ buffering and efficiently sequester subplasmalemmal Ca2+ and consequently facilitate capacitative Ca2+ entry. Hence, these data point to different contribution of mitochondria in the process of ER Ca2+ refilling based on the presence or absence of IP3, which represents the turning point for the dependence or autonomy of ER Ca2+ refilling from trans-mitochondrial Ca2+ flux.     

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.     

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.     

Uptake and release of Ca2+ by the endoplasmic reticulum contribute to the oscillations of the cytosolic Ca2+ concentration triggered by Ca2+ influx in the electrically excitable pancreatic B-cell.

The role of intracellular Ca2+ pools in oscillations of the cytosolic Ca2+ concentration ([Ca2+]c) triggered by Ca2+ influx was investigated in mouse pancreatic B-cells. [Ca2+]c oscillations occurring spontaneously during glucose stimulation or repetitively induced by pulses of high K+ (in the presence of diazoxide) were characterized by a descending phase in two components. A rapid decrease in [Ca2+]c coincided with closure of voltage-dependent Ca2+ channels and was followed by a slower phase independent of Ca2+ influx. Blocking the SERCA pump with thapsigargin or cyclopiazonic acid accelerated the rising phase of [Ca2+]c oscillations and increased their amplitude, which suggests that the endoplasmic reticulum (ER) rapidly takes up Ca2+. It also suppressed the slow [Ca2+]c recovery phase, which indicates that this phase corresponds to the slow release of Ca2+ that was taken up by the ER during the upstroke of the [Ca2+]c transient. Glucose promoted the buffering capacity of the ER and amplified the slow [Ca2+]c recovery phase. The slow phase induced by high K+ pulses was not affected by modulators of Ca2+- or inositol 1,4,5-trisphosphate-induced Ca2+ release, did not involve a depolarization-induced Ca2+ release, and was also observed at the end of a rapid rise in [Ca2+]c triggered from caged Ca2+. It is attributed to passive leakage of Ca2+ from the ER. We suggest that the ER displays oscillations of the Ca2+ concentration ([Ca2+]ER) concomitant and parallel to [Ca2+]c. The observation that thapsigargin depolarizes the membrane of B-cells supports the proposal that the degree of Ca2+ filling of the ER modulates the membrane potential. Therefore, [Ca2+]ER oscillations occurring during glucose stimulation are likely to influence the bursting behavior of B-cells and eventually [Ca2+]c oscillations.     

Properties of intracellular Ca2+ waves generated by a model based on Ca(2+)-induced Ca2+ release.

Cytosolic Ca2+ waves occur in a number of cell types either spontaneously or after stimulation by hormones, neurotransmitters, or treatments promoting Ca2+ influx into the cells. These waves can be broadly classified into two types. Waves of type 1, observed in cardiac myocytes or Xenopus oocytes, correspond to the propagation of sharp bands of Ca2+ throughout the cell at a rate that is high enough to permit the simultaneous propagation of several fronts in a given cells. Waves of type 2, observed in hepatocytes, endothelial cells, or various kinds of eggs, correspond to the progressive elevation of cytosolic Ca2+ throughout the cell, followed by its quasi-homogeneous return down to basal levels. Here we analyze the propagation of these different types of intracellular Ca2+ waves in a model based on Ca(2+)-induced Ca2+ release (CICR). The model accounts for transient or sustained waves of type 1 or 2, depending on the size of the cell and on the values of the kinetic parameters that measure Ca2+ exchange between the cytosol, the extracellular medium, and intracellular stores. Two versions of the model based on CICR are considered. The first version involves two distinct Ca2+ pools sensitive to inositol 1,4,5-trisphosphate (IP3) and Ca2+, respectively, whereas the second version involves a single pool sensitive both to Ca2+ and IP3 behaving as co-agonists for Ca2+ release. Intracellular Ca2+ waves occur in the two versions of the model based on CICR, but fail to propagate in the one-pool model at subthreshold levels of IP3. For waves of type 1, we investigate the effect of the spatial distribution of Ca(2+)-sensitive Ca2+ stores within the cytosol, and show that the wave fails to propagate when the distance between the stores exceeds a critical value on the order of a few microns. We also determine how the period and velocity of the waves are affected by changes in parameters measuring stimulation, Ca2+ influx into the cell, or Ca2+ pumping into the stores. For waves of type 2, the numerical analysis indicates that the best qualitative agreement with experimental observations is obtained for phase waves. Finally, conditions are obtained for the occurrence of "echo" waves that are sometimes observed in the experiments.     

Inositol 1,4,5-trisphosphate and the endoplasmic reticulum Ca2+ cycle of a rat insulinoma cell line

Regulation of endoplasmic reticulum (ER) Ca2+ cycling by inositol 1,4,5-trisphosphate (IP3) was studied in saponin-permeabilized RINm5F insulinoma cells. Cells were incubated with mitochondrial inhibitors, and medium Ca2+ concentration established by nonmitochondrial pool(s) (presumably the ER) was monitored with a Ca2+ electrode. IP3 degradation accounted for the transience of the Ca2+ response induced by pulse additions of the molecule. To compensate for degradation, IP3 was infused into the medium. This resulted in elevation of [Ca2+] from about 0.2 microM to a new steady state between 0.3 and 1.0 microM, depending on both the rate of IP3 infusion and the ER Ca2+ content. The elevated steady state represented a bidirectional buffering of [Ca2+] by the ER, as slight displacements in [Ca2+], by small aliquots of Ca2+ or the Ca2+ chelator quin 2, resulted in net uptake or efflux of Ca2+ to restore the previous steady state. When IP3 infusion was stopped, [Ca2+] returned to its original low level. Ninety per cent of the Ca2+ accumulated by the ER was released by IP3 when the total Ca2+ content did not exceed 15 nmol/mg of cell protein. Above this high Ca2+ content, Ca2+ was accumulated in an IP3-insensitive, A23187-releasable pool. The maximal amount of Ca2+ that could be released from the ER by IP3 was 13 nmol/mg of cell protein. The data support the concept that in the physiological range of Ca2+ contents, almost all the ER is an IP3-sensitive Ca2+ store that is capable of finely regulating [Ca2+] through independent influx (Ca2+-ATPase) and efflux (IP3-modulated component) pathways of Ca2+ transport. IP3 may continuously modulate Ca2+ cycling across the ER and play an important role in determining the ER Ca2+ content and in regulating cytosolic Ca2+ under both stimulated and possibly basal conditions.     

Simulation of the fertilization Ca2+ wave in Xenopus laevis eggs.

In the preceding paper Fontanilla and Nuccitelli (Biophysical Journal 75:2079-2087 (1998)) present detailed measurements of the shape and speed of the fertilization Ca2+ wave in Xenopus laevis eggs. In order to help interpret their results, we develop here a computational technique based on the finite element method that allows us to carry out realistic simulations of the fertilization wave. Our simulations support the hypothesis that the physiological state of the mature egg is bistable, i.e., that its cytoplasm can accommodate two alternative physiological Ca2+ concentrations: a low concentration characteristic of the prefertilization state and a greatly elevated concentration characteristic of the state following the passage of the wave. We explore this hypothesis by assuming that the bistability is due to the release and re-uptake properties of the endoplasmic reticulum (ER) as determined by inositol trisphosphate (IP3) receptor/Ca2+ channels and sarcoendoplasmic reticulum calcium ATPase (SERCA) pumps. When combined with buffered diffusion of Ca2+ in the cytoplasm, our simulations show that inhomogeneities in the Ca2+ release properties near the plasma membrane are required to explain the temporal and spatial dependences of the shape and speed of these waves. Our results are consistent with an elevated IP3 concentration near the plasma membrane in the unfertilized egg that is augmented significantly near the site of fertilization. These gradients are essential in determining the concave shape of the Ca2+ fertilization wave front.     

Analytical calculation of intracellular calcium wave characteristics

We present a theoretical analysis of intracellular calcium waves propagated by calcium feedback at the inositol 1,4,5-trisphosphate (IP3) receptor. The model includes essential features of calcium excitability, but is still analytically tractable. Formulas are derived for the wave speed, amplitude, and width. The calculations take into account cytoplasmic Ca buffering, the punctate nature of the Ca release channels, channel inactivation, and Ca pumping. For relatively fast buffers, the wave speed is well approximated by V(infinity) = (J(eff)D(eff)/C0)1/2, where J(eff) is an effective, buffered source strength; D(eff) is the effective, buffered diffusion constant of Ca; and C(0) is the Ca threshold for channel activation. It is found that the saturability and finite on-rate of buffers must be taken into account to accurately derive the wave speed and front width. The time scale governing Ca wave propagation is T(r), the time for Ca release to reach threshold to activate further release. Because IP3 receptor inactivation is slow on this time scale, channel inactivation does not affect the wave speed. However, inactivation competes with Ca removal to limit wave height and front length, and for biological parameter ranges, it is inactivation that determines these parameters. Channel discreteness introduces only small corrections to wave speed relative to a model in which Ca is released uniformly from the surface of the stores. These calculations successfully predict experimental results from basic channel and cell parameters and explain the slowing of waves by exogenous buffers.     

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.     

Two roles of Ca2+ in agonist stimulated Ca2+ oscillations.

We propose a mechanism for agonist-stimulated Ca2+ oscillations that involves two roles for cytosolic Ca2+: (a) inhibition of inositol-1,4,5-trisphosphate (IP3) stimulated Ca2+ release from the endoplasmic reticulum (ER) and (b) stimulation of the production of IP3 through its action on phospholipase C (PLC), via a Gq protein related mechanism. Relying on quantitative experiments by Parker, I., and I. Ivorra (1990. Proc. Natl. Acad. Sci. USA. 87:260-264) on the inhibition of Ca2+ release from the ER using caged-IP3, we develop a kinetic model of inhibition that allows us to simulate closely their experiments. The model assumes that the ER IP3 receptor is a tetramer of independent subunits that can bind both Ca2+ and IP3. Upon incorporation of the action of Ca2+ on PLC that leads to production of IP3, we observe in-phase-oscillations of Ca2+ and IP3 at intermediate values of agonist stimulation. The oscillations occur on a time scale of 10-20 s, which is comparable to the time scale for inhibition in Xenopus oocytes. Analysis of the mechanism shows that Ca(2+)-inhibition of IP3-stimulated Ca2+ release from the ER is an essential step in the mechanism. We also find that the effect of Ca2+ on PLC can lead to an indirect increase of cytosolic Ca2+, superficially resembling "Ca(2+)-induced Ca(2+)-release." The mechanism that we propose appears to be consistent with recent experiments on REF52 cells by Harootunian, A. T., J. P. Y. Kao, S. Paranjape, and R. Y. Tsien. (1991. Science [Wash. DC]. 251:75-78.) and we propose additional experiments to help test its underlying assumptions.     

Impact of mitochondrial Ca2+ cycling on pattern formation and stability.

Energization of mitochondria significantly alters the pattern of Ca2+ wave activity mediated by activation of the inositol (1,4,5) trisphosphate (IP3) receptor (IP3R) in Xenopus oocytes. The number of pulsatile foci is reduced and spiral Ca2+ waves are no longer observed. Rather, target patterns of Ca2+ release predominate, and when fragmented, fail to form spirals. Ca2+ wave velocity, amplitude, decay time, and periodicity are also increased. We have simulated these experimental findings by supplementing an existing mathematical model with a differential equation for mitochondrial Ca2+ uptake and release. Our calculations show that mitochondrial Ca2+ efflux plays a critical role in pattern formation by prolonging the recovery time of IP3Rs from a refractory state. We also show that under conditions of high energization of mitochondria, the Ca2+ dynamics can become bistable with a second stable stationary state of high resting Ca2+ concentration.