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Caffeine-induced [Ca²⁺] oscillations in neurones of frog sympathetic ganglia

Zoltán Cseresnyés, Alexander I. Bustamante and Martin F. Schneider

Received 14 April 1998; accepted after revision 28 September 1998.

	ABSTRACT

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1. Single cell fluorimetry was used to monitor caffeine-induced oscillations of cytosolic [Ca²⁺] in frog sympathetic ganglion neurones in 2·0 mM K⁺ Ringer solution.

2. [Ca²⁺] oscillations decreased in frequency and exhibited three different amplitude patterns after the first large peak of [Ca²⁺]: (a) a series of big oscillations (BOs) of constant large amplitude (300-400 nM), (b) a series of much smaller oscillations (SOs) (40-60 nM), or (c) a series of decaying oscillations (DOs) of rapidly decreasing amplitude.

3. A model in which the oscillation amplitude was determined by the Ca²⁺ content of the endoplasmic reticulum (ER) whereas the oscillation frequency was controlled by how rapidly the cytosolic [Ca²⁺] reached the threshold for Ca²⁺-induced Ca²⁺ release (CICR) was able to simulate each observed pattern by varying the level of activity of the ER Ca²⁺ pump (SERCA), CICR and release-activated Ca²⁺ transport (RACT). A cumulative, cytosolic Ca²⁺-dependent inactivation of the plasma membrane (PM) Ca²⁺ influx or of the Ca²⁺-sensitive leak coefficient of the ryanodine receptors caused the oscillation frequency to decrease in the model.

4. Transitions between BOs and SOs and changes in [Ca²⁺] oscillations caused by ryanodine, thapsigargin, lanthanum and FCCP could also be simulated.

5. We conclude that RACT, SERCA, CICR and Ca²⁺-dependent PM Ca²⁺ influx are major mechanisms underlying [Ca²⁺] oscillations in these neurones.

	INTRODUCTION

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Oscillations of cytosolic [Ca²⁺] (Berridge, 1990) in response to constant application of extracellular agonists is a form of Ca²⁺ signalling (Putney, 1998) present in a wide range of cell types (Nieman & Eisner, 1985; Foskett et al. 1991; Harootunian et al. 1991; Friel & Tsien, 1992a; Li et al. 1994; Tse et al. 1994; Friel, 1995b; Swann & Lai, 1997). The potential importance of [Ca²⁺] oscillations is that cells may respond to constant, elevated levels of extracellular agonists with a periodic intracellular signal. This periodic cytosolic signal can be sensed by intracellular mechanisms that decode the information transferred by the oscillation (e.g. Ca²⁺-calmodulin-dependent protein kinase, see Hanson et al. 1994; De Koninck & Schulman, 1998).

In neurones of bullfrog sympathetic ganglia, rhythmic hyper- and depolarizations of the plasma membrane in the presence of caffeine have been attributed to caffeine-induced oscillations of cytosolic [Ca²⁺] (Kuba & Nishi, 1976). Early theoretical models considered calcium-induced calcium release (CICR) together with an active Ca²⁺ uptake system to be the main intracellular mechanisms underlying such [Ca²⁺] oscillations (Kuba & Takeshita, 1981). More recent studies showed that ryanodine receptors (RyRs; McPherson et al. 1991; McPherson & Campbell, 1993) of the endoplasmic reticulum (ER; Vertel et al. 1992) participate in the generation of fast Ca²⁺ release from the ER via CICR (McPherson et al. 1991; Friel & Tsien, 1992a, b; Friel, 1995a). As for the Ca²⁺ reuptake mechanism, the ATP-dependent Ca²⁺ pump in the ER membrane (SERCA) has generally been considered to be the major uptake system contributing to maintained [Ca²⁺] oscillations (Friel & Tsien, 1992a, b; Friel, 1995a). However, neurones of frog sympathetic ganglia may also exhibit a non-SERCA-type fast Ca²⁺ uptake mechanism which transfers Ca²⁺ from the cytosol to the ER and is only activated by Ca²⁺ release from the ER (Cseresnyés et al. 1997). This mechanism, called release-activated Ca²⁺ transport or RACT, has been shown to be highly effective in preventing Ca²⁺ loss from the cell via plasma membrane (PM) Ca²⁺ transporters. It thus seems probable that RACT would contribute to the maintained [Ca²⁺] oscillations observed in these neurones.

In the present study we show that three kinetically distinct patterns of [Ca²⁺] oscillations exist in frog sympathetic ganglia neurones. Moreover, using a computer model which included both the SERCA and RACT contribution to Ca²⁺ reuptake and the CICR contribution to fast Ca²⁺ release, we were able to simulate each of the three different oscillation patterns experimentally observed in these neurones.

	METHODS

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Cell isolation and single cell fluorimetry

Neurones were isolated from the sympathetic ganglia of adult grass frogs (Rana pipiens) using methods described previously (Cseresnyés et al. 1997). Briefly, ganglia were dissected from animals killed by decapitation and pithing. Isolated ganglia were cleaned and incubated in collagenase and trypsin at 35·5°C for 50 min and 10 min, respectively, and were triturated every 10 min to dissociate individual neurones. Neurones were then plated in Petri dishes, which had 15 mm holes cut from the bottom capped with micro coverglasses (VWR Scientific) coated with poly-L-lysine (Sigma, diluted 1 : 10). Cells were maintained in Ringer solution (for composition of solutions see Cseresnyés et al. 1997) with 2 mM [Ca²⁺] mixed with an equal amount of Leibovitz L-15 culture medium (Gibco BRL) for 4-6 days at either room temperature (22-24°C) or at 4°C. Fresh mixtures of Ringer solution and L-15 were added to the Petri dishes every 2 days.

Single cell fluorimetry was performed as described previously (Cseresnyés et al. 1997). The Ca²⁺ indicator fura-2 AM (2 µM) was applied for 20 min at room temperature in Ringer solution to load fura-2 into the cytosol to monitor cytosolic [Ca²⁺]. To let the AM form of fura-2 be converted into the Ca²⁺-sensitive form by endogenous esterase, cells were stored in dye-free Ringer solution for about 30 min before starting experiments. After such loading procedures, the spatial distribution of fura-2 fluorescence has been shown to be predominantly cytosolic (Cseresnyés et al. 1997). For simple [Ca²⁺] transients, the fura-2 fluorescence signals were usually excited at both 358 nm (the isosbestic wavelength) and 380 nm (a Ca²⁺-sensitive wavelength) at a data acquisition rate of 2 s per point and the fluorescence ratio was calculated. However, to resolve the time course of the relatively fast [Ca²⁺] oscillations, the fura-2 fluorescence signal was monitored only at 380 nm, using a 0·5 s per point acquisition rate. The 358 nm fluorescence was measured in the same cell immediately before and after the high acquisition rate sequence, and the average value of the two readings at 358 nm was used to calculate the fluorescence ratio during the entire period of fluorescence monitoring with 380 nm excitation. To avoid the bleaching of fura-2, which would lead to a decrease of the 358 nm fluorescence during the high rate acquisition and result in faulty fluorescence ratio values, a low transmittance neutral density filter was used to reduce the light intensity of the Xe arc lamp. In five neurones, successive responses to caffeine (n = 4) or high K⁺ (n = 1) were measured using sampling at either 0·5 s per point or at a five times higher rate (0·1 s per point) and exhibited no significant difference in rising or falling phase time course, indicating that the 0·5 s per point acquisition rate used here produced negligible distortion of the fluorescence signals during stimulation.

Cytosolic [Ca²⁺] was calculated from fura-2 fluorescence ratio signals, as described previously (Grynkiewicz et al. 1985; Cseresnyés et al. 1997). Briefly, fura-2 fluorescence was measured at two excitation wavelengths: 380 nm for the Ca²⁺-sensitive and 358 nm for the Ca²⁺-insensitive (isosbestic) signal. The ratio of these fluorescence values (R) was then used to calculate the cytosolic concentration of free Ca²⁺:

[Ca²⁺] = (K_D)((R - R_min)/(R_max - R)). (1)

K_D was assumed to be 135 nM, R_max was measured in living cells by exposing them to 4 µM ionomycin and 1 mM Ca²⁺ and R_min was determined in Ca²⁺-free Ringer solution in the presence of 4 µM ionomycin and 1 mM EGTA.

Model simulation of Ca²⁺ fluxes

The equations describing Ca²⁺ fluxes in frog neurones used by Friel (1995a) were modified to include release-activated calcium transport (RACT) as described in our previous paper (Cseresnyés et al. 1997). We have also now added the possibility of explicitly including the additional mechanism of CICR in our previous model. To calculate the time course of the store [Ca²⁺] (c_s), the cytosolic [Ca²⁺] (c_i) and the RACT transport rate constant (k_RACT; Cseresnyés et al. 1997) for a system including RACT and CICR, a set of first-order differential equations had to be solved. The equations for c_s and c_i were:

dc_s/dt = k_SERCAc_i + k_RACTc_i - k_RyR(c_s - c_i), (2)

and

dc_i/dt = k_RyR(c_s - c_i) + k_PM(c_o - c_i) -

k_SERCAc_i - k_RACTc_i - k_PMCAc_i. (3)

k_SERCA is the SERCA rate constant, k_RACT is the RACT rate constant, k_RyR is the rate coefficient for Ca²⁺ efflux via the RyRs (see eqn (6)), c_o is the extracellular [Ca²⁺] and is the ratio of the volume occupied by the ER lumen to the entire volume of the cytosol. k_PM is the plasma membrane leak coefficient, k_PMCA is the rate coefficient of the plasma membrane Ca²⁺-ATPase.

The rate constant of the mechanism behind RACT is presumed to be controlled by both local and global [Ca²⁺], and was described by the following equation:

dk_RACT/dt = k_on,R(k_RACT,max - k_RACT)c_lR - k_off,Rk_RACT. (4)

k_on,R and k_off,R are the 'on' and 'off' rate constants for Ca²⁺ binding to hypothetical regulatory sites on RACT, and kRACT,max is the maximum value for the flux coefficient for RACT. In eqn (4), the local concentration of [Ca²⁺] (c_lR) at the hypothetical Ca²⁺ binding regulatory sites for RACT, which are assumed to be in close proximity to the RyRs, is given by:

c_lR = c_i + (c_s - c_i)k_RyR. (5)

transforms the ER Ca²⁺ flux into a local increment of extraluminal [Ca²⁺] and k_RyR is defined as an instantaneous function of cytosolic [Ca²⁺]:

k_RyR = k_RyR,0 + ((k_RyR,1)/(1 + (K_D/c_i)ⁿ)). (6)

k_RyR,0 and (k_RyR,0 + k_RyR,1) are the flux coefficients for the RyR at zero and full activation of CICR, and K_D and n are the Ca²⁺ dissociation constant and the apparent co-operativity of the RyR regulatory sites for CICR.

In bullfrog neurones the decrease in Ca²⁺ influx resulting from lowering extracellular [Ca²⁺] has been shown to decrease the frequency of caffeine-induced [Ca²⁺] oscillations in partially depolarized neurones (Friel, 1995a). In the present studies we observed a continual decrease in oscillation frequency during caffeine application to non-depolarized neurones (Results). Therefore, in order to simulate the observed progressive slowing of the oscillation frequency during continued exposure to caffeine, we arbitrarily introduced a hypothetical negative Ca²⁺ feedback mechanism to control the coefficient k_PM for the Ca²⁺ flux via the PM Ca²⁺ channels so as to gradually decrease the rate of Ca²⁺ influx with time:

dk_PM/dt = k_on,PM(k_PM,max - k_PM)c_i - k_off,PMk_PM. (7)

k_on,PM and koff,PM represent the 'on' and 'off' rate constants for Ca²⁺ binding to a hypothetical Ca²⁺-binding regulatory site on the PM Ca²⁺ channel and kPM,max is the maximum value of the PM flux coefficient.

The starting conditions were determined by solving the steady-state equations which were obtained from eqns (2), (3), (4) and (7), making the time derivatives equal zero. The Levenberg-Marquardt algorithm was applied to complete this calculation, using Mathcad 7 Professional (Mathsoft, Inc., Cambridge, MA, USA). The time courses of c_s, c_i, k_RACT and k_PM were calculated from eqns (2)-(7), using the Rosenbrock method in Mathcad 7. The starting values of the parameters appearing in eqns (2)-(7) were as in our previous paper (Cseresnyés et al. 1997), with the additions of n = 3, k_RyR,0 = 0·03 and k_RyR,1 = 2. The parameter values were then adjusted to produce simulated curves resembling the observed data.

	RESULTS

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RACT contributes to fast removal of Ca²⁺ after Ca²⁺ release

A brief application of high K⁺ solution causes elevation of cytosolic [Ca²⁺] due to Ca²⁺ influx via voltage-activated plasma membrane Ca²⁺ channels. The decay of [Ca²⁺] after a high K⁺-induced Ca²⁺ influx is characterized by a biphasic time course (Fig. 1A, peak 1). A brief application of caffeine shortly after the end of a second high K⁺ pulse causes an additional [Ca²⁺] peak due to Ca²⁺ release from intracellular stores via caffeine-sensitive Ca²⁺ release channels (Fig. 1A, peak 2), which is followed by a fast decay of [Ca²⁺] and then a secondary rise of [Ca²⁺] (hump of [Ca²⁺] following peak 2). The fast decay and subsequent slow rise of [Ca²⁺] which occur after Ca²⁺ release from ER (e.g. after peak 2 in Fig. 1A) can be accounted for by the existence of a fast Ca²⁺ reuptake mechanism, which is activated by Ca²⁺ release and the resulting local increase in the concentration of Ca²⁺ around the ER. This mechanism, called release-activated Ca²⁺ transport or 'RACT', has been described in our previous paper (Cseresnyés et al. 1997). An important possible functional role of RACT may be to restore Ca²⁺ to the ER immediately after Ca²⁺ release from ER Ca²⁺ stores, thereby conserving store Ca²⁺.

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Figure 1. Different oscillation patterns evoked by prolonged caffeine exposures in frog sympathetic neurones A, the response of a sympathetic neurone to 50 mM K+ (peak 1; filled vertical bar beneath record), 50 mM K+ followed by a short pulse of 10 mM caffeine (peak 2; open vertical bar) and 10 mM caffeine applied for 10 min (peak 3 and after; open horizontal bar; gap corresponds to 1 min) are shown, followed by the response to a repeated 50 mM K+ exposure (peak 4; gap indicates 3·5 min). The large [Ca2+] oscillations induced by the prolonged caffeine pulse (termed 'big oscillations' or BOs) were terminated by 20 µM ryanodine (Ry) added to the caffeine solution (filled horizontal bar). B, another neurone was tested with a protocol similar to the one shown in A (the gap corresponds to 1 min). The [Ca2+] oscillations started with large peaks (BOs) and then continued with small transients, termed 'small oscillations' or SOs. Twenty micromolar ryanodine blocked the small oscillations. C, in another neurone, 10 mM caffeine induced oscillations which consisted of [Ca2+] peaks of decaying amplitude ('decaying oscillations' or DOs). D, the time course of cytosolic [Ca2+] in a neurone in which a prolonged application of caffeine induced [Ca2+] oscillations which were BOs but the oscillation frequency was much smaller than in the previous examples. Basal [Ca2+] increased gradually in the interpeak regions before the next [Ca2+] spike was initiated. The dashed line beneath the start of the record indicates the zero level of [Ca2+].

Prolonged application of 10 mM caffeine induces [Ca²⁺] oscillations

Earlier studies have shown that when RyRs are activated over a prolonged period of time, the initial [Ca²⁺] transient is in many cases followed by subsequent additional periodic increases and decreases of [Ca²⁺] (Kuba & Nishi, 1976; Nohmi et al. 1992). In neurones, when 10 mM caffeine was applied together with elevated extracellular K⁺, [Ca²⁺] oscillations were induced and maintained for periods of 13-14 min (Lipscombe et al. 1988a, b; Friel, 1995a). In this case, Ca²⁺ influx across the plasma membrane presumably contributes to maintaining the Ca²⁺ content of the cell. However, even without the additional influx of Ca²⁺ activated by depolarization due to an elevated level of K⁺, oscillations at frequencies of 0·55-0·83 min^-1 have been observed to last for at least 7-8 min in the presence of 3-10 mM caffeine in bullfrog sympathetic neurones (Nohmi et al. 1992). In the present experiments, 10 mM caffeine was administered to frog sympathetic neurones bathed in Ringer solution containing only 2 mM K⁺, and the resulting oscillations of cytosolic [Ca²⁺] were monitored.

Application of 10 mM caffeine for 9·5 min to the neurone in Fig. 1A (bar under record) caused a series of [Ca²⁺] oscillations in which a first very large peak of [Ca²⁺] (1·2 µM, peak 3) was followed by a series of big [Ca²⁺] transients ('big oscillations' or BOs; n = 21) of similar amplitude (about 350 nM). When 20 µM ryanodine was added to the caffeine solution (Fig. 1A), the oscillations ceased after three additional peaks, indicating the involvement of RyRs in maintaining the [Ca²⁺] oscillations. Prior to ryanodine application the interpeak interval slowly increased during exposure to 10 mM caffeine, and the addition of ryanodine further increased the intervals. However, the neurone did not deteriorate significantly during the long caffeine and ryanodine exposure, as indicated by the similarity of the high K⁺ responses after (Fig. 1A, peak 4) and before (peak 1) the caffeine exposure and the resulting oscillations. Note that in order to resolve the time course of the fast [Ca²⁺] transients during the oscillations, the data acquisition rate was four times higher when the oscillations were recorded (compare the time scales during the oscillations and for the start and end of the record in Fig. 1A; see Methods).

In another neurone, the strong activity and relatively rapid turn off of RACT were again indicated, respectively, by a rapid decline of [Ca²⁺] followed by a delayed rise of [Ca²⁺] when caffeine was applied briefly immediately after a high K⁺ exposure (Fig. 1B, peak 1 and hump following peak 1). Prolonged exposure of the same neurone to caffeine induced [Ca²⁺] oscillations, which were again recorded at a four times higher time resolution (Fig. 1B, after break in record). During the long exposure to 10 mM caffeine, an initial large and fast [Ca²⁺] transient was evoked (peak 2), and was followed by a series of fast [Ca²⁺] peaks of approximately equal amplitude of about 350 nM. As a new phenomenon, a small peak, corresponding to a rise of [Ca²⁺] of about 35-45 nM, appeared between each pair of large peaks in this record. After 2·5 min, the large peaks disappeared but the small oscillations (SOs) continued (n = 5). Ryanodine (bar beneath the record) was less effective in terminating the small amplitude oscillations than in terminating the big oscillations. It took 2 min and 13 small oscillations before the transients disappeared. The ryanodine effect on the small oscillations (SOs) may also be due to the depletion of the ER Ca²⁺ stores. This may explain why it takes longer for ryanodine to stop the small amplitude oscillations than the big oscillations.

In another cell, the oscillation pattern consisted of spikes of decaying amplitude ('decaying oscillations' or DOs, n = 7) following the first initial [Ca²⁺] transient during the long caffeine exposure (Fig. 1C, peak 1). After about 3 min the oscillations continued with small peaks. Peak 2 might contain an artificial component and a small and fast spike superimposed, the unusually wide transient being caused for example by a small piece of fluorescent tissue floating in front of the lens.

There was no sign of deterioration of neurones despite the appearance of small amplitude [Ca²⁺] oscillations, as shown in other neurones by comparing the shapes of high K⁺ responses before and after the long caffeine exposure (not shown).

Decreasing oscillation frequencies characterize [Ca²⁺] oscillations

The interpeak intervals were measured for every data record by using a peak-search routine, and the oscillation frequencies were calculated as the inverse of the intervals. Figure 2A-C shows the time dependence of the oscillation frequencies for the experimental records shown, respectively, in Fig. 1A-C. The BOs were characterized by a nearly linear decrease in oscillation frequency with time, with ryanodine treatment causing the curve to flatten (Fig. 2A). When analysing the more complex scenario shown in Fig. 1B, the first part of the record (BOs) showed a linear time dependence, whereas after the switch to small oscillations (SOs) the frequency decayed more rapidly with time (Fig. 2B). However, the absolute values of the oscillation frequencies were significantly higher for SOs than for BOs (compare square symbols with circles in Fig. 2B). In the presence of ryanodine, the few oscillations that continued before the cessation of oscillations exhibited no clear tendency that could be tracked (filled symbols in Fig. 2B).

When the decaying oscillations (DOs) were tested for the time dependence of the oscillation frequencies (Fig. 2C), it was found that the frequency values decreased 2·5-4 times more rapidly than those of the BOs during the first 100 s, after which the frequency curve flattened (Fig. 2C). In DOs, the small amplitude spikes were less frequent than the transients related to SOs (compare Fig. 2C with B).

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Figure 2. Time dependence of oscillation frequency for the records shown in Fig. 1 A, the peak-to-peak time intervals of the record in Fig. 1A were measured and the oscillation frequencies were calculated as the inverse of the time intervals. Values corresponding to BOs before ryanodine exposure (the start of ryanodine exposure is indicated by the arrow) are displayed as open circles whereas frequencies in the presence of ryanodine (before cessation of oscillations due to ryanodine; cf. Fig. 1) are shown as filled circles. The continuous and dotted line is the linear regression fitted to the open symbols. B, frequency data of the record shown in Fig. 1B are plotted as open circles (BOs), open squares (SOs without ryanodine) and filled squares (SOs in the presence of ryanodine). The start of ryanodine exposure is indicated by the arrow. The continuous and dotted straight line is the linear regression of the BO data while the continuous and dotted curve is a single exponential plus constant fit of the SO points ( = 52·6 s). C, the time dependence of the oscillation frequency for the record shown in Fig. 1C (DOs) is plotted with open triangles. The continuous and dotted curve is a single exponential plus constant fit, the time constant of which was 39·3 s.

Interpeak frequencies were measured for all the experimental records of BOs, SOs and DOs, and the time and spike-number dependence of the frequencies were plotted in Fig. 3. Both the time and the spike-number dependence showed that the collected data fell into two apparently separate groups: significantly higher frequencies characterized the SO group, with only very few SO points falling into the region of the lower-frequency group. The BOs and DOs were both characterized by lower frequencies and the data belonging to BOs and DOs fell into the same region on the frequency plots (Fig. 3). These data may indicate that the DOs are more similar to BOs than to SOs.

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Figure 3. Time and spike-number dependence of the oscillation frequency for all neurones A, interpeak intervals were measured in every record of oscillations and the frequency was plotted as a function of the elapsed time. Data corresponding to big oscillations are presented as filled circles whereas small oscillations are shown by open circles. The data corresponding to DOs are represented by circles with a cross. The time scale starts at the peak of the first transient following the initial large [Ca2+] response. B, the same data as in A plotted as a function of the spike number. Spike no. 1 is the first [Ca2+] transient following the initial, large response. BOs are represented by filled circles, SOs by open circles and DOs by circles with a cross.

Model simulations of BOs, SOs and DOs

Numerical solutions of eqns (2)-(7) provided the simulated time courses of the cytosolic and store [Ca²⁺]. The model used in our earlier studies (Cseresnyés et al. 1997) was able to simulate the neuronal responses not only to short depolarizations and brief exposures to caffeine (Cseresnyés et al. 1997) but also to long caffeine pulses as well. However, our experimental data showed that the frequency of all three types of oscillations (BOs, SOs and DOs) decreased with elapsed time or increasing spike number, which the original model could not reproduce. A new mechanism was therefore needed to enable the model to simulate the observed slow-down of the [Ca²⁺] oscillations. The best candidate appeared to be a Ca²⁺ influx via the PM (see Discussion). The model simulation shown in Fig. 4A-C incorporated a Ca²⁺-dependent inactivation of the PM Ca²⁺ influx (eqn (7), Methods) as an additional mechanism in order to gradually decrease the frequency of the [Ca²⁺] oscillations.

The simulation in Fig. 4A (model parameters listed in Table 1) corresponds to the experimental situation in Fig. 1A. A short depolarization induced an abrupt rise of [Ca²⁺] (Fig. 4A, peak 1) which then declined along a biphasic decay of [Ca²⁺] when the PM leak conductance was returned to the steady-state value. A brief application of caffeine, following a short depolarization, was simulated (Fig. 4A, peak 2) by decreasing the K_D of the RyR Ca²⁺ activation site to 1/15 of its initial resting value. The model system responded by a sharp rise of [Ca²⁺], corresponding to the Ca²⁺ release from the ER, followed by a fast decay and then a delayed rise of [Ca²⁺]. The simulated response was generally similar to that of the experimental data shown in Fig. 1A. When a long exposure to caffeine was simulated by the same but continued change in K_D, the system responded with a large and sharp peak of [Ca²⁺] (Fig. 4A, peak 3), followed by large periodic transients. The frequency of these oscillations decreased with elapsed time, in accordance with the experimental findings. The effect of ryanodine was simulated by decreasing k_RyR,1 by 40 %, which eventually resulted in cessation of the oscillations. The slow rise in [Ca²⁺] which preceded each oscillation in the simulation (Fig. 4A) was generally not observed in the experimental records (e.g. Fig. 1A). We have been unable to reproduce oscillations without a preceding slow rise in [Ca²⁺] using the present model (see Discussion), although all other aspects of the oscillations were well reproduced by the model.

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Figure 4. Computer model simulations of the experimental data represented in Fig. 1 A, the experimental records of Fig. 1A have been simulated using the parameters shown in Table 1. The calculations were executed as described in Methods. The parameter values not shown in Table 1 were constant in this panel, in panels B and C of this figure and in Fig. 8. These values were: kRyR,1 = 2·0, kPM = 1·2 × 10-6, co = 2000 µM, kPMCA = 0·03, n = 3, kon,PM = 0·0035, kon,R = 0·02, koff,R = 0·03, = 6·0. Units are s-1 for flux coefficients and 'on' rate constants, µM-1 s-1 for 'off' rate constants, µM for KD while (Table 1) and are dimensionless. The high K+ effect (peak 1) was simulated as a 50-fold, step-like increase of the PM leak coefficient for the duration indicated by the length of the filled bar beneath the simulated records. The caffeine effect (peak 2) was simulated as a decrease of the KD of CICR to 1/15 of the initial value for a time period indicated by the open bar under the record. The long application of caffeine was simulated by the same drop of KD for a correspondingly longer time period (peak 3 and after). The ryanodine effect (labelled with the filled bar beneath the model curve) was simulated as a 40 % decrease of the RyR leak coefficient (kRyR,1). The time scale and the [Ca2+] scales of this figure are the same as those of Fig. 1. B, when the parameters in row 2 of Table 1 were substituted into the computer model, the response of the system to high K+ and elevated caffeine (peak 1) was similar to that shown in panel A of this figure. However, the effect of a simulated longer duration exposure to caffeine (peak 2 and after) was different from the one shown in A. During the first 200 s the model system responded with big oscillations, but there were 1-3 small peaks between every pair of BOs. After the first 200 s, the system switched to the small amplitude mode (SOs). The effect of ryanodine was simulated as described in A. C, with the set of parameters in row 3 of Table 1, the model system reproduced the appearance of decaying oscillations (DOs). After the first large transient (peak 1), the amplitude of oscillations decreased until it reached a small level. Very small changes of the koff,PM made these small peaks stable or disappearing; in this panel a value was chosen which resulted in stable conditions for the very small oscillations. D, simulation of BOs with decaying frequency using another version of our computer model, where the Ca2+-sensitive leak coefficient of the RyR (kRyR,1) was inactivated by cytosolic Ca2+. The 'on' and 'off' rate constants for the kRyR,1 inactivation site were 1·5 × 10-3 s-1 and 1 × 10-4 µM-1 s-1, respectively (see also row 4 of Table 1 for other parameter values).

In order to simulate the appearance of SOs, as well as the transitions between BOs and SOs, the RACT rate constants had to be increased and the SERCA rate constants decreased (see Table 1) so that the RACT mechanism for Ca²⁺ reuptake into the ER after Ca²⁺ release was increased (compare k_RACT and k_SERCA in Table 1). The appearance of the depolarization-induced transient followed by a brief application of caffeine (Fig. 4B, peak 1) resembled the shape of the experimental record (see Fig. 1B, peak 1). Decreasing K_D to 1/15 of the initial value to simulate the long caffeine exposure gave rise to a complex [Ca²⁺] oscillation pattern (Fig. 4B). The large initial [Ca²⁺] transient (peak 2) was followed by two fairly large [Ca²⁺] peaks (BOs), after which the simulation produced the appearance of 1-3 small spikes between each pair of large transients. After about 200 s the oscillation pattern changed: the large peaks disappeared and the system switched to the SOs. Application of ryanodine was again simulated as a drop in the RyR leak coefficient, which then decreased the amplitude of SOs and the oscillations finally ceased. The simulation pattern presented in Fig. 4B is in good agreement with the experimental findings shown in Fig. 1B.

Table 1. Values of the model parameters used for the simulations presented in Fig. 4

Panel	kSERCA (s-1)	kRACT (s-1)	KD (µM)	kRyR,0 (s-1)	koff,PM (µM-1 s-1)
A	0·60	2·0	3·0	0·024	1·8 × 10-4	0·6
B	0·25	3·5	4·0	0·012	3·6 × 10-4	0·265
C	0·10	3·65	4·0	0·014	1·8 × 10-4	0·4
D	0·60	2·0	3·0	0·015	n.a. *	0·6

As was shown in Fig. 3, the position of DOs on the frequency plot indicated that DOs might be more similar to BOs than to SOs. The model simulation of DOs was therefore started with the parameter values corresponding to BOs. After adjusting the major model parameters (see Table 1), the model simulations produced the pattern shown in Fig. 4C. Following the initial transient (peak 1), the amplitude of each subsequent [Ca²⁺] transient decreased continuously until the peak amplitude became very small. The frequency of these small oscillations was significantly smaller than that of the SOs (see Fig. 4B), in accordance with our expectations of DOs being more similar to BOs than to SOs (see Fig. 3). The simulation of DOs (Fig. 4C) was in fair qualitative agreement with the experimental data (Fig. 1C).

We also tested the effect of a 50 % increase and a 50 % decrease in each of the 12 individual parameter values in the model on the oscillation frequency and amplitude, as well as on the width of the [Ca²⁺] spikes. The results of these tests are shown in Table 2 for the six parameters which were adjusted to make the simulations similar to the experimental data (Table 2, upper 6 entries) and for the six parameters which remained constant throughout the model simulations represented in this study (Table 2, lower 6 entries). The + and ++, or the - and -- signs correspond to moderate or major changes, respectively. The peak amplitudes of both the initial large transient and of the secondary smaller oscillations were measured and are presented in Table 2, respectively, by the first and second symbols separated by /. As the table shows, only two parameters can change the oscillation frequency without affecting the peak amplitude or width, the PM leak coefficient (k_PM) or the Ca²⁺-sensitive leak coefficient of the RyR release channels (k_RyR,1). The model presented here (Methods) uses the PM leak coefficient to account for the experimentally observed time-dependent decrease of the oscillation frequency. However, based on the data in Table 2, we modified the model to include a cytosolic [Ca²⁺]-dependent inactivation of k_RyR,1 with constant PM Ca²⁺ influx coefficient, to account for the spontaneous decrease of oscillation frequency. In this case an equation similar to eqn (7), but with k_RyR,1 as a substitute for k_PM, was used to calculate the Ca²⁺ inactivation of the leak coefficient of the RyR release channels. The experimental conditions shown in Fig. 1A were simulated with the modified model and the result is shown in Fig. 4D. The similarity between the simulated curve in Fig. 4D and the data curve in Fig. 1A or the k_PM-based simulation in Fig. 4A indicates that either the k_RyR,1-related or the PM-related inactivation mechanism can account for our data quite well. Thus, progressive slowing of the oscillations could be attributed either to a gradual decline in PM Ca²⁺ influx or a steady decrease in RyR sensitivity to Ca²⁺ activation.

For simplicity we have assumed that Ca²⁺ activation of Ca²⁺ efflux via RyR release channels is regulated by global cytosolic [Ca²⁺] (c_i). However, we have also modified our basic model so as to make the Ca²⁺-dependent flux coefficient k_RyR,1 for Ca²⁺ release be dependent on the local [Ca²⁺] (c_lR) at the ryanodine receptor, rather than on global [Ca²⁺] as in the standard model. Exhaustive tests of this model indicated that the modified model was unable to produce oscillations, even when the parameters were chosen from a relatively wide range around the values used in our other simulations (Cseresnyés et al. 1997, and this study). A possible explanation for the lack of oscillations with this model may be that in this model the RyR release channels are all activated in a basically all-or-none manner due to local positive feedback, eliminating the interactions with global [Ca²⁺] which underlie the oscillations in the standard model.

Table 2. Effect of a 50 % increase or a 50 % decrease in the value of each adjusted (top 6 entries) and unadjusted (bottom 6 entries) model parameter on oscillation properties

	50 % increase			50 % decrease
	Frequency	Amplitude	Width	Frequency	Amplitude	Width
kSERCA	--	+/+	+	++	0/-	0
kRACT	-*	++/+	+	--*	--/-	--
KD(CICR)	--	0/0	-	+	0/--	++
kRyR,0	++	-/--	0	--	++/+	+
koff,PM	--	-/0	-	0	+/0	+
	--	++/+	+	++	--/--	-
kon,R	- *	+/0	+	-*	--/0	-
koff,R	0	-/0	0	-	++/0	+
kPM	+	0/0	0	-	+/0	0
kRyR,1	+	0/0	0	--	0/0	0
kon,PM	--	+/0	0	++	+/0	0
kPMCA	++	+/0	-	--	-/0	+

Phase plane diagrams of experimental and simulated records of BOs, SOs and DOs

Plotting the time derivative of [Ca²⁺] as a function of [Ca²⁺] (phase plane plot) provides a very sensitive tool both to characterize the stability of the oscillation patterns and to reveal further details of the similarities or differences between the model simulations and the experimental data. The time derivatives were calculated numerically for both the simulated and measured sets of data and plotted as phase plane diagrams in Fig. 5. Each oscillation cycle corresponds to one full counterclockwise loop in the phase diagrams. The phase diagrams corresponding to the observed (Fig. 1A) and simulated (Fig. 4A) BOs are shown, respectively, in Fig. 5A left and right. Both plots cross the zero level of [Ca²⁺]/t (labelled with a dashed line) in the 250-350 nM range, which corresponds to the relative peak amplitude of the oscillations. The negative values of the phase plots coincide with the decay component of the [Ca²⁺] transients. The value of the derivative became more negative at [Ca²⁺] levels below 150 nM, corresponding to an accelerated Ca²⁺ uptake, driven by RACT late in the decay phase of each oscillation.

The combined appearance of BOs and SOs, shown in Figs 1B (observed) and 4B (simulated), are characterized by the phase diagrams shown in Fig. 5B, the left panel corresponding to the experimental data and the right panel referring to the model simulation. The shapes of these two phase plots were generally similar to those in Fig. 5A. However, the negative parts of the curves occurred at more negative values, and a separate small cycle was present in the diagrams, corresponding to SOs.

The instability of DOs was displayed by the phase diagrams as well, since the successive loops corresponding to consecutive smaller amplitude [Ca²⁺] transients formed a converging system of increasingly smaller cycles (Fig. 5C). The phase plot of the simulated DOs data (Fig. 5C, right) showed a close resemblance to the measured DOs (Fig. 5C, left), especially in the positive territory of [Ca²⁺]/t.

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Figure 5. Phase plane plots of experimental and simulated records of oscillations A, the numerical time derivative of cytosolic [Ca2+], calculated as [Ca2+]/t where [Ca2+] is the difference in [Ca2+] at successive 0·5 s time points and t is 0·5 s, was plotted as a function of [Ca2+]. The left panel shows the experimental data, the right panel corresponds to the simulated oscillations (Figs 1A and 4A, respectively). Background fluctuations of the experimental record around the steady-state [Ca2+] level were filtered out digitally in a routine written in Mathcad 7 Professional. B, the phase diagrams of experimental and simulated [Ca2+] oscillations in Figs 1B and 4B were generated as described in A. C, phase plane plots of experimental and simulated DOs from Figs 1C and 4C were calculated as above.

Neurones not exhibiting [Ca²⁺] oscillations

In 9 cells out of 42, prolonged exposure to caffeine did not initiate maintained oscillations of [Ca²⁺]. Two representative examples of the experimental records from such cells are shown in Fig. 6Aa and Ba. The response of each non-oscillating cell to a high K⁺ pulse was a large increase of [Ca²⁺] followed by an unusually fast decay of [Ca²⁺] after removal of high K⁺ (Fig. 6Aa and Ba, peaks 1). When caffeine was applied during the decay phase of a second high K⁺ response, the caffeine-induced rise of [Ca²⁺] (panels Aa and Ba, peaks 2) was followed by a decay of [Ca²⁺] which did not have a significantly faster rate constant than the high K⁺ response alone. Prolonged application of 10 mM caffeine to these neurones gave rise to only a single [Ca²⁺] transient (panels Aa and Ba, peaks 3), with no appearance of [Ca²⁺] oscillations. The observed behaviour of the other seven non-oscillating cells was similar to those represented in Fig. 6 in exhibiting a rapid decline in [Ca²⁺] after removal of high K⁺ and having usually none but at most one [Ca²⁺] peak after the initial [Ca²⁺] transient during continuous exposure to caffeine.

In contrast with all other figures which presented either only experimental records or only simulations, Fig. 6Ab and Bb presents the model simulations of the experimental records from the non-oscillating neurones (Fig. 6Aa and Ba). To simulate these experimental observations, it was necessary to use the modified model where the Ca²⁺ efflux coefficient of the RyRs (k_RyR,1) was controlled by local, rather than global, [Ca²⁺] (see description of Fig. 4 above). This model was able to reproduce the large high K⁺ response with a fast decay component (Fig. 6Ab and Bb, peaks 1), as well as the absence of an accelerated decay of [Ca²⁺] after a brief caffeine pulse during the decay of a high K⁺ response (panels 6Ab and Bb, peaks 2). As previously mentioned (description of Fig. 4 above), the modified model where k_RyR,1 is controlled by local [Ca²⁺] rather than by global [Ca²⁺] as in the standard model, was unable to produce [Ca²⁺] oscillations. Thus, when this model was used to simulate a prolonged application of caffeine, the result was the appearance of a single transient of [Ca²⁺] with no appearance of [Ca²⁺] oscillations (panels Ab and Bb, peaks 3), as observed experimentally (panels Aa and Ba).

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Figure 6. Experimental observations and model simulations of [Ca2+] responses in cells not exhibiting [Ca2+] oscillations Aa and Ba, two individual neurones, representative of a total of 9 neurones not exhibiting oscillations, were exposed to 50 mM K+ (peaks 1) and 50 mM K+ followed by a brief pulse of 10 mM caffeine (peaks 2). Each neurone was characterized by a large and rapidly decaying high K+ response and a non-potentiated decay of [Ca2+] after the short caffeine pulse following exposure to 50 mM K+. None of these neurones produced maintained [Ca2+] oscillations when subsequently exposed to 10 mM caffeine for an extended period of time (peaks 3). Ab and Bb, respective model simulations corresponding to panels Aa and Ba. The model was modified to include kRyR,1 controlled by local, rather than global, [Ca2+]. The model parameters used in these simulations were: kSERCA = 1 and = 0·24 (panel A) or kSERCA = 0·6 and = 0·4 (panel B) and kRACT = 2, KD = 3, kRyR,0 = 0·024, koff,PM = 1·8 × 10-4, kon,RyR,1 = 0·1, koff,RyR,1 = 3. kon,RyR,1 and koff,RyR,1 are the 'on' and 'off' rate constants of the binding sites for local Ca2+ controlling the RyR Ca2+ efflux rate coefficient.

The standard model, in which k_RyR,1 is controlled by global [Ca²⁺], was also used to try to reproduce the experimental records shown in panels Aa and Ba. The unusually fast decay of [Ca²⁺] after a high K⁺-induced transient rise of [Ca²⁺] could be simulated by increasing k_RyR,0, the Ca²⁺-independent efflux coefficient of the RyR using the standard model. In this simulation (not shown) the increased background leak from the ER (controlled by k_RyR,0) prevented significant accumulation of extra Ca²⁺ in the Ca²⁺ store, decreasing the simulated efflux of Ca²⁺ from the ER during the decay phase of the simulated high K⁺ response and resulting in a rapid, monophasic decay of [Ca²⁺] in the simulation, as observed experimentally. However, since the high background efflux from the Ca²⁺ store prevented the store from accumulating Ca²⁺ under steady-state conditions as well, simulation of a caffeine application during resting conditions resulted in only a very small release of Ca²⁺, which was not in accord with the experimental observations (Fig. 6Aa and Ba). In contrast, when k_RyR,1 was controlled by local [Ca²⁺] the steady-state efflux from the Ca²⁺ store could be kept low, allowing the ER to accumulate Ca²⁺ and generate large amplitude simulated caffeine responses even under resting conditions, as well as the fast decay of [Ca²⁺] after a simulated high K⁺ response (Fig. 6Ab and Bb).

Cellular mechanisms contributing to [Ca²⁺] oscillations

To investigate the importance of the plasma membrane Ca²⁺-ATPase (PMCA) in Ca²⁺ removal during the [Ca²⁺] oscillations, La³⁺ was applied to block the PMCA, and records before and after La³⁺ were compared. A neurone was exposed to 50 mM K⁺ (Fig. 7A, peak 1) and 50 mM K⁺ followed by 10 mM caffeine (peak 2). Strong activity of RACT was indicated by the fast decay and delayed rise of [Ca²⁺] after peak 2. The cell was then exposed to 10 mM caffeine and after recording three [Ca²⁺] transients, 1 mM La³⁺ was added to the 10 mM caffeine solution (bar beneath the record in Fig. 7A). This concentration of La³⁺ was previously shown to inactivate the PMCA in neurones, as indicated by the decrease of the rate of decay of [Ca²⁺] after a high K⁺ response in the presence of La³⁺ (Herrington et al. 1996; Cseresnyés et al. 1997). A slight increase in the amplitude of the [Ca²⁺] oscillations was detected when 1 mM La³⁺ was added to the caffeine-containing solution (Fig. 7A). The individual [Ca²⁺] spikes became wider as a result of the La³⁺ exposure (see Discussion). Note that the oscillation records in Fig. 7, as well as their simulations in Fig. 8, are presented on a more expanded time scale than that used in the preceding figures.

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Figure 7. The importance of various cellular mechanisms in [Ca2+] oscillations A, a neurone was exposed to 50 mM K+ (peak 1), 50 mM K+ followed by a brief (peak 2) and a prolonged exposure to 10 mM caffeine. After the second peak following the initial [Ca2+] transient, the PMCA blocker La3+ (1 mM) was added to the caffeine solution (filled horizontal bar beneath record). Note the expanded time scale for the oscillation records in this and the next figure compared with previous figures. B, in another neurone, prolonged application of 10 mM caffeine induced [Ca2+] oscillations which ceased after 4 peaks. Addition of 2 µM thapsigargin (filled bar under record) to the caffeine solution re-initiated the oscillations with decaying amplitude. After peak 4, the oscillations ceased. C, to test for the possible importance of mitochondria in [Ca2+] oscillations, the mitochondria uncoupler FCCP (5 µM) was applied together with the mitochondrial ATP synthase inhibitor oligomycin (10 µM; filled bar beneath record). In this neurone, the [Ca2+] oscillations without mitochondrial agents exhibited a stable sequence, whereas addition of the two drugs led to a larger [Ca2+] oscillation which was then followed by a delayed rise of [Ca2+] (peak 2). The oscillations stopped after peak 2. Note the different [Ca2+] scale bar for panel C.

The contribution of SERCA pumps in the return of released Ca²⁺ to the ER is significant. In our previous paper (Cseresnyés et al. 1997) it was shown that after a caffeine-induced [Ca²⁺] transient, SERCA pumps represented about 40 % of the total Ca²⁺ reuptake flux, the remaining 60 % being assigned to RACT. The well-known SERCA pump inhibitor thapsigargin (TG) was used to test the SERCA contribution during [Ca²⁺] oscillations in the continuous presence of caffeine. A neurone was exposed to 10 mM caffeine (Fig. 7B), which resulted in a large initial response followed by three oscillations of equal peak amplitude after which the oscillations ceased. Two micromolar TG was then added to the 10 mM caffeine solution (bar under record). After 30 s in TG the oscillations restarted, but the successive peaks became smaller (Fig. 7B, peaks 1-4). The decay rate of [Ca²⁺] after peaks 1-4 was 0·49-0·56 s^-1, compared with the decay rate of the control peaks, 0·81 s^-1. The decreasing amplitude can probably be explained by depletion of the ER Ca²⁺ stores (model simulation, see below), which resulted from the uncompensated loss of Ca²⁺ from the ER in the absence of active SERCA pumps (Thastrup et al. 1990; Cseresnyés et al. 1997). The immediate decrease of the [Ca²⁺] reuptake rate after adding TG and the quantitative value of the decrease in uptake rate are in accord with the previously determined values of the RACT and SERCA rate constants and with the TG independence of RACT (Cseresnyés et al. 1997). The TG concentration used in these experiments (2 µM; n = 3) equalled the highest concentration used in our previous studies (Cseresnyés et al. 1997), and should have been high enough to promptly and completely block the SERCA pumps, whereas the TG insensitivity of the RACT mechanism (Cseresnyés et al. 1997) allowed Ca²⁺ reuptake to function until the ER Ca²⁺ stores were depleted of Ca²⁺, after which the [Ca²⁺] oscillations finally ceased (Fig. 7B, after peak 4). Note that since cytosolic [Ca²⁺] was rising whereas store [Ca²⁺] was falling after TG addition, the resumption of oscillations after TG addition in Fig. 7B indicates that oscillations are initiated by elevated cytosolic [Ca²⁺] rather than by elevated store [Ca²⁺].

Mitochondria have been shown to participate in buffering Ca²⁺ after high Ca²⁺ loads (Gunter & Pfeiffer, 1990; Rizzuto et al. 1993, 1994; Hehl et al. 1996; Herrington et al. 1996), and also in releasing the Ca²⁺ taken up during high Ca²⁺ loads in bullfrog sympathetic neurones (Friel & Tsien, 1994). Moreover, mitochondria play a very important role in providing ATP for a range of energy-consuming cell functions, including the operation of the ATP-dependent Ca²⁺ pumps in the ER and plasma membranes. It has also been shown that mitochondrial inhibition by carbonyl cyanide p-trifluoromethoxy-phenyl hydrazone (FCCP) or carbonyl cyanide m-chlorophenyl hydrazone (CCCP) (Friel & Tsien, 1994; Budd & Nicholls, 1996; Herrington et al. 1996; Huang & Chueh, 1996) leads to a very fast decline in the ATP supply of the cell (Budd & Nicholls, 1996). This shortage of ATP could directly result in lower Ca²⁺-ATPase activity. In our experiments, cells reacted to FCCP exposure with a cessation of [Ca²⁺] oscillations. In Fig. 7C, a neurone was exposed to 10 mM caffeine, and after the first four regular [Ca²⁺] transients were recorded, 5 µM FCCP and 10 µM oligomycin were added to the caffeine-containing solution (bar under record). The subsequent [Ca²⁺] transient was higher than the previous one, and was followed by a large second rise of [Ca²⁺] (Fig. 7C, peak 2). The rise of [Ca²⁺] (peak 2) is probably a result of Ca²⁺ release from the mitochondria, caused by the blocking agents FCCP and oligomycin. The decay rate of [Ca²⁺] after peak 2 was slower than that of the control oscillations (0·46 s^-1 vs. 0·74 s^-1). After the mitochondrial Ca²⁺ release, the oscillations ceased. Since neither RACT (Cseresnyés et al. 1997) nor SERCA is related to mitochondrial function, the lack of oscillations after blocking mitochondria is probably explained by the fast depletion of cytosolic ATP. If so, these data would provide evidence for the involvement of ATP-consuming mechanisms underlying the [Ca²⁺] oscillations, possibly including both SERCA and RACT.

Model simulations of the contributions of different cellular mechanisms to [Ca²⁺] oscillations

To investigate how well the model would describe the drug effects which were presented in Fig. 7, the partial block of PMCA, of SERCA and of SERCA and RACT were simulated by the model. The effect of La³⁺ as a PMCA blocker was simulated by decreasing k_PMCA by 60 % in the model (Fig. 8A) after the first two peaks following the initial large [Ca²⁺] transient. The last three peaks, in the presence of the decreased PMCA rate constant, were of slightly higher amplitude than the control peaks and were significantly wider than the controls. This change of peak width is in good agreement with the experimental data (see Fig. 7A).

The thapsigargin effect was simulated by setting the SERCA rate constant (k_SERCA) of the model to zero. In Fig. 8B, the first three peaks after the initial [Ca²⁺] transient served as controls, after which the oscillations ceased, as in the corresponding experimental record (Fig. 7B). The next four peaks (peaks 1-4) were then produced in the simulation as a result of decreasing k_SERCA to zero to simulate the effect of TG. The re-establishment of the oscillations after blocking the SERCA pump resulted from a rise in cytosolic [Ca²⁺] due to Ca²⁺ efflux from the ER, which was now no longer compensated for by SERCA transport back to the ER. Peak 1 in Fig. 8B was larger than the controls because of the elevated net release of Ca²⁺ from the ER as a consequence of the decreased reuptake due to the complete elimination of SERCA Ca²⁺ transport. The slower rate of [Ca²⁺] decay characterizing peak 1 was also the result of eliminating the SERCA contribution to Ca²⁺ reuptake. Peaks 2-4 in Fig. 8B were of successively decreasing amplitude and had a slow decay component, as observed experimentally (Fig. 7B). The Ca²⁺ depletion of the ER Ca²⁺ store accounted for the successively smaller amplitudes of peaks 2-4, while the lack of contribution from SERCA slowed down the Ca²⁺ reuptake combined with a less active RACT because of the smaller ER Ca²⁺ release. The general tendency shown by the simulation closely resembled the experimental data (Fig. 7B).

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Figure 8. Computer simulations of the drug effects demonstrated in Fig. 7 A, the computer model was started from conditions similar to those in Fig. 4A. The effect of the PMCA blocker La3+ was simulated by decreasing the PMCA rate constant (kPMCA) by 60 % after the second peak of oscillations (filled bar under curve). B, the effect of TG was simulated by decreasing kSERCA to zero (filled bar) after the original oscillations ceased spontaneously. The [Ca2+] transients generated by the model with kSERCA = 0 are shown as peaks 1-4. C, to simulate the effect of mitochondrial inhibition on oscillations of the model system, a second intracellular Ca2+ store was introduced into the system (see Results). In the simulation presented here, the model system produced five [Ca2+] transients after the initial response (peak 1) with the original parameter settings. At this point, the rate constant characterizing the Ca2+ uptake into the second Ca2+ store was set to zero, resulting in a first-order release of Ca2+ from the second Ca2+ store to simulate the FCCP effect on inducing Ca2+ liberation from the mitochondria. Simultaneously, kSERCA and kRACT were set to zero while kPMCA was decreased by 40 %. After the resulting [Ca2+] transient and a secondary rise of [Ca2+] (peak 2), the oscillations ceased. The model parameters in these simulations were: kSERCA = 0·6, kRACT = 1, kRyR,0 = 0·024, koff,PM = 3 × 10-4 (panel A) or kSERCA = 0·9, kRACT = 2·75, kRyR,0 = 0·024, koff,PM = 8 × 10-5 (panel B) or kSERCA = 1·2, kRACT = 2, kRyR,0 = 0·015, koff,PM = 1·8 × 10-4 (panel C), KD = 3 and = 0·6.

Since the mitochondrial Ca²⁺ fluxes may be relatively minor compared with other fluxes generating the oscillations (Friel & Tsien, 1994; Herrington et al. 1996; Huang & Chueh, 1996; Cseresnyés et al. 1997), the effect of the mitochondrial blockers FCCP and oligomycin may be more related to the depletion of the cell's ATP reserves than to blocking a direct mitochondrial contribution to the fast Ca²⁺ fluxes underlying [Ca²⁺] oscillations. If the ATP/ADP ratio drops when mitochondria are blocked, the Ca²⁺ transport mechanisms which require ATP will be slowed down significantly. To simulate the effect of a massive drop in the cell's ATP supply, the rate constants of SERCA and RACT were set to zero and k_PMCA was decreased by 40 % after the first five [Ca²⁺] spikes following the initial transient (Fig. 8C, peak 1). The remaining 60 % of the total Ca²⁺ efflux via plasma membrane Ca²⁺ transporters would correspond to Ca²⁺ movements via the Na⁺-Ca²⁺ exchanger, which is significant in these neurones (see Cseresnyés et al. 1997) and would not be directly abolished by a decrease in cytosolic ATP levels. In addition, the direct effect of mitochondrial inhibition on mitochondrial Ca²⁺ storage was simulated as a first-order release of Ca²⁺ from a hypothetical second intracellular Ca²⁺ store which for simplicity was assumed not to participate in the preceding Ca²⁺ movements so as not to influence the model oscillations prior to mitochondrial inhibition. The resulting release of Ca²⁺ from the hypothetical second store roughly mimicked the release of mitochondrial free Ca²⁺ after the mitochondria were inhibited by FCCP and oligomycin. The result of this simulation was similar to the experimental effects of mitochondrial inhibition (Fig. 7C) in exhibiting a secondary rise of [Ca²⁺] (Fig. 8C, peak 2) followed by a slow decay of [Ca²⁺] and the elimination of any further oscillations. In other simulations (not shown), the same simulated release of Ca²⁺ from the second intracellular store but without inhibition of ATP-dependent pumps produced a similar rise and fall in [Ca²⁺], after which the oscillations resumed, indicating that simple release of extra Ca²⁺ from a second store would not halt the oscillations.

	DISCUSSION

Top Abstract Introduction Methods Results Discussion References

The present report describes the existence and properties of three distinct patterns of caffeine-induced [Ca²⁺] oscillations in frog sympathetic ganglion neurones. Two patterns exhibited constant amplitude [Ca²⁺] oscillations, the big amplitude oscillations (BOs) and small amplitude oscillations (SOs), whereas the third pattern exhibited declining amplitudes (DOs). However, each type of pattern of oscillation was characterized by a decreasing frequency of oscillation with time during the oscillations.

A single computer model was capable of simulating the BOs, SOs and DOs by varying the values of the rate constants and Ca²⁺ affinities of several Ca²⁺ transport pathways out of the cytosol and Ca²⁺ flux pathways into the cytosol. The parameters actually adjusted to achieve the simulations of the three patterns of oscillations were k_SERCA, k_RACT, K_D, k_RyR,0, koff,PM and (see Table 1). The similarity between the experimental data and the model simulations after these adjustments of parameter values was generally quite good. In the case of the modelling of BOs and SOs, both the ER Ca²⁺ content and the amount of the cytosolic free Ca²⁺ decreased abruptly after a large initial [Ca²⁺] transient. However, in both cases the subsequent simulated [Ca²⁺] transients corresponded to a steady-state situation: the ER Ca²⁺ content and the cytosolic free Ca²⁺ returned to about the same interpeak values, resulting in sustained steady-state oscillations of approximately constant amplitude. In contrast, in the case of DOs the set of model parameters corresponded to a situation where the ER did not reload completely between consecutive simulated [Ca²⁺] peaks and where a net loss of cytosolic free Ca²⁺ increased continuously from peak to peak until the system switched to the small peak mode (model simulation, data not shown).

Decline in oscillation frequency with time

A decline in the oscillation frequency with elapsed time during a series of BOs, SOs or DOs was a consistent finding in these experiments. The time dependence of the decline in oscillation frequency was linear for BOs (Fig. 2A and B), while the SOs and DOs exhibited an exponential decay. However, ignoring the small peaks, the time course of decline in the DO frequency values would also have been considered to be linear. Since the initial phase of an exponential function can be approximated by a linear function, the apparent discrepancy between the linear and exponential time dependence could be resolved if the individual cells were characterized by different time constants. In this case, BOs in Fig. 2A and B might have been cells where the mechanism behind the decline of the oscillation frequency had a time constant much longer than the time of the experiment, giving an apparently linear time dependence over the initial phase of the exponential decline. The cells where SOs and DOs were detected (Fig. 2B and C), however, might have a smaller time constant and thus exhibited an exponential decline in oscillation frequency. In Fig. 3, which represents all the oscillation frequency data, it can be seen that the SOs group is characterized by higher frequencies of oscillation than BOs or DOs. The values corresponding to DOs are well within the area of the BO values, indicating that DOs are not significantly different from BOs with regard to the oscillation frequency, but are distinct from SOs.

The actual mechanism underlying the decline of the oscillation frequency is not known. Other reports in the literature (Homa & Swann, 1994; Tse et al. 1994; Swann & Lai, 1997) have described a similar slow-down of oscillation frequency in human and mouse oocytes and in gonadotrophs. However, previous reports have not provided a satisfactory explanation for the slowing, nor has any model simulation of the slowing been presented. In the literature, the frequency of oscillations is dependent either on how quickly the ER Ca²⁺ stores refill with Ca²⁺ or on how fast the cytosolic [Ca²⁺] reaches the threshold for ER Ca²⁺ release by CICR (Berridge, 1990; Stucki & Somogyi, 1994; Friel, 1995a, b; Lukyanenko et al. 1996). In our model, in the case of BOs, the mechanism underlying the slow-down of the oscillation frequency had to leave the oscillation amplitude constant, as observed experimentally, which led to the conclusion that the loading status of the ER Ca²⁺ stores had to be the same before each [Ca²⁺] spike. A mechanism which progressively decreases the rate of increase of cytosolic [Ca²⁺] prior to the initiation of each oscillation thus seemed to be a likely possibility for the slow-down of the oscillations observed here. Experimental evidence indicates that abruptly decreasing the rate of Ca²⁺ entry into a neurone by lowering extracellular [Ca²⁺] during caffeine-induced oscillations in partially depolarized neurones does decrease the oscillation frequency (Friel, 1995a). Thus, a natural candidate for producing a gradual decrease in oscillation frequency would be a gradual decrease of the rate of Ca²⁺ entry into the cell over the course of the oscillations. We achieved this effect in the model by introducing a cumulative Ca²⁺-dependent inactivation of the Ca²⁺ flux into the neurone via the PM Ca²⁺ channels. We assumed that a system such as calcineurin might be involved in the inactivation process of the PM Ca²⁺ channels (Armstrong, 1989; Lukyanetz, 1997), and that the cumulative slow inactivation of the plasma membrane Ca²⁺ influx could be the consequence of the integrative action of calcineurin. However, by modifying our model we were able to show that a continuous decline in the sensitivity of the RyR Ca²⁺ release channel to activation by cytosolic [Ca²⁺] could also account (Fig. 4D) for the observed decrease in oscillation frequency. It is possible that the simulated slow decline in the RyR release coefficient, and the consequent decrease in oscillation frequency, could be somehow related to the adaptation process of the RyR (Györke & Fill, 1993; Keizer & Levine, 1996), but this remains to be established. Without further studies, it is impossible to provide conclusive evidence regarding the actual biochemical mechanism behind the frequency slow-down.

Transport and flux systems underlying the oscillation

Release-activated Ca²⁺ transport (RACT) was recently discovered and described in frog sympathetic neurones (Cseresnyés et al. 1997). The RACT system is activated when large amounts of Ca²⁺ are released from the Ca²⁺ stores of the ER and effectively translocates Ca²⁺ from the cytosol into the ER. Other pieces of evidence, which specified the location and properties of RACT more closely (see Cseresnyés et al. 1997), showed that an important possible functional role of RACT might be to restore Ca²⁺ to the ER immediately after Ca²⁺ release from ER Ca²⁺ stores, thereby conserving store Ca²⁺ after activation of Ca²⁺ release. Based on this possible role of RACT, the concept of RACT being involved in maintaining [Ca²⁺] oscillations occurs naturally, since RACT may provide a very effective mechanism for saving and then re-using Ca²⁺ during [Ca²⁺] oscillations.

Friel (1995a) has shown that a model system with SERCA and CICR, but without RACT, can simulate large amplitude oscillations, similar to the BOs in our present study, if the leak coefficient of the plasma membrane Ca²⁺ influx is elevated during the simulated effect of caffeine application. This would correspond to his experimental conditions in which caffeine was applied to neurones in partially elevated extracellular [K⁺]. However, in our experiments caffeine was applied without elevated extracellular [K⁺] and the model simulations were performed using the original low value for the plasma membrane leak coefficient (Friel, 1995a; Cseresnyés et al. 1997). Under these conditions, maintained big oscillations were reproduced only when RACT was also active; without RACT, the simulations shown in Fig. 4A and D have produced only three [Ca²⁺] transients, after which the oscillations would cease (simulation not shown). By gradually elevating k_RACT, the number of simulated [Ca²⁺] transients preceding the end of the oscillations was also found to increase.

The presence of an active RACT system in the model was very crucial when attempting to simulate the experimental observations in Fig. 1B and C. The appearance of the small oscillations between each pair of big [Ca²⁺] transients (Figs 1B and 4B), as well as the switch of the system from BOs to SOs, were reproduced only when RACT was active. As Table 1 indicates, DOs are also characterized by an active RACT, with the decaying amplitude of oscillations being the result of the relatively low SERCA activity, resulting in a net loss of Ca²⁺ between successive oscillations (see Results).

In a subgroup of cells, prolonged application of caffeine did not induce maintained [Ca²⁺] oscillations (see Fig. 6). To simulate the unusual response of these non-oscillating cells to 50 mM K⁺ and to brief or prolonged caffeine exposures, the original model had to be modified (see Results). In the altered model, k_RyR,1 was controlled by local, rather than global, [Ca²⁺] and the simulations performed using this model accounted for all the major characteristics of these cells (see Fig. 6). The cellular mechanism which alters the Ca²⁺ dependence of the efflux coefficient of the CICR is not known. However, a hypothesis can be formed which considers that possible structural changes of the ER might alter the mode of Ca²⁺ dependence of CICR. For example, the extraluminal volume within which the Ca²⁺ released from the ER can freely diffuse might possibly be changed when the structure of the ER or of other elements of the cellular structure in the immediate vicinity of the RyRs is altered. The nine non-oscillating cells, two of which are presented in Fig. 6, may correspond to such an altered cellular structure. The reason why certain cells may possess such an altered structure is not known, but might reflect differences in the in vivo position or function of neurones within the ganglia, although changes in the cellular structure during the culture process cannot be excluded. Further studies will be required to determine the actual mechanism behind the special behaviour of these non-oscillating cells.

The effects of various pharmacological agents (Fig. 7) were simulated fairly well by our model (Fig. 8). The slight increase of the oscillation amplitude when PMCA was blocked could simply be explained by having less efflux during the repetitive [Ca²⁺] cycles, leading to better loaded ER Ca²⁺ stores. The wider peaks appeared as a result of the slower re-loading process of the ER Ca²⁺ stores. As shown by the computer simulations, when k_PMCA was decreased, the slower efflux of cytosolic Ca²⁺ increased the level of Ca²⁺-dependent inactivation of the plasma membrane Ca²⁺ channels, resulting in a continuous net loss of cytosolic free Ca²⁺ (simulated data, not shown).

The effect of TG could be explained by abolished SERCA pump activity while RACT was still fully functional. The insensitivity of RACT to TG (Cseresnyés et al. 1997) and previous evidence for TG-independent Ca²⁺ pumps involved in SR/ER Ca²⁺ uptake and [Ca²⁺] oscillations (Foskett et al. 1991; Tanaka & Tashjian, 1993) provide an additional background to this argument. We have observed that addition of TG to the system following the cessation of oscillations re-initiates [Ca²⁺] oscillations (e.g. Fig. 7B). A possible explanation for this phenomenon is that TG resulted in an extra net efflux of Ca²⁺ from the ER, which in turn increased [Ca²⁺] around the RyRs of the ER, elevating the level of [Ca²⁺] above the CICR threshold (model simulation in Fig. 8B). Other examples of TG-induced oscillations, related to net release of Ca²⁺ from intracellular stores, can also be found in the literature (see e.g. Foskett et al. 1991).

The elimination of [Ca²⁺] oscillations after the combined application of the mitochondrial uncoupler FCCP and mitochondrial ATP synthase inhibitor oligomycin might appear surprising since mitochondrial Ca²⁺ fluxes are not included in the model used to simulate the oscillations. However, mitochondria have been shown to be relatively slow Ca²⁺ buffers which would be incapable of transferring Ca²⁺ sufficiently rapidly to participate significantly in fast Ca²⁺ events such as [Ca²⁺] oscillations (Friel & Tsien, 1994; Herrington et al. 1996; Huang & Chueh, 1996; Cseresnyés et al. 1997). Mitochondrial Ca²⁺ fluxes would thus not appear to play a major role in the system underlying the observed oscillations. An alternative explanation for the observed effect of mitochondrial blockers might be based on the ATP-synthesizing function of the mitochondria, which also ceases when the mitochondrial H⁺ gradient is eliminated by FCCP. Even if the reverse mode of action of the mitochondrial ATP synthase is blocked by oligomycin, in the absence of replenishment of the cell's ATP reserves, ATP depletion might cause intracellular ATPase function to cease fairly soon after the mitochondria were blocked (Budd & Nicholls, 1996). The model simulation based on this assumption (Fig. 8C) reproduced the experimental observation (Fig. 7C) fairly well.

Limitations of the present model

An obvious limitation of the present model is the treatment of the cytosol as a single pool of uniform [Ca²⁺]. This eliminates the possibility of modelling the effects of local gradients in cytosolic [Ca²⁺] and possible spatial propagation of [Ca²⁺] signals. Along these lines, it is interesting to note that the simulations in Fig. 4 display a slow rise in [Ca²⁺] between the oscillations, which was usually (e.g. Fig. 1A-C) but not always (Fig. 1D) absent from the experimental records. Although the reason for this discrepancy is not known, it might possibly be related to the lack of consideration of spatial non-uniformities in cytosolic [Ca²⁺], which may be present in the experimental situation but are not included in the model. Thus, an elevation of cytosolic [Ca²⁺] in one region of a neurone might locally initiate a propagated [Ca²⁺] oscillation in the neurone without producing a measurable global change prior to the oscillation, whereas a model with uniform cytosolic [Ca²⁺] as used here may require a gradual rise in [Ca²⁺] to initiate the next oscillation. Future simulations including spatial non-uniformities of cytosolic [Ca²⁺] will be required to further investigate this possibility, as well as other possible effects of non-uniform cytosolic [Ca²⁺].

For simplicity, we have assumed in our model that CICR is regulated by global, not local, cytosolic [Ca²⁺], which would be the case if individual ER release channels or small clusters of channels are not sufficiently close to each other to interact via local Ca²⁺ near an open release channel. As indicated in the Results, when the simulations incorporated only a local [Ca²⁺] dependence of the Ca²⁺-sensitive leak coefficient of RyR release sites (k_RyR,1), the model system was not capable of reproducing maintained oscillations. This indicates that assuming CICR to be regulated by global [Ca²⁺], rather than local [Ca²⁺], was not an unreasonable simplification of the model system.

In conclusion, prolonged applications of 10 mM caffeine induced three different patterns of oscillations: BOs, SOs and DOs. A computer model was used to simulate the experimental data. The model, which included SERCA, RACT, PMCA and RyRs, as well as plasma membrane Ca²⁺ channels which exhibited a cumulative Ca²⁺-dependent inactivation, could account for most of the experimental findings.

	REFERENCES

Top Abstract Introduction Methods Results Discussion References

Armstrong, D. L. (1989). Calcium channel regulation by calcineurin, a Ca2+-activated phosphatase in mammalian brain. Trends in Neurosciences 12, 117-122.	[Medline]
Berridge, M. J. (1990). Calcium oscillations. Journal of Biological Chemistry 265, 9583-9586.	[Medline]
Budd, S. L. & Nicholls, D. G. (1996). A reevaluation of the role of mitochondria in neuronal Ca2+ homeostasis. Journal of Neurochemistry 66, 403-411.	[Abstract]
Cseresnyés, Z., Bustamante, A. I., Klein, M. G. & Schneider, M. F. (1997). Release-activated Ca2+ transport in neurons of frog sympathetic ganglia. Neuron 19, 403-419.	[Medline]
De Koninck, P. & Schulman, H. (1998). Sensitivity of CaM kinase II to the frequency of Ca2+ oscillations. Science 279, 227-230.	[Abstract/Full Text]
Foskett, J. K., Roifman, C. M. & Wong, D. (1991). Activation of calcium oscillations by thapsigargin in parotid acinar cells. Journal of Biological Chemistry 266, 2778-2782.	[Abstract]
Friel, D. D. (1995a). [Ca2+]i oscillations in sympathetic neurons: An experimental test of a theoretical model. Biophysical Journal 68, 1752-1766.	[Abstract]
Friel, D. D. (1995b). Calcium oscillations in neurons. In Calcium Waves, Gradients, and Oscillations, ed. Bock, G. R. & Ackrill, K. Ciba Foundation Symposium, vol.188, pp. 210-234. John Wiley & Sons Ltd, Chichester.
Friel, D. D. & Tsien, R. W. (1992a). Phase-dependent contributions from Ca2+ entry and Ca2+ release to caffeine-induced [Ca2+]i oscillations in bullfrog sympathetic neurons. Neuron 8, 1109-1125.	[Medline]
Friel, D. D. & Tsien, R. W. (1992b). A caffeine- and ryanodine-sensitive Ca2+ store in bullfrog sympathetic neurons modulates effects of Ca2+ entry on [Ca2+]i. Journal of Neuroscience 14, 4007-4024.	[Abstract]
Friel, D. D. & Tsien, R. W. (1994). An FCCP-sensitive Ca2+ store in bullfrog sympathetic neurons and its participation in stimulus-evoked changes in [Ca2+]i. Journal of Neuroscience 14, 4007-4024.	[Abstract]
Grynkiewicz, G., Poenie, M. & Tsien, R. Y. (1985). A new generation of Ca2+ indicators with greatly improved fluorescence properties. Journal of Biological Chemistry 260, 3440-3450.	[Abstract]
Gunter, T. E. & Pfeiffer, D. R. (1990). Mechanisms by which mitochondria transport calcium. American Journal of Physiology 258, C755-786.	[Medline]
Györke, S. & Fill, M. (1993). Ryanodine receptor adaptation: control mechanism of Ca2+-induced Ca2+ release in heart. Science 260, 807-809.	[Medline]
Hanson, P. I., Meyer, T., Stryer, L. & Schulman, H. (1994). Dual role of calmodulin in autophosphorylation of multifunctional CaM kinase may underlie decoding of calcium signals. Neuron 12, 943-956.	[Medline]
Harootunian, A. T., Kao, P. Y., Paranjape, S. & Tsien, R. Y. (1991). Generation of calcium oscillations in fibroblasts by positive feedback between calcium and IP3. Science 251, 75-78.	[Medline]
Hehl, S., Golard, A. & Hille, B. (1996). Involvement of mitochondria in intracellular calcium sequestration by rat gonadotropes. Cell Calcium 20, 515-524.	[Medline]
Herrington, J., Park, Y. B., Babcock, D. F. & Hille, B. (1996). Dominant role of mitochondria in clearance of large Ca2+ loads from rat adrenal chromaffin cells. Neuron 16, 219-228.	[Medline]
Homa, S. T. & Swann, K. (1994). A cytosolic sperm factor triggers calcium oscillations and membrane hyperpolarizations in human oocytes. Human Reproduction 9, 2356-2361.	[Abstract]
Huang, W.-C. & Chueh, S.-H. (1996). Calcium mobilization from the intracellular mitochondrial and nonmitochondrial stores of the rat cerebellum. Brain Research 718, 151-158.	[Medline]
Keizer, J. & Levine, L. (1996). Ryanodine receptor adaptation and Ca2+-induced Ca2+ release-dependent Ca2+ oscillations. Biophysical Journal 71, 3477-3487.	[Abstract]
Kuba, K. & Nishi, S. (1976). Rhythmic hyperpolarizations and depolarization of sympathetic ganglion cells induced by caffeine. Journal of Neurophysiology 39, 547-563.	[Medline]
Kuba, K. & Takeshita, S. (1981). Simulation of intracellular Ca2+ oscillation in a sympathetic neuron. Journal of Theoretical Biology 93, 1009-1031.