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Spatial Distribution of Ca²⁺ Signals during Repetitive Depolarizing Stimuli in Adrenal Chromaffin Cells

Department of Physiology, UCLA School of Medicine, Los Angeles, California 90095

Correspondence: Address reprint requests to Jonathan R. Monck, Dept. of Physiology, Center for Health Sciences, 53-263, UCLA School of Medicine, 10833 Le Conte Ave., Los Angeles, CA 90095. Tel.: 310-825-0932; Fax: 310-206-3788; E-mail: jrmonck{at}mednet.ucla.edu.

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Exocytosis in adrenal chromaffin cells is strongly influenced by the pattern of stimulation. To understand the dynamic and spatial properties of the underlying Ca²⁺ signal, we used pulsed laser Ca²⁺ imaging to capture Ca²⁺ gradients during stimulation by single and repetitive depolarizing stimuli. Short single pulses (10–100 ms) lead to the development of submembrane Ca²⁺ gradients, as previously described (F. D. Marengo and J. R. Monck, 2000, Biophysical Journal, 79:1800–1820). Repetitive stimulation with trains of multiple pulses (50 ms each, 2Hz) produce a pattern of intracellular Ca²⁺ increase that progressively changes from the typical Ca²⁺ gradient seen after a single pulse to a Ca²⁺ increase throughout the cell that peaks at values 3–4 times higher than the maximum values obtained at the end of single pulses. After seven or more pulses, the fluorescence increase was typically larger in the interior of the cell than in the submembrane region. The pattern of Ca²⁺ gradient was not modified by inhibitors of Ca²⁺-induced Ca²⁺ release (ryanodine), inhibitors of IP₃-induced Ca²⁺ release (xestospongin), or treatments designed to deplete intracellular Ca²⁺ stores (thapsigargin). However, we found that the large fluorescence increase in the cell interior spatially colocalized with the nucleus. These results can be simulated using mathematical models of Ca²⁺ redistribution in which the nucleus takes up Ca²⁺ by active or passive transport mechanisms. These results show that chromaffin cells can respond to depolarizing stimuli with different dynamic Ca²⁺ signals in the submembrane space, the cytosol, and the nucleus.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Ca²⁺ is a widely used intracellular signaling molecule that controls a large number of cellular processes (Berridge et al., 2000; Brini and Carafoli, 2000). Ca²⁺ controls short-term events on the millisecond timescale, such as synaptic transmission and muscle contraction, and also controls events that may last hours, such as transcription and synaptic long-term potentiation. The processes that Ca²⁺ controls are located in different parts of the cell, some near the plasma membrane, where they are particularly sensitive to Ca²⁺ entry, and some deep in the cell, where there may be delays in the signal transduction process. In addition, some Ca²⁺-dependent processes are located in organelles, such as the mitochondria and nucleus, where the Ca²⁺ concentration might not be entirely independent of the cytosolic Ca²⁺ concentration but may change in a distinct way that depends on the dynamics and spatial organization of the cytosolic Ca²⁺ signal.

To understand how a particular cellular stimulus, electrical or chemical, regulates a large number of processes in an apparently distinct manner with high fidelity and without unnecessary crossover, we must understand the dynamics and the spatial organization of the Ca²⁺ signal. To do this, we must be able to measure Ca²⁺ at precise locations and at precise times, and in the case of excitable cells at early times. In practice it is difficult to do this for rapid events, as there is always a tradeoff between temporal resolution and spatial resolution. The best methods for measuring high resolution Ca²⁺ signals all have different tradeoffs. Thus, confocal spot detection gets excellent time resolution at a single optically limited location, whereas pulsed laser imaging gets high resolution spatial information at a single time; successive measurements can then be made at different locations or times, respectively (DiGregorio et al., 1999; DiGregorio and Vergara, 1997; Escobar et al., 1994; Marengo and Monck, 2000; Monck et al., 1994). Alternatively confocal line scan can get good time resolution, but the spatial information is limited to one direction (Hernández-Cruz et al., 1990; Nohmi et al., 1992; Segal and Manor, 1992). Each method has distinct advantages and disadvantages, and the most suitable technique will depend on the type of data required and the geometry of the cell. Even with these methods used under optimal conditions, there are still limitations. The amount of data that can be collected is limited by the high intensity laser illumination, the spatial resolution is limited by the optics of the microscope, and the pattern of Ca²⁺ signal is perturbed by the presence of the Ca²⁺ indicator, which binds significant amounts of Ca²⁺ and alters the dynamics of the spatial redistribution of Ca²⁺.

A more recent approach is to use a combination of high-resolution Ca²⁺ measurement and mathematical modeling (e.g., Fink et al., 2000; Issa and Hudspeth, 1996; Marengo and Monck, 2000; Sala and Hernández-Cruz, 1990; Smith et al., 1998). The measurements of the dynamics and spatial distribution of the Ca²⁺ signal are used to build a virtual cell that can reproduce the measured pattern of Ca²⁺ changes. The model can then be used to interpolate between data points. More importantly, the model can also be used to extrapolate to situations that are not experimentally amenable, either to spaces very close to a Ca²⁺ channel or to predict the physiological Ca²⁺ signal in the absence of the Ca²⁺ indicator. In addition, the model can be used to help with experimental design or to make predictions about the properties of endogenous Ca²⁺ buffers or other cellular parameters.

Our interest in this approach came from our interest in the regulation of exocytosis by Ca²⁺ in adrenal chromaffin cells, where several phases of the process, including vesicle fusion from the readily releasable pool and vesicle mobilization to this pool, are thought to be Ca²⁺ dependent. In a previous study, using pulsed laser Ca²⁺ imaging, we found that, on opening of Ca²⁺ channels, the Ca²⁺ gradients develop relatively slowly, in terms of magnitude and rate of spread to the center of the cell (20–30 ms), and dissipate over hundreds of milliseconds, indicating that most of the Ca²⁺ is being bound to an immobile endogenous Ca²⁺ buffer (Marengo and Monck, 2000). By developing a model to explain the development of the Ca²⁺ gradient during the depolarizing pulse and the dissipation after the pulse we were able to make predictions about the properties of an endogenous poorly mobile high capacity Ca²⁺ buffer, and to estimate the kinetics of the Ca²⁺ signal near the cell membrane in the absence of Ca²⁺ indicator (Marengo and Monck, 2000).

Here we extend the study to consider the pattern of Ca²⁺ gradient development, dissipation, and clearance in response to repetitive (train) stimuli. We use the measured Ca²⁺ distributions to develop a virtual cell that can simulate the measured fluorescence changes. We were able to identify three spatially localized Ca²⁺ signals with distinct dynamic properties in adrenal chromaffin cells: a rapid Ca²⁺ spike just beneath the subplasma membrane, a cytosolic signal that increased in a stepwise fashion with each depolarizing pulse, and a slower, delayed increase in the nucleus.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Cell preparation and solutions
Chromaffin cells were prepared from bovine adrenal medullae by enzymatic digestion (Burgoyne et al., 1988) and incubated 1–4 days in culture medium (Marengo and Monck, 2000). For experiments, chromaffin cells were washed in an extracellular medium comprising 120 mM NaCl, 20 mM Hepes, 4 mM MgCl₂, 5 mM CaCl₂, 5 mg/ml glucose, and 1 µM tetrodotoxin (pH 7.25). The standard internal solution used in the patch-clamp pipettes contained 125 mM Cs D-glutamate, 30 mM Hepes, 8 mM NaCl, 1 mM MgCl₂, 2 mM Mg-ATP, 0.3 mM GTP, 0.3 mM Cs-EGTA, and 0.2mM rhod-2 (pH 7.2). These solutions allow measurement of Ca²⁺ currents because Na⁺ and K⁺ currents are prevented. The holding potentials have not been corrected for junction potentials (Neher, 1992).

Measurement of Ca²⁺ gradients with pulsed laser imaging
Ca²⁺ gradients were measured using pulsed laser Ca²⁺ imaging of whole-cell patch-clamped cells, as previously described (Marengo and Monck, 2000; Monck et al., 1994). We used the Ca²⁺ indicator rhod-2 (Minta et al., 1989) and estimate the changes in Ca²⁺ concentration from the fractional fluorescence change (stimulus/control ratio, F_t/F_o) (Monck et al., 1988, 1994). We used a value of 1880 nM for the K_d (Escobar et al., 1997) and 0.013 for (the ratio of the fluorescence of free and Ca²⁺-bound rhod-2, determined in vitro using internal solution with "zero" Ca²⁺ (10 mM EGTA) and saturating Ca²⁺, respectively). Assuming a value of 100 nM for the resting Ca²⁺ concentration, these values give Ca²⁺ concentrations of 240 and 410 nM for F_t/F_o values of 2 and 3, respectively (see Marengo and Monck, 2000, for a discussion of the calibration).

Simulation of the spatial organization of the Ca²⁺ signal
Mathematical model for Ca²⁺ entry, diffusion, and buffering
To simulate the changes in concentration of free Ca²⁺ and other species (e.g., free buffers and buffer-Ca²⁺ complexes) as a function of time and radial distance, we developed a radial diffusion model, which is described fully in Marengo and Monck (2000). This model assumes a uniform entry of Ca²⁺ through Ca²⁺ channels in a spherical cell, and is based on the model of Nowycky and Pinter (1993).

The cell is modeled as a sphere composed of concentric shells of equal thickness (0.1 µm). A simplifying assumption is that each shell represents a well-mixed system and that diffusion within the shell can be neglected. Diffusion of Ca²⁺ and buffers is assumed to occur solely at the shell interfaces and can be described by a function involving shell thickness (i.e., diffusional distance), shell surface areas (inner and outer), and diffusion coefficient. Given these assumptions, Eq. 1 can be represented as a system of first-order, ordinary differential equations describing the concentration of Ca²⁺ (and other diffusible species) in each shell, where the first shell is the outer shell and the Nth shell is the innermost. For the ith shell of N shells, the diffusion equation takes the form:

(1)

where [Ca²⁺]_i is the concentration of free Ca²⁺ in the ith shell, D_Ca is the diffusion coefficient for Ca²⁺, is the shell thickness, V_i the shell volume, and A_i and A_i-1 are the surface areas of the inner and outer surfaces of the ith shell. P_i is a permeability factor for each shell surface; the value ranges from zero, to represent an impermeable membrane, to 1, to represent free diffusion. So for most shell surfaces where there is no membrane or boundary condition, P_i = 1. The boundary conditions specify that diffusion does not occur across the outermost spherical boundary or out of the innermost shell, which is spherical. The boundary conditions were achieved by setting P₀ (outer boundary of first shell) and P_N (inner boundary of Nth shell) to zero.

The permeability factor is also used to make a membrane permeable to one or more species. We used this to make the nuclear membrane permeable to Ca²⁺ and mobile Ca²⁺ buffers (see below) and for making the plasma membrane permeable to Ca²⁺ in the presence of ionomycin. In addition, the permeability factor was used to simulate diffusion between the pipette solution and the cytosol by making the plasma membrane partially permeable (in proportion to the pipette tip size). We assumed that the pipette-cytosol exchange is relatively slow and that we could simulate the diffusional exchange between the pipette and the outer shell of the cytosol as a simple two-compartment model.

The final model also includes components for Ca²⁺ entry through Ca²⁺ channels, Ca²⁺ leak, and Ca²⁺ extrusion, and for Ca²⁺ binding to mobile and immobile Ca²⁺ buffers. The following is a first-order differential equation to describe the change in Ca²⁺ concentration in each shell:

(2)

The three terms of the form d[Ca²⁺]_i/dt)_B^x represent the change in Ca²⁺ concentration due to binding to three Ca²⁺ binding buffers (B^A–B^C), which is calculated with the equation: where [CaB^x] is the concentration of Ca²⁺ bound to buffer X, [B^x] is the concentration of unbound buffer, and k₊₁ and k_-1 are the forward and reverse rate constants for the binding of Ca²⁺ to the buffer. The three Ca²⁺ buffers considered are the Ca²⁺ indicator, EGTA, and endogenous buffer. The last three terms, for Ca²⁺ influx, leak, and extrusion, are only present in the outer shell, i.e., they are zero when i 1. A set of similar equations can be developed for the change in the concentration of Ca²⁺-buffer complex and free buffer for each diffusible buffer:

(3)

(4)

Equation 4 is different from that used previously (Marengo and Monck, 2000), where we make the additional assumption that the diffusion coefficients for Ca²⁺-buffer complex and unbound buffer are equal, so that the total concentration of buffer in each shell is constant and equal to the initial total concentration of buffer. Using this assumption eliminated the need to have a set of equations for the change in concentration of unbound buffer (so Eq. 4 simplified to). The current modification was made to enable us to explore the effect of alternating the restricted diffusion across the nuclear membrane using relative permeabilities.

For selection of values for diffusion coefficients, affinities, and kinetic properties of exogenous and endogenous Ca²⁺ buffers, we used the same values that we previously determined to best simulate the measured Ca²⁺ gradients (Marengo and Monck, 2000). Thus we used 100 µm²·s^-1 for the diffusion coefficient for rhod-2 and Ca²⁺, 800 for the buffer capacity of endogenous buffer, which was assumed to have a K_d of 1 µM and a dissociation rate constant of 0.05 ms^-1. As this buffer is assumed to be immobile, the diffusion coefficient was set to zero. In some simulations, the endogenous Ca²⁺ buffer exhibited positive cooperativity. In these cases, the endogenous buffer was given four Ca²⁺ binding sites, with the same properties as used before and keeping the total number of binding sites constant. For this we set up equations for three additional equilibria: Ca²⁺ binding to buffer with one, two, or three sites occupied. By increasing the affinity of the Ca²⁺ binding to buffer with three occupied sites, we were able to simulate positive cooperativity. For the simulations in Fig. 7, B and C, the affinity of this site was increased to 10 nM. We used a Ca²⁺ current of 210 pA, as previously determined (Marengo and Monck, 2000). Ca²⁺ channel rundown was simulated empirically from the measured decrease in Ca²⁺ current with pulse number. For example, the Ca²⁺ currents were reduced to 88.6 ± 1.33% (n = 15) and 74.0 ± 2.1% of the initial values after 5 pulses and 10 pulses, respectively. All other Ca²⁺ buffer and Ca²⁺ transport parameters were as given in Marengo and Monck (2000).

View larger version (37K): [in this window] [in a new window]   FIGURE 7  Simulation of dynamics of Ca2+ gradients during repetitive stimuli. A virtual cell describing the pattern of Ca2+ distribution after stimulation with repetitive depolarizing stimuli was used to simulate fluorescence and Ca2+ distributions under experimental protocols similar to those used for the measurements in Figs. 1 and 5. This model extends the model of Marengo and Monck (2000) by introducing three new features: Ca2+ channel inactivation (see Methods), Ca2+ clearance by the patch pipette (see Methods and Fig. 6), and a centrally located nucleus. Three different mechanisms were used to try and replicate the experimentally observed results. (A) The nucleus was given active Ca2+ transport mechanisms for uptake and efflux, both with first-order dependence on Ca2+. Here we used a Vmax of 50 pmol·cm-2·s-1 for both Ca2+ uptake and efflux and a Km of 0.2 µM and 0.75 µM, respectively. To simulate our experimental conditions, we included 0.3 mM rhod-2 and 0.2 mM EGTA as exogenous mobile Ca2+ buffers that are introduced through the patch pipette, and assumed an endogenous immobile buffer with the properties previously estimated (0.968 mM concentration with Kd = 1 µM, kon = 50m M-1·ms-1 and kon = 0.05 ms-1 to give a buffer capacity of 800). The nucleus was given 1% of the cytosolic Ca2+ buffer concentration. (Left) Time course of simulated changes in fluorescence (expressed as Ft/Fo). The different lines represent the time courses in the outer 100 nm shell and shells 1, 2, 3 (cytosolic), 4, 5, and 6 (nuclear) µm from the cell membrane. (Middle) Profiles of simulated fluorescence gradients taken after each pulse (black lines) and at 20-s intervals thereafter (colored lines). (Right) Profiles of simulated fluorescence gradients after accounting for the blurring effect of out-of-focus light introduced by the imaging optics. (B) Simulation using a model with a passive mechanism for the nuclear Ca2+ distribution is used instead of an active mechanism. Here we assume that the nucleus is permeable to Ca2+ and mobile buffers to an extent that movement is restricted to 0.2% of that occurring by diffusion without the nuclear membrane. To get the gradient in the nucleus, we assume that the Ca2+-rhod-2 complex binds to nuclear constituents resulting in net accumulation of indicator. In this simulation, 53% of the Ca2+-indicator complex and 0.5% of the free indicator are bound to nuclear sites at steady state. In these simulations, the endogenous buffer in the cytosol was given four binding sites and positive cooperativity introduced for binding of the fourth Ca2+ ion, as described in Methods. This positive cooperativity increases the buffer capacity at higher Ca2+ concentrations, which explains the smaller changes later in the train of pulses in B and C (compared to A). (C) Simulation using a model with a mechanism where the fluorescence difference between the cytosol and the nucleus was generated by assuming different properties of the indicator in the nucleus. In this case, the Fmax/Fmin was five times larger in the nucleus. Increasing this ratio did not increase the difference between the cytosol and nucleus. As in the simulation shown in B, the nucleus permeability to Ca2+ and mobile buffers is 0.2% of that occurring by free diffusion, the cytosolic Ca2+ buffer was given four binding sites, and positive cooperativity for binding the fourth Ca2+ ion.

Simulation of the Ca²⁺ signal in the nucleus
A nucleus centered on the center of the cell was simulated by introducing a barrier between two shells at the appropriate location (usually 40 shells from the cell surface, giving a nuclear radius of 2.1 µm). This barrier was either completely impermeable or given a partial permeability by changing the permeability factor for the surface representing the position of the nuclear membrane, e.g., for 1% of free diffusion we used P_Nuc = 0.01 (subscript "Nuc" refers to the position of the nucleus, i.e., when i = 40). In some cases, the permeability of the nuclear membrane to Ca²⁺-bound indicator was set to different values depending on whether the diffusion was into or out of the nucleus. In this case, Eq. 4 was modified as follows:

(5)

and where P_Nuc was modified depending on the direction of movement. This modification allowed us to explore some passive mechanisms for changes in nuclear Ca²⁺ concentration.

Active nuclear Ca²⁺ transport was modeled using first-order processes dependent on Ca²⁺ on the cytosolic side and nuclear side of the membrane:

(6)

(7)

where V_max and K_m are the maximum rate and the Michaelis-Menten constants for the Ca²⁺-uptake (superscript "Up") and efflux (superscript "Eff") processes, and the subscript "Nuc - 1" refers to the last cytosolic shell before the nuclear membrane and the subscript "Nuc" refers to the first nuclear shell (the inner surface of this shell, A_Nuc, represents the nuclear membrane). No assumptions about the mechanism are made, apart from the first-order Ca²⁺ dependence. To provide a steady-state Ca²⁺, a constant leak was defined as being equal and opposite to the net Ca²⁺ transport determined by the steady-state Ca²⁺ uptake and efflux at the resting cytosolic Ca²⁺ concentration, calculated using Eqs. 6 and 7.

We also incorporated binding of Ca²⁺ indicator to nuclear constituents, designated as indicator binding constituent (IBC). For this we set up equations for three additional eqiuilibria: binding of free indicator (B^D) to IBC, binding of Ca²⁺ indicator complex (CaB^D) to IBC, and Ca²⁺ binding to indicator bound to IBC. As these three equilibria form a cycle with the Ca²⁺ binding to free indicator, we ran the simulation to achieve a new steady-state before initiating Ca²⁺ entry through Ca²⁺ channels.

Simulating the fluorescence changes and the blurring introduced by the optics
The fluorescence, F, of a fluorescent indicator dye is given by

(8)

where is the ratio of the fluorescence of the free (B^D) and Ca²⁺-bound (CaB^D) species of the indicator. The proportionality constant drops out when the fractional fluorescence change (F_t/F₀) is calculated.

An important component of the model is that it is directly comparable with the measured fluorescence data. However, we cannot directly compare the fluorescence simulations with the experimental images because the observed fluorescence images were obtained with an epifluorescence microscope and are contaminated with out-of-focus information. On the other hand, the simulations provides a "nonblurred" ideal representation of the fluorescence gradients. Therefore, to allow a better comparison with experimental data, we constructed a three-dimensional model of the fluorescence simulations and "blurred" it using the theoretical point spread function of the microscope, as previously described (Marengo and Monck, 2000; Monck et al., 1992).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
We studied the pattern of Ca²⁺ distribution during single and repetitive depolarizing stimuli in patch-clamped adrenal chromaffin cells loaded with fluorescent Ca²⁺ indicators. We used pulsed laser Ca²⁺ imaging to capture Ca²⁺ gradients, which were measured as dynamic fluorescence ratios (F_t/F_o) between the image obtained after the single or multiple depolarizing pulses and an image obtained just before the start of the stimulus.

Ca²⁺ gradients during single and repetitive depolarizing pulses
Fig. 1 shows the pattern of Ca²⁺ distribution after stimulation of patch-clamped adrenal chromaffin cells with different numbers of depolarizing pulses, 50 ms steps from -70 mV to +20 mV at 500 ms intervals (2 Hz). As we have shown before (Marengo and Monck, 2000; Monck et al., 1994), the pattern after a single pulse is a prominent submembrane Ca²⁺ gradient (Fig. 1, A and B, left), with the Ca²⁺ decreasing progressively toward the center of the cell, where there was only a small increase. These Ca²⁺ distributions can be accounted for by Ca²⁺ entry, binding to buffers and by diffusion of Ca²⁺ and the Ca²⁺ buffers, as described in detail (Marengo and Monck, 2000). There is no contribution from Ca²⁺ and IP₃-sensitive intracellular Ca²⁺ stores, as the changes are not affected when intracellular stores are inhibited or depleted. Inhibition of Ca²⁺ and IP₃-induced Ca²⁺ release with ryanodine (five cells) or xestospongin (three cells) resulted in maximum fluorescence changes at the cell border of 1.92 ± 0.12 and 2.06 ± 0.12, respectively, compared to 1.94 ± 0.12 for controls (13 cells). Likewise, the cellular spatial averages were 1.50 ± 0.09, 1.60 ± 0.02, and 1.49 ± 0.06 with ryanodine, xestospongin, and in control cells. In addition, when thapsigargin (n = 6) was added to reduce endoplasmic reticulum Ca²⁺ content, no changes were observed in comparison with control condition (1.87 ± 0.18 and 1.44 ± 0.12 for the maximum signal at border and spatial average, respectively), in agreement with our previous study.

View larger version (24K): [in this window] [in a new window]   FIGURE 1  Dynamics of Ca2+ distribution during repetitive depolarizing stimuli. Ca2+ images and Ca2+ currents were measured during a train of 10 depolarizing pulses (50 ms duration, from -70 to +20 mV at 500 ms intervals (2 Hz)). (A) Dynamic fluorescence ratios representing the Ca2+ distribution after 1, 2, 4, and 5 pulses. (B) Dynamic fluorescence ratios captured after 1, 3, 5, and 10 pulses in a different cell. Fluorescence images were captured before the stimuli (control) and immediately after the pulses (stimulus image) using a pulsed laser imaging protocol (see Methods). Below each image is the fluorescence cross-sectional profile, measured along the black line shown superimposed on the images. Assuming a value of 100 nM for the resting Ca2+ concentration, Ft/Fo values of 2 and 3 give Ca2+ concentrations of 240 and 410 nM, respectively. Note how the prominent Ca2+ gradient apparent after a few pulses is gradually replaced by a more global increase. After 10 pulses, there is a prominent increase in the cell interior. This is typically seen after 7 or more pulses. More examples of the Ca2+ distribution after 10 pulses are shown in Fig. 2.

View larger version (44K): [in this window] [in a new window]   FIGURE 2  The Ca2+ increase in the cell interior colocalizes with the nucleus. The distribution of Ca2+ signal was measured after 10 depolarizing pulses (50 ms duration, from -70 to +20 mV) in four different cells. (Top) Dynamic ratio images, representing the change in Ca2+ distribution, along with corresponding cross-sectional profiles through cell. (Bottom) Bright-field images of the same cells showing the nucleus. The fluorescence images were captured just after the 10th pulse (A, B, and C) or just before the 10th pulse (D). The cells in A, C, and D were stimulated at 2 Hz and the cell in B at 1 Hz. Assuming a value of 100 nM for the resting Ca2+ concentration, Ft/Fo values of 1.8, 3.7, and 5.0 give Ca2+ concentrations of 210, 540, and 830 nM, respectively. Note how the large fluorescence increase appears to colocalize with the position of the nucleus.

Fig. 3 shows an analysis of the fluorescence changes in the cytosolic and nuclear regions, as well as the cellular spatial average. The data are pooled from a number of cells, after stimulation with different numbers of depolarizing pulses. Analysis of the fluorescence changes in the cytosolic and nuclear regions from data recorded from nine cells shows that the nuclear signal lags behind the cytosolic signal for the first five pulses and then becomes larger thereafter (Fig. 3 A). The F_t/F_o values in the "nuclear region" and the "cytosolic region" of the cell after 10 pulses were 3.18 ± 0.17 and 2.75 ± 0.12, respectively, and the difference was highly significant (0.43 ± 0.06, p < 0.001, n = 19). Most of the variation is due to differences in the size of the changes observed in different cells, as the relative time courses of the cytosolic and nuclear fluorescence changes can be seen more clearly when the data are normalized by expressing the changes in the cytosol and nucleus as a percentage of the spatially averaged change throughout each cell (Fig. 3 B).

View larger version (14K): [in this window] [in a new window]   FIGURE 3  Analysis of fluorescence changes during repetitive stimulation. The average fluorescence changes in the whole cell, and the cytosolic and nuclear regions, were measured from images like those shown in Figs. 1 and 2. (A) Average fluorescence changes in the cytoplasm (red circles) and the nuclear region (green circles) after different numbers of pulses during 2 Hz stimulation with 50 ms depolarizing pulses. The data were analyzed from recordings in nine cells, but not every time point was taken in all cells (1 pulse, n = 6; 2 pulses, n = 5; 4 pulses, n = 3; 5 pulses, n = 5, 7 pulses, n = 3; 10 pulses, n = 7). (B) Relative changes in the cytosol and nucleus after normalization for the size of the average fluorescence change in each cell. The changes in the cytosol and nucleus were calculated as a percentage of the spatially averaged change measured throughout each cell before averaging the data for different cells. The lower variation seen after this normalization indicates that most of the variation observed in A is due to differences in the size of the changes observed in different cells. Note that in several cases, the error bars are within the size of the symbols. (C) Cell average data superimposed over the simulated fluorescence gradients (after blurring to allow a realistic comparison) using the model previously developed (Marengo and Monck, 2000). Note that the measured fluorescence increase appears to saturate after 5 or 6 pulses, which is not accounted for in this version of the model.

Role of intracellular Ca²⁺ stores
To study the possibility that the prominent F_t/F_o increase in the cell interior was due to Ca²⁺ release from intracellular stores, we performed a series of experiments using specific inhibitors (Fig. 4). First, the characteristic pattern of a significantly larger Ca²⁺ increase in the nuclear region was not modified qualitatively when the endoplasmic reticulum was depleted with thapsigargin, an inhibitor of reticular Ca²⁺-ATPases (eight measurements obtained in five cells). Second, we observed the same pattern when Ca²⁺-induced Ca²⁺ release was inhibited with ryanodine (10 measurements obtained in 5 cells). Third, the pattern was also unaffected when IP₃ induced Ca²⁺ release was blocked with xestospongin (four measurements in four cells). In addition, inhibition of mitochondria with FCCP plus oligomycin, which will inhibit mitochondrial uptake and deplete any mitochondrial Ca²⁺ stores, had no effect on the pattern of Ca²⁺ distribution (nine measurements in six cells). This latter result is complicated by the fact that the FCCP/oligomycin treatment inhibits the Ca²⁺ current, since the integral of I_Ca during the train in these experiments was 66 ± 11 pC (n = 6), compared to 98 ± 12 (n = 21) in controls. However, although this resulted in a reduction of the spatially averaged Ca²⁺ signal in presence of FCCP (1.94 ± 0.30, n = 6, compared to 2.77 ± 0.16, n = 21, for the controls), the large intracellular Ca²⁺ increase in the nuclear region was still observed.

View larger version (34K): [in this window] [in a new window]   FIGURE 4  The Ca2+ increase in the vicinity of the nucleus is not due to Ca2+ release from perinuclear Ca2+ stores. Histogram of average fluorescence changes for the cytoplasm and the region containing the nucleus under various pharmacological treatments: control; ryanodine (1 mM), to inhibit Ca2+-induced Ca2+ release; xestospongin (10 µM), to inhibit IP3 sensitive stores; thapsigargin (1 µM), to inhibit Ca2+ uptake into reticular stores; and FCCP (1 µM with the addition of 0.2 µM oligomycin), to prevent uptake and release of Ca2+ by mitochondria. The Ft/Fo values for the nuclear and cytosolic regions after 10 pulses were 3.18 ± 0.17 and 2.75 ± 0.12, respectively for controls (difference 0.43 ± 0.06, p < 0.001, n = 19), 2.90 ± 0.27 and 2.65 ± 0.28 for ryanodine (difference 0.25 ± 0.03, p < 0.01, n = 5), 3.16 ± 0.46 and 2.58 ± 0.26 for xestospongin (difference 0.57 ± 0.20, p < 0.07, n = 4), 2.70 ± 0.24 and 2.40 ± 0.21 for thapsigargin (difference 0.29 ± 0.07, p < 0.02, n = 5), and 2.13 ± 0.34 and 1.85 ± 0.28 for FCCP (difference 0.28 ± 0.08, p < 0.02, n = 6).

To confirm that the increase in the nuclear region occurred progressively during the repetitive stimulation and was not just a transient increase during depolarization, we made a series of measurements (eight measurements in five cells) where the images were captured just before the 10th pulse of a 10-pulse train (i.e., 450 ms after the end of the ninth pulse). The Ca²⁺ distribution in these experiments also showed the typical pattern with the pronounced Ca²⁺ increase in the nuclear region (e.g., Fig. 2 D). Moreover, the difference between "nuclear region" and "cytosolic region" was even more pronounced under these conditions (0.69 ± 0.12, n = 5). This suggests that the prominent increase of the signal in the "nuclear region" is produced by a gradual process that occurs throughout the train.

Ca²⁺ clearance and decay of Ca²⁺ signals
After stimulation, the Ca²⁺ concentration returns slowly to resting values. To study this decay of intracellular Ca²⁺ after the train, we obtained images at various times after the end of the last depolarizing pulse. Fig. 5 shows an example of such kind of experiment. The distribution of the fluorescence signal is shown in the images in Fig. 5 A. It can be seen that the fluorescence signal in all parts of the cell decays slowly over several minutes, although the differences in fluorescence signal between cytosol and nucleus remain until the signal has almost returned to resting levels. Fig. 5 B shows the spatially averaged values of fluorescence signal measured in the whole cell area, cytosolic area, and nuclear area for the cell shown of the experiment represented above. The decay of the nuclear signal is delayed a few seconds with respect to the cytosolic signal, presumably reflecting the fact that the nuclear Ca²⁺ changes are after the cytosolic Ca²⁺ concentration changes. Data pooled from several cells show that during the first 4 s after train stimulation ends, the cytosolic signal decreases significantly compared to the values obtained at the end of the 10th pulse (0.31 ± 0.06, n = 6, p < 0.01), whereas there was no significant decrease of the nuclear signal during this period (0.15 ± 0.10, n = 6).

View larger version (26K): [in this window] [in a new window]   FIGURE 5  Ca2+ clearance after stimulation with repetitive depolarizing pulses. Ca2+ images were measured after a train of 10 depolarizing pulses (50 ms duration, from -70 to +20 mV, 2 Hz) to investigate the rate of Ca2+ clearance. (A) Dynamic fluorescence ratios, representing the Ca2+ distribution, captured at various times after the end of the 10th pulse. The control image used for all dynamic ratios was captured just before the first depolarizing pulse. (B) Analysis of fluorescence changes occurring during Ca2+ clearance measured in the same cell as shown in A. The spatial averages for the whole cell (black circles), the cytoplasm (red triangles), and nuclear regions (green triangles) are shown. The decay of spatially average values for the whole cell was fitted both to a single exponential equation (dotted line) of the type (A = 1.78 ± 0.04; = 32.34 ± 1.62; r = 0.996; the asymptote was fixed at 1) and to a double exponential equation (continuous line) (A1 = 0.73 ± 0.41; 1 = 14.90 ± 6.38; A2 = 1.10 ± 0.42; 2 = 49.29 ± 11.70; r = 0.999). The latter avoids the small persistent deviations between the theoretical curve and experimental values seen at the longer times with the single exponential fitting. However, correlation coefficients were very good for both type of equations and we did not find significant differences between them (Fisher test, K. Diem, Scientific Tables, 6th ed, Geigy, Ardsley, NY, 1962). (C) Clearance rates obtained from the fitting of the normalized values from spatial averages in series of measurements obtained from six cells. The continuous lines represent the result of a double exponential fitting. The parameters were A1 = 0.35 ± 0.10, 1 = 7.74 ± 3.46 s, A2 = 0.66 ± 0.10, 2 = 67.77 ± 15.09 s, n = 64, r = 0.953; whereas for single exponential fitting, the parameters were A1 = 0.94 ± 0.02, = 38.76 ± 2.69 ms, r = 0.9333204. (D) Clearance rates obtained from the fitting of the normalized values from cytoplasm and nuclear regions. The continuous lines represent the result of a double exponential fitting performed on the all the individual data points. For clarity, the figure shows the cytosolic and nuclear experimental results expressed as averages taken from data points binned over 2-s intervals between 0 and 20 s, 10-s intervals between 20 and 40 s, and 20-s intervals between 40 and 120 s. The parameters for the shown curves were, for cytoplasm, A1 = 0.27 ± 0.06, 1 = 6.11 ± 2.50 s, A2 = 0.60 ± 0.06, 2 = 61.50 ± 9.61 s, n = 61, r = 0.966; and for nuclear region, A1 = 0.44 ± 0.22, 1 = 11.67 ± 6.81 s, A2 = 0.73 ± 0.22, 2 = 73.27 ± 16.45 s, n = 61, r = 0.947.

We also investigated the possibility that mitochondrial Ca²⁺ uptake could modify the pattern of Ca²⁺ removal from the cell. In these experiments (n = 4), FCCP and oligomycin were used to inhibit the mitochondrial Ca²⁺ uptake. However, these inhibitors did not lengthen the time constant associated with the decay of the spatially averaged signal after the train ( = 34.26 ± 1.77 s). In addition, we studied the effect of Na⁺ removal from external and internal solutions to inhibit the participation of plasma membrane Na⁺/Ca²⁺ exchange mechanism. This treatment also had no effect on the rate of fluorescence decay after the end of the train (A = 0.98 ± 0.03, = 43 ± 0.7 s, r = 0.943, n = 36). However, if we consider only the first 8 s after the end of the train, the cytosolic Ca²⁺ signal decays slower when Na⁺ is removed (slopes were -0.057 ± 0.005 s^-1 and -0.030 ± 0.001 s^-1 for control and zero Na⁺, respectively). These experiments suggest that neither Na⁺/Ca²⁺ exchange nor mitochondrial Ca²⁺ uptake plays a major role in Ca²⁺ clearance under our experimental conditions, although Na⁺/Ca²⁺ exchange may play a minor role.

Our experiments were performed in cells patch-clamped in the whole-cell configuration, where there will be diffusion between the cell and the pipette. To investigate the possible role of diffusional exchange between the cell and pipette, we compared the time constant for Ca²⁺ clearance for individual cells, , with the access resistance, which has been shown to control diffusional exchange between the pipette and the cytosol of patch-clamped cells (Pusch and Neher, 1988). A plot of 1/ against the access conductance G_A is shown in Fig. 6 A. Pusch and Neher (1988) have previously shown that diffusion between a cell and a patch pipette yields a linear plot of 1/ vs. G_A for many water-soluble molecules, including fluorescent Ca²⁺ indicators. There is a good linear fit (slope = 0.25 ± 0.02 s^-1·M, r > 0.99) between 1/ and G_A when the conductance is larger than 90 nS, but for higher resistances (>10 M), the clearance rate deviates from the linear relationship. This suggests that in most of our regular whole-cell conditions, the main mechanism of Ca²⁺ removal from cytosol after the large gradients close to the membrane have dissipated is passive diffusion into the patch pipette, and that it is only when the access resistance is high that the physiological cellular mechanisms predominate.

View larger version (12K): [in this window] [in a new window]   FIGURE 6  Relationship between the Ca2+ clearance rate and the access resistance of the patch pipette. (A) The clearance time constants were measured from the decay of the spatially averaged fluorescence change after repetitive stimulation (single exponential decays determined as described in Fig. 5). The inverse of these clearance rates was plotted against the access conductance of the patch pipette (GA) to allow direct comparison with the data of Pusch and Neher (1988). The parameters for the fit of the straight line through the points with GA > 90 nS were: slope = 0.25 ± 0.02 s-1·M, r = 0.99. (B) The effect of patch pipette access resistance on Ca2+ clearance rate was simulated by calculating diffusion into a pipette of different sizes, mimicking different access conductances. The resulting clearance rates were plotted against pipette area (expressed as a percentage of the total cell surface area), which is proportional to the access conductance (GA). Several curves are shown for different activities of a cellular Ca2+ clearance mechanism. In these simulations, we simulated a plasma membrane Ca2+-ATPase with a Km of 0.83 µM and a Vmax of variously 0 (square symbols), 2 (triangles), 4 (circles), and 10 (inverted triangles) pmol·cm-2·s-1. (C) Effect of patch pipette access resistance on measured clearance rate. The time constants of the experimentally derived clearance rates are plotted against the access conductance (inverse of access resistance). Note that the experimental data are closest to the simulations using a Vmax of 4 pmol·cm-2·s-1, which plateaus at slightly >50 s-1. As the measured clearance rates plateau at slightly <50 s-1, a cellular clearance rate of 5 pmol·cm-2·s-1 (not shown) would best describe the experimental measurements of the clearance rate.

Simulation of Ca²⁺gradients during and after repetitive stimuli
One of the goals of this study is to develop a "virtual cell" describing dynamic and spatial aspects of Ca²⁺ signaling in adrenal chromaffin cells. Our original reason was to use this to investigate the Ca²⁺-dependent regulation of depolarization-induced exocytosis, but the model will also be used to investigate potential mechanisms for the larger fluorescence increases in the nuclear region (see later). We want to use the experimental data on the time course and spatial distribution of the Ca²⁺ increases after depolarizing stimuli to develop a computer model that accurately reproduces the physiological responses. We have previously developed a radial diffusion model that describes the development and dissipation of Ca²⁺ gradients in response to short depolarizing pulses (Marengo and Monck, 2000). This model accounts for the distribution of the Ca²⁺ entering through voltage-activated Ca²⁺ channels by diffusion and binding to endogenous and exogenous Ca²⁺ buffers. Here we extend the model to take account of the Ca²⁺ distribution during repetitive stimulation. In Fig. 3 C, the average values for the whole cell are superimposed over a simulation of the pattern of Ca²⁺ gradients, using the parameters determined to best reproduce the pattern of Ca²⁺ gradients during development and dissipation during and after a single depolarizing pulse (Marengo and Monck, 2000). Although the averages match the simulation well for the first four or five depolarizing pulses, the simulation significantly overestimates the fluorescence changes for seven or more pulses. These results suggest that a more complete model must account for additional mechanisms limiting the total increase in fluorescence. One possible mechanism is Ca²⁺ channel rundown, which usually occurs during a train stimulus. Some Ca²⁺ channel rundown is apparent in Fig1 B, although the extent is less than average in these cells. In our experiments, the Ca²⁺ current is reduced to 88.6 ± 1.33% (n = 15) of the initial value after five pulses and to 74.0 ± 2.1% after 10 pulses. We have simulated the rundown empirically, as described in Methods, but the reduced Ca²⁺ influx is insufficient to account for the smaller fluorescent changes after 7–10 pulses (data not shown). Other mechanisms that could reduce the fluorescence changes during repetitive stimulation are the Ca²⁺ clearance mechanisms for restoring resting Ca²⁺ levels, which, as discussed in the last section, involves mainly diffusional exchange with the pipette under our experimental conditions. The pipette Ca²⁺ clearance is included in the simulation shown in Fig. 7 A, but is also insufficient to account for the fluorescence changes observed. We found that the best way of reducing the Ca²⁺ changes was to use an endogenous Ca²⁺ buffer with four binding sites and introduce positive cooperativity for the fourth Ca²⁺ bound (see Fig. 7, B and C). The rationale for this was that most EF-hand Ca²⁺ binding proteins have four Ca²⁺ binding sites, and cooperativity has been observed in several cases (Iida, 1988; Leathers et al., 1990; Morimoto and Ohtsuki, 1994; Olwin and Storm, 1985; Teleman et al., 1983). However, we stress that these changes were introduced so that our simulations better reproduced the measured fluorescence changes in the cytosol and not because we have any experimental evidence that the endogenous Ca²⁺ binding protein in adrenal chromaffin cells has four Ca²⁺ binding sites or exhibits positive cooperativity.

We used the computer simulations of the expected fluorescence changes as a tool to explore putative mechanisms to account for the larger fluorescence increase in the nuclear region. As shown earlier, comparison of the fluorescent images mapping the Ca²⁺ distribution with bright-field images showed that the large fluorescence increase inside the cell colocalized with the nucleus. We also showed pharmacological evidence indicating that Ca²⁺ release from perinuclear Ca²⁺ stores was unlikely to be involved. An alternative explanation is that this larger internal increase occurs due to the presence of a distinct nuclear compartment. To investigate this possibility, we considered several different mathematical models to explain the spatial distribution of the measured fluorescence changes, notably the delayed increase and the large increases at the end of the train. Fig. 7 shows simulations of the fluorescence changes obtained with three types of potential mechanisms that were able to successfully simulate the observed experimental results: one involving active nuclear Ca²⁺ transport mechanisms, the second using a passive mechanism involving diffusion and accumulation of bound Ca²⁺-indicator complex in the nucleus, and the third mechanism with different fluorescence properties of the Ca²⁺ indicator in the nucleus.

Fig. 7 A shows a simulation performed using the modified radial diffusion model of a cell with a nucleus placed in the center of the cell. The nucleus was given active Ca²⁺ transport mechanisms for uptake and efflux, both with first-order dependence on Ca²⁺. Here we used a V_max of 50 pmol·cm^-2·s^-1 for both Ca²⁺ uptake and efflux and a K_m of 0.2 µM and 0.75 µM, respectively. To simulate our experimental conditions, we included 0.3 mM rhod-2 and 0.2 mM EGTA as exogenous mobile Ca²⁺ buffers that are introduced through the patch pipette, and assumed an endogenous immobile buffer with the properties previously estimated (0.968 mM concentration with K_d = 1 µM, k_on = 50 m M^-1·ms^-1, and k_on = 0.05ms^-1 to give a buffer capacity of 800). These were the conditions established in our previous study (Marengo and Monck, 2000) and used in the simulation shown in Fig. 3 C. The nucleus was given 1% of the endogenous cytosolic Ca²⁺ buffer concentration. The rationale for the lower buffer capacity is that the Ca²⁺ binding proteins that are candidate Ca²⁺ buffers are mainly cytosolic proteins (Burgoyne and Geisow, 1989; Heizmann, 1992). The value used is not critical, as when using 10% for the nuclear Ca²⁺ buffer, the nuclear fluorescence and Ca²⁺ changes were suppressed by <5% relative to Fig. 7 A (data not shown). However, similar quantitative results can be obtained with higher or lower nuclear buffer by changing the capacities of the Ca²⁺ transport mechanisms.

The time course of the fluorescence changes simulated with the model (Fig. 7 A) shows many features of the measured fluorescence changes observed during a train of depolarizing pulses. Early on there are prominent submembrane gradients with the increase in the nucleus lagging behind. Then there is the progressively increasing cytosolic signal, and finally the appearance of a larger nuclear increase. The "blurred" fluorescence profiles (Fig. 7 A, right) show that an increase in the nucleus, which appears as an abrupt step increase with respect to the cytosol in the simulated profiles (Fig. 7 A, middle), would be observed as a smooth increase slightly larger than the cytosol due to the blurring effect of the microscope optics.

The second type of mechanism involves passive diffusion of Ca²⁺ and indicator into the nucleus. Restricted diffusion of Ca²⁺ and indicator across the nucleus envelope provides the delayed fluorescence increase, and accumulation of the Ca²⁺-indicator complex in the nucleus accounts for the larger fluorescence increase seen late in the train. Fig. 7 B shows a model simulation where the latter is achieved by assuming that the Ca²⁺-indicator complex binds to intranuclear constituents more than the free form of the indicator. Other studies have indicated that substantial fractions of the Ca²⁺ indicator may be bound to intracellular constituents, particularly in skeletal muscle myoplasm (Baylor and Hollingworth, 1988; Harkins et al., 1993; Konishi et al., 1988), although we know of no specific reports for indicator binding in the nucleus. This model is similar to that shown in Fig. 7 A, except that the passive model for the nuclear Ca²⁺ and indicator distribution is used instead of a mechanism involving active Ca²⁺ transport. Here we assume that the nucleus is permeable to Ca²⁺ and mobile buffers to an extent that movement is restricted to 0.2% of that occurring by diffusion without the nuclear membrane, consistent with what we might expect for diffusion through the nuclear pores. In this simulation, 50% of the Ca²⁺-indicator complex is bound, whereas <1% of the free indicator is bound. The result is net accumulation of the Ca²⁺-indicator complex and a larger fluorescence increase in the nucleus.

A third possible explanation for the larger fluorescence increase in the nucleus, which also involves passive movement of Ca²⁺ and indicator across the nuclear envelope, is shown in Fig. 7 C. Here we assume that the fluorescence properties of the Ca²⁺ indicator are different in the nucleus, so that the fluorescence of the Ca²⁺-bound indicator is increased (i.e., F_max/F_min, the ratio of the Ca²⁺-saturated and free indicator, is increased in the nucleus). This phenomenon has been reported for the Ca²⁺ indicator fluo-4 (Thomas et al., 2000). To reproduce the delay before the large nuclear increase was observed, we also had to assume that the nucleus was partially permeable to Ca²⁺, EGTA, and indicator. As before, we assumed that the permeability allowed diffusion at 0.2% of the rate that occurred for diffusion in the cytosol. Unlike the previous two mechanisms, the larger fluorescence increase is not due to a higher Ca²⁺ concentration in the nucleus, but is solely due to the properties of the indicator fluorescence.

We also used computer simulations to consider a number of other potential mechanisms that we thought might be able to explain the difference in the fluorescence changes observed in the cytosol and nucleus. Mechanisms tested included models involving differences in accessible volume in the cytosol and nucleus, differences in the assumed resting Ca²⁺ concentration in the cytosol and nucleus, differences in diffusion coefficient of Ca²⁺ and/or mobile buffers, differences in affinity or buffer capacity of endogenous buffer in cytosol and nucleus, and differences in the K_d of the Ca²⁺ indicator. However, we were unable to adequately reproduce the observed experimental results with any of these mechanisms. We have only shown the three types of mechanism that were able to reasonably reproduce the relative fluorescence changes in the cytosol and nucleus. The relative merits of these mechanisms as possible explanations for the larger fluorescence increase in the nucleus will be discussed later (see Discussion).

Effect of ionomycin
Fig. 8 shows an experiment where the Ca²⁺ ionophore ionomycin was used to elevate the Ca²⁺ concentration. The ionomycin caused a slow fluorescence increase over 3–10 min (Fig. 8 A) and, as with electrical stimulation, there was a larger fluorescence increase in the nucleus (4.3 ± 0.4 compared to 3.1 ± 0.3, n = 6). The ionomycin treatment gives a larger relative increase in the nucleus (1.38 ± 0.01, n = 6) than electrical stimulation (1.15 ± 0.02, n = 19). As the ionomycin experiments were over longer time spans, the larger F_t/F_o change in the nucleus after ionomycin treatment may be due to slow accumulation of Ca²⁺-indicator complex in the nucleus due to binding, as illustrated by the simulation shown in Fig. 8 B using the same model as described for Fig. 7 B. This simulation also reproduces the larger relative increase in the nucleus with ionomycin than with electrical stimulation (compare Fig. 8 B with Fig. 7 B). Alternatively, the measured results can also be reproduced by a simulation using the model described for Fig. 7 C where the fluorescence properties of indicator are different in the nucleus (Fig. 8 C).

View larger version (20K): [in this window] [in a new window]   FIGURE 8  Effect of ionomycin on the distribution of Ca2+ indicator fluorescence. The Ca2+ ionophore, ionomycin (10 µM), was added to the extracellular medium, and images taken before and at various times afterward. (A) Ft/Fo images calculated from the images taken 4, 6, and 10 min after ionomycin addition, using the image taken before ionomycin addition as the reference (Fo). The profiles through the nucleus along the line indicated are shown beneath. (B) (Left) Simulation of fluorescence time course using the model described for Fig. 7 B, where the higher nuclear fluorescence is due to accumulation of bound Ca2+-indicator complex. In these simulations, the plasma membrane was made permeable to Ca2+ by setting the permeability factor to 0.00015 (see Methods). Note that the changes in the cytosol and nucleus are almost uniform so the lines superimpose for the cytosolic shells (0, 10, 20, and 30 (blue)) and the nuclear shells (40, 50, and 60 (magenta)). (Right) Profiles of simulated fluorescence gradients at 100-s intervals after addition of ionomycin. The profiles were blurred to mimic the effect of out-of-focus light introduced by the imaging optics. (C) (Left) Simulation of fluorescence time course using the model described for Fig. 7 C, where the higher nuclear fluorescence is due to the fluorescence properties of the Ca2+ indicator. (Right) Blurred profiles of simulated fluorescence gradients at 100-s intervals after addition of ionomycin.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

Ca²⁺ signals during repetitive stimulation of adrenal chromaffin cells
Short single depolarizations (10–100 ms) lead to the development of submembrane Ca²⁺ gradients, which dissipate to leave a homogenously elevated cytoplasmic Ca²⁺ concentration. The gradient dissipation comprises a fast phase (tens of milliseconds), mainly due to diffusion, and a slow phase (hundreds of milliseconds), mainly due to slow release of Ca²⁺ from intracellular Ca²⁺ buffers (Marengo and Monck, 2000). The homogenously elevated Ca²⁺ decays to rest relatively slowly (see later for discussion of clearance mechanism). Under these conditions, we can clearly distinguish a fast localized Ca²⁺ signal beneath cell membrane and a slower "global" cytosolic Ca²⁺ signal that persists for seconds.

Stimulation with repetitive stimuli, which might better represent the physiological signal, reveals a different pattern of Ca²⁺ signals. A second, third, or fourth stimulus results in a Ca²⁺ gradient, similar to that after the first pulse, on top of the homogenously elevated "residual" Ca²⁺ that remains after dissipation of the previous gradient. As the number of pulses increases, a larger fluorescence increase in a region near the center of the cell becomes visible and is prominent after 7–10 pulses. At intermediate times the results were variable, with an edge-to-center gradient still clear in some cells (e.g., Fig. 1), and a larger increase in the cell interior in other cells. After 10 pulses, the fluorescence increase in the center of the cell was usually larger than that measured at the cell periphery, and was typically 2–4 times higher than the maximum values obtained for fluorescence gradients at the end of single pulses (Fig. 1).

The large Ca²⁺ increase occurs near the center of the cell, but not at the geometric center. Comparison of the fluorescent images mapping the Ca²⁺ distribution with bright-field images showed that the large fluorescence increase in the cell interior colocalized with the nucleus (Fig. 2). Analysis of the fluorescence changes in the cytosolic and nuclear regions from several cells shows that the nuclear signal lags behind the cytosolic signal for the first five pulses and the then becomes larger thereafter (Fig. 3 A).

One possible explanation for the large fluorescence increase in the vicinity of the nucleus is that there is release of Ca²⁺ from intracellular stores in the perinuclear region. The nucleus is surrounded with endoplasmic reticulum, which serves as intracellular Ca²⁺ stores (Burgoyne et al., 1989; O'Sullivan et al., 1989). In addition, IP₃ induced release of Ca²⁺ from the nuclear envelope has been reported (Gerasimenko et al., 1995; Stehno-Bittel et al., 1995). Thus it is possible that Ca²⁺ release from such stores might contribute to the large Ca²⁺ increase in the cell interior. The presence of out-of-focus light, due to the optical limits of fluorescent microscopy, means that we cannot definitively distinguish between colocalization with the nucleus and colocalization with, for example, perinuclear endoplasmic reticulum or the nuclear envelope. To investigate this possibility, we performed some pharmacological experiments to inhibit or empty such Ca²⁺ stores. However, the pattern of Ca²⁺ gradient was not modified by inhibition of Ca²⁺-induced Ca²⁺ release with ryanodine, inhibition of IP₃-induced Ca²⁺ release with xestospongin, or depletion of intracellular Ca²⁺ stores with thapsigargin, as shown in Fig. 4. In addition, inhibition of mitochondria had no effect. Thus, release of Ca²⁺ from perinuclear Ca²⁺ stores is unlikely to explain the larger fluorescence increase in the vicinity of the nucleus. Furthermore, the measured spatially averaged Ca²⁺ changes after 5–10 pulses were smaller than expected based on predictions with our diffusional model (Fig. 3 C), which argues against an additional source of Ca²⁺ entering the cytosol. Other possible explanations for the observation that the change in nuclear fluorescence becomes larger than the change in cytosolic fluorescence will be discussed later.

Ca²⁺ clearance mechanisms in patch-clamped cells
After the formation of Ca²⁺ gradients, the gradients dissipate to leave a homogenously elevated cytosolic Ca²⁺ concentration (see (Marengo and Monck, 2000)). This elevated Ca²⁺ slowly returns to resting levels (Fig. 5). The most important Ca²⁺ clearance mechanism under our experimental conditions is usually diffusional exchange of Ca²⁺ and Ca²⁺ complexes with mobile buffers in the cytosol with the solution in the patch pipette. As shown in Fig. 6 A, our measured time constant for Ca²⁺ clearance from the cytosol is inversely proportional to access conductance (G_A). A previous study of the rate of diffusional exchange between the cytosol of small cells and patch pipettes, which measured diffusion of fluorescent molecules into patch-clamped adrenal chromaffin cells, found that the inverse of the diffusion time constant (1/) was proportional to the access conductance with a proportionality constant that was determined by the diffusion coefficient and size of the diffusing molecule (Pusch and Neher, 1988). This relationship can be used to estimate the diffusion constant in our experiments. Since most of the Ca²⁺ is bound to endogenous and exogenous Ca²⁺ buffers, the main diffusing species will be the Ca²⁺ complexes with the mobile Ca²⁺ buffers, which are rhod-2 and EGTA in our whole-cell experiments. According to this study by Pusch and Neher (1988), the diffusion coefficient, D = (78.4 ± 6.6)/(G_A). Using the data in Fig. 6 from the five cells that fit the linear relationship, we estimate a diffusion coefficient of 120 µm²/s^-1, after correcting for cell size according to the equations given by Pusch and Neher (1988). This diffusion coefficient is in reasonably good agreement with the 100 µm²/s^-1 that we use in our simulations.

In some experiments, when the access resistance is high, the measured clearance rate is faster than predicted by the theory just described. The slowest clearance rates have time constants of 40-50 s. We attribute this Ca²⁺ clearance to physiological mechanisms. It is difficult to study the physiological Ca²⁺ clearance mechanism under our experimental conditions, because the pipette resistance dominates Ca²⁺ clearance in most of our experiments. Increasing the pipette resistance is not practical as then we don't get good diffusional exchange of the Ca²⁺ indicator, which is necessary for the Ca²⁺ measurements. In addition, our experiments generally involve small stimuli under strongly buffered conditions, so the measured Ca²⁺ changes are relatively small. Other studies using stronger stimulating protocols have variously implicated a role for plasma membrane Na⁺/Ca²⁺ exchange and mitochondrial mechanisms (Herrington et al., 1996; Pan and Kao, 1997; Tang et al., 2000). This is not inconsistent with our experiments. As described in Results, there is a slight slowing of clearance immediately after stimulation when extracellular Na⁺ is removed suggesting that Na⁺/Ca²⁺ exchange may participate