Dynamics of Signaling between Ca²⁺ Sparks and Ca²⁺- Activated K⁺ Channels Studied with a Novel Image-Based Method for Direct Intracellular Measurement of Ryanodine Receptor Ca²⁺ Current

Calcium ions, which serve as signals for a wide range of cellular processes, can enter the nucleus and cytosol either from outside the cell or from the endoplasmic reticulum/sarcoplasmic reticulum. Two types of Ca²⁺ release channels mediate release from the endoplasmic reticulum/sarcoplasmic reticulum.; ryanodine receptors (RyRs) and inositol 1,4,5-trisphosphate receptors. The activation of inositol 1,4,5-trisphosphate receptors or RyRs generates highly localized Ca²⁺ transients, called “Ca²⁺ puffs” and “Ca²⁺ sparks,” respectively (Parker and Yao 1991; Cheng et al. 1993). In many cases these constitute the elementary building blocks underlying global increases in intracellular Ca²⁺ concentration ([Ca²⁺]_i). In addition, these transients can function as signals that achieve specificity by activating targets solely in the vicinity of the release, i.e., targets that are colocalized with the release sites in a microdomain. A possible consequence of such proximity is that a target with relatively low affinity for Ca²⁺ will respond only to local Ca²⁺ release and remain protected from global Ca²⁺ elevations of lower amplitude. Hence, an analysis of the functional and spatial relationship between localized Ca²⁺ transients and their targets is critical for understanding the specificity of Ca²⁺ signaling.

Smooth muscle cells provide an especially useful system to study the relationship between local Ca²⁺ release events and targets within their microdomains because at least two of the targets are ion channels that are readily monitored at high temporal resolution with patch-clamp recording. In smooth muscle cells, Ca²⁺ sparks induce spontaneous transient outward currents (STOCs) by activating Ca²⁺-activated K⁺ channels (Nelson et al. 1995; Mironneau et al. 1996; Bolton and Gordienko 1998; ZhuGe et al. 1998, ZhuGe et al. 1999) as well as spontaneous transient inward currents by opening Ca²⁺-activated Cl⁻ channels (ZhuGe et al. 1998). Because the STOCs are blocked by iberiotoxin and their activation is voltage sensitive, it has been concluded that large conductance Ca²⁺-activated K⁺ channels (BK channels) underlie the STOCs (Nelson et al. 1995; ZhuGe et al. 1999). Interest in STOCs has heightened since the pioneering work of Nelson et al. 1995(see also Brenner et al. 2000), which provided strong evidence that STOCs regulate vascular tone in cerebral arteries. Hence, the underlying Ca²⁺ sparks have an important physiological role in their own right, in contrast to serving simply as building blocks for global elevations in Ca²⁺. Similarly, ZhuGe et al. 1998 have suggested that sparks generating spontaneous transient inward currents regulate contractility in airway smooth muscle.

Studies of the quantitative relationship between Ca²⁺ sparks and STOCs have focused largely on establishing and corroborating the causal link between them (Nelson et al. 1995; Mironneau et al. 1996; Bolton and Gordienko 1998; ZhuGe et al. 1998, ZhuGe et al. 1999; Perez et al. 1999). However, the mechanisms by which the STOC is generated and the nature of the functional relationship between RyRs and BK channels in the spark microdomain have not been established in detail. For example, do one or more RyRs contribute to a spark? To what degree do the local [Ca²⁺], the kinetics of the underlying Ca²⁺ flux through the RyRs, and the kinetics of BK channel gating determine the spark–STOC relationship? In the present mechanistic study, we address questions of this sort.

To date, studies of Ca²⁺ sparks have measured changes in fluorescence relative to background (F/F₀ or 100 × (F − F₀)/F₀), usually with fluo-3, as an index of alterations in Ca²⁺ concentration. In the present study, we use a measure of the quantity of Ca²⁺ released during a spark, a measure similar to the signal mass unit that Sun et al. 1998 devised to analyze Ca²⁺ puffs in oocytes. Using a confocal linescan system, Sun et al. 1998 measured F/F₀ in the usual way and computed the total fluorescence based on a model of the extent of the puff. In the present study, we have developed a new method for the direct measure of the total increase in fluorescence due to entry of Ca²⁺ into the cytosol. This is made possible by the use of a widefield digital imaging system that can capture the increase in fluorescence over a sufficiently large volume and with sufficiently low noise to allow detection of the total increase in fluorescence because of a localized rise in cytosolic Ca²⁺.

The present study is the first application of a direct signal mass approach to the study of Ca²⁺ sparks in any system. The use of the signal mass approach affords three advantages. First, since this measure discloses the total Ca²⁺ released (i.e., the integrated flux) over a known time, the Ca²⁺ flux or, in terms of charge, the Ca²⁺ current through the RyRs during a spark (i.e., I_Ca(spark)) can be determined. Second, it is uncertain whether fluorescent indicators are capable of reporting the [Ca²⁺] in the microdomain, where the BK channels underlying a STOC reside, since equilibrium conditions between released Ca²⁺ and indicator may not be reached there (Stern 1992; Naraghi and Neher 1997). Hence, an uncertain measure of concentration can be replaced by a measure of the signal mass and Ca²⁺ flux or current, which can be related to the STOCs. Third, using two-dimensional widefield imaging, as was done in this study, the signal mass is essentially independent of the z-axis location of the spark relative to the microscope's plane of focus.

Major results of the present study are as follows. First, most sparks result from the concerted opening of a number of RyRs. Second, 21% of sparks fail to cause detectable STOCs. Third, a given I_Ca(spark) leads to STOCs of different magnitude because of, at least in part, different ratios of RyRs to BK channels in the spark microdomains. Fourth, the rate of STOC activation is relatively constant in the face of large differences in I_Ca(spark). Fifth, STOC decay is approximated by a single exponential function that is independent of the magnitude of the Ca²⁺ signal mass and close to the value of the mean open time of the BK channels at the same potential. These findings suggest a model of the STOC in which the spark presents to the BK channels a step increase in [Ca²⁺] to levels well above the EC₅₀ for the BK channels. In this model, the rise and fall of the STOC is determined by the kinetics of the BK channels and not by diffusion of Ca²⁺ to the BK channels or by the rate of rise or fall of [Ca²⁺]_i. The signal mass approach coupled with widefield microscopy should provide insights into focal Ca²⁺ transients elsewhere, for example, in striated muscle or in dendritic spines of neurons.

Single smooth muscle cells were enzymatically dispersed from the stomach muscularis of Bufo marinus as described previously (Fay et al. 1982). Membrane currents were recorded using the tight-seal, whole-cell patch recording configuration. The extracellular solution contained (in mM): 130 NaCl, 3 KCl, 1.8 CaCl₂, 1 MgCl₂, 10 HEPES, and the pH was adjusted to 7.4 with NaOH. The pipet solution contained the following (in mM): 137 KCl, 3 MgCl₂, 10 HEPES, 3 Na₂ATP, 0.05 fluo-3 (unless otherwise noted), and the pH was adjusted to 7.2 with KOH. All experiments were carried out at room temperature. Whole-cell currents were recorded and low pass–filtered using the Axopatch 1D amplifier (200-Hz cutoff) and digitally sampled at 1 kHz or, in some instances, the Axoclamp 2A amplifier (100-Hz cutoff, then digitally sampled at 300 Hz), and stored for analysis. Events were counted as STOCs if they exceeded a threshold of 10 pA, as detected by a custom-automated algorithm that also measured their amplitude and frequency. The events were checked by visual inspection to eliminate anomalies such as multiple events overlapping in time or excessively noisy traces.

The following two measures of Ca²⁺ sparks were used: the conventional fluorescence ratio, ΔF/F₀; and the change in total fluorescence F^T − F₀^T, which is related to the total Ca²⁺ released into the cytosol, also termed the signal mass. The two measures differ not only in the way they are computed, but also in the area from which the fluorescence is collected. The ratio measure is tracked for a single pixel, whereas the signal mass is collected over a much larger area. For each measure, fluorescent images were obtained using fluo-3 as the calcium indicator and a custom built widefield, high speed digital imaging system that is described in detail elsewhere (ZhuGe et al. 1999). Rapid imaging was made possible by using a cooled high sensitivity, charge-coupled device camera (128 × 128 pixels) developed in conjunction with MIT Lincoln Laboratories. The camera was interfaced to a custom-made, inverted microscope equipped with a 40× oil immersion lens (NA 1.3); each pixel covered a 333 × 333-nm area of the cell. The 488-nm line of a multiline Argon laser provided fluorescence excitation for the indicator fluo-3. Emission of the Ca²⁺ indicator was imaged at wavelengths >500 nm. To obtain a constant concentration of Ca²⁺ indicator, 50 μM fluo-3 was delivered through the patch pipet, and measurements were not commenced until 10–15 min after breakthrough of the patch. After this time, no significant change in background fluorescence was detected. Subsequent image processing and analysis were performed off-line using a custom-designed software package, running on a Silicon Graphics workstation.

For this measure, the fluo-3 images were first smoothed by convolution with a 3 × 3-pixel approximation to a two-dimensional Gaussian:

Fluorescence ratio images were calculated and expressed as a percentage on a pixel to pixel basis from the equation:

where F is the fluorescence at each pixel in the time series, and F₀ is the resting level derived from the fluorescence time series by computing the median pixel value during quiescent times at each F(x, y). The ΔF/F₀ traces in the figures follow the time course of the single pixel that had the highest fluorescence ratio, which we call the epicenter pixel. For an event to qualify as a Ca²⁺ spark, it had to meet two criteria. First, the fluorescence ratio at the epicenter pixel had to be equal to or >5%, and it had to last for at least two consecutive time frames of 10 ms. The second criterion was based on the signal mass, which is described in detail in the next section.

During a spark, free Ca²⁺ (diffusion coefficient, D = 250 μm²/s) and Ca²⁺ bound to fluo-3 (D = 22 μm²/s; Smith et al. 1998) quickly diffuse away from the spark release site as Ca²⁺ continues to be discharged. To quantify the total fluorescence arising from the binding of fluo-3 to the discharged Ca²⁺(i.e., the Ca²⁺ signal mass), the increase in fluo-3 fluorescence ) must be collected from a sufficiently large volume to provide a measure of the total quantity of Ca²⁺ released. Custom software was used to process the images and extract signal mass information for each spark event. The signal mass time course for each spark was computed from the two-dimensional, widefield fluorescence images of fluo-3 according to the following equations.

Total fluorescence,

The fluorescence F is summed over a 13.7-μm square region (41 pixels on a side in the x-y plane) surrounding the spark epicenter pixel (x,y) as determined from the ΔF /F₀ images from .

Signal mass,

The signal mass sm(t) is the change in total fluorescence F^T(t) over the baseline fluorescence F^T(t₀) times the detector gain G (see below). The time t₀ corresponds to the image immediately preceding the beginning of the spark. The beginning of the spark event was identified as the first image having a flux, i.e., an increase in total fluorescence (F^T) relative to the preceding image, exceeding 2 SDs of the noise in the flux measurement, which were calculated according to the following equations:

Pixel noise,

Total noise,

Fluorescence flux,

Flux noise,

Spark threshold,

(Note that the flux is proportional to the Ca²⁺ current through the RyRs, and the signal mass is proportional to the integrated Ca²⁺ current or total charge carried by Ca²⁺ during the spark. See Eqs. 9 and 10.) The high speed CCD camera was previously calibrated as having a linear response to light with a gain (G) of five detected photons per digital count and an RMS readout noise (N) equivalent to five detected photons at each pixel. In and , Δt = 10 ms is the time between two consecutive images. defines the threshold Ca²⁺ flux required to be considered as a spark. Therefore, t₀ refers to the image immediately before the first significant flux is observed. The end of the spark event was taken as the last consecutive image having a significant change in total fluorescence, using the same criterion as for the beginning of the event. Finally, the peak signal mass was calculated as the difference in the total fluorescence between the end image and that preceding the beginning of the event. Since the total noise depends on the absolute fluorescence of the pixels in the image, the threshold noise level may vary from spark to spark.

With a widefield imaging system, photons emitted from fluo-3 molecules both at the plane of focus and outside of it are collected by the optics and imaged onto the camera. Clearly, not all the sparks detected will be centered in the plane of focus, and so the fluorescence from them will not be focused as sharply on the CCD camera, but appear as a blur and hence occupy a larger area. Thus, the area of collection must be large enough so that a negligible fraction of photons from an out of focus spark escape detection. In addition, the area of collection must be large enough to allow for the diffusional spread of Ca²⁺ and Ca²⁺ bound to fluo-3. The size of the area for the measurement was chosen by expanding the area around the epicenter for each spark in the entire data set by increments of 4 pixels on a side. The mean value of the signal mass for the spark population began to level off for areas larger than 17 × 17 pixels, and further increase was negligible for areas larger than 41 × 41 pixels. A larger area was not used to avoid decreasing the signal to noise ratio; i.e., the total noise (σ^T) in increases with an increase in measurement area, whereas the signal mass in only increases if additional discharged Ca²⁺ is encompassed. To validate this empirical choice, we also used simulations as described in the next section.

We recorded a total of 365 local Ca²⁺ transients in 31 cells that met the criteria for a Ca²⁺ spark as defined above. Of these, 75 generated no STOCs; 110 generated STOCs where measurement of amplitude was uncertain because of contamination by other STOCs or noise in the records; and 180 generated STOCs whose amplitude was clearly measurable. Of these 180 sparks, 34 had STOCs with noise in the current trace at their onset, which made it impossible to determine the time point of STOC initiation. Thus, 146 sparks with their corresponding STOCs were used to determine the spark–STOC relation based on signal averaging as shown in Fig. 5 and Fig. 9. In addition, we recorded 2,348 STOCs in 15 additional cells in the absence of fluo-3 in the pipet for the comparison made in Fig. 6.

To obtain a calibration factor for converting fluorescence to quantity of Ca²⁺, we used the resting or basal fluorescence since the resting [Ca²⁺] in these cells is accurately known from earlier studies using fura-2 (Drummond and Fay 1996). We first determined the fluorescence, or photon count, due to the resting [Ca²⁺] as follows. Basal fluo-3 fluorescence emanating from a volume subtended by a 5.67-μm (17 × 17 pixels) square area about each spark epicenter pixel was measured just before each spark in the data set. The mean basal fluorescence for the entire population was determined to be 2.73 × 10⁵ detected photons. Given a total fluo-3 concentration of 50 μM, K_d = 1.1 μM (Harkins et al. 1993) and equilibrium with a resting [Ca²⁺] of 100 nM, the concentration of Ca²⁺-bound fluo-3 in the cells was 4.08 μM, and the Ca²⁺-free fluo-3 was 45.92 μM. Given that Ca²⁺-bound fluo-3 is 200 times brighter than the Ca²⁺-free, the Ca²⁺-bound fluo-3 contributed 94.7% of the basal fluorescence. The basal fluorescence due to just the Ca²⁺ bound fluo-3 was therefore 2.58 × 10⁵ detected photons.

Since photons emitted from fluo-3 molecules both at the plane of focus and outside of it are collected by the optics and imaged onto the camera, the actual imaged volume subtended by the 5.67 μm square measurement area must be calculated. We assume that sparks occur at random across the two-dimensional image of the cell, and the average of the cell thickness at all possible spark positions is 8 μm and, thus, an average volume of light collection is ∼257 μm³. At a concentration of 4.08 μM, the number of Ca²⁺-bound fluo-3 molecules within this volume was calculated to be 6.29 × 10⁵ molecules.

Dividing the calculated number of Ca²⁺-bound molecules in this volume by their measured mean basal fluorescence signal gave a calibration factor of 2.44 Ca²⁺ ions, bound to fluo-3, per detected photon. The signal mass (sm) of was converted into moles of Ca²⁺ using the formula:

Ca²⁺ -bound fluo-3 moles=0.41×10⁻²³·smt.

Similarly the flux, f(t) of is converted to Ca²⁺ current using the formula:

I_Casparkamps=7.9×10⁻¹⁹·fluxt.

The average detection threshold for all sparks was a flux equal to ∼0.89 × 10⁻²⁰ mol of Ca²⁺ in 10 ms (or ∼0.19 pA). The smallest detection threshold, due to variations in the basal fluorescence, was equal to ∼0.47 × 10⁻²⁰ mol Ca²⁺ in 10 ms (or ∼0.1 pA).

To determine whether the fluo-3 was able to track the Ca²⁺ released in a spark, we used two sets of simulations. In each case, finite difference approximations were used to solve a set of partial differential equations for the reaction–diffusion kinetics in a cylindrical coordinate system. The details of this approach are described elsewhere (Kargacin and Fay 1991; Zou et al. 1999). In the first set of simulations, we examined the result of a 30-ms long period of Ca²⁺ influx (10, 1, or 0.1 pA) from a point source into the cytosol of a cylindrical cell (length = 30 μm and radius = 6 μm) containing 50 mM fluo-3 (i.e., the concentration in the patch pipet). 30 ms was chosen because this was the approximate duration of the longest time to peak for the development of the spark signal mass (see results). The results of these simulations are shown in Fig. 1 A for 1 pA, and the parameters are provided in the figure legend. As can be seen, fluo-3 binds Ca²⁺ rapidly enough to track the Ca²⁺. In the absence of endogenous stationary buffer, the fluorescence reports virtually all the Ca²⁺ entering the cytosol; i.e., virtually all the Ca²⁺ (i.e., >90%) is in the bound form. Endogenous mobile buffers should dialyze away through the patch pipet so they were not included in the simulation. When 230 μM of fixed buffer was included (Robertson et al. 1981; Bond et al. 1984; Kargacin and Fay 1991), the signal mass was reduced in amplitude, but its onset and peak were unaltered. If the K_d was sufficiently low, the time course of the rising phase was unaffected, but a sag appeared after the cessation of the current. (For each of the stationary buffers used in the simulation, the k_on was diffusion limited and the k_off was varied to give the K_d's shown [Fig. 1 A, legend]). There is reason to believe that the stationary buffer in these cells has only a small effect in the face of 50 μM fluo-3 (see discussion).

Similar simulations were carried out with Ca²⁺ currents of 0.1 and 10 pA. Over the range of Ca²⁺ currents from 0.1 to 10 pA, the fluo-3 tracked the total Ca²⁺ in a proportional fashion under each of the buffer conditions. Fig. 1 B shows the total Ca²⁺ bound to fluo-3 at the end of a 30-ms pulse of each of these three values of Ca²⁺ current in the presence and absence of the same fixed buffer shown in Fig. 1 A. Hence, the increase in fluorescence is proportional to the quantity of Ca²⁺ released over a range of two orders of magnitude ∼1 pA. We expect the Ca²⁺ current to be in the 1-pA range based on previous estimates (ZhuGe et al. 1999; Zou et al. 1999) and on the results obtained here (see results).

In the first set of simulations just described, the entire cell was used as the collection volume, assuming perfect capture of all the fluorescence throughout the z-axis (i.e., the properties of the imaging system and its point spread function [PSF] were not included in the simulation). A second set of simulations refined the first in two ways: the fluorescence collection area was restricted to a 13.7-μm square area centered on the release site; and an empirically determined PSF was incorporated to examine the effect when the spark was as much as 6 mm removed from the z-plane of focus. (This distance is sufficient for a cell of the thickness used in this study, given that we sought to focus at the cell's center.) The results of the second set of simulations for 1 pA are shown in Fig. 1 C; the simulations were limited to the case where there was no fixed buffer. It is clear that with the 13.7-μm square collection area almost all the fluorescence is captured both for sparks in the focal plane and out of it. (In the worst case, i.e., farthest from the plane of focus, 84% of the fluorescence is monitored.) Finally, it should be noted that, with the widefield system, the time course of the signal mass trace is not affected by the position of the spark release site in the z-axis.

All chemicals except fluo-3 (Molecular Probes) were purchased from Sigma-Aldrich.

Ca²⁺ sparks and the STOCs elicited by them were simultaneously monitored using a widefield digital imaging system with high sensitivity, low noise, and high temporal resolution in combination with whole-cell patch recording. (See materials and methods and the results of simulations in Fig. 1.) Fig. 2 illustrates a typical recording of a single Ca²⁺ spark and the STOC it elicits. In Fig. 2 A, a small region of the smooth muscle cell is shown, and a single Ca²⁺ spark is represented on a pseudocolor scale in the bottom row of images and by a contour plot also incorporating the same pseudocolor scale in the top row. (The height of the contour plot provides a measure of relative intensity without introducing subjective color impressions.) In Fig. 2 B, the top trace records the STOC; and the middle trace records the conventional measure of spark amplitude (the fluorescence ratio, ΔF/F₀) for the single pixel (333 × 333 nm) where the fluorescence ratio reaches its highest value (i.e., the epicenter pixel). The bottom trace in Fig. 2 B tracks the signal mass, i.e., the increase in total fluorescence over an area 13.7 μm square (i.e., 41 pixels on a side) and throughout the entire thickness of the cell (∼8 μm on average). A collection volume of this size was sufficient both to prevent loss of fluorescence because of diffusion of Ca²⁺ and bound fluo-3 away from the point of release and to capture 84% or more of the fluorescence from sparks originating outside the plane of focus (Fig. 1). Hence, the signal mass is proportional to the total quantity of cytosolic Ca²⁺ accumulated over time, i.e., the integral of net Ca²⁺ current into the cytosol. Here, as elsewhere, the signal mass is given in terms of moles of Ca²⁺ using the calibration described in materials and methods. This calibration assumes that there are no significant buffers other than fluo-3 acting over this time frame so that the value for the quantity of Ca²⁺ constitutes a lower bound (see discussion). It is important to note that the signal mass is not a measure of Ca²⁺ concentration. The slope of the signal mass trace is proportional to the net Ca²⁺ current into the cytosol from the SR through the RyRs or, in terms of charge, the net Ca²⁺ current into the cytosol. We refer to this as the spark Ca²⁺ current or I_Ca(spark); as with the signal mass, the value given for I_Ca(spark) is a minimum. The spark current is a useful measure since it provides a way of examining the Ca²⁺ current of the RyRs in the cell under physiological conditions as opposed to recordings in an artificial bilayer system.

The record of signal mass, unlike that of ΔF/F₀ at the spark epicenter pixel, does not return to baseline, but rather remains at a plateau level for the period shown. The half-time for decay of the fluorescence ratio was ∼15 ms in this example, whereas the half-time for the decline of the signal mass was well in excess of 100 ms. For the entire population of sparks analyzed, the average half-time of decay for the fluorescence ratio was 16 ± 0.4 ms, whereas the signal mass had not decayed to half its peak value even after 100 ms. Hence, it appears that diffusion into the surrounding cytosol accounts for most of the decline in Ca²⁺ at the spark epicenter. This result is consistent with estimates for Ca²⁺ sparks in cardiac cells where diffusion accounts for ∼80% of the decay in spark amplitude (Gomez et al. 1996). Moreover, the existence of the plateau phase indicates that the volume subtended by the area over which the fluorescence is monitored is sufficiently large to capture virtually all the fluorescence due to bound Ca²⁺. If the monitored area was not large enough, then there would be a decay as the Ca²⁺ and bound fluo-3 diffused away. Finally, the rising phase of signal mass lasted 20 ms or less in most cases and exceeded 30 ms only in a few instances.

The signal mass measure, when implemented with widefield microscopy, is affected minimally by the z-axis location of the spark in cells of the thickness used here, given the area of the x-y plane from which fluorescence is collected and the PSF of the widefield digital system (see Fig. 1 C and materials and methods). That is, virtually the entirety of the fluorescence is captured by this system whether or not the spark is in focus. Moreover, since the system captures sparks over the entire x-y plane lying within the field, no distortion is introduced in this plane for either the signal mass measure or for the fluorescence ratio. In sum, the widefield system is ideally suited for the signal mass approach. A widefield system is also suited for the study of sparks in a cell like smooth muscle and neurons where the location of the sparks is not known a priori as it is in striated cells with their well demarcated t-tubular system.

The error bars in the middle and bottom traces of Fig. 2 B represent the SD due to the calculated photon noise. Two points deserve mention. First, our initial criterion for identifying an event as a Ca²⁺ spark is an increase of 5% in the fluorescence ratio ΔF/F₀ (lasting two or more frames), which is a level equal to 1 SD above the noise (Fig. 2 B, middle trace). Second, the signal to noise ratio, which is approximately equal to the square root of the total fluorescence, is higher in the signal mass record than in the record of fluorescence ratio since more photons are collected in the former. The low noise in the signal mass is also due to the high signal to noise ratio of the digital imaging system and CCD camera.

Although sparks have been studied previously in a number of smooth muscle types (Nelson et al. 1995; Mironneau et al. 1996; Bolton and Gordienko 1998; ZhuGe et al. 1998, ZhuGe et al. 1999; Pabelick et al. 1999; Collier et al. 2000), distributions of parameters characterizing the sparks have not been reported. We examined the properties of a population of 365 sparks in 31 smooth muscle cells (Fig. 3). The percent change in fluorescence (Fig. 3 A) displayed a distribution with a single peak at 11.6% and an extended tail, giving a range of one order of magnitude. The distribution of the signal mass for each spark is given in Fig. 3 B. It has a single peak, an extended tail, and a total range of >13-fold, thus, resembling the distribution in Fig. 3 A. Both distributions are consistent with a continuum rather than with several discrete populations in a hierarchy, and resemble Ca²⁺ puffs in this respect (Sun et al. 1998; Thomas et al. 1998). It is also noteworthy that the range in the distribution for the signal mass is somewhat greater than that for fluorescence ratio. Since the signal mass is essentially independent of focus, the observed spark variability in this is real and not simply a result of variation with respect to location of the spark site in the z-plane. Also shown are the distributions of full-width at half maximum amplitude (Fig. 3 C) and the half-time of decay (Fig. 3 D), both based on the fluorescence ratio (ΔF/F₀).

To analyze the relationship between the underlying I_Ca(spark) through the RyRs during a spark and the corresponding STOCs, we wished to examine the kinetics of each. To do so, we carried out the signal averaging procedure illustrated in Fig. 4. The procedure is illustrated in Fig. 4 for five different STOCs (left) and the signal mass of the corresponding sparks (right). First, the STOCs are all aligned at time 0 when their three-point smoothed signal reached the 5-pA level above baseline, as determined from custom-made software. Time 0 is taken as the initiation point for the STOC, and the group of STOCs is averaged over time with respect to this initiation point (Fig. 4, bottom left). For each corresponding record of signal mass, the same time point is assigned as the zero time (Fig. 4, right). The signal mass traces are averaged with respect to this zero point, yielding the mean trace (Fig. 4, bottom right). The zero time for the averaged signal mass is the initiation time for the STOC not the spark. As would be expected, the signal mass begins to rise before the initiation point for the STOC and, hence, the onset of the increase in signal mass corresponds to a negative time along the x-axis.

Do sparks with Ca²⁺ signal mass of varying amplitudes have different underlying Ca²⁺ currents? If the larger signal mass is due simply to a single RyR opening for a longer time, then the underlying I_Ca(spark) will be the same; if the sparks are due to the concerted opening of multiple RyRs, I_Ca(spark) will vary. To examine this question, we grouped the sparks into quarters based on the magnitude of the signal mass for each spark. Then, we used the signal averaging technique outlined in Fig. 4. The results are shown in Fig. 5, with the signal mass shown in A and B, the latter on an expanded scale; the corresponding STOC traces are shown below in C and D. The slopes of the plots in Fig. 5 B, which are proportional to the mean I_Ca(spark) for each of the groups, differ by more than fivefold. Thus, not all sparks have underlying Ca²⁺ currents of the same amplitude; rather the sparks of larger signal mass are generated by a larger mean I_Ca(spark). The data in Fig. 5 B are useful since they provide an estimate of the range of values for I_Ca(spark) over the population of sparks. The slopes in Fig. 5 B are 0.08, 0.23, 0.23, and 0.45 × 10⁻²⁰ mol Ca²⁺/ms, which correspond, respectively, to 0.15, 0.44, 0.44, and 0.87 pA of Ca²⁺ current. Assuming that each RyR acts as a single pore, the more than fivefold range in these values indicates that a substantial fraction of the sparks are due to the opening of multiple RyRs. The values for I_Ca(spark) calculated in Fig. 5 B provide a minimum estimate since buffers other than fluo-3 and the action of ion pumps and exchangers, if they have a substantial effect, will decrease the measured signal mass. At the acquisition rate used, our measurements disclose no clear evidence for anything other than a constant slope on the rising phase of the signal mass, i.e., a constant I_Ca(spark) (but see discussion). The simplest conclusion is that the Ca²⁺ current approximates a step function. Assuming that the underlying Ca²⁺ currents are step functions at least over the first 10 ms of the spark, low pass filtering because of the image acquisition rate leads to an underestimate of the current by about one third. Correcting for such filtering leads to values of mean I_Ca(spark) equal to 0.23, 0.66, 0.66, and 1.31 pA. For comparison, Mejia-Alvarez et al. 1999 have recently estimated that the Ca²⁺ current through a single cardiac RyR in a bilayer is 0.35 pA. We consider in greater detail in the discussion how the values found in this study compare to single RyR Ca²⁺ currents measured in bilayers and to sparks in other systems. It is clear that certain features of the data in Fig. 5 speak to the relationship between a Ca²⁺ spark and the STOC that it generates. This will be considered in more detail in the next section.

A comparison was made between the STOCs recorded in the presence and absence of fluo-3 (50 μM) in the patch pipet. The results are shown in Fig. 6. There was no apparent difference in the two populations (P = 0.244, t test). Hence, fluo-3 at this concentration does not change the [Ca²⁺] at the interior surface of the BK channels enough to affect their activation.

Is the relative [Ca²⁺] at the peak of a spark, as estimated by ΔF/F₀ at the epicenter pixel, a good predictor of the corresponding STOC? Fig. 7 A shows a plot relating these two parameters for 255 sparks. Those sparks that did not generate STOCs are assigned a value of 0 and plotted on the abscissa. Although the correlation between ΔF/F₀ and STOC amplitude is significant, it is evident from the plot that the correlation is quite weak (r = 0.163 and P = 0.026; Spearman rank order coefficient). (In calculating the correlation coefficient [r], the STOC-less sparks appearing on the abscissa are omitted; including these points would further weaken the correlation.) The FWHM, as determined from the fluorescence ratio (Fig. 7 B) is also weakly correlated with STOC amplitude (r = 0.158 and P = 0.031). These relatively poor correlations might result from the fact that the percent change in fluorescence is affected by the plane of focus (z-axis) in which the spark occurs. Hence, we examined the correlation for those sparks that appeared at the lateral edges of the cell in two-dimensional images. Since we attempted to focus on the center of the cell, these sparks were more likely to lie in the plane of microscope focus. But for this data set, the correlation between STOCs and either parameter did not grow stronger (not shown). Another possible way to correct for this problem is to use the signal mass as a measure of spark intensity since it is almost completely insensitive to the z-plane in which the spark occurs. Using the signal mass, the correlation improves somewhat (Fig. 7 C), but it remains weak and is a poor predictor of spark amplitude (r = 0.40 and P = 0.001; Spearman rank order coefficient).

Although most Ca²⁺ sparks triggered STOCs, 21% did not and these are plotted on the abscissa in Fig. 7. Two such STOC-less sparks are illustrated in Fig. 8; the spark shown in Fig. 8 A lies at the edge of the cell. Among sparks that clearly lay at the cell's edge, 23% failed to elicit STOCs. Thus, the failure to cause STOCs cannot simply be attributed to spark generation at a site far from the membrane. (The same conclusion about STOC-less sparks emerged from an earlier study on a different smooth muscle preparation. In that case, 3-D imaging was used to locate the sparks unambiguously, and the STOC-less sparks were somewhat closer to the membrane than the average [Kirber et al. 1998].) We asked whether the sparks that triggered STOCs (a total of 290) differed from those that did not (a total of 75). The following significant differences were found (mean ± SEM) for sparks with STOCs and sparks without STOCs, respectively: ΔF/F₀ (in percent), 12.6 ± 0.5 vs. 10.5 ± 0.5, P = 0.004; FWHM, 2.7 ± 0.1 μm vs. 2.2 ± 0.1 μm, P = 0.001; signal mass, 6.2 ± 0.3 × 10⁻²⁰ mol Ca²⁺ vs. 4.0 ± 0.2 × 10⁻²⁰ mol Ca²⁺, P = 0.001; and t_1/2 of decay, 16.0 ± 0.5 vs. 15.4 ± 0.91, P = 0.269. Even though the two spark populations are significantly different by these measures, the overlap in their distributions is substantial as can be seen in Fig. 7, where the STOC-less sparks appear on the x-axis. Thus, relatively small sparks may generate STOCs, and relatively large ones may fail to do so. This suggested to us that the coupling between RyRs and BK channels might be variable, with the STOC-less sparks lying at one extreme.

Are larger STOCs caused by I_Ca(spark) of greater amplitude? To address this question, we divided the population of STOCs into quarters, grouped from smallest to largest so that the smallest STOCs all fell into the first quarter and the largest into the fourth quarter. This was done to maximize the observable differences in I_Ca(spark) underlying STOCs of different amplitudes. The same signal averaging procedure, as shown in Fig. 4, was carried out for each quarter of the STOC population. The averaged STOCs for each quarter are shown in Fig. 9 A, and the time course of the corresponding mean signal mass in Fig. 9 B. The temporal alignment of the signal mass traces here is determined by the STOCs, as described above for Fig. 4.

The peak STOC amplitude for the four groups varies by a factor of four (Fig. 9 A), whereas the corresponding signal mass peak varies only by a factor of two (Fig. 9 B). Although the mean time to peak (TTP) for the larger STOCs and the corresponding signal mass (Fig. 9A and Fig. B) tend to be longer, the longer duration cannot fully account for larger STOC amplitude. This becomes apparent on examination of the 5-ms time point designated by open circles on the traces. At this point, it can be seen that the signal mass for the four groups varies by only a small amount (Fig. 9 B, circles) whereas the STOC amplitude varies by almost a factor of three (Fig. 9 A, circles). At this time point the mean signal mass for the smallest group of sparks (black line) reaches its peak and the others continue to rise. Hence, at this point, approximately the same mean signal mass and the same mean I_Ca(spark) gives rise to a STOC current that varies by about threefold for the four groups. The mean I_Ca(spark) for each of the four groups was calculated explicitly from the slope of a straight line fitted to the data points beginning at the onset of the rise in signal mass and ending at the time that the signal mass reaches its peak (Fig. 9 D). As can be seen, the mean I_Ca(spark) varies by only a small amount for the four groups, with the largest difference lying between the smallest quarter and the others. Moreover, the rank order of the mean I_Ca(spark) for the same four groups is not the same as that of the STOC amplitude at the 5-ms time point.

We term the ratio of signal mass to STOC current the “coupling ratio.” The large variation in coupling ratio at the 5-ms time point indicated by the circles in Fig. 9 could be explained in two fundamental ways. The first is that the number of BK channels (N) per RyR is variable. The second is that the number of BK channels (per RyR) does not vary, but the probability of their being in the open state (P_o) does. In turn, this variability in P_o may occur for two reasons. First, the BK channels at different spark sites may have different kinetic properties. For example, because of the presence of different BK channel isoforms; or second, the BK channels may lie at different distances from the RyRs at different spark sites. Consider the possibility that P_o varies because of variation in the kinetic properties of the BK channels. In this case, a larger fraction of a constant number of BK channels (per RyR) would be activated in the same period of time because of faster kinetics. The kinetics of the rising phase of the four groups of STOCs are analyzed in Fig. 9 C; for each group, the data points (open circles) were fitted by the equations and parameters given in the figure legend (solid lines). We chose these expressions because they were previously used by Markwardt and Isenberg 1992 to fit the responses of smooth muscle BK channels in excised inside-out patches to rapid jumps in [Ca²⁺] (see discussion). The kinetics of the rising phase for the four groups does not vary systematically from smallest to largest; and there is little difference among the three smallest groups. Moreover, the rate of rise for the largest group of STOCs is slowest and that for the smallest group is fastest. This is the opposite of the expected order if differences in BK channel kinetics were to underlie the differences in STOC amplitudes caused by the same Ca²⁺ current.

Consider next the possibility that P_o varies because of variability in the distance between the RyRs and BK channels at different spark sites. In this case, the smaller STOCs should result from a greater distance between BK channels and RyRs; such smaller STOCs should arise from the exposure of BK channels to lower [Ca²⁺]_i and, hence, the P_o should be lower and the kinetics slower. Here again, the fact that the smallest group of STOCs has the fastest kinetics, and the largest group the slowest kinetics, argues against this alternative. We conclude that P_o for the BK channels is not different at the different spark sites. Rather, the first of the alternatives is correct, i.e., the number of BK channels per RyR is not constant but variable.

These results also place a restriction on the role of Ca²⁺ diffusion as a factor in the variability in coupling ratio. Since the mean I_Ca(spark) is the same at the 5-ms point for the four groups, the spatial profile of [Ca²⁺] would appear to be the same at that point in time. This rules out recruitment of BK channels due to diffusional spread of Ca²⁺ as the cause of the difference in coupling ratios, at least up to this time point.

Another factor apparently contributes to the larger STOCs at points later than the 10-ms time point as marked in Fig. 9 A. As noted above, the TTP is longer for the larger STOCs, 8.6 ± 0.7, 11.0 ± 0.8, 12.0 ± 0.9, and 13.9 ± 0.9 ms for the four groups (P < 0.001 by analysis of variance). This is apparently due to the fact that the Ca²⁺ current duration is greater for the longer STOCs. Since the STOCs should begin to decay when the Ca²⁺ current turns off, the larger STOCs should also have later times for the onset of their decay. In fact, this is the case with the mean lapse in time from the onset of the STOC to the onset of decay for the four groups being 9.6 ± 0.9, 12.4 ± 1.0, 15.6 ± 1.2, and 19.1 ± 1.6 ms (P < 0.001 by analysis of variance). These time points are indicated by the arrowheads in the STOC traces of Fig. 9 A; the arrowheads in Fig. 9 B mark the corresponding points on the signal mass traces.

The qualitative relationship between sparks and STOCs agrees with the conclusions that emerge from an examination of Fig. 5; i.e., the mean Ca²⁺ signal mass at its peak varied by more than fivefold, whereas the mean peak STOC amplitude varied by less than a factor of two. At the 5-ms time point (Fig. 5A and Fig. C, circles), this discrepancy is also evident, with an approximate threefold difference in signal mass among the groups but a 1.67-fold difference in STOC amplitude. Again, since this comparison is made for the same point in time, differences in the time to peak of the spark signal mass (i.e., differences in duration of I_Ca(spark)) cannot account for the difference in coupling ratio at this time point. Moreover, large variations in I_Ca(spark) and Ca²⁺ signal mass of the spark did not alter the BK channel kinetics during the rising phase of the STOC. Since the differences in mean signal mass (Fig. 5 A) and I_Ca(spark) (Fig. 5 B) were substantial among the four groups of data, it was possible to examine the effect of signal mass and I_Ca(spark) on the rising phase of the STOCs (Fig. 5 D). Here, the kinetics of the rising phase did not vary systematically among the groups (from smallest to largest) despite a fivefold difference in the mean I_Ca(spark) (Fig. 5 B) over the first 10 ms. Finally, Ca²⁺ currents that are considerably larger than the ones in Fig. 9 D can be monitored by this system, as is evident from Fig. 5 B, confirming the simulations illustrated in Fig. 1.

Does the rate of decay of the STOC depend on the magnitude of the spark signal mass or the underlying I_Ca(spark)? To address this question, the rate of STOC decay was studied by using the grouping in Fig. 5. The results are shown in Fig. 10 where the data points (circles) during the decay for each group of STOCs was fit by a single exponential with the time constants given in the figure legend. As was shown in Fig. 5, both the mean I_Ca(spark) and mean signal mass vary more than fivefold among the four groups. Nevertheless, as is evident from Fig. 10, the rate of STOC decay is indistinguishable among three of the four groups, and the time constants do not vary in a systematic fashion from small to large among the groups. These time constants are close to values for the mean open time of BK channels in the same cells in the presence of 1 or 10 μM Ca²⁺, which were 20–40 ms (Singer and Walsh 1987) and quite insensitive to [Ca²⁺]. Moreover, the time constants are roughly the same as Markwardt and Isenberg 1992 found for BK channels in inside-out patches at the end of a rapid step change in [Ca²⁺] at 0 mV in a different smooth muscle preparation. In that study, the decay was well fit by a single exponential with a time constant at 0 mV, which, on average, was 37 ms and was not sensitive to the preceding [Ca²⁺]. These findings are consistent with a drop in [Ca²⁺] at the BK channels to subactivating levels upon the termination of I_Ca(spark), a drop which is rapid in comparison to the slower deactivation kinetics of the BK channels. Finally, the agreement of the decay time constant with the mean open time of BK channels in this preparation is another piece of evidence that BK channels are responsible for STOCs.

How rapidly is the steady state [Ca²⁺] profile established in the vicinity of the Ca²⁺ release site? How elevated is the concentration? How rapidly is it dissipated? And how fast is this establishment and dissipation in comparison to the STOC kinetics? To answer these questions, we simulated the consequences of a 15-ms pulse of Ca²⁺ current flowing into the cytosol. This approximates the average time for the signal mass to reach its peak, i.e., the time from onset to termination of the I_Ca(spark). Based on the measurements given in Fig. 5, we used values of 0.2 and 1 pA for the Ca²⁺ current in the absence of fixed buffer, and 0.9 and 4.5 pA in the presence of 230 μM fixed buffer with the highest Ca²⁺ affinity (Fig. 1). (These represent the two extremes of possible conditions, i.e., the condition where fixed buffer is negligible and where the fixed buffer is of the highest likely concentration and affinity for Ca²⁺.) We used a step function for I_Ca(spark) since the rate of rise of the signal mass was well fit by a straight line. The results are shown in Fig. 11 A. (The heavy black line in each panel indicates the isoconcentration line for 2 μM Ca²⁺, the approximate EC₅₀ for BK channels in this preparation at 0 mV [Singer and Walsh 1987].) In each case, the steady state concentration at a radial distance of 200 nm or less reaches its near-final level within 1–2 ms of the onset of I_Ca(spark). This is faster than the rise time of the STOCs (Fig. 5 and Fig. 9). After the first 1–2 ms at radial distances of 200 nm or less, there is little or no increase in [Ca²⁺]. Subsequent small increases in [Ca²⁺] at this distance are most evident in the presence of fixed buffer at higher current levels (Fig. 11 A, c and d). But in this case, the concentrations are sufficiently high that a [Ca²⁺] of 10 μM or more is achieved within 1–2 ms. Thus, within 200 nm, a [Ca²⁺] is quickly established that is either constant or well in excess of the EC₅₀.

This can be more readily appreciated in Fig. 11 B, where [Ca²⁺] is plotted as a function of time at a constant distance of 200 nm. The dashed lines indicate the [Ca²⁺]_EC50 of the BK channels for Ca²⁺. Either the [Ca²⁺] rises quickly to a near constant level or it creeps up more slowly, but only after exceeding the EC₅₀ within 1–2 ms. In either event, the BK channels will respond as though the [Ca²⁺] is unchanging after the first 1–2 ms. Thus, a step of Ca²⁺ current (i.e., I_Ca(spark)) produces, within a microdomain of 200 nm or less in radius, a condition similar to applying a rapid step change in [Ca²⁺] to BK channels in an excised inside-out patch, as Markwardt and Isenberg did (1992). Finally, if the BK channels lie close enough to the release site (e.g., within 100 nm), then for all levels of Ca²⁺ current, the BK channels will be exposed to [Ca²⁺] well in excess of the EC₅₀ within 1–2 ms. This could account for the similarity of the kinetics of the rising phase of the STOCs at all levels of I_Ca(spark) (Fig. 5).

Examination of the [Ca²⁺] profile at the end of the I_Ca(spark) pulse shows a continuing presence of high levels of Ca²⁺ in the presence of the high affinity fixed buffer (Fig. 11 A, c and d). We used the concentration and affinity of the fixed buffer shown to represent a possible extreme effect on the STOC. However, it appears that the effect of fixed buffer is less than that shown in Fig. 11 A (c and d). The reason for this is that the time constant of decay of the STOC is independent of the magnitude of the I_Ca(spark) (Fig. 10), and it corresponds to the mean open time of the BK channels in this preparation (Singer and Walsh 1987). This appears to be incompatible with a continued presence of substantial levels of Ca²⁺ at the offset of the current pulse as found with a fixed buffer of the type and concentration shown. Hence, the condition in the spark microdomain would seem to resemble more closely the conditions modeled in Fig. 11 A (a and b), where fixed buffer has relatively little effect and the main buffer is fluo-3.

In this paper, we have developed a new approach to the analysis of Ca²⁺ sparks. This approach takes its inspiration from the very perceptive work of Sun et al. 1998, but differs from it in that our approach is more direct. Sun et al. 1998 set out to determine the total Ca²⁺ (i.e., signal mass) released during a Ca²⁺ puff using confocal microscopy. To do so, they first estimated the [Ca²⁺] using the measured fluorescence, and then modeled the extent of the puff to obtain an estimate of signal mass (i.e., total Ca²⁺ released). Their starting point was an estimate of [Ca²⁺] since the confocal microscope is appropriate to make that measure in a restricted region. In contrast, we used a widefield system, with high spatiotemporal resolution and signal to noise ratio, to measure the signal mass directly by simply collecting the total increase in fluorescence over a sufficiently large region. The first derivative of the signal mass is the Ca²⁺ current or, when multiplied by a constant, the Ca²⁺ current flowing through RyRs at the spark site, I_Ca(spark); and we have been able to make a measurement of this Ca²⁺ current. Because the measure of signal mass is direct, it is free from the necessity of 3-D modeling of the spark and the assumptions involved therein. Moreover, this approach provides a measure of the Ca²⁺ current through the RyRs under physiological conditions in the cell with Ca²⁺ as the current carrier. Hence, this measure of I_Ca(spark) provides a complement to measures of RyR currents recorded in bilayers.

It has been controversial whether the opening of a single RyR or the concerted opening of a cluster of multiple RyRs is responsible for a Ca²⁺ spark in smooth, cardiac, and skeletal muscle (Cheng et al. 1993; Lipp and Niggli 1996; Blatter et al. 1997; Gollasch et al. 1998; Shirokova et al. 1998; Fill et al. 1999; Schneider 1999; Shtifman et al. 2000). In the present study, we found a range of I_Ca(spark) that varies by more than a factor of five; hence, we conclude that most sparks are due to the concerted opening of a number of RyRs. Mejia-Alvarez et al. 1999 recently measured single cardiac RyR channel currents in artificial bilayers under ionic conditions approximating the physiological and concluded that the current is <0.6 pA, probably on the order of 0.35 pA. Those values were for a lumenal free [Ca²⁺] of ∼1 nM. Measurements of lumenal [Ca²⁺] in the cells used here indicate a value on the order of 150 μM (ZhuGe et al. 1999), so we expect that the single RyR current in these cells is smaller than 0.35 pA, perhaps one tenth as small. The smallest mean I_Ca(spark) that we detected is 0.15 or 0.23 pA. Do the smallest sparks arise from the opening of a single RyR? This remains uncertain. If the single-channel RyR Ca²⁺ currents in the cells used here are on the order of that seen by Mejia-Alvarez et al. 1999, then the smallest currents we found are likely due to a single RyR. If the single-channel currents are a tenth the value, then even the smallest sparks arise from a number of RyRs on the order of 10 and the largest ones from a number on the order of 50.

One of the most striking features of the time course of the signal mass is the prolonged plateau once the peak of the signal mass is reached (Fig. 2). This plateau indicates that virtually all of the Ca²⁺ remains in the cytosol for the period of the plateau that is several times longer than the time to peak. This is consistent with what has been concluded for sparks in cardiac cells where diffusion accounts for >80% of the decay in fluorescence (Gomez et al. 1996). The plateau observed in the present study means that significant removal or sequestration of Ca²⁺ by pumps, exchangers, or entry into mitochondria does not occur after the termination of the Ca²⁺ current during the time of the plateau. Such removal would cause a decline rather than a plateau. If removal by these mechanisms is significant, it must occur during the rising phase of the signal mass. Hence, these Ca²⁺ removal mechanisms have a limited time to exert their effects, which, in turn, places constraints on their contribution. This fact may be pertinent when considering the existence and function of restricted spaces lying between SR and plasma membrane (Lederer et al. 1990; Van Breeman et al. 1995). The failure of removal mechanisms to exert a discernible effect during the time of the plateau is consistent with the low cytosolic concentrations of Ca²⁺ to be expected as Ca²⁺ quickly diffuses over an increasing volume with the dimensions of microns.

Although there is an extensive literature on STOCs, there is relatively little information on the kinetics of their rise and decay (Bolton and Imaizumi 1996). Part of the reason for this may be that individual STOCs are somewhat noisy (Fig. 4). The signal averaging technique that we used here allowed us to examine the kinetics for groups of large and small STOCs (Fig. 9 C) as well as kinetics for groups of STOCs corresponding to large and small values of mean I_Ca(spark) (Fig. 5 D). We found little variation in the kinetics of the rising phase, even with large differences in I_Ca(spark) (Fig. 5). One interpretation of this data is that the BK channels are exposed to a high enough [Ca²⁺] that their activation rate has reached a maximum, even when I_Ca(spark) is relatively small. This would be the case if the BK channels lie close to the release site (See below).

The STOC decay was well fit by a single exponential with a time constant of 24–30 ms. This is in good agreement with the value of ∼30 ms for the effective mean open time at 0 mV for BK channels in excised patches from the same cells used here (Singer and Walsh 1987). The activation rate for the STOCs is much faster, with time constants on the order of 3–4 ms for each of the independent subunits in the model used (Fig. 8 A and 4 C). Hence, if activating levels of Ca²⁺ persisted for a significant period of the decay period, the time of decay should be significantly longer than the mean open time. Therefore, it appears that the [Ca²⁺] at the Ca²⁺ binding site of the BK channels drops rapidly (i.e., within a few milliseconds) upon termination of the Ca²⁺ current.

It is of interest to compare the kinetics of the STOCs with BK channels studied in other preparations. However, this is difficult because of the variability in the BK channel sensitivity to Ca²⁺, due in part to the presence or absence of β subunits and perhaps other factors. Most appropriate for the present study is a comparison to the behavior of BK channels examined by Markwardt and Isenberg 1992 in excised inside-out patches from guinea pig urinary bladder smooth muscle cells. The work of Markwardt and Isenberg 1992 is most relevant to the present study since, to the best of our knowledge, it is the only report of the response of BK channels in excised patches to rapid concentration jumps of Ca²⁺. It appears both from simulations of Ca²⁺ diffusion and from the conclusions drawn in the previous paragraphs that during a spark the BK channels are exposed to a change in [Ca²⁺] that is more rapid than the BK channel kinetics. At the offset of a [Ca²⁺] jump at 0 mV, Markwardt and Isenberg find an exponential decay of BK channel activity with a time constant of 37 ms (Fig. 9 B in Markwardt and Isenberg 1992) that is independent of [Ca²⁺] to which the channels were previously exposed. This result is in remarkably good agreement with our findings (Fig. 10). For the activation of the BK channels at the onset of a [Ca²⁺] jump, Markwardt and Isenberg 1992 used a Hodgkin-Huxley type of formulation to fit their data, based on three independent Ca²⁺ binding subunits. We used the same formulation to fit the time course of STOC activation, simply as a way of fitting the data to facilitate comparisons among the different groups of STOCs and with the experiments of Markwardt and Isenberg. Our data were well fit with time constants that did not vary systematically either with the amplitude of the STOC (Fig. 9 C) or with the amplitude of the I_Ca(spark) (Fig. 5 D). We used time constants of ∼3–4 ms which, in the work of Markwardt and Isenberg, resulted from a [Ca²⁺] jump in excess of 20 μM (Fig. 9 A in Markwardt and Isenberg 1992). (Although those BK channels may be somewhat less sensitive to [Ca²⁺] than the ones underlying the STOCs in the present study [Fig. 7 in Markwardt and Isenberg 1992 versus Fig. 6 in Singer and Walsh 1987], the difference appears to be small.) Markwardt and Isenberg found that at jumps to [Ca²⁺]'s in excess of 20 μM, where the kinetics of activation were fastest, the diffusion of Ca²⁺ to the patch within the pipet became rate limiting. The maximal [Ca²⁺] to which the BK channels can be exposed in our experiments is 150 μM, which is the free concentration measured in the SR of these cells (ZhuGe et al. 1999). Hence, it would appear that the BK channels are exposed to a [Ca²⁺] between 20 and 150 μM during a spark in the cells studied here, but experimental evidence is necessary to establish this point with certainty.

Two general views of STOC generation might be considered. In the first of these, the spark microdomain is simply the whole cell writ small. According to this view, the amplitude of the STOC is indicative of the level of submembranous [Ca²⁺]; that is, with higher [Ca²⁺], the P_o of the BK channels is increased and the STOCs are larger. Hence, a relationship between [Ca²⁺] in the spark microdomain and STOC amplitude is to be expected. This view depends on several assumptions. First, the concentration of BK channels at each spark site must be the same. Second, the [Ca²⁺] to which the BK channels are exposed must be below saturating levels so that P_o is not always 1 during a spark. Third, there must be sufficient time during a spark for equilibrium to be achieved between the [Ca²⁺] and the channel, i.e., the BK kinetics must be relatively fast. Hence, according to this view, the rising phase of the STOC reflects the rise in [Ca²⁺] at the BK channels during the spark. In summary, this view does not need to take account of BK channel kinetics because the relationship between P_o and [Ca²⁺] at equilibrium explains the variability in STOC amplitude. In this case, the rise in [Ca²⁺] is the rate-limiting step, and the BK channels track this rise.

An alternative view emerging from the data presented here arises from the special properties of a microdomain where the RyR and the BK channels lie close together. If these two proteins are close enough, then the [Ca²⁺] will be sufficiently high in every case that the equilibrium P_o of the BK channels will always be one. Moreover, the [Ca²⁺] in this microdomain can reach a steady state level very quickly, too quickly for the BK channels to be in equilibrium as the [Ca²⁺] rises. On this view, the rise in the STOC and its decay reflect the BK channel kinetics as the [Ca²⁺] in the microdomain rises rapidly at the onset of the Ca²⁺ current and dissipates rapidly on its termination. In this case, the relationship between the Ca²⁺ current and the amplitude of the STOC will be largely independent of the magnitude of the I_Ca(spark). However, the amplitude of the STOC for a given magnitude of the I_Ca(spark) will vary depending on the density of the BK channels. And the STOC amplitude will increase the longer the duration of the I_Ca(spark) since a greater fraction of BK channels will activate with time given their relatively slow kinetics. In this case, the BK channel kinetics are the rate-limiting factor after the rapid, switchlike changes in [Ca²⁺] from very low levels to saturating levels and back. The controlling factor is the ability of [Ca²⁺] to very rapidly reach a very high steady state level within the microdomain.

If this second view is correct, then why is there a relationship, however weak, between the Ca²⁺ signal mass and the magnitude of the STOC? First, the signal mass will be larger for Ca²⁺ currents of longer duration, and the STOC will continue to rise as long as the Ca²⁺ current persists until a P_o of one is reached. A second possible, though admittedly speculative, reason for the correlation between signal mass and STOC amplitude may be lie in the molecular architecture of the spark microdomain. One of the most striking findings in the present study is that the same Ca²⁺ current over the same period of time yields STOCs that vary several-fold in amplitude. The most straightforward interpretation of this result, given that the kinetics of the accompanying STOCs are the same, is that the ratio of RyRs to BK channels varies from spark site to spark site. One way to account for this is to postulate two types of RyRs, one type linked to BK channels and another type not linked. In this way, there is a constant proportionality between RyRs of the first type and BK channels, but this proportionality will be weakened by RyRs of the second type. In this way, a weak correlation will emerge between spark signal mass and STOC amplitude. One interesting feature of this sort of mechanism is that it suggests a physical linkage, direct or indirect, between RyRs and BK channels reminiscent of the link between RyRs and L-type Ca²⁺ channels in skeletal muscle.

We would like to thank Ian Parker, Karl Magleby, Michael Stern, Michael Kirber, and Catherine O'Reilly for their thoughtful reading of the manuscript and helpful comments and discussion. We thank Jeffrey Carmichael, Rebecca McKinney, and Paul Tilander for excellent technical assistance, and Stephen Baker for help with the statistical analysis.

This study was supported by a grant from the National Institutes of Health (HL 61297-01) and grants from the National Science Foundation (DBI-9724611 and DIR9200027).