Correspondence to: John V. Walsh, Jr., Department of Physiology, University of Massachusetts Medical Center, Worcester, MA 01655-027. Fax:(508) 856-5997 E-mail:john.walsh{at}umassmed.edu.
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Abstract |
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Ca2+ sparks are highly localized cytosolic Ca2+ transients caused by a release of Ca2+ from the sarcoplasmic reticulum via ryanodine receptors (RyRs); they are the elementary events underlying global changes in Ca2+ in skeletal and cardiac muscle. In smooth muscle and some neurons, Ca2+ sparks activate large conductance Ca2+-activated K+ channels (BK channels) in the spark microdomain, causing spontaneous transient outward currents (STOCs) that regulate membrane potential and, hence, voltage-gated channels. Using the fluorescent Ca2+ indicator fluo-3 and a high speed widefield digital imaging system, it was possible to capture the total increase in fluorescence (i.e., the signal mass) during a spark in smooth muscle cells, which is the first time such a direct approach has been used in any system. The signal mass is proportional to the total quantity of Ca2+ released into the cytosol, and its rate of rise is proportional to the Ca2+ current flowing through the RyRs during a spark (ICa(spark)). Thus, Ca2+ currents through RyRs can be monitored inside the cell under physiological conditions. Since the magnitude of ICa(spark) in different sparks varies more than fivefold, Ca2+ sparks appear to be caused by the concerted opening of a number of RyRs. Sparks with the same underlying Ca2+ current cause STOCs, whose amplitudes vary more than threefold, a finding that is best explained by variability in coupling ratio (i.e., the ratio of RyRs to BK channels in the spark microdomain). The time course of STOC decay is approximated by a single exponential that is independent of the magnitude of signal mass and has a time constant close to the value of the mean open time of the BK channels, suggesting that STOC decay reflects BK channel kinetics, rather than the time course of [Ca2+] decline at the membrane. Computer simulations were carried out to determine the spatiotemporal distribution of the Ca2+ concentration resulting from the measured range of ICa(spark). At the onset of a spark, the Ca2+ concentration within 200 nm of the release site reaches a plateau or exceeds the [Ca2+]EC50 for the BK channels rapidly in comparison to the rate of rise of STOCs. These findings suggest a model in which the BK channels lie close to the release site and are exposed to a saturating [Ca2+] with the rise and fall of the STOCs determined by BK channel kinetics. The mechanism of signaling between RyRs and BK channels may provide a model for Ca2+ action on a variety of molecular targets within cellular microdomains.
Key Words: widefield digital microscope, sarcoplasmic reticulum, microdomain, STOC, smooth muscle release
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INTRODUCTION |
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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)1 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 (
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 (
Studies of the quantitative relationship between Ca2+ sparks and STOCs have focused largely on establishing and corroborating the causal link between them (
To date, studies of Ca2+ sparks have measured changes in fluorescence relative to background (F/F0 or 100 x (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
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., ICa(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 (
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 ICa(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 ICa(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.
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MATERIALS AND METHODS |
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Preparation of Cells and Patch-Clamp Recording
Single smooth muscle cells were enzymatically dispersed from the stomach muscularis of Bufo marinus as described previously (
Detection and Measurement of Ca2+ Sparks
The following two measures of Ca2+ sparks were used: the conventional fluorescence ratio, F/F0; and the change in total fluorescence FT - F0T, 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 (
Fluorescence Ratio
For this measure, the fluo-3 images were first smoothed by convolution with a 3 x 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:
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(1) |
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 F/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.
Ca2+ Quantity or Signal Mass
During a spark, free Ca2+ (diffusion coefficient, D = 250 µm2/s) and Ca2+ bound to fluo-3 (D = 22 µm2/s;
Total fluorescence,
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(2) |
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 F /F0 images from Equation 1.
Signal mass,
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(3) |
The signal mass sm(t) is the change in total fluorescence FT(t) over the baseline fluorescence FT(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 (FT) 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,
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(4) |
Total noise,
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(5) |
Fluorescence flux,
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(6) |
Flux noise,
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(7) |
Spark threshold,
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(8) |
(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 Equation 6 and Equation 7, t = 10 ms is the time between two consecutive images. Equation 8 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 x 17 pixels, and further increase was negligible for areas larger than 41 x 41 pixels. A larger area was not used to avoid decreasing the signal to noise ratio; i.e., the total noise (T) in Equation 5 increases with an increase in measurement area, whereas the signal mass in Equation 3 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 sparkSTOC 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.
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Calibration of Signal Mass into Moles of Ca2+
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 (
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 x 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 Equation 3 was converted into moles of Ca2+ using the formula:
Ca2+ -bound fluo-3 (moles)=0.41x10-23·sm(t).
Similarly the flux, f(t) of Equation 6 is converted to Ca2+ current using the formula:
ICa(spark)(amps)=7.9x10-19·flux(t).
The average detection threshold for all sparks was a flux equal to 0.89 x 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 x 10-20 mol Ca2+ in 10 ms (or
0.1 pA).
The Fraction of Free Ca2+ Detected
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 reactiondiffusion kinetics in a cylindrical coordinate system. The details of this approach are described elsewhere (
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 (
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.
Reagents
All chemicals except fluo-3 (Molecular Probes) were purchased from Sigma-Aldrich.
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RESULTS |
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The Quantity of Ca2+ Released into the Cytosol by a Ca2+ Spark Can Be Determined Using High Temporal Resolution, Widefield Digital Microscopy
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, F/F0) for the single pixel (333 x 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 ICa(spark); as with the signal mass, the value given for ICa(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 F/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 (
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 F/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.
Characterization of Ca2+ Sparks
Although sparks have been studied previously in a number of smooth muscle types (F/F0).
Signal Averaging Based on STOCs Makes Possible a Kinetic Analysis of Ca2+ Signal Mass
To analyze the relationship between the underlying ICa(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.
Ca2+ Sparks Are Caused by the Concerted Opening of Multiple Ryanodine Receptors
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 ICa(spark) will be the same; if the sparks are due to the concerted opening of multiple RyRs, ICa(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 ICa(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 ICa(spark). The data in Fig 5 B are useful since they provide an estimate of the range of values for ICa(spark) over the population of sparks. The slopes in Fig 5 B are 0.08, 0.23, 0.23, and 0.45 x 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 ICa(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 ICa(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 ICa(spark) equal to 0.23, 0.66, 0.66, and 1.31 pA. For comparison,
STOC Amplitudes in the Presence and Absence of 50 µM Fluo-3
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.
Fluorescence Ratio Estimate of Ca2+ Concentration during a Spark Is a Poor Predictor of STOC Amplitude
Is the relative [Ca2+] at the peak of a spark, as estimated by F/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
F/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).
Many Ca2+ Sparks Fail to Cause STOCs
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 [ F/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 x 10-20 mol Ca2+ vs. 4.0 ± 0.2 x 10-20 mol Ca2+, P = 0.001; and t1/2 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.
Variation in Signal MassSTOC Coupling Ratio Is due in part to Variation in Ratio of RyRs/BK Channels
Are larger STOCs caused by ICa(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 ICa(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 ICa(spark) gives rise to a STOC current that varies by about threefold for the four groups. The mean ICa(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 ICa(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 ICa(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 (Po) does. In turn, this variability in Po 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 Po 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
Consider next the possibility that Po 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 Po 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 Po 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 ICa(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.
STOC Activation Kinetics Are Not Altered by Variations in Mean ICa(spark)
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 ICa(spark)) cannot account for the difference in coupling ratio at this time point. Moreover, large variations in ICa(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 ICa(spark) (Fig 5 B) were substantial among the four groups of data, it was possible to examine the effect of signal mass and ICa(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 ICa(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.
The Decay Rate of STOCs Corresponds to the BK Channel Open Time and Is Independent of the Magnitude of the Signal Mass and ICa(spark)
Does the rate of decay of the STOC depend on the magnitude of the spark signal mass or the underlying ICa(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 ICa(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 2040 ms (
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Simulations of Changes in [Ca2+] in the Spark Microdomain Based on Measured ICa(spark)
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 ICa(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 ICa(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 [
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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 12 ms. In either event, the BK channels will respond as though the [Ca2+] is unchanging after the first 12 ms. Thus, a step of Ca2+ current (i.e., ICa(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 12 ms. This could account for the similarity of the kinetics of the rising phase of the STOCs at all levels of ICa(spark) (Fig 5).
Examination of the [Ca2+] profile at the end of the ICa(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 ICa(spark) (Fig 10), and it corresponds to the mean open time of the BK channels in this preparation (
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DISCUSSION |
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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
Ca2+ Sparks Are due to the Concerted Opening of Multiple RyRs
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 (1 nM. Measurements of lumenal [Ca2+] in the cells used here indicate a value on the order of 150 µM (
Clearance of Ca2+ Liberated by a Ca2+ Spark
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 (
The Kinetics of STOCs
Although there is an extensive literature on STOCs, there is relatively little information on the kinetics of their rise and decay (
The STOC decay was well fit by a single exponential with a time constant of 2430 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 (
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 ß subunits and perhaps other factors. Most appropriate for the present study is a comparison to the behavior of BK channels examined by 34 ms which, in the work of Markwardt and Isenberg, resulted from a [Ca2+] jump in excess of 20 µM (Fig 9 A in
The Mechanism of STOC Generation by Ca2+ Sparks: Two Views
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 Po 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 Po 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 Po 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 Po 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 ICa(spark). However, the amplitude of the STOC for a given magnitude of the ICa(spark) will vary depending on the density of the BK channels. And the STOC amplitude will increase the longer the duration of the ICa(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 Po 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.
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Footnotes |
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R. ZhuGe and K.E. Fogarty contributed equally to this work.
1 Abbreviations used in this paper: BK channel, large conductance Ca2+-activated K+ channel; FWHM, full width at half maximum; PSF, point spread function; RyR, ryanodine receptor; I(Ca)spark, Ca2+ spark Ca2+ current; STOC, spontaneous transient outward current; TTP, time to peak.
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Acknowledgements |
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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).
Submitted: 19 September 2000
Revised: 24 October 2000
Accepted: 25 October 2000
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References |
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