Calcium sparks: single-channel vs. multiple-channel hypothesis
Determining the nature of calcium sparks is one of the most critical issues for studies of excitation-contraction coupling. If sparks represent single openings of SR calcium release channels, then they offer a direct observation of the calcium release process at the smallest physiological length scale. If, on the other hand, sparks are due to regenerative gating of multiple release channels, then channel properties can only be inferred indirectly from spark data, in a model-dependent way. We attempted to distinguish between these two possibilities by studying the effect of reducing SR calcium stores. We reasoned that, if sparks are due to a calcium-mediated regenerative process, they might be abolished altogether by a modest reduction in the amount of released calcium which would reduce the positive feedback gain below the threshold for local regeneration. This did not occur: sparks were robustly observed, albeit at reduced frequency and amplitude, when SB calcium was depleted by nearly 2/3. Since the effect of SR depletion was quantitative rather than qualitative, definitive interpretation of the observed effects requires a correction for the major sampling bias introduced by confocal linescan imaging. After this correction (see below), the total number of sparks estimated was equal to the number of sparks (of amplitude greater than 1.22) present under control conditions, as if the only effect of SR depletion were to reduce the amplitude of all sparks by a constant factor (s). This result is what would be expected if sparks represent single openings of a channel whose opening rate is independent of the unitary calcium release flux, and is not modulated by [Ca2+] inside the SR. Further, when the same correction was used to estimate the mean amplitude of all sparks with amplitudes greater than 1 + 0.22s, it was found to be linearly correlated to releasable SR calcium content, which is a satisfying result, although it is not necessarily required that SR luminal [Ca2+] be linearly related to total releasable calcium, or that release channel unitary calcium flux be linearly proportional to luminal [Ca2+]. The results of this study, as interpreted in the light of our simple statistical model of the spark detection process, are favourable to the single-channel hypothesis of spark generation. Even without statistical assumptions, our data show clearly that any model of the spark as due to multi-channel local regenerative CICR must be sufficiently robust to produce regenerative events even when only about 1/3 of the normal resting SR calcium load is present.
This may be understood more clearly with reference to the theoretically predicted behaviour of a cluster of CICR channels. Three regimes can be defined as a function of increasing unitary release flux (related to the releasable SR calcium content). In regime I the unitary release flux is small (relative to CICR sensitivity), so there is only a small probability that a spontaneous channel opening will recruit other channels in the cluster. In this regime, the frequency of events is independent of the permeating flux, and will depend on SR content only to the extent that the latter can directly influence release channel gating. The amplitude of fluorescence events, which is roughly proportional to release flux (G. Smith & H. Cheng, unpublished calculations), will be proportional to the unitary release flux. The apparent amplitude and frequency of detected events will be determined by the interaction of this proportional scaling with detectability, so that the estimated amplitude and frequency obtained by our correction procedure will give constant frequency and linear amplitude dependence, as we observed. In regime II the unitary flux is large enough to recruit additional CICR channels. For a sufficiently large cluster, there will be a narrow, threshold-like range of unitary flux over which the amplitude of events increases at a greater than linear rate from the amplitude characteristic of a single channel to that of the whole cluster. If, as suggested by Lipp & Niggli (1996), the single-channel events are too small to detect, then apparent frequency will rise rapidly in this regime, even after ‘correction’ by our method which assumes linear scaling of the amplitude distribution. Finally, in regime III, every opening of a channel triggers a regenerative activation of all the channels in the cluster. In this regime, the amplitude will again rise only linearly with unitary flux, since the number of activated channels is constant. The event statistics in regime III will therefore resemble those in regime I, except that the apparently ‘elementary’ event is actually a stereotyped cluster regeneration. The practical upper limit of regime III comes at the point where activation can spread to neighbouring clusters. In terms of these ideas, we can say that our data show that the range of SR loading between 36 and 100% of the normal resting value must lie entirely in regime I (single-channel openings) or entirely in regime III (robust cluster regenerations).
At first glance, our conclusions seem to be at odds with the observation by Parker, Zang & Wier (1996) that a majority of calcium sparks involves multiple sites hundreds of nanometres apart within the same Z-line zone. However, it is well-known that a continuum of behaviour of intracellular calcium dynamics can be observed under the ‘same’ experimental conditions (Wier, Cannell, Berlin, Mar ban & Lederer, 1987; Cheng et al. 1996a; Lukyanenko et al. 1996), presumably due to cellular inhomogeneity in calcium load. In rat ventricular myocytes, which exhibit spontaneous calcium waves and sparks, correlating observations with the frequency of waves and sparks seemed to us provide a practical way for a meaningful integration of results from different studies. Cells chosen in the present study were all quiescent during a 1 min observation period (see Methods) and had a rate of spontaneous sparks from 0.35 to 4.26s−1(100 μm)−1 whereas spark rate in the study of Parker et al. (1996) appears to be much higher (31 and 48s−1 (100 μm)−1, estimated from their Figs 1 and 3, respectively). Besides, our own data show rare radial or longitudinal regeneration of calcium sparks in rat and mouse ventricular myocytes (Cheng et al. 1996b) except in cells showing higher frequency of calcium waves and calcium sparks (H. Cheng, unpublished observations). Therefore, the apparently conflicting observations could be reconciled, e.g. by a difference in SR loading conditions in these studies.
If our results are interpreted in favour of single-channel spark generation, then it becomes necessary to deal with a paradox of independence. How can single CICR channels gate independently when it is known that they are located in dense clusters? Simple diffusion calculations show that the local [Ca2+] in the vicinity of an open release channel will be large compared to the global value produced by photorelease in the experiments of Lipp & Niggli (1996) in which CICR was observed without discrete sparks. Local [Ca2+] at the cardiac diad junction is expected to be comparable to the levels required for steady-state activation of the cardiac RyRs in lipid bilayers, even in the presence of physiological [Mg2+] (Valdivia, Kaplan, Ellis-Davies & Lederer, 1995; Langer & Peskoff, 1996). Under these conditions it is difficult to imagine that RyRs act independently (regime I).
Optical sampling error and the correction algorithm
The confocal linescan samples fluorescence along a single line parallel to the long axis of the myocyte. While SR release channels are located almost exclusively at the plane of the Z-line of the sarcomere (Carl et al. 1995), there is no evidence that they have any preferred location within that plane. If sparks are located randomly within the plane of the Z-line, then the number of sparks located within a given perpendicular distance from the scan line will increase as the square of that distance. Calculations using simulated spark fluorescence profiles show that this would result in a distribution of apparent spark amplitudes which is monotonically decreasing, without a mode (E. Ríos, M. Stern & H. Cheng, unpublished results), and that it is nearly impossible to get a modal distribution using any plausible spark fluorescence profile (M. Stern & E. Ríos, unpublished results). Despite this, most published studies of calcium sparks selected by eye show a modal or multi-modal amplitude distribution.
To investigate this paradox, we developed an objective computer algorithm to identify and measure calcium sparks in confocal linescan images. This algorithm finds roughly twice as many sparks as are identified by eye (1.50 versus 0.73–0.85 s−1 (100 μm)−1 under control conditions; Cheng et al. 1996a,b; Lukyanenko et al. 1996), and they are predominantly small in amplitude, so that the resulting distributions both before and after thapsigargin are strongly skewed to the low-amplitude end. This distribution pattern is compatible with the theoretical prediction of a monotonically decreasing amplitude distribution, if we take the detection efficiency into account. Given the detectability function (Fig. 2D), it is possible to ‘correct’ the observed amplitude distribution to estimate the number of sparks which actually occurred with amplitudes greater than 1.22. In order to correct spark statistics during SR depletion, a further assumption is needed. It is necessary to extrapolate the number of sparks of amplitude less than 1.22, for which there is no information in the measured distribution from SR-depleted cells. In order to make this extrapolation in the least model-dependent way possible, we used the control amplitude distribution as an extrapolating function. This was done by assuming that the effect of SR depletion on spark amplitude is a uniform scaling of the amplitudes ΔF/Fo by a factor s between zero and one. The applicable factor was determined by a least-squares fit of the scaled control amplitude distribution to the measured amplitude distribution from SR-depleted cells. The goodness of fit was measured by the χ2 test, which showed that the observed amplitude distributions from thapsigargin-treated cells were compatible with this scaling hypothesis. The scaled control distribution was then used to estimate the number of unobserved sparks which were present with amplitudes from 1 + 0.22s to 1.22. As discussed above, this correction procedure significantly altered the scenario in interpreting data for SR calcium depletion. This methodology should be useful for future studies on physiological and pharmacological modulation of elementary release events.
Comparison with previous studies
Our finding that depletion of SR calcium reduced the apparent spark frequency is in agreement with the observation in rabbit ventricular myocytes in which both the SR calcium content and spark frequency are gradually decreased during rest after regular electrical stimulation (Satoh, Blatter & Bers, 1997). Previous in vitro studies using cell-free systems suggest that SR calcium may modulate RyRs (a) through direct or indirect (via calsequestrin) interaction from the luminal side (Fabiato, 1985; Ikemoto, Ronjat, Meszaros & Koshita, 1989; Kawasaki & Kasai, 1994; Györke, Lukyanenko & Györke, 1997), or (b) when released, binding to activation and inactivation sites of RyRs on the cytosolic side (Tripathy & Meissner, 1996). Since the resting [Ca2+]cyto and the corrected rate of spark occurrence were unchanged when SR calcium was highly depleted, the present results indicate that SR intraluminal calcium content is not a major physiological modulator of ryanodine receptor gating in vivo under our experimental conditions (i.e. depletion of SR calcium). This underscores the importance of studying regulation of RyRs in intact cells and in the physiological context. Nevertheless, it should be pointed out that our data do not exclude the possibility that at elevated calcium load, luminal calcium could affect RyR gating (Fabiato, 1985; Stern, Capogrossi & Lakatta, 1988; Cheng et al. 1996a; Györke et al. 1997). In this regard, studies in cells challenged with 10 mm external Ca showed that a 30% increase in SR calcium is associated with a fourfold increase in the spark frequency (Cheng et al. 1996a; Lukyanenko et al. 1996). The increase in spark frequency is in part accounted for by increased [Ca2+]cyto, as we proposed previously (Cheng et al. 1996a). In the light of the present results, the spark frequency increase may also be attributable to an enhanced detectability, since spark amplitudes are increased under calcium overload conditions.
Furthermore, the present data on elementary release events fit nicely with our previous findings at the whole-cell level that calcium transients elicited by L-type calcium current and the gain function of SR calcium release are linearly correlated with the caffeine-induced calcium transient (Janczewski & Lakatta, 1993; Janczewski, Spurgeon, Stern & Lakatta, 1995), as if the total number of release units recruited was unchanged but each had a proportionally reduced amount of released calcium.
The results of this study, when contrasted with those of other studies of spark statistics, in which sparks were identified by eye, show that the distributions of spark parameters are subject to strong observer selection bias, which can create an apparently normal distribution from events whose amplitudes are distributed monotonically. The criteria used in our spark identification algorithm were simple, and based largely on the amplitude of the event. It is possible that a more sophisticated method could discriminate nearby sparks from those farther from the scan line (for example, the rise time of nearby sparks ought to be faster); this would restore the ability to determine the mode (if any) of the underlying distribution of calcium release events. Model calculations show that this will be difficult with the present generation of fluorescent probes and detection hardware; more sophisticated methods need to be devised to determine the true nature of calcium sparks. In the meanwhile, it is necessary to be wary of the effects of selection bias in spark studies.