Relationship between L-type Ca2+ current and unitary sarcoplasmic reticulum Ca2+ release events in rat ventricular myocytes

Authors

  • Mei Lin Collier,

    1. Department of Physiology, Allegheny University of the Health Sciences and *Department of Pathology, Anatomy and Cell Biology, Thomas Jefferson University, Philadelphia, PA, USA
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  • Andrew P. Thomas,

    1. Department of Physiology, Allegheny University of the Health Sciences and *Department of Pathology, Anatomy and Cell Biology, Thomas Jefferson University, Philadelphia, PA, USA
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  • Joshua R. Berlin

    1. Department of Physiology, Allegheny University of the Health Sciences and *Department of Pathology, Anatomy and Cell Biology, Thomas Jefferson University, Philadelphia, PA, USA
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  • Author's present address

    A. P. Thomas: Department of Pharmacology and Physiology, University of Medicine and Dentistry of New Jersey, 185 S. Orange Avenue, Newark, NJ 07103, USA.

Corresponding author J. R. Berlin: Department of Pharmacology and Physiology, University of Medicine and Dentistry of New Jersey, 185 S. Orange Avenue, Newark, NJ 07103, USA. Email: berlinjr@umdnj.edu

Abstract

  • 1The time courses of Ca2+ current and Ca2+ spark occurrence were determined in single rat ventricular myocytes voltage clamped with patch pipettes containing 0.1 μM fluo-3. Acquisition of line-scan images on a laser scanning confocal microscope was synchronized with measurement of Cd2+-sensitive Ca2+ currents. In most cells, individual Ca2+ sparks were observed by reducing Ca2+ current density with nifedipine (0.1-8 μM).
  • 2Ca2+ sparks elicited by depolarizing voltage-clamp pulses had a peak [Ca2+] amplitude of 289 ± 3 nM with a decay half-time of 20.8 ± 0.2 ms and a full width at half-maximum of 1.40 ± 0.03 μm (mean ± s.e.m., n= 345), independent of the membrane potential.
  • 3The time between the beginning of a depolarization and the initiation of each Ca2+ spark was calculated and data were pooled to construct waiting time histograms. Exponential functions were fitted to these histograms and to the decaying phase of the Ca2+ current. This analysis showed that the time constants describing Ca2+ current and Ca2+ spark occurrence at membrane potentials between -30 mV and +30 mV were not significantly different. At +50 mV, in the absence of nifedipine, the time constant describing Ca2+ spark occurrence was significantly larger than the time constant of the Ca2+ current.
  • 4A simple model is developed using Poisson statistics to relate macroscopic Ca2+ current to the opening of single L-type Ca2+ channels at the dyad junction and to the time course of Ca2+ spark occurrence. The model suggests that the time courses of macroscopic Ca2+ current and Ca2+ spark occurrence should be closely related when opening of a single L-type Ca2+ channel initiates a Ca2+ spark. By comparison with the data, the model suggests that Ca2+ sparks are initiated by the opening of a single L-type Ca2+ channel at all membrane potentials encountered during an action potential.

Electrically stimulated intracellular Ca2+ ([Ca2+]i) transients in mammalian cardiac muscle are largely due to release of Ca2+ from the sarcoplasmic reticulum (Bers, 1991). One step in the mechanism that links membrane depolarization to release of intracellular Ca2+ stores is the influx of Ca2+ via L-type Ca2+ channels (Fabiato, 1985; Näbauer et al. 1989). This pathway for Ca2+ influx is routinely measured as the macroscopic Ca2+ current (ICa) and many investigations have demonstrated that the membrane potential (Vm) dependence of ICa can be similar to the Vm dependence of the [Ca2+]i transient (Cannell et al. 1987; Beuckelmann & Wier, 1988; Cleeman & Morad, 1991). Even so, more recent reports have shown that the relationship between ICa and [Ca2+]i transient amplitude is Vm dependent in a manner that suggests the efficacy of excitation-contraction (E-C) coupling is a function of single Ca2+ channel current amplitude rather than the total influx of Ca2+ during ICa (López-López et al. 1995; Santana et al. 1996) This apparent divergence between ICa amplitude and control of sarcoplasmic reticulum (SR) Ca2+ release is thought to be evidence in support of the ‘local control’ formalism for the Ca2+-induced Ca2+ release mechanism which postulates that localized changes of [Ca2+] in the dyad cleft, rather than global changes of [Ca2+]i, regulate SR Ca2+ release (Stern, 1992). If this is correct, measurements of ICa, by themselves, do not represent an accurate means to access the processes controlling localized increases in [Ca2+]i that trigger SR Ca2+ release. Thus, in the absence of single Ca2+ channel current measurements, a reasonable means must be found to extrapolate between ICa and events at the single channel level in order to understand how Ca2+ influx triggers SR Ca2+ release.

Localized increases of [Ca2+]i in resting myocytes, termed ‘Ca2+ sparks’ (Cheng et al. 1993) have been observed during stimulated increases of [Ca2+]i (López-López et al. 1994, 1995; Berlin, 1995; Cannell et al. 1995; Lipp & Niggli, 1996) and are thought to represent unitary SR Ca2+ release events, even if several functionally coupled ryanodine receptors actually contribute to Ca2+ release flux during each event (Lipp & Niggli, 1996). At the most basic level, the global increases in [Ca2+]i that occur during a [Ca2+]i transient can be thought of as the summation of these localized, unitary release events.

The ability to observe Ca2+ sparks offers a new avenue to study how opening of sarcolemmal Ca2+ channels and the subsequent Ca2+ influx regulate SR Ca2+ release. In this regard, several questions remain to be answered about the manner in which Ca2+ influx triggers unitary SR Ca2+ release events. For example, recent electron microscopic studies in developing chick heart have observed clusters of intramembrane particles localized in the surface membrane of the dyadic cleft (Protasi et al. 1996). By analogy to studies with skeletal muscle, these particles are presumed to be sarcolemmal Ca2+ channels, i.e. dihydropyridine receptors (Protasi et al. 1998). If correct, these results suggest that the dyad includes clusters of surface membrane Ca2+ channels in close apposition to clusters of ryanodine receptors on junctional SR membranes.

The presence of clusters of L-type Ca2+ channels in the dyadic junction raises the possibility that unitary SR Ca2+ release events are triggered by opening of multiple surface Ca2+ channels. In addressing this possibility, Cannell et al. (1995) and, more recently Santana et al. (1996), showed that an e-fold increase in the amplitude of Ca2+ current and incidence of ‘Ca2+ sparks’ occurred over approximately 7 mV in the range of Vm near the threshold for L-type Ca2+ channel opening. The similar voltage dependence for activation of these two processes suggests that the opening of a single Ca2+ channel on the surface membrane is sufficient to trigger a Ca2+ spark (Santana et al. 1996). Since E-C coupling normally occurs at more depolarized potentials, these authors also examined the relationship between ICa amplitude and the probability of Ca2+ spark occurrence over a wide range of Vm. By assuming that (1) single Ca2+ channel ion flux rates can be approximated using the Goldman-Hodgkin-Katz constant field equation and (2) instantaneous open probability of the SR release channel is a square function of dyadic [Ca2+], Santana et al. (1996) concluded that opening of a single L-type Ca2+ channel was sufficient to trigger a Ca2+ spark over a broad range of Vm values. However, given the difficulty in verifying these crucial assumptions, a more straightforward means to examine the relationship between ICa and Ca2+ spark occurrence is needed. Thus, in this study, the kinetics of ICa and Ca2+ spark occurrence were measured in voltage-clamped rat ventricular myocytes. Using Poisson statistics to describe ICa in terms of L-type Ca2+ channel openings, we were then able to analyse directly how changes in ICa related to the appearance of Ca2+ sparks during voltage-clamp depolarizations.

This work has appeared, in part, as preliminary communications (Collier et al. 1997, 1998).

METHODS

General procedures

Hearts were obtained from male Sprague-Dawley rats (150-250 g) anaesthetized by intraperitoneal injection with pentobarbital (50 mg kg−1) in accordance with procedures approved by the Institutional Animal Care and Use Committee of The Graduate Hospital. Single rat ventricular myocytes were isolated enzymatically as previously described (Konishi & Berlin, 1993) and placed in a chamber mounted on an inverted Olympus microscope (Olympus Inc., Melville, NY, USA). The whole-cell patch-clamp configuration was used to measure membrane currents with a Dagan 8900 amplifier (Dagan Corporation, Minneapolis, MN, USA). Series resistance was compensated electronically, when necessary, to less than 1.5 MΩ. Patch pipettes were pulled using a Flaming-Brown puller (Sutter Instrument Co., Novato, CA, USA) to give resistances of 1-2 MΩ and filled with a solution containing (mM): 130 caesium glutamate, 10 NaCl, 10 Hepes (caesium salt), 5 dextrose, 20 TEACl, 0.33 MgCl2, 0.1 Tris-GTP, 4 Mg-ATP, 5 Tris2-creatine phosphate and 0.1 fluo-3 (pentapotassium salt), pH 7.2. During experiments cells were continuously superfused with a Hepes-buffered Tyrode solution composed of (mM): 137 NaCl, 5 KCl, 1.5 CaCl2, 5 Hepes, 1 NaH2PO4, 1.2 MgCl2, pH 7.4. Prior to measuring ICa, the external solution was changed to a modified Tyrode solution containing equimolar CsCl instead of KCl, 10 mM TEACl and 4 mM 4-aminopyridine to block K+ channels, 0.03 mM tetrodotoxin to block Na+ channels and 1 mM CaCl2. To observe individual Ca2+ sparks, ICa was reduced in many experiments by addition of nifedipine (0.1-8.0 μM) to the modified Tyrode solution. All experiments were performed at room temperature.

Steady-state SR Ca2+ load was maintained by delivering three conditioning depolarizations of 100 ms duration from -80 to 0 mV at 1 Hz. Following the conditioning pre-pulses, the cell was depolarized to -50 mV with a 500 ms ramp to promote Na+ channel inactivation and then depolarized to various membrane potentials for 200 ms. This protocol was repeated 30-40 times in each cell examined. All membrane current data were analysed using pCLAMP software, version 6.0.3 (Axon Instruments). Difference currents were obtained after linear leak subtraction. ICa could be blocked by substituting CaCl2 with 200 μM CdCl2.

Recording and analysis of Ca2+ sparks

Fluo-3 fluorescence was measured with a laser scanning confocal microscope (Biorad MRC 600, Cambridge, MA, USA) using a plan-apo, ×60 oil-immersion objective lens, NA 1.4, during illumination with 488 nm light. To minimize cell damage by photobleaching, illumination was limited to 300 ms periods with an electronic shutter. A neutral density filter allowing 1 % transmission was also placed between the Ar-Kr laser and the confocal scan-head. Initiation of laser light scanning across the cell was synchronized with voltage-clamp steps and opening of the electronic shutter. Line-scan images were obtained by repeatedly scanning the laser beam along a single raster line oriented with the long axis of a cell at 2 ms intervals (Cheng et al. 1993; Berlin, 1995; Cannell et al. 1995). Pixel size was equal to 0.138 μm. After acquisition, line-scan images were low pass filtered, averaging 3 pixels in each scan line and 2 pixels across scan lines (MetaMorph, Universal Imaging, West Chester, PA, USA). Events exhibiting both a rapid rise in fluorescence intensity (≤10 ms) and an increase in fluorescence intensity of greater than or equal to 2 standard deviations above mean baseline fluorescence intensity were analysed for amplitude, duration and waiting time (time from the beginning of the depolarizing pulse to the leading edge of increased fluorescence intensity) using custom-designed software. [Ca2+]i was calculated from fluo-3 fluorescence using the previously described pseudo-ratio equation (Cheng et al. 1993), assuming that the in situKD of fluo-3 for Ca2+ was 2.5 μM (Harkins et al. 1993) and basal [Ca2+]i was 100 nM.

Ca2+ sparks were treated as a representative sample of a population of randomly distributed stochastic events. This assumption allowed the application of analytical procedures analogous to those previously applied to study single ion channel kinetics. To determine the kinetics of the process controlling SR Ca2+ release events, waiting times for all Ca2+ sparks in a cell were tabulated into a cumulative waiting time histogram (Colquhoun & Hawkes, 1993) and an exponential function was fitted to the resulting data. Table 2 reports the mean ±s.e.m. of the exponential time constants determined in these calculations. For display purposes only, histograms were constructed by pooling waiting times into 10 ms bins (López-López et al. 1995). These histograms include data from all experiments using a normalization procedure that accounts for the number of Ca2+ sparks observed in each cell (see description in Results).

Table 2. The time course of Ca2+ current and Ca2+ spark occurrence
Voltage step (mV)No. of experimentsτ of ICa decay (ms)τ of Ca2+ spark occurrence* (ms)Student's t test (P value)
  1. TI, time independent.* The time constant of the expontential function fitted to the cumulative waiting time histogram; † in the absence of nifedipine; ‡ significantly different at P < 0.05.

−304TITI
+20625 ± 131 ± 60.30
+30525 ± 230 ± 70.50
+50†556 ± 696 ± 110.017‡

Statistics

A two-tailed ANOVA was used to establish significant differences among multiple groups and pairwise comparisons were carried out with Student's t test. Differences were considered to be statistically significant if the resulting P value was less than 0.05. Linear and non-linear curve fitting was carried out with least significant difference routines available in commercial software (SigmaPlot, Jandel Scientific, San Rafael, CA, USA). Data are presented as means ±s.e.m.

RESULTS

Rat ventricular myocytes were whole-cell voltage clamped with patch pipettes containing the K+ salt of fluo-3. Figure 1A shows that after allowing the dye to diffuse into the cytosol, fluorescence across the cell was uniform except for a few areas of increased fluorescence, such as the nuclei. In some cells, occasional local Ca2+ transients, termed ‘Ca2+ sparks’ (Cheng et al. 1993) were observed. Since spontaneous Ca2+ sparks share similar kinetics with Ca2+ sparks evoked by membrane depolarization (Cannell et al. 1995; López-López et al. 1995), only cells which exhibited a low number of spontaneous Ca2+ sparks were used in subsequent experiments. When ICa was reduced with 1 μM nifedipine, a step depolarization to +20 mV elicited Ca2+ sparks during the voltage-clamp pulse (Fig. 1B left). With subsequent addition of 200 μM cadmium, a blocker of Ca2+ channels, Ca2+ sparks were observed only very infrequently during the depolarizing step (Fig. 1B right). In a typical cell, Ca2+ sparks in the presence of cadmium were approximately 3 % of total Ca2+ sparks elicited during test depolarizations to +20 mV (3 of 95 in the cell shown in Fig. 1). Such a low incidence of spontaneous events is unlikely to affect significantly analysis of Ca2+ spark occurrence measured during test depolarizations.

Figure 1.

The effect of Ca2+ channel blockade on depolarization-induced Ca2+ sparks

A, a confocal image of a rat ventricular myocyte loaded with fluo-3 and voltage clamped at -80 mV in the absence of nifedipine. The raster line that was scanned to construct line-scan images in panel B of this figure is indicated by the horizontal white line through the image. B, line-scan images were obtained after the cell had been superfused for 3 min with nifedipine-containing modified Tyrode solution in the absence (left) and presence (right) of cadmium. Depolarizations of 200 ms duration to +20 mV were elicited at times indicated by bars to the left of the images.

Properties of Ca2+ sparks during test depolarizations

Initial experiments examined whether Ca2+ sparks evoked during depolarizing voltage-clamp pulses displayed Vm-dependent properties. In these experiments, peak amplitude together with spatial and temporal properties of Ca2+ sparks observed at each test depolarization were calculated. Figure 2 shows line-scan images of Ca2+ sparks activated during membrane depolarizations to -30 and +30 mV in different cells. Cumulative data from 40 depolarizations in the cell depolarized to -30 mV showed that [Ca2+]i at the peak of the Ca2+ spark was 295 ± 5 nM (n= 126), the full width at half-maximum (FWHM) was 1.4 ± 0.1 μm, and the decay half-time was 20.5 ± 0.9 ms. In the cell depolarized to +30 mV, peak [Ca2+]i was estimated to be 268 ± 4 nM (n= 100) with a FWHM of 1.4 ± 0.1 μm and decay half-time of 21.3 ± 1.3 ms. These data and others from cells subjected to depolarizations to +20 and +50 mV are summarized in Table 1. Although peak amplitude varied from one cell to another at each test potential, no Vm-dependent pattern was discernible. As a result, all data were pooled together and the mean Ca2+ spark amplitude was calculated to be 289 ± 3 nM (n= 345). Likewise, at all membrane potentials tested, Ca2+ spark FWHM and decay half-time were very similar (Table 1). Thus, in agreement with previous reports (Cannell et al. 1995; López-López et al. 1995) properties of Ca2+ sparks do not appear to be Vm dependent.

Figure 2.

Comparison of Ca2+ sparks at two membrane potentials

Line-scan images were acquired during depolarizations to membrane potentials of -30 and +30 mV. The images are oriented so that time is on the horizontal axis.

Table 1. The properties of depolarization-induced Ca2+ sparks
Voltage step (mV)No. of Ca2+ sparksCa2+ spark amplitude (nM)Decay half-time (ms)FWHM (μm)
−30126295 ± 520.5 ± 0.91.4 ± 0.06
+2042277 ± 620.8 ± 0.81.5 ± 0.05
+30100268 ± 421.3 ± 1.31.4 ± 0.05
+5077311 ± 521.2 ± 0.61.5 ± 0.06
Mean 289 ± 320.8 ± 0.21.4 ± 0.03

Effect of nifedipine on Ca2+ sparks

The Ca2+ channel blocker nifedipine was used in many experiments. As a result, the effects of this dihydropyridine on the relationship between ICa and Ca2+ spark occurrence was also examined. Figure 3 shows the amplitude and time course of ICa and representative line-scan images recorded during depolarizations to +50 mV in the absence and presence of 0.1 μM nifedipine. In this cell, peak ICa amplitude was reduced from 105 to 33 pA and the exponential time constant for current decay was changed from 51 to 63 ms with the addition of nifedipine (Fig. 3A and B, top). The time course of ICa was examined in several cells. In the presence of nifedipine, the time constant for current decay was 56 ± 6 ms (n= 5), a value not significantly different from the time constant of 68 ± 5 ms (n= 6) determined in the absence of nifedipine. These results are consistent with previous reports suggesting that dihydropyridines decrease ICa by reducing Ca2+ channel availability without altering the kinetics of single channel openings (Kawashima & Ochi, 1988; Méry et al. 1996).

Figure 3.

The effect of nifedipine on L-type Ca2+ current and Ca2+ sparks

A and B show Ca2+ current (top) and line-scan images (bottom) from a cell depolarized to a membrane potential of +50 mV during superfusion with modified Tyrode solution in the absence and presence of 0.1 μM nifedipine, respectively. The top panel in C shows voltage-clamp depolarization to +50 mV. The bottom panel in C shows the change in spatial mean [Ca2+]i expressed as the ratio (F/F0) of fluorescence intensity (F) divided by the fluorescence prior to depolarization (F0). Average fluorescence intensity was measured over a 35 μm wide region of a cell in the presence (+) and absence (-) of 0.1 μM nifedipine. The increase in F/F0 produced by depolarization was reduced in the presence of nifedipine.

Line-scan images showed that the number of Ca2+ sparks observed during a depolarization also declined in the presence of nifedipine. This result can most easily be appreciated in the bottom panels of Fig. 3A and B by noting that the number of locations showing localized increases in [Ca2+]i upon cell depolarization to +50 mV was greatly reduced in the presence of 0.1 μM nifedipine.

To determine if nifedipine has a direct effect on the ability of L-type Ca2+ channel openings to trigger SR Ca2+ release, the effect of nifedipine on the relationship between ICa and Ca2+ spark occurrence was examined. For this purpose, the ‘coupling ratio’ was calculated as the number of Ca2+ sparks divided by the integral of L-type Ca2+ current during the voltage step. This coupling ratio was calculated for depolarizations to +50 mV during the first 10 ms of the voltage step (at the time of peak ICa) in the presence and absence of nifedipine. During the first 10 ms of the voltage clamp pulse in the absence of nifedipine, the integral of ICa was 2.6 ± 0.2 pC and the number of Ca2+ sparks was 10 ± 2 (n= 4). The coupling ratio calculated from these data was 4.0 ± 0.6 pC−1 (n= 4). In the presence of 0.1 μM nifedipine, these calculations yielded a coupling ratio of 3.6 ± 1.1 pC−1 (n= 5). These values are not significantly different, consistent with the suggestion that nifedipine does not change the ability of L-type Ca2+ channel opening to trigger SR Ca2+ release.

Nifedipine also affects the level of spatial mean [Ca2+] reached during voltage-clamp depolarizations. In the absence of nifedipine, [Ca2+]i increased during the depolarization to +50 mV, even in those regions of the cell that did not display clear instances of local Ca2+ release (line-scan image in Fig. 3A). To quantify this increase, spatial mean [Ca2+] was measured over a 35 μm wide region in each cell that did not display any obvious Ca2+ spark activity. Initially, spatial mean [Ca2+] increased during the depolarization until a maintained plateau level was observed (Fig. 3A). The abrupt increase in spatially averaged [Ca2+] at the end of the depolarization was due to the occurrence of a Ca2+ transient triggered by membrane repolarization, as previously reported (Cannell et al. 1995). In five cells, the plateau level of spatially mean [Ca2+] during the depolarization was 265 ± 28 nM. By comparison, Fig. 3A also shows that the increase in [Ca2+]i was smaller in the presence of nifedipine, even though the time course of the increase was similar. In six cells, the final level of spatially averaged [Ca2+] was 168 ± 11 nM in the presence of nifedipine. Similar measurements carried out with depolarizations to +20 and +30 mV in the presence of nifedipine showed that the plateau levels of spatial mean [Ca2+] were 168 ± 11 nM (n= 6) and 165 ± 25 nM (n= 5), respectively. Thus, nifedipine reduced the rise in spatial mean [Ca2+] during test depolarizations to positive Vm values, presumably by decreasing ICa and the number of Ca2+ sparks occurring out of the plane of focus.

Relationship between ICa and Ca2+ spark occurrence

Figure 4 shows representative records of ICa (B), line-scan images (C) and Ca2+ spark waiting time histograms (D) for test depolarizations to -30 mV (left) and +30 mV (right) in the presence of micromolar concentrations of nifedipine. Test depolarizations to -30 mV produced a small ICa that displayed little or no inactivation during the course of the 200 ms voltage-clamp pulse. A representative line-scan image (Fig. 4A, left) showed that Ca2+ sparks occurred throughout the depolarizing pulse.

Figure 4.

L-type Ca2+ current and Ca2+ spark occurrence

A, voltage-clamp depolarizations to membrane potentials of -30 mV and +30 mV were applied to cells superfused with modified Tyrode solution containing nifedipine. B, Ca2+ currents averaged from 30 voltage-clamp depolarizations to -30 mV and 40 depolarizations to +30 mV are shown. The decaying phase of the Ca2+ current at +30 mV was fitted with a single exponential function (dashed curve). C, representative line-scan images obtained during a depolarization to -30 mV (left) and +30 mV (right). D, normalized Ca2+ spark waiting time histograms are shown. Ca2+ spark waiting times (see text) were pooled into 10 ms bins and normalized to the total number of Ca2+ sparks in each cell. Each bin of the histogram shows the average of the normalized data accumulated for 4 cells depolarized to -30 mV and 5 cells depolarized to +30 mV. The dashed curve is an exponential function that uses the mean time constant in Table 2 for depolarizations to +30 mV.

To determine if this behaviour was consistently observed for all experiments, normalized waiting time histograms of Ca2+ spark occurrence were constructed. The time from the beginning of the depolarization to the initial rapid increase in fluorescence during each Ca2+ spark, termed ‘Ca2+ spark waiting time’, was determined with custom-designed computer software. Calculated waiting times were then accumulated into 10 ms bins and are displayed as histograms of normalized Ca2+ spark occurrence. Normalization, to allow for comparison of data between different cells, was accomplished by dividing the number of Ca2+ sparks in each bin by the total number of Ca2+ sparks observed in a cell. The displayed values in each bin of Fig. 4A are the mean values of normalized Ca2+ spark occurrence for four cells.

Consistent with the line-scan image shown in the left panel of Fig. 4A, Ca2+ spark occurrence was similar throughout the depolarizing step (Fig. 4A, left). This point was confirmed by a regression analysis that showed that the slope of the best-fit line through the data was not significantly different from zero. Thus, neither ICa nor the occurrence of Ca2+ sparks displayed a clear time dependence during depolarizations to -30 mV.

With depolarizations to +30 mV, ICa was larger and displayed a time-dependent decay (Fig. 4A, right) that could be fitted with an exponential function. In five experiments, the best-fit time constant for current decay was 25 ± 2 ms (Table 2). The sample line-scan image also shows that most of the SR Ca2+ release events occurred at the beginning of the depolarization (Fig. 4A, right). This same behaviour was observed in all cells subjected to depolarizations to +30 mV, as is shown by the histogram of normalized Ca2+ spark waiting times accumulated for all cells (Fig. 4A, right). The greatest number of Ca2+ sparks occurred in the first 10 ms bin, corresponding to the time of peak ICa. Thereafter, Ca2+ spark occurrence decreased rapidly, again analogous to the time course of ICa. To estimate the kinetics of the process controlling the appearance of Ca2+ sparks, waiting times for SR Ca2+ release events in each cell were compiled into cumulative histograms and fitted with exponential functions. In five cells, the time constant for Ca2+ spark waiting times calculated with this fitting procedure was 30 ± 7 ms (Table 2). The dotted curve in Fig. 4A is an exponential function with a time constant of 30 ms that has been scaled to the normalized data to show that the process determining Ca2+ spark waiting times is well described by this exponential function. Importantly, the time constants describing ICa and the occurrence of Ca2+ sparks were not significantly different. Similar experiments with depolarizations to +20 mV also showed that the time constants for Ca2+ current and unitary SR Ca2+ release events were not significantly different (Table 2). As pointed out in the Discussion, these data suggest that opening of a single L-type Ca2+ channel is responsible for triggering Ca2+ sparks even at Vm as positive as +20 or +30 mV.

Figure 4D also shows a low incidence of Ca2+ spark occurrence during the latter portion of depolarizations to +30 mV even after current had reached a pseudo-steady-state level. These Ca2+ sparks late during the depolarization are presumably triggered by re-opening of sarcolemmal Ca2+ channels that have been observed in single L-type Ca2+ channel recordings (Rose et al. 1992) or represent a low rate of spontaneous Ca2+ spark occurrence.

Relationship between ICa and Ca2+ spark occurrence in the absence of nifedipine

The experiments in Fig. 4 were conducted in the presence of micromolar concentrations of nifedipine to reduce Ca2+ channel availability. These dihydropyridine concentrations are so high that one could argue, even if L-type Ca2+ channels are clustered in the sarcolemma at the dyad, the chance of more than one channel opening within a cluster would be remote. Thus, it would not be surprising if our previous experiments suggested that Ca2+ influx through single sarcolemmal Ca2+ channels regulated unitary SR Ca2+ release events. A more pertinent question might be whether opening of a single sarcolemmal channel will regulate SR release events even when L-type Ca2+ availability is high.

To address this question, experiments must be performed in the absence of Ca2+ channel inhibitors. As already demonstrated in Fig. 3, depolarizations to +50 mV allowed individual Ca2+ sparks to be visualized even in the absence of nifedipine. Experiments at +50 mV also have three advantages for the question raised above. First, at +50 mV, open probability for L-type channels is maximal (McDonald et al. 1994), increasing the likelihood that more than one channel will open in any cluster of L-type Ca2+ channels. Second, the coupling efficiency between sarcolemmal Ca2+ channel opening and Ca2+ spark initiation is low (Santana et al. 1996) so that increased Ca2+ influx due to multiple Ca2+ channel openings in the surface membrane at the dyad would be expected to increase the coupling efficiency. Third, inactivation of ICa is complete under steady-state conditions (Cohen & Lederer, 1988; Richard et al. 1993), so that triggered Ca2+ sparks would be expected to decrease to zero with very long depolarizations. This last point simplified curve-fitting procedures because the exponential function fit to ICa could be assumed to decay to zero. In the light of these assumptions, the relationship between ICa and Ca2+ sparks was examined in myocytes depolarized to +50 mV.

Figure 5 shows a representative tracing of membrane current along with a line-scan image recorded during a depolarization to +50 mV in a cell that was not exposed to nifedipine. The amplitude of ICa was quite small, but the time course of current decay could still be fitted with an exponential function (Fig. 5A). Likewise, individual line-scan images (Fig. 5A) indicated that most Ca2+ sparks occurred in the early portion of the depolarization. Normalized waiting time histograms constructed from SR release events recorded in five cells showed that Ca2+ spark occurrence was time dependent (Fig. 5A). To determine the kinetics of Ca2+ spark occurrence in these cells, cumulative waiting time histograms were constructed for each cell and the time constant for the best-fit exponential function was determined to be 96 ± 11 ms (n= 5). The dotted curve in Fig. 5A is an exponential function with this time constant. Although more variability is present from one bin to the next, owing to a lower number of total events, the exponential curve generally follows the data in the normalized waiting time histogram.

Figure 5.

L-type Ca2+ current and Ca2+ spark occurrence in the absence of nifedipine

Top panel in A shows the voltage-clamp depolarization to +50 mV. Bottom panel in A shows Ca2+ current averaged from 30 voltage-clamp depolarizations in a cell superfused with nifedipine-free modified Tyrode solution. The dashed curve is an exponential fit to the decaying phase of the current. B, a representative line-scan image obtained during a depolarization. C, normalized waiting time histogram of Ca2+ spark occurrence averaged for 5 cells. The dashed curve was drawn with the time constant shown in Table 2.

As presented earlier, the time constant for ICa during depolarizations to +50 mV was 56 ± 6 ms (n= 5). Student's t test showed that this value is significantly different from the time constant describing Ca2+ spark occurrence. The variability of the time constants for ICa and Ca2+ spark occurrence is greater at this potential due to the smaller amplitude of ICa and lower number of Ca2+ sparks. Even so, simulations presented in the Discussion suggest that when the time constant of Ca2+ spark occurrence is equal to or slower than the time constant for ICa, Ca2+ sparks are being triggered by opening of one L-type Ca2+ channel. Thus, our experiments in the presence and absence of nifedipine suggest that opening of a single sarcolemmal Ca2+ channel is sufficient to activate localized SR Ca2+ release events at all Vm values tested.

DISCUSSION

Prior to investigating the relationship between Ca2+ influx during ICa and localized SR Ca2+ release, the effects of experimental manoeuvres on the properties of Ca2+ sparks were examined in this study. Unitary SR Ca2+ release events triggered at Vm from -30 to +50 mV appear to have similar amplitude, spatial and temporal properties, in agreement with previous reports (Cannell et al. 1995; López-López et al. 1995). Given the wide difference of L-type Ca2+ channel currents predicted over this range of Vm, these results suggest that the properties of localized SR Ca2+ release are independent of the triggering event, as could be anticipated for a process that includes a high degree of amplification (Stern, 1992). Alternatively, the Ca2+ binding properties of fluo-3 may obscure the actual waveform of local SR Ca2+ release to a degree that diffusion of the Ca2+ bound indicator (Escobar et al. 1997) and origin of the release event relative to the plane of focus (Pratusevich & Balke, 1996; Shirokova & Ríos, 1997; Smith et al. 1998) may be the only processes dominating the observed properties of Ca2+ sparks.

Analysis of Ca2+ sparks was limited to events which displayed an amplitude greater than or equal to two standard deviations above baseline fluorescence. Events of smaller amplitude are likely to occur in cardiac myocytes (Song et al. 1997); however, they are difficult to distinguish from background noise in our system. We infer that the properties of these low amplitude events are independent of Vm based on our observation that the properties of the analysed Ca2+ sparks are unchanged with Vm.

Nifedipine also appeared to have little effect on the relationship between ICa and Ca2+ spark occurrence at +50 mV, even though ICa density was reduced greatly. This result is consistent with previous reports suggesting that dihydropyridines decrease channel availability but have little effect on open channel kinetics (Kawashima & Ochi, 1988; Méry et al. 1996). In this case, channel opening in the presence and absence of nifedipine would, on average, be able to support the same Ca2+ flux into the junctional space of the dyad so that the relationship between Ca2+ influx through L-type Ca2+ channels and individual Ca2+ release events would not be fundamentally altered even though fewer Ca2+ sparks are observed.

The principal result of this study is that the time course of ICa is similar to the rate of occurrence of Ca2+ sparks during a voltage-clamp depolarization. When ICa is relatively time independent, as observed at -30 mV, the occurrence of Ca2+ sparks is also unchanged throughout 200 ms depolarizations. Likewise, at Vm values where ICa is time dependent, the rate of Ca2+ spark occurrence peaks early in the depolarization and thereafter decreases. López-López et al. (1995) reported similar results, except that ICa was not measured in their experiments. We show that exponential time constants describing ICa decay and the time dependence of Ca2+ spark occurrence are not significantly different in the presence of nifedipine. With depolarizations to +50 mV in the absence of nifedipine, ICa decays more rapidly than the rate of Ca2+ spark occurrence. The significance of this finding is dependent on understanding the relationship between macroscopic ICa and the underlying single Ca2+ channel openings that comprise the ensemble current.

Relationship between macroscopic ICa, localized Ca2+ influx at the dyad and Ca2+ sparks

Previous studies have shown that mean open time of single L-type Ca2+ channels is considerably less than 1 ms when Ca2+ is the charge carrier (Yue et al. 1990; Rose et al. 1992). Given the much longer time course of ICa, it is clear that the kinetics of the macroscopic current decay must either be due to the latency for channel opening or the rate of channel re-opening prior to inactivation. In fact, Rose et al. (1992) found evidence that both factors play a role in the time course of ICa, the former in determining the rate of rapid current decay and the latter in the maintained, slowly inactivating portion of the current. The similarity of the time constant for the decay of ICa and the occurrence of Ca2+ sparks in the present study also suggests that latency to first opening of the L-type Ca2+ channel is important for determining the timing of Ca2+ sparks.

A low incidence of Ca2+ sparks was observed in the latter portion of depolarizations to +30 mV when ICa had reached a steady amplitude. These late Ca2+ sparks could be triggered by re-opening of L-type Ca2+ channels or, alternatively, could result from spontaneous SR Ca2+ release events.

To interpret the role of sarcolemmal Ca2+ channel openings in triggering Ca2+ sparks in this study, macroscopic ICa must be understood in terms of single channel events. The macroscopic current represents the ensemble average of single channel activity for a population of channels (Colquhoun & Hawkes, 1993). For time-dependent current, such as ICa, relative changes in single channel open probability (Po) during the decay of the macroscopic current can be estimated as:

display math(1)

where τ is the time constant for decay of current and P′ is maximum Po at the peak of ICa (assumed to occur at time zero in this calculation). Although eqn (1) relates changes in macroscopic current density to average microscopic Po, the likelihood of one or more L-type Ca2+ channels opening in a dyad is not elaborated by this equation.

Given that each dyad contains a cluster of ryanodine receptors apposed with many L-type Ca2+ channels (Protasi et al. 1996) and that the sarcolemmal channels have a low open probability (Bean & Rios, 1989; Rose et al. 1992; Bers & Stiffel, 1993), a straightforward way to evaluate the possibility that opening of one, two, or more L-type Ca2+ channels occur in a dyad is to construct a model using the Poisson distribution (Goldstein, 1964):

display math(2)

where λ is the average rate of occurrence of channel opening and r is equal to number of open channels (from 1 to n) in the dyad. For the present simulations, λ equals the ensemble open probability for sarcolemmal Ca2+ channels in a dyad at any time, i.e. nPo(t). To satisfy the assumption underlying the Poisson distribution that open events are very rare (Goldstein, 1964), nPo is constrained to be less than 1. For ICa, the value of λ relative to peak current is equal to Po(t)/P′ so that combining eqns (1) and (2) yields:

display math(3)

Each time an L-type Ca2+ channel opens, a Ca2+ spark can be triggered with some probability, Ps, that will depend on a transmission factor, Pi (López-López et al. 1995; Santana et al. 1996). Yet, if two, three or more channels open coincidentally, there is no a priori reason to assume that Pi stays constant. Therefore, to take into account possible changes in Pi when multiple sarcolemmal Ca2+ channels open in the dyad, the expression relating Ps to open channel probability is:

display math(4)

where Pi,r is the transmission factor for the condition where r Ca2+ channels are open. To understand how this expression relates the time course of ICa to the time dependence of Ca2+ spark occurrence, Fig. 6 shows the simulated changes in relative ICa and Ps for r equal to one to three open L-type Ca2+ channels.

Figure 6.

Model simulations relating the time course of Ca2+ current and Ca2+ spark occurrence to the number of open L-type Ca2+ channels in a dyad

Ca2+ current is assumed to decay with a time constant of 25 ms from t= 0. The relative time-dependent decrease in the open probability (Po) of L-type Ca2+ channels is shown as the continuous curve. The time course of Ca2+ spark occurrence was simulated using Poisson statistics (see text). The assumptions for this simulation were as follows: nPo at time 0 was 0.5, and the transmission factor Pi,r was directly proportional to the number of open Ca2+ channels. Simulations for the time course of Ca2+ spark occurrence are shown when a minimum of one (……), two (–––) or three (–¨–¨) open Ca2+ channels are required to activate a Ca2+ spark.

In Fig. 6, the decay of the ICa (continuous curve) from peak current at time zero is assumed to occur with a time constant of 25 ms. Additional curves show the calculated decay of Ca2+ spark occurrence when opening of a minimum of one, two or three L-type Ca2+ channels is required to trigger a Ca2+ spark. The simulation was run assuming that the probability of L-type Ca2+ channel opening in a cluster of sarcolemmal channels is low, i.e. nPo= 0.5, and that Pi,r is directly proportional to the number of open L-type Ca2+ channels. This simulation predicts that, if opening of one or more L-type Ca2+ channels is needed to trigger a Ca2+ spark, then the time constant describing the time-dependent decrease in Ca2+ spark occurrence (τspark) is similar to the time constant describing the decay of ICacurrent). When two of more L-type Ca2+ channels were required to trigger a Ca2+ spark, the decay of Ca2+ spark occurrence would precede the decay of ICa, i.e. τspark < τcurrent. Since the dependence of Ps on Ca2+ influx is unknown, simulations were also performed in which Pi,r was (a) independent of or (b) a square function of the number of open L-type Ca2+ channels. The latter relationship between Ca2+ influx and Ps was postulated by Santana et al. (1996). The outcome predicted for these simulations was similar to that shown in Fig. 6. Additional simulations were run where nPo was allowed to approach a value of 1. In all cases, Ca2+ spark occurrence decreased considerably more rapidly than ICa whenever the opening of two or more sarcolemmal Ca2+ channels was required to trigger a Ca2+ spark.

In the present experiments, the time constant for the decay of Ca2+ spark occurrence was either not statistically different or was slower than the decay of ICa, i.e. τspark≥τcurrent. If Ca2+ sparks are activated by the opening of two or more L-type Ca2+ channels, the model predicts that τspark should be less than τcurrent. Thus, these simulations suggest that opening of only one L-type Ca2+ channel is needed to trigger a Ca2+ spark in the range of depolarized Vm tested. Together with the data from Santana et al. (1996), these data indicate that Ca2+ influx through one sarcolemmal Ca2+ channel is sufficient to trigger a Ca2+ spark over the entire range of Vm for inward ICa. Alternatively, these data might suggest that the incidence of multiple Ca2+ channel openings in a single dyad junction is so low that they do not substantively contribute to the total number of observed Ca2+ sparks. If this alternative explanation is correct, clustering of sarcolemmal Ca2+ channels at the level of the single dyad might represent an adaptation to maximize the possibility that at least one L-type Ca2+ channel opens in each dyad during an action potential, thereby insuring an efficient E-C coupling mechanism.

The time-dependent decrease of Ca2+ spark occurrence in the absence of nifedipine was slower than the decay of ICa when cells were depolarized to +50 mV. Equation (4) predicts such a result when nPo approaches 1 and Pi,r is independent of the number of L-type Ca2+ channel openings. However, these conditions seem unrealistic. Previous reports (López-López et al. 1994; Santana et al. 1996) and our own data (not shown) suggest that Pi,r would be small at more positive Vm because single Ca2+ channel current amplitude is small. Thus, at +50 mV, Pi,r is likely to be more dependent on the number of open L-type Ca2+ channels than at other Vm. An alternative explanation for this result is that Pi,r increased during the depolarization. In this regard, it is notable that spatial mean [Ca2+]i during depolarizations to +50 mV increased to much higher levels in the absence than the presence of nifedipine. Higher [Ca2+]i could increase Pi,r by increasing SR Ca2+ loading (Lukyanenko et al. 1996) and/or ryanodine receptor Ca2+ sensitivity (Sitsapesan & Williams, 1994). An apparent increase in Pi,r couldc also occur if Ca2+ spark detection efficiency (Satoh et al. 1997) improves as a result of the increased cytosolic [Ca2+]. Both of these possible explanations require further investigation. In any case, it should be emphasized that the slower decrease of Ca2+ spark occurrence at +50 mV in the absence of nifedipine is compatible with our interpretation that one L-type Ca2+ channel opening is sufficient to trigger a Ca2+ spark.

Summary

The present study shows a close temporal relationship between the time course of macroscopic ICa and the occurrence of Ca2+ sparks when the probability of Ca2+ spark occurrence is low. By relating macroscopic ICa to L-type Ca2+ channel openings at the level of the single dyad, we interpret these data as suggesting that the opening of a single L-type Ca2+ channel is sufficient to trigger localized SR Ca2+ release at all membrane potentials encountered during the cardiac action potential.

Acknowledgements

We thank Marguarita Schmid for technical assistance and Dr L. D. Robb-Gaspers for his assistance with the confocal microscope. This work is supported by funds from the NIH (HL43712 to J.R.B. and DA06290 to A.P.T.) and the Southeastern Pennsylvania affiliate of the American Heart Association.

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