One calcium ion may suffice to open the tetrameric cardiac ryanodine receptor in rat ventricular myocytes

Abstract

1. The release of Ca²⁺ from sarcoplasmic reticulum in response to Ca²⁺ entering through L-type Ca²⁺ channels was studied in isolated voltage clamped rat ventricular myocytes at room temperature using the fluorescent Ca²⁺ indicators fluo-3 and Oregon Green 488 Bapta 5N.

2. Depolarizations to positive potentials elicited fluo-3 Ca²⁺ transients with rates of rise that were linearly related to the magnitude of the peak measured Ca²⁺ current in the presence of Cs⁺-containing pipette solutions.

3. Further experiments utilizing prepulses to preactivate a constant number of channels also revealed a linear relationship between the Ca²⁺ transient rate of rise and the magnitude of entering Ca²⁺ current at positive potentials. Under these conditions as well, the maximal rates of rise of global myoplasmic Ca²⁺ transients were due primarily to Ca²⁺ release from the sarcoplasmic reticulum as revealed by effects of ryanodine and caffeine on the Ca²⁺ transients. Using such prepulses, linearity between the Ca²⁺ transient rate of rise and the magnitude of the peak Ca²⁺ current was found under a variety of pulse protocols.

4. Using one such pulse protocol, linearity between the Ca²⁺ transient rate of rise and the magnitude of the peak Ca²⁺ current was also found when Ca²⁺ currents assessed at one potential were reduced in magnitude during the onset of block by application of Co²⁺. Using the same pulse protocol, linearity between the Ca²⁺ transient rate of rise and the magnitude of the peak Ca²⁺ current was also found when use of Cs⁺ was avoided by blocking K⁺ currents with extracellular TEA and 4-aminopyridine. Linearity in the relationship between the Ca²⁺ transient rate of rise and the magnitude of the peak Ca²⁺ current was also found when Ca²⁺ transients were measured using the low affinity Ca²⁺ indicator Oregon Green 488 Bapta 5N in place of fluo-3.

5. These results appear to indicate that the cardiac ryanodine receptor is capable of being activated by only one calcium ion. Alternative interpretations of the data are discussed.

Considering its importance, it is surprising that few experiments have been directed at determining the number (n) of calcium ions required to activate Ca²⁺ release through cardiac ryanodine receptors (RyRs). In light of the fact that the RyR consists of four identical subunits in the sarcoplasmic reticulum (SR) membrane, it is uncertain whether the tetrameric foot structure could be activated by one calcium ion binding to a site on any monomer or whether a site on each monomer needs to be occupied in order to activate Ca²⁺ release. On the one hand, the rate of RyR activation in reconstitution experiments increased only 10.5-fold for a 10-fold increase in Ca²⁺ concentration (Schiefer et al. 1995), consistent with only one calcium ion required for activation. On the other hand, the closely related InsP₃ receptor (InsP₃R) is reported to require binding of four molecules of InsP₃ in order to activate release (Marchant & Taylor, 1997). In addition to these most likely possibilities, it is conceivable that some intermediate number of binding sites need to be occupied (2 or 3) in order to activate release.

Although extensively studied in planar lipid bilayers, activation of the cardiac RyR by Ca²⁺ has not yielded this sort of information for several reasons: (1) heterogeneity from channel to channel (Ma, 1995; Copello et al. 1997) makes it difficult to pool data together, (2) most experiments have been performed under non-physiological conditions (absence of Mg²⁺, ATP and other modulators), (3) the experiments have generally been performed in the steady state and therefore might not be indicative of the more physiologically significant transient behaviour of the channel, and (4) in many cases a Ca²⁺-dependent inactivation process (Fabiato, 1985) makes it difficult to assess the saturating level of activation of the channel. Only one titration has been reported under transient activation conditions (Györke & Fill, 1993) and the small number of data points prevents a rigorous steepness analysis of the titration curve. Flux experiments with isolated cardiac membrane vesicles are less compromised by factors 1 and 2 above, yet rapid mixing is not always fast enough to simulate the physiological event (Kim et al. 1987; Meissner & Henderson, 1987), and results are still complicated by the presence of the inactivation process at higher cytoplasmic Ca²⁺ values (Chu et al. 1993). Given that the unmeasured local [Ca²⁺] around the mouth of a conducting channel could represent the critical Ca²⁺ level for inactivation, uncertainties persist. Measurements of the characteristics of local Ca²⁺ transients (sparks) in isolated myocytes have led to a conclusion that n = 2 (Santana et al. 1996). These experiments were performed in the presence of organic Ca²⁺ channel blockers that greatly changed the voltage dependence of release (and thus the relationship between Ca²⁺ release and Ca²⁺ current). These measurements, carried out under a number of assumptions which could not be verified, might still not reflect the release activation process under true physiological conditions.

The relationship between Ca²⁺ current across the myocardial surface membranes and the Ca²⁺ release it elicits has been examined using a variety of different protocols, but, for a variety of reasons, it has not been used to analyse critically the number of calcium ions required to activate release. Early studies of Ca²⁺ transients in myocytes suggested that the relationship between Ca²⁺ release and Ca²⁺ current was fairly linear, but these measurements did not analyse release flux (Cannell et al. 1987; Beuckelmann & Wier, 1988). More recent measurements which extracted release flux parameters from the data suggested that the relationship between flux and Ca²⁺ current was highly non-linear, particularly at values near the threshold for activating Ca²⁺ current (Wier et al. 1994). For the purposes of determining the stoichiometry of release activation, ideally one would have measurements in which the measured variable (Ca²⁺ current) was linearly related to the more critical related but unmeasured variable (microscopic Ca²⁺ current determined by the driving force on Ca²⁺ entry through individual channels). Unfortunately, in the most recent experiments alluded to, different numbers of channels were being activated near the threshold for activation, and thus macroscopic Ca²⁺ current would not have mirrored the more relevant microscopic Ca²⁺ current.

In order to examine this process in greater detail, we have attempted to correct this shortcoming of the macroscopic Ca²⁺ current/global Ca²⁺ transient recording system. We have done so by inserting before the test pulse a short prepulse to E_Ca, the Ca²⁺ equilibrium potential. This manoeuvre was designed to activate the maximum number of channels while still not permitting Ca²⁺ release activation or significant Ca²⁺ current inactivation. Under these circumstances the Ca²⁺ current early in the test pulse should be carried through a constant number of channels, and the macroscopic Ca²⁺ current should mirror the microscopic Ca²⁺ current. The results of these measurements are reported here. A preliminary report of these findings has been communicated previously (Fan & Palade, 1998).

METHODS

Experiments were carried out according to procedures submitted to and approved by the Animal Care and Use Committee of the University of Texas Medical Branch. All experiments were performed on ventricular myocytes acutely dissociated from the hearts of 200-300 g male Sprague-Dawley rats using collagenase (Yakult Pharmaceuticals, Tokyo, Japan; Yazawa et al. 1990). Rats were administered with i.p. heparin 30 min prior to anaesthesia with i.p. 30-35 mg pentobarbital sodium per animal. After all reflex activity had ceased, the animal was killed by opening the chest and rapidly removing the heart. Myocytes were stored at 4°C in a high potassium, low sodium, KB-like solution (Isenberg & Klockner, 1982) until use. Experiments were carried out at room temperature (20-22°C) on cells that had been previously exposed to 2 μM fluo-3 AM (Molecular Probes, Eugene, OR, USA; or Teflabs, Austin, TX, USA) for 5-15 min prior to washing.

All experiments were performed under conventional whole-cell recording conditions with a List EPC-7 patch clamp, recording fluorescence from nearly the entire cell (but not the micropipette) using an Oriel photomultiplier tube, optical filters from Omega Optical (Brattleboro, VT, USA; Yasui et al. 1994) and electronic filtering at 200 Hz. Bleaching was made negligible by the use of an electronic shutter synchronized so that cells were illuminated only during each actual 100 ms measurement. Ca²⁺ transients were expressed as F/F_o, calculated as the ratio between the peak fluorescence upon stimulation divided by the resting fluorescence of the cell. Background fluorescence passing through the optical system was subtracted from both these values by recording the fluorescence response to shutter opening when no cell was in the field. Recordings from an individual cell were rarely extended beyond 10 min in order to reduce as much as possible both escape of dye from the cell and Ca²⁺ current run-down. External solution in the bath was normal Tyrode (1 mM Ca²⁺) with Cs⁺ substituted for K⁺ for the purposes of blocking inward rectifier K⁺ currents in most experiments. The internal solution in the pipette contained 120 mM caesium aspartate supplemented with 20 mM CsCl, 3 mM Na₂ATP, 3.5 mM MgCl₂ and 5 mM Hepes. The experiments in Fig. 7 utilized potassium aspartate and KCl substituted for caesium aspartate and CsCl, respectively. The holding potential was -40 or -50 mV.

Figure 7. Ca²⁺ currents and the Ca²⁺ transients they elicited in a myocyte patched with a pipette filled with K⁺ internal solution instead of Cs⁺.

In A-C, the upper set of traces represents the Ca²⁺ transients, the middle set the Ca²⁺ currents, and the lower set the voltage clamp protocol. A, records obtained in normal Tyrode solution. B, records obtained in Tyrode solution + 3 mM Co²⁺. C, subtraction of currents in B from those in A to yield the Co²⁺-sensitive transient and current. D, relationship between the maximal rate of release and the peak Ca²⁺ current.

When used, 1.5-3 mM Co²⁺, 2 mM caffeine and 10 μM ryanodine, or 20 mM TEACl and 6 mM 4-aminopyridine were added to the external solution, maintaining constant osmolarity. Data are presented as means ±s.d. While most figures employed subtraction procedures to generate Co²⁺-sensitive Ca²⁺ transients and Ca²⁺ currents, plots of rates of rise of fluorescence versus_Ca utilized Co²⁺-sensitive Ca²⁺ currents but uncorrected Ca²⁺ transients. This procedure was followed in order to avoid the additional noise introduced by the subtraction of traces. Since Ca²⁺ transients in the presence of Co²⁺ were minimal and extremely slow to rise, minimal distortion of the relationship would have been introduced.

RESULTS

Normal whole-cell recording at room temperature with Cs⁺ present intracellularly provided quite a good isolation of Ca²⁺ currents elicited by depolarizing voltage clamp pulses. The Ca²⁺ transients obtained were small when the Ca²⁺ currents were small and large when the Ca²⁺ currents were large (Fig. 1). When a comparison was made between the maximum rate of rise of the Ca²⁺ transient (dictated primarily by the rate of release of Ca²⁺ from the SR) and the peak Ca²⁺ current, the relationship was quite linear at positive potentials (Fig. 1D). However, for reasons mentioned in the Introduction, Ca²⁺ currents at potentials below 0 mV were carried through different numbers of open channels, and they required different periods of time to activate. This made it impossible to meaningfully compare the Ca²⁺ transients at different potentials.

Figure 1. Ca²⁺ currents and the Ca²⁺ transients they elicited in myocytes stimulated by simple depolarizing pulses.

A, the Ca²⁺ transient response. B, the Ca²⁺ current response. C, the voltage clamp protocol. The myocyte was held at -40 mV at room temperature and then stimulated as indicated in C. D, the relationship between maximal rate of rise of the Ca²⁺ transient and the peak Ca²⁺ current. ▪, values obtained at 0 mV and positive potentials; □, values obtained at negative potentials.

Accordingly, we introduced a prepulse to E_Ca (+90 mV) before the test pulses. The prepulse was designed to minimize both effects mentioned above. First, it activated a constant number of channels that would continue to conduct at least during the early stages of the test pulse. Second, by preactivating the channels, the variation in activation kinetics was abolished. However, this procedure also introduced a greater contamination of the whole-cell Ca²⁺ current records by capacitative currents. This in turn necessitated a better subtraction of capacitative currents from the Ca²⁺ current records, accomplished in our case by a repetition of the measurements in the presence of 3 mM Co²⁺ added to the external solution. Figure 2A shows the Ca²⁺ current and transient records obtained in normal Tyrode solution, Fig. 2B shows those obtained in the presence of Co²⁺, and Fig. 2C the Co²⁺-sensitive currents and the transients they elicited. Finally, the filled symbols in Fig. 2E show the relationship between the maximum rate of rise of the Ca²⁺ transient and the peak Ca²⁺ current at each potential. The relationship was clearly linear over most of the positive potential range explored.

Figure 2. Ca²⁺ currents and the Ca²⁺ transients they elicited in myocytes first preactivated by a very strong depolarization and then stepped to successively less positive potentials.

In A-D, the upper set of traces represents the Ca²⁺ transients, the middle set the Ca²⁺ currents, and the lower set the voltage clamp protocol. A, records obtained in normal Tyrode solution. B, records obtained in Tyrode solution + 3 mM Co²⁺. C, subtraction of currents in B from those in A to yield the Co²⁺-sensitive transient and current. D, use of two exponentials to extrapolate Co²⁺-sensitive current back to the start of the test pulse. E, relationship between maximal rate of rise of the Ca²⁺ transients and the peak Ca²⁺ current. •, raw data points as shown in C; ▵, data extrapolated to values at the start of the test pulse as indicated in D.

In these experiments there was a finite ‘settling time’ (Isenberg & Han, 1994) required to achieve the command potential, and the rise of the tail transients reflects the time required to reach the command potential. During the first 1-2 ms following the change in potential, the membrane potential would have been at a value intermediate between +90 mV and the test pulse potential. This reduced the driving force on Ca²⁺ entry through open channels during this period, resulting in rising phases in the tail currents. Since the command potential was not achieved instantaneously, the currents measured still accurately reflect the peak currents attained.

Nevertheless, because the theoretically achievable tail current was not attained during the settling time, we fitted our tail currents to the sum of two exponentials, in order to extrapolate to the possible tail currents at t = 0 after the repolarization, as seen in Fig. 2D. As could have been predicted, the correction was minimal at positive potentials, where little inactivation or deactivation took place, but was significant at potentials near 0 mV, where there was a clear inactivation during the test pulse. This resulted in a slightly less steep relationship between the Ca²⁺ transient rate of rise (unaffected by the correction) and the larger Ca²⁺ tail currents, as shown by the open symbols in Fig. 2E. Linearity was maintained with both analyses.

The Ca²⁺ transients under these conditions were still primarily determined by Ca²⁺ release from the SR. As shown in Fig. 3 and Table 1, application of 2 mM caffeine and 10 μM ryanodine for a period of 2-3 min while stimulating at 0.5 Hz, followed by washout of the caffeine and ryanodine, led to a major decrease in the Ca²⁺ transient and its rate of rise (88.6 %) even though the Ca²⁺ current amplitude was much less affected (12.7 %). The caffeine and ryanodine were washed out because we noted in these experiments that maintenance of caffeine in the solutions decreased the amplitude of the Ca²⁺ currents (e.g. Zahradnik & Palade, 1993). As noted by these authors, the rate of Ca²⁺ current decline was slowed in the presence of ryanodine, and the effects attributed to ryanodine were not reversible.

Figure 3. Effects of temporary exposure to caffeine and ryanodine to deplete SR of Ca²⁺.

A, Ca²⁺ transients, Ca²⁺ currents and voltage clamp protocol obtained in normal Tyrode solution. B, Ca²⁺ transients and Ca²⁺ currents obtained in normal Tyrode solution following a 2-3 min exposure to 2 mM caffeine plus 10 μM ryanodine during stimulation at 0.5 Hz and subsequent washout.

Table 1.

Effects of ryanodine and caffeine on Ca²⁺ currents and rates of rise of Ca²⁺ transients

	Control		Ry + Caf		Percentage reduction after Ry + Caf
Cell number	ICa (pA)	RR (ms−1)	ICa (pA)	RR (ms−1)	ICa	RR
1	−1030	0.0406	−972	0.0036	5.7	91.1
2	−806	0.0199	−669	0.0017	17.0	91.5
3	−1133	0.0220	−918	0.0026	19.0	88.2
4	−635	0.0185	−513	0.0029	19.2	84.5
5	−1597	0.1145	−1558	0.0138	2.4	87.9
Mean	−1040	0.0431	−926	0.0049	12.7	88.6
S.D.	±367	±0.0409	±399	±0.0050	±8.0	±2.8

Ry, ryanodine; Caf, caffeine; RR, rate of rise of Ca²⁺ transient. All data were obtained with pulses to +10 mV from cells treated with 10 μM ryanodine and 2 mM caffeine for 2–3 min prior to washout.

Unlike the situation in Fig. 1, where small depolarizations were followed by progressively larger depolarizations, the records in Fig. 2 were obtained with the larger test pulse depolarizations applied first, and the depolarizations to less positive potentials applied only afterwards, when the SR might have had some chance of being depleted by the earlier test pulses which elicited a large release. Accordingly, two additional pulse protocols were employed. As shown in Fig. 4, if the small depolarizations were applied first, the release-current relationship at positive potentials was still linear, as it also was if the train of test pulses was begun at 0 mV instead (not shown).

Figure 4. Ca²⁺ currents and the Ca²⁺ transients they elicited in a myocyte first preactivated by a very strong depolarization and then stepped to 0 mV and successively more positive potentials.

In A-C, the upper set of traces represents the Ca²⁺ transients, the middle set the Ca²⁺ currents, and the lower set the voltage clamp protocol. A, records obtained in normal Tyrode solution. B, records obtained in Tyrode solution + 3 mM Co²⁺. C, subtraction of currents in B from those in A to yield the Co²⁺-sensitive transient and current. D, relationship between the maximal rate of release and the peak Ca²⁺ current.

The second alternative protocol involved preceding each prepulse-test pulse combination with a train of moderate depolarizing pulses designed to guarantee that the SR would be equally loaded prior to each test pulse. The results of this intervention are shown in Fig. 5. Again, the relationship between Ca²⁺ release and current at positive potentials was still linear. This protocol was not routinely used because it took significantly longer to perform the experiment, which could lead to results being influenced by current run-down more than in the other protocols.

Figure 5. Ca²⁺ currents and the Ca²⁺ transients they elicited in a myocyte using the same voltage clamp protocol as in Fig. 2 with each test pulse preceded by a 0.5 Hz train of four 50 ms depolarizing pulses to -10 mV to ensure equivalent SR loading.

A, records obtained in normal Tyrode solution. B, records obtained in Tyrode solution + 3 mM Co²⁺. C, subtraction of currents in B from those in A to yield Co²⁺-sensitive transient and current. D, relationship between the maximal rate of release and the peak Ca²⁺ current.

To rule out contributions from any possible voltage-dependent Ca²⁺ release (Hobai et al. 1997; Howlett et al. 1998) linearity between Ca²⁺ release and Ca²⁺ influx was additionally assessed using a protocol that did not depend on changing the membrane potential. For these experiments, the entry of Ca²⁺ through individual dihydropyridine receptors (DHPRs) was decreased using Co²⁺ as a low affinity Ca²⁺ channel blocker. The response of cells to application of Co²⁺ was monitored. As the Co²⁺ inhibited the Ca²⁺ currents over the course of 1-2 min of application, so too did it inhibit the Ca²⁺ transients. As shown in Fig. 6, diminished rates of rise of the transients were then plotted against the diminished currents in the same fashion as for previous figures. In all three experiments in which this test was employed, the relationship was linear. Discounting (subtracting) the subthreshold current for inducing release, a doubling of the current caused the rate of rise of the transient to increase by a factor of two.

Figure 6. Ca²⁺ currents and the Ca²⁺ transients they elicited in a myocyte during the onset of perfusion with Tyrode solution + 1.5 mM Co²⁺.

Currents in the steady state in Co²⁺ were subtracted from each current trace. A, Ca²⁺ transients, Ca²⁺ currents and voltage clamp protocol during exposure to Co²⁺. B, relationship between the maximum rate of rise of the Ca²⁺ transients and the peak Ca²⁺ current.

The experiments detailed so far were all carried out in the presence of high concentrations of intracellular Cs⁺ introduced via the patch pipette. Several reports have claimed that substitution of Cs⁺ for K⁺ intracellularly causes large reductions in the amplitude of phasic tension responses and Ca²⁺ transients, as well as alterations in their voltage dependencies (Han et al. 1994; Levi et al. 1996; Wasserstrom & Vites, 1996). In contradistinction to our study, all these results were obtained at 35-37°C, conditions which have been shown to enhance the contribution of reverse Na⁺-Ca²⁺ exchange to cardiac excitation-contraction coupling (Vornanen et al. 1994; Wasserstrom & Vites, 1996). Nevertheless, to exclude side effects of Cs⁺ on the relationship between Ca²⁺ currents and the rate of rise of Ca²⁺ transients, several experiments were performed at room temperature in the absence of Cs⁺ in our solutions. For these experiments, K⁺ currents were partly blocked by the use of an external solution containing 20 mM TEACl and 6 mM 4-aminopyridine, and addition of 3 mM Co²⁺ to this solution was used to block Ca²⁺ currents. As shown in Fig. 7, the relationship between the Ca²⁺ transient rate of rise and the tail Ca²⁺ current was linear under these conditions as well.

If the time constant of our optical measurements with fluo-3 was rate limiting or if the dye was close to saturation in some traces, it could have had minimal effects on the results obtained at slow maximal rates of rise, but might have seriously attenuated the results obtained at the faster rates of rise. To assess the possible effect of dye kinetics, we also made measurements with higher concentrations (1 mM) of the faster, much lower affinity indicator Oregon Green 488 Bapta 5N (Molecular Probes; K_d = 31 μM; Song et al. 1998) introduced by way of the patch pipette. As shown in Fig. 8 and two other experiments not shown here, the relationship between current and maximal rate of rise of fluorescence was still linear. We also ruled out similar artifacts due to our 200 Hz electronic filter. In this case, optical records were filtered less heavily, at 1000 Hz, and the data then analysed. The relationship between peak current and maximal rate of rise of the Ca²⁺ transient remained linear (data from 3 cells, not shown).

Figure 8. Ca²⁺ currents and the Ca²⁺ transients they elicited in a myocyte containing Oregon Green 488 Bapta 5N.

Instead of incubating the cells with fluo-3 AM, Oregon Green 488 Bapta 5N was added to the patch pipette internal solution at a concentration of 1 mM. A, records obtained in normal Tyrode solution. B, records obtained in Tyrode solution + 3 mM Co²⁺. C, subtraction of currents in B from those in A to yield the Co²⁺-sensitive transient and current. D, relationship between the maximal rate of rise of the Ca²⁺ transients and the peak Ca²⁺ current.

DISCUSSION

We have chosen to compare the rates of rise of the Ca²⁺ transients with the peak Ca²⁺ currents that we measured, under the assumption that the peak current would trigger the fastest release. Alternative analyses could be applied to our data. Beuckelmann & Wier (1988) chose to compare the amplitudes of their Ca²⁺ transients with a 20 ms integral of their Ca²⁺ currents. If we apply the same procedure to our data, we still observe a linear relationship. In fact, our results at positive potentials appear in all ways similar to those of Beuckelmann & Wier (1988). However, our results stand in contrast to those of Wier et al. (1994), in which the peak amplitude of release flux was related to a 25 ms integral of Ca²⁺ current elicited by simple depolarizing pulses applied as in our Fig. 1. We suggest that the true relationship between entry and release can be accurately assessed only when maximal SR Ca²⁺ release flux or rate of rise of the Ca²⁺ transient is compared with peak I_Ca, and when the release is both synchronously triggered and occurring at maximal rates. Once release rates start to decline, Ca²⁺ currents might no longer be as effective in triggering Ca²⁺ release.

We have confined our analysis to the region of positive membrane potentials, since rapid deactivation of tails at negative potentials might have reduced the duration of the entering Ca²⁺ trigger to a point where it might not have been able to activate release. Indeed, Vélez et al. (1997) have claimed that spikes associated with the release of Ca²⁺ by DM-nitrophen are not sufficient to activate Ca²⁺ release from isolated RyRs incorporated into planar lipid bilayers. While not shown here, the amplitude of the Ca²⁺ transients frequently declined at negative membrane potentials using the prepulse procedure in this study, although the rates of rise of the transient were less affected. Accordingly, the relationship between the rate of rise of the transient and the peak tail current either saturated or showed modest declines, in contrast to the increases reported by Wier et al. (1994). The settling time of a typical patch clamp used on these large cells could lead to an artificially large inward current at very positive potentials when simple depolarizing pulses are used, due to activation of a larger current at more moderate potentials prior to attainment of the final command voltage. This would distort the relationship between current and transient at these potentials more than the prepulse procedure we have utilized.

Our results indicate that very small Ca²⁺ currents near E_Ca are insufficient to activate release, perhaps because they are too small or because the release flux generated at these potentials is still too small to overcome resequestration by the Ca²⁺ pumps in the system. Once release becomes activated by tail currents above a critical threshold, the relationship between maximum release rate and superthreshold peak current becomes linear and eventually saturates. We interpret the remaining linear portion of the relationship between current and release to indicate that a doubling of any superthreshold current value will generate a doubling of the maximum rate of rise of the Ca²⁺ transient. Since the linear relationship between the maximum rate of rise of the transient and the peak Ca²⁺ tail current was unexpected, we wish to address several possible biological factors which might have rendered a higher order relationship linear under our measurement conditions.

SR Ca²⁺ load

While the SR load under our experimental conditions might not have been as high as that of Han et al. (1994) when they observed indications of regenerative behaviour, we have established that the rate of rise of the Ca²⁺ transient is determined mostly by SR Ca²⁺ release. If the load was unphysiologically low, it could have rendered the SR more susceptible to depletion, particularly when release rates were relatively high. To determine the SR Ca²⁺ load and to allow comparison with the results of other investigators, we estimated the gain, defined by some investigators as the ratio at some potential between Ca²⁺ release and Ca²⁺ entry. If we assume that 87.3 % of the Ca²⁺ current (remaining after SR depletion) accounted for all 11.4 % of the rate of rise of the Ca²⁺ transient that remained after SR depletion, then 100 % of the current would account for 13 % of the rate of rise of the transient, and the remaining 87 % of the rate of rise with SR normally loaded would be contributed by SR Ca²⁺ release. This would be equivalent to a gain of 87/13 = 6.7. While less than similar previous estimates of gains of 10 or higher in rat myocytes (Cannell et al. 1987; Wier et al. 1994), this represents only a lower limit to the gain because we cannot be certain that our exposures to caffeine and ryanodine were sufficient to deplete the SR completely. Run-down of Ca²⁺ currents in our experiments precluded longer term exposures.

Variable efficiency of triggering

If variable gain had made an inherently non-linear relationship appear more linear in our measurements, it would have required a higher contribution of SR Ca²⁺ release to the Ca²⁺ transient (gain) at +10 mV and a lower contribution (gain) at +30 mV. However, in four cells we calculated lower limits for gain of 7.7 at +10 mV and 8.1 at +30 mV after identical extents of SR Ca²⁺ depletion. The relationship appeared non-linear only at very positive potentials where the Ca²⁺ currents were very small.

DHPR domain overlap

One DHPR might not provide an effective trigger if another nearby DHPR had already activated all RyRs in the vicinity, a possibility rendered more likely by the activity manifest by two L-type channels within an individual myocyte patch (Imredy & Yue, 1992). We have observed an increase in subthreshold current if some of the L-type channels are inactivated by holding at -30 or -20 mV (not shown). This may indicate that with low unitary currents, two or more channels may contribute to activating a cluster of release channels. However, depolarized holding potentials which reduced the current to 0.2-0.3 times normal did not make the relationship between Ca²⁺ current and the rate of rise of fluorescence non-linear (4 cells, not shown).

Non-linear buffering

Possible selective buffering of larger Ca²⁺ influxes is difficult to rule out in these experiments, but is very unlikely to contribute to the linear Ca²⁺ dependence of activation rates in in vitro purified RyR experiments (Schiefer et al. 1995), which led to a similar conclusion that only one calcium ion is required to activate the cardiac RyR. The present study extends those findings to conditions much nearer to physiological conditions in situ.

Release inactivation

The relationship between Ca²⁺ current and the rate of rise of the Ca²⁺ transient could be altered by some Ca²⁺-dependent release inactivation process more likely to occur when release rates are higher. Release rates through individual RyRs should be comparable, but local Ca²⁺ levels could be higher if additional RyRs were contributing Ca²⁺ to the local environment. A release inactivation process with a time constant of 15 ms for rat ventricular myocytes has been described by Yasui et al. (1994). Lukyanenko et al. (1998) have described faster termination of local Ca²⁺ release (sparks) from myocytes when release flux was greater.

In the present more macroscopic study, the time course of decline of the first derivatives of the Ca²⁺ transients speeded up from a τ of 14.6 ± 0.8 ms at +30 mV with smaller transients to 6.6 ± 2.0 ms at 0 mV where the transients were larger (3 cells), but this closely paralleled the time course of decline in the Ca²⁺ current (τ of 18.7 ± 2.0 ms at +30 mV and 6.7 ± 0.3 at 0 mV in the same cells). Although this correlation suggests that release is simply deactivated by removal of its trigger, an alternative explanation of faster release inactivation at 0 mV cannot at present be ruled out. If the turning off of release is attributed to inactivation, measured release rates might underestimate the maximum rates attainable in the absence of inactivation. Extrapolation of the first derivatives of transients to the time when the transients began to rise would cause a significant increase by a factor of 1.66 ± 0.37 (3 cells) in the maximum rate of rise at +30 mV, and a larger 2.51 ± 0.21-fold increase in the same cells at 0 mV. Correction of our linear curves by such factors would render them non-linear.

Conclusions of others regarding stoichiometry of RyR activation

Our tentative conclusion that only one calcium ion is required to activate RyRs is in disagreement with an n = 2 determined by Santana et al. (1996) from spark data in the presence of nifedipine. Those measurements were performed under the assumption that on the time scale of the measurements nifedipine either blocked an individual spark or left it unaffected. However, given that the nifedipine greatly altered the apparent voltage dependence of release, it might not have been safe to make that assumption. If nifedipine had reduced the single channel current, it could have altered this relationship. However, M. D. Stern (personal communication) has indicated to us that a local control model which includes Ca²⁺ activation of the cardiac RyR by two calcium ions can be significantly linearized due to reduction of the gain near 0 mV by any of the following: (1) SR Ca²⁺ depletion, (2) Ca²⁺-dependent inactivation of the L-type channels, and (3) other great reductions of L-type channel densities. Thus, the data presented here still deserve to be interpreted with caution, particularly since the lack of apparent release at strongly positive potentials would also be consistent with a higher order reaction.

Comparisons with coupling in other systems

With regard to other intracellular Ca²⁺ release channels, the activation of skeletal RyRs appears to require the movement of four equivalent charges (Simon & Hill, 1992). Given that four DHPRs may sit atop alternate RyR tetramers (Block et al. 1988), this arrangement might indicate that all four DHPRs require activation prior to activation of the tetrameric RyR. However, the fourth power relation may also be accounted for by movement of one set of dipoles within each of the four sets of transmembrane segments of an individual DHPR. This interpretation would be equivalent to activation of the tetrameric RyR at any one of its monomeric subunits, as suggested here for activation of cardiac RyRs by Ca²⁺. Similarly, controversy persists with regard to the stoichiometry of activation of the closely related tetrameric InsP₃R by InsP₃, for which activation by one (Hirose et al. 1998) or four InsP₃ molecules (Marchant & Taylor, 1997) has been claimed. Both studies provided evidence that Ca²⁺ was additionally required for activation, and Hirose et al. (1998) claimed that their data were better fitted with an assumption that two calcium ions were bound per InsP₃R.

If only one calcium ion is required to activate release through a RyR, modelling of Ca²⁺ movements in cardiac myocytes performed under the assumption that n = 2 (Stern, 1992; Cannell & Soeller, 1997) may have to be re-explored. In addition activation by only one calcium ion leads to one of several surprising conclusions, namely: (i) the RyR can be opened by activating one Ca²⁺ activation site on any of the four identical subunits, (ii) there is only one Ca²⁺ activation site composed of portions of all four subunits, (iii) three of the four identical sites are rendered non-functional at some post-translational modification step, or (iv) three of the sites become occupied at resting free Ca²⁺ levels without opening the release channels. Similar surprising conclusions may be called for in the event that two calcium ions are required for activation.