Single canine cardiac ryanodine receptor channels were incorporated into planar lipid bilayers. Single-channel currents were sampled at 1–5 kHz and filtered at 0.2–1.0 kHz. Channel incorporations were obtained in symmetrical solutions (20 mM HEPES-Tris, pH 7.4, and pCa 5). Unitary Ca2+ currents were monitored when 2–30 mM Ca2+ was added to the lumenal side of the channel. The relationship between the amplitude of unitary Ca2+ current (at 0 mV holding potential) and lumenal [Ca2+] was hyperbolic and saturated at ∼4 pA. This relationship was then defined in the presence of different symmetrical CsCH3SO3 concentrations (5, 50, and 150 mM). Under these conditions, unitary current amplitude was 1.2 ± 0.1, 0.65 ± 0.1, and 0.35 ± 0.1 pA in 2 mM lumenal Ca2+; and 3.3 ± 0.4, 2.4 ± 0.2, and 1.63 ± 0.2 pA in 10 mM lumenal Ca2+ (n > 6). Unitary Ca2+ current was also defined in the presence of symmetrical [Mg2+] (1 mM) and low [Cs+] (5 mM). Under these conditions, unitary Ca2+ current in 2 and 10 mM lumenal Ca2+ was 0.66 ± 0.1 and 1.52 ± 0.06 pA, respectively. In the presence of higher symmetrical [Cs+] (50 mM), Mg2+ (1 mM), and lumenal [Ca2+] (10 mM), unitary Ca2+ current exhibited an amplitude of 0.9 ± 0.2 pA (n = 3). This result indicates that the actions of Cs+ and Mg2+ on unitary Ca2+ current were additive. These data demonstrate that physiological levels of monovalent cation and Mg2+ effectively compete with Ca2+ as charge carrier in cardiac ryanodine receptor channels. If lumenal free Ca2+ is 2 mM, then our results indicate that unitary Ca2+ current under physiological conditions should be <0.6 pA.

Introduction

Muscle contraction is activated by a sudden increase in cytosolic [Ca2+] caused by Ca2+ release from the sarcoplasmic reticulum (SR).1 Ca2+ release from the SR is mediated by a large tetrameric Ca2+ channel known as the ryanodine receptor (RyR). Ca2+ release during normal excitation–contraction coupling is triggered in the heart by a small extracellular Ca2+ influx through voltage-dependent L-type Ca2+ channels and in skeletal muscle by a presumably mechanical action of dihydropyridine receptors in the transverse tubule. A complete understanding of these control mechanisms has been prevented, among other reasons, by the paucity of knowledge concerning unitary Ca2+ current through single RyR channels under physiological conditions. A better definition of this current has become critically necessary to interpret the local Ca2+ release events termed Ca2+ sparks (Cheng et al., 1993), and in particular whether they arise from the opening of a single RyR channel or the concerted opening of several RyR channels.

Unitary Ca2+ currents through the RyR channel have been measured in lipid bilayer studies under relatively simple ionic conditions (Smith et al., 1988; Fill and Coronado, 1988). To optimize the signal-to-noise ratio, unitary Ca2+ current is typically recorded in the presence of large Ca2+ concentrations (e.g., ∼50 mM). In cells, however, the intralumenal SR Ca2+ concentration is thought to be near 1 mM (Bers, 1991; Chen et al., 1996; Shannon and Bers, 1997). Single RyR channel studies have also revealed that the RyR channel is a rather poorly selective Ca2+ channel. Consequently, unitary Ca2+ currents are usually recorded in the absence of competing ions. In cells, however, Mg2+ and K+ are found at concentrations that allow them to compete effectively with Ca2+ for occupancy of the RyR pore. These considerations indicate that the unitary Ca2+ current in the cell must be considerably less than that predicted from measurements of unitary Ca2+ current under the typical RyR channel recording conditions.

In this study, unitary Ca2+ currents through single cardiac RyR channels were measured in the presence of competing ions at lumenal Ca2+ concentrations ranging from 2 to 30 mM. Unitary Ca2+ currents were recorded in the presence of different concentrations of competing cations (Cs+ and/or Mg2+). Competing cation concentration was symmetrical across the membrane and the Ca2+ currents were recorded at 0 mV. Our data indicate that, under conditions that roughly mimic the physiological condition (i.e., 1–2 mM lumenal Ca2+, 1 mM Mg2+, 150 mM monovalent salt, 0 mV membrane potential), the amplitude of the Ca2+ current through a single RyR channel will be considerably <0.6 pA.

Methods

Heavy SR microsomes were isolated from canine ventricular muscle using previously described methods (Tate et al., 1985). Single SR Ca2+ release channels were reconstituted by fusing heavy SR microsomes into artificial planar lipid bilayers. Channel incorporation was evidenced by the sudden appearance of single-channel activity.

Planar bilayers were formed across a 150-μm diameter aperture in a Delrin partition. Bilayer-forming solution contained a mixture of phosphatidylethanolamine and phosphatidylcholine (7:3, 50 mg/ml of decane; Avanti Polar Lipids). Heavy SR microsomes were added to one side of the bilayer (cis). The cis chamber contained the cytoplasmic side of the channel (Tu et al., 1994). The other side of the bilayer, trans, was held to ground. The transmembrane potential was always held at 0 mV. The standard solution contained 20 mM HEPES-Tris, pH 7.4, and 10 μM added free Ca2+. Unitary currents were measured after addition of different Ca2+ (or Ba2+) concentrations (2–30 mM) to the lumenal side of the channel. The attenuating effect on unitary Ca2+ currents induced by symmetric concentrations of Mg2+ (1 mM) and/or Cs+ (5, 50, and 150 mM) was defined. The buffering effect of CH3SO3 on free [Ca2+] was quantified with a Ca2+-selective electrode. Those measurements were conducted under conditions of constant ionic strength (with equivalent [Cl]'s).

Unitary currents were recorded with a conventional patch clamp amplifier (Axopatch 200B; Axon Instruments). The current signal was digitized at a rate of 4 kHz with a 32 bit AD/DA converter (Digidata 1200; Axon Instruments), filtered with a Bessel filter at 1 kHz, and stored for later analysis. Current amplitudes were determined either by measuring individually long opening events or by fitting gaussian functions to the total amplitude histograms. Data acquisition, unitary current measurements, statistical analysis, and data processing were performed using commercially available software packages (pClamp V6.0; Axon Instruments, Excel 97; Microsoft Corp., and Origin V5.0; Microcal Software, Inc.). Experimental data shown here as mean ± SEM were obtained from a total of 53 bilayers. Opening events are shown as downward deflections.

Results

Unitary Ca2+ Current in the Absence of Competing Ions

Single RyR channel activity was measured in the presence of different lumenal Ca2+ concentrations ranging from 2 to 30 mM. A sample single-channel recording in the presence of 2 mM Ca2+ is illustrated in Fig. 1 A. The free Ca2+ concentration on the cytoplasmic side of the channel was ∼10 μM and no competing ions (Cs+ or Mg2+) were present. The recording shown here demonstrates that under these relatively simple ionic conditions, the signal-to-noise ratio of the recording system is sufficient to clearly resolve single-channel openings in the presence of such low lumenal Ca2+ concentrations. The unitary current amplitude was determined from the corresponding total amplitude histogram (Fig. 1 A, right). The histogram was fit by the sum of two gaussian functions (describing the closed and open current levels). The difference between the means of the gaussian components (i.e., unitary current amplitude) was 1.37 pA. To confirm the identity of the ion channel responsible for the single-channel activity recorded, we tested its sensitivity to the plant alkaloid ryanodine and to ruthenium red. Fig. 1 B illustrates an experiment where addition of 20 μM ryanodine to the cytoplasmic side of a channel induced the typical effects described for the cardiac RyR channel on both permeation and gating kinetics. The addition of 5 μM ruthenium red to the cytoplasmic side of a channel induced a significant decrease of the RyR channel activity (Fig. 1 C). These results confirmed that the channel activity we recorded in the presence of 2 mM lumenal Ca2+ arose from a typical cardiac RyR.

Unitary Ca2+ Current Attenuation Induced by Symmetrical Monovalent Cations

To estimate the impact of monovalent cations on Ca2+ permeation through the RyR channel, unitary Ca2+ current carried by 2 mM Ca2+ was recorded in the presence of 150 mM symmetrical Cs+ and without Mg2+ (Fig. 2). A sample single-channel recording obtained under these conditions is illustrated in Fig. 2 A. In this case, since the current signal was filtered at 300 Hz, fast single-channel openings were significantly attenuated; however, the amplitude of long single-channel events was essentially unaffected. The selected sample record illustrates such long single-channel openings. The corresponding total amplitude histogram (Fig. 2 B) indicates that the unitary Ca2+ current amplitude was 0.35 pA. This result and that shown in Fig. 1 A indicate that the presence of permeable monovalent cations (i.e., Cs+) significantly attenuates the unitary Ca2+ current (from 1.37 to 0.35 pA). Current attenuation is most likely due to competition between Cs+ and Ca2+ ions for occupation of the RyR pore. Unitary Ca2+ current attenuation induced by Cs+ depended on both the lumenal Ca2+ and Cs+ concentrations. The relationship between the lumenal Ca2+ and Cs+ concentration is illustrated in Fig. 3. At every Cs+ concentration (5, 50, and 150 mM), unitary Ca2+ current amplitude could be fitted by a hyperbolic function of lumenal Ca2+ concentration (between 0 and 10 mM). Higher Cs+ concentrations resulted in smaller unitary Ca2+ currents. To investigate how much of this effect resulted from [Ca2+] buffering by CH3SO3, we measured the free [Ca2+] in our solutions at different [CH3SO3]'s (data not shown). Our results indicated that, acting as a low affinity Ca2+ buffer, CH3SO3 did not induce a significant decrease of the Ca2+ current amplitude when measured at low lumenal [Ca2+] (between 0 and 2 mM).

At high Cs+ concentrations (150 mM; Fig. 3, ▵), it was impossible to reliably record single-channel events at lumenal Ca2+ concentration below 2 mM. The data were plotted as a function of lumenal Ca2+ to facilitate extrapolation to lower Ca2+ concentrations. For example, it is clear that unitary Ca2+ current at 1 mM lumenal Ca2+ in the presence of 150 mM Cs+ will be <0.5 pA.

Cs+ Attenuates Unitary Current Regardless of Current Carrier Identity

If the mechanism of Cs+ attenuation is competition for occupation of the RyR pore, then Cs+ should attenuate unitary current in a similar way for other current carriers. Therefore, we measured unitary Ba2+ currents in the presence of different Cs+ symmetrical concentrations. The relationship of the current amplitude with Ba2+ and Cs+ concentrations is illustrated in Fig. 4. Unitary Ba2+ current was attenuated by Cs+ in a dose-dependent fashion. At all Cs+ concentrations (5, 50, and 150 mM), unitary Ba2+ current was a hyperbolic function of lumenal Ba2+ concentration (0–10 mM). Like the Ca2+ data presented in Fig. 3, unitary Ba2+ current was scaled by the competing Cs+ concentration. High Cs+ concentrations resulted in smaller unitary Ba2+ currents. These data indicate that physiological levels of a permeable monovalent cation are sufficient to attenuate unitary Ca2+ or Ba2+ to <0.5 pA. The Ba2+ data (Fig. 4) also indicate that the competition between Cs+ and the current carrier was independent of the ionic species used.

Unitary Ca2+ Current Attenuation by Symmetrical Mg 2+

It has been reported that the concentration of free Mg2+ in muscle cells falls in the millimolar range, and that the RyR channel is permeable to Mg2+ (Smith et al., 1988). Thus, the unitary Ca2+ current through the RyR channel is also likely to be attenuated by Mg2+. The extent of current attenuation induced by 1 mM symmetrical Mg2+ was also measured here. Sample single-channel records at different lumenal Ca2+ concentrations (2, 5, and 10 mM) in the absence (Fig. 5, left) and presence (Fig. 5, right) of 1 mM Mg2+ are shown. All these measurements were conducted in the presence of low monovalent cation concentration (<5 mM Cs+). Single-channel records were selected to illustrate differences in the unitary current amplitude. The action of Mg2+ on the open probability of the channel was not evaluated. Nevertheless, the data presented in Fig. 5 clearly illustrates that the amplitude of unitary Ca2+ current was significantly reduced in the presence of 1 mM Mg2+. Additionally, an apparent reduction of the noise level was a frequent observation after addition of Mg2+.

Unitary Ca2+ Current Attenuation by Simultaneous Presence of Symmetrical Mg2+ and Cs+

At this point, our results indicated that unitary Ca2+ current was attenuated by both Cs+ and Mg2+. In addition, we found that the extent of attenuation depended on both the Cs+ and Mg2+ concentrations. We then investigated the effect of those competing ions on the unitary Ca2+ current amplitude when they were present simultaneously. The main results of those experiments are illustrated in Fig. 6. Unitary Ca2+ current amplitude was plotted as a function of lumenal Ca2+ concentration to allow direct extrapolation to lower Ca2+ concentrations. In the absence of both competing ions (Mg2+ and Cs+; Fig. 6, •; n = 6), unitary Ca2+ current amplitude was described by a single rectangular hyperbolic function of lumenal Ca2+ concentration (0–30 mM). When only Mg2+ (1 mM) was added to both sides of the channel, the amplitude of the unitary Ca2+ current was significantly reduced to ∼50% of the original amplitude (Fig. 6, ○; n = 5). When Mg2+ (1 mM) and Cs+ (50 mM) were added simultaneously, the attenuation of the unitary Ca2+ current appeared additive, as revealed by an ∼70% reduction of the current (Fig. 6, shaded triangles; n = 2). Due to the large reduction of the current amplitude induced by the presence of both Mg2+ and Cs+, it was impossible to reliably measure the amplitude of unitary Ca2+ current when [Cs+] was larger than 50 mM. As it is shown in Fig. 6 A (shaded triangles), in the presence of 1 mM Mg2+ and 50 mM Cs+, the minimum resolvable current amplitude was 0.8 pA with 10 mM lumenal [Ca2+]. Since current amplitude measurements at lower lumenal [Ca2+]'s were not reliable, we could not precisely fit a hyperbolic function in this range. Thus, to extrapolate the value of unitary Ca2+ current amplitude at lower lumenal [Ca2+]'s, we scaled the curve obtained for the no competing ions data set and applied it to the competing ion data set.

In addition, no dramatic differences in the apparent gating kinetics were observed when both Mg2+ and Cs+ were present. The single-channel trace shown in Fig. 6 B illustrates such a condition (10 mM lumenal Ca2+, 1 mM symmetrical Mg2+ and 50 mM symmetrical Cs+). As in previous figures, the corresponding total amplitude histogram was fitted with two gaussian functions. The difference of the peaks revealed a mean opening level with an amplitude of ∼0.7 pA.

Discussion

The goal of this work was to measure the amplitude of unitary Ca2+ current through single cardiac RyR channel, under concentrations of Ca2+, monovalent cations, and Mg2+ that are assumed to be present in the intact cell. Our results indicate that physiological levels of monovalent cations and Mg2+ significantly attenuate unitary Ca2+ current. The unitary Ca2+ current carried by 2 mM lumenal Ca2+ was <0.6 pA in the presence of either 150 mM Cs+ or 1 mM Mg2+. Attenuation of the unitary Ca2+ current was most likely due to the competition of permeable ions for occupancy of the RyR pore. This assumption was favored by the observation that when Cs+ and Mg2+ were present simultaneously, the attenuating effect on the current amplitude was even larger. These data indicate that unitary Ca2+ current through a single RyR channel in a cell (i.e., with both monovalent cations and Mg2+ present) would be considerably <0.6 pA. Nevertheless, the physiological relevance of this measurement should be drawn cautiously, since the role of multiple factors existing in the cell that clearly modify the permeation properties of RyR (i.e., polyamines, FKBP12, etc.) were absent in our study. Likewise, the potential impact on the RyR permeation of other intracellular ions such as Na+, Cl, polyamine, etc., was not addressed in this work.

Significance of Using Cs+ as Representative Monovalent Cation

Single RyR channels were incorporated into planar lipid bilayers by fusion of heavy SR microsomes that contained the RyR channel. The SR microsomes are known to also contain Cl and K+ channels (Cukierman et al., 1985; Hamilton et al., 1989). Therefore, the use of Cs+ as a charge carrier allowed us to identify the bilayers with RyR channel before the addition of divalent charge carriers, without the interference of K+ channels. An impermeable anion substitute (CH3SO3) was used to avoid currents due to the presence of Cl channels. This strategy for recording single RyR channels is commonly employed. The results presented here can therefore be directly compared with other studies using this common RyR channel fusion method. Additionally, studies on purified RyR channels show that PCa/PCs and PCa/PK ratios are almost identical. This implies that Cs+ and K+ compete with Ca2+ almost equally for occupancy of the RyR pore. Thus, few disadvantages of using Cs+ instead of K+ as the competing monovalent ion in this study were outweighed by the ability to prescreen bilayers for RyR channels.

Unitary Ca2+ Current Amplitude under Simple Ionic Conditions

Unitary Ca2+ current in most single RyR studies has been defined in the presence of large lumenal Ca2+ concentrations and/or in the absence of permeable competing ions. In our study, unitary Ca2+ current (at 0 mV) in 30 mM lumenal Ca2+ was 3.5 ± 0.4 pA (see Fig. 6, •). For comparison, Smith et al. (1988) reported that unitary Ca2+ current (at 0 mV) in 54 mM lumenal Ca2+ was ∼4.2 pA. Tinker et al. (1992) reported that unitary Ca2+ current (at 0 mV) in 210 mM lumenal Ca2+ was ∼5.5 pA. Thus, the unitary Ca2+ currents observed here in the absence of permeable competing ions are consistent with previously published values. Therefore, we conclude that the small amplitudes measured in the presence of competing ions reported here are not due to selection of RyR channels with unusually small unitary conductance. The characteristic behavior of the channels used in this study was further confirmed by their ryanodine sensitivity when conducting 2 mM Ca2+ (Fig. 1 B).

Unitary Ca2+ Current Amplitude in the Presence of Competing Ions

The monovalent cation and Mg2+ concentrations on both sides of the channel were equal in this study. Thus, there was no net monovalent or Mg2+ current at 0 mV where all our single-channel measurements were made. On the other hand, the free Ca2+ concentration was asymmetric across the bilayer (2–30 mM trans; 0.01 mM cis), creating a 100-fold Ca2+ gradient across the channel. Thus, the net current (inward by convention) through the RyR channel at 0 mV was carried by Ca2+. Experiments were done at 0 mV to mimic what is thought to represent the physiological potential across the SR (García and Miller, 1984). The interpretation of our data is based on the assumption that, even in the absence of a net monovalent or Mg2+ current, these permeant ions will effectively compete for occupancy of the pore. Thus, attenuation of net Ca2+ current would be expected in the presence of other permeant ions as those ions compete with Ca2+ for occupancy of the conduction pore. This interpretation is consistent with the relatively low selectivity of the RyR channel (Smith et al., 1988).

Our results show that physiologically relevant concentrations of monovalent cation (150 mM Cs+) or Mg2+ (1 mM) significantly attenuate Ca2+ current through single RyR channels. Assuming that lumenal free Ca2+ inside the SR is between 1 and 2 mM (Bers, 1991; Chen et al., 1996; Shannon and Bers, 1997), our data indicate that unitary Ca2+ current will be <0.6 pA in the presence of a competing monovalent cation (Cs+). The data also show that the attenuation of the current due to 1 mM Mg2+ is close to that induced by 150 mM Cs+. The large noise inherent to planar bilayer studies made it technically impossible to directly measure the unitary Ca2+ current in the simultaneous presence of high concentrations of both competing ions (Cs+ and Mg2+). However, with high Ca2+ concentrations (10 mM, lumenal), we were able to evaluate the effect of these competing ions (50 mM Cs+ and 1 mM Mg2+) when added together (Fig. 6, shaded triangles). As expected, under these conditions the current attenuation was greater than the effect induced separately by each ion. Thus, we conclude that unitary Ca2+ current in the intact cell in the presence of physiological salts must be considerably <0.6 pA.

This conclusion has two interesting implications. First, the value we observed is about fourfold smaller than a previously published estimate of the unitary Ca2+ current through the cardiac RyR channel under quasi-physiological conditions (∼1.4 pA in 1.2 mM lumenal Ca2+; Tinker et al., 1993). Second, the amplitude of the unitary current through the RyR is critical to the interpretation of the “Ca2+ spark” observed in scanning confocal imaging studies exploring local control of SR Ca2+ release.

Comparison with Previous Estimations

Tinker et al. (1993) first explored how unitary Ca2+ current through single RyR channels may be impacted by the presence of other permeant ions. They measured net currents in a quasi-physiological mixture of ions (symmetrical 120 mM K+, 0.5 mM Mg2+, 10 mM lumenal Ca2+) and fit those data using an Eyring-rate model for RyR permeation (Tinker et al., 1992). Their model predicted that unitary Ca2+ current through RyR (at 0 mV) would be ∼1.4 pA at a more physiological lumenal Ca2+ concentration (1.2 mM). There is a fourfold discrepancy between this model prediction (1.4 pA) and our experimental measurements (0.35 pA, measured with 2 mM lumenal Ca2+, 150 mM symmetrical Cs+, and no Mg2+).

A very simple argument can be made suggesting that the single-channel current must be <1.4 pA. It is well established that [Ca2+] in the lumen of the SR does not exceed 2 mM and is probably in the range of 1–1.5 mM (Chen et al., 1996). Since the channel exhibits ion selectivity and discrete gating, the permeation path must pass through a true pore with a radius r0 well under 1 nm. If we assume that Ca2+ ions entering the pore on the lumenal side converge by spherically symmetrical diffusion down to a radius of r0, and diverges similarly from a radius r0 on the cytosolic side, then the minimum possible transmembrane [Ca2+] gradient when passing a unitary current i, at zero transmembrane potential, is i/(DF r0), where D is the diffusion coefficient of Ca2+ and F is the faraday constant. If we use the liberal values r0 = 1 nm and D = 0.78 × 10−5 cm2/s (the value in free aqueous solution), this minimum gradient is 3 mM, even without considering the resistance of the true pore. Therefore, our measurements of unitary current amplitude are much more consistent with diffusion theory than previous estimates. This was also pointed out by Tinker et al. (1992), who found that their Eyring-rate permeation model required that the association rate of Ca2+ to the potential wells at the mouth of the pore exceed the diffusion limit by about one order of magnitude.

To clearly understand these estimates of physiologic unitary current, we should consider possible mechanisms that might enhance the diffusion-limited permeability. Two such mechanisms, not mutually exclusive, are (a) electrostatic focussing and (b) the existence of a multibarrel channel. The electrostatic focussing mechanism is based on an electric field produced by fixed negative charges in the lumenal vestibule of the channel (Tu et al., 1994). This electric field would increase the local [Ca2+], resulting in a larger transmembrane driving force. Fields of this nature only exist within a Debye length of the fixed charges (∼1 nm in physiological ionic strength). The RyR channel contains many anionic amino acid residues (Takeshima et al., 1989). Thus, specific structural arrays may exist that act as a negatively charged, Ca2+-permeable “sponge”, which would function as an “electrostatic funnel” to enhance diffusion-limited permeability. In the  Appendix, we present the simplest possible model of this effect. In this case, the sponge is modeled as a homogeneously charged sphere that creates a Donnan equilibrium potential. By making extreme assumptions (i.e., r0 = 1 nm, free diffusion of Ca2+ within the sponge, ionization of all acidic residues, effective radius of the sponge set at an optimum) it is possible to reduce the diffusion gradient to 0.33 mM, again without including the resistance of the true pore. This suggests that, while electrostatic focussing might assist permeation, it probably could not fully account for a current of 1.4 pA under more realistic assumptions. The second enhancing mechanism, a multibarrel channel, has been suggested by Ondrias et al. (1996). This mechanism is based on their observation of 1/4 conductance states when FKBP12 is removed from the channel, as well as single openings of multiple conductance (up to six times normal) when several channels are in the bilayer in the presence of FKBP12. On this model, each RyR monomer would have its own permeation path. In the presence of FKBP12, the possibility of synchronous gating of the different pores (within and among tetramers) is somehow favored. Given the large size of the tetramer, this could reduce the diffusion gradient by nearly a factor of 4. Our estimate of unitary current of <0.6 pA substantially reduces the need to include these enhancing mechanisms in our model. Assuming a diffusion coefficient of 0.39 × 10−5 cm2/s and a true pore capture radius of 1 nm, the unassisted diffusion gradient for a unitary current of 0.4 pA is 1.7 mM. Therefore, the existence of any permeability-enhancing mechanisms would make the necessary Ca2+ gradient across the SR considerably <1.7 mM.

Physiologic Release Flux

Taking advantage of the detailed morphometry that has been conducted on skeletal muscle membranes, we tested whether our estimates of single-channel current could account for the release flux measured in whole-cell experiments. According to Eisenberg and Peachey (1975), the lumenal length of T-tube per unit fiber volume is 0.82 μm/μm3. If 80% of that is junctional and there are 60 channels per micrometer on each side of the junction, then there are 76 channels/μm3. Assuming that our estimate is valid for skeletal muscle (where these geometric relationships have been better defined), a unitary current of 0.35 pA per channel would yield 27 pA/μm3, or 135 mM/s when all channels are open. If we consider an accessible aqueous volume of 70%, the effective release flux density would be 193 mM/s. This flux would provide enough Ca2+ to saturate troponin (240 μM; Baylor et al., 1983) in <2 ms, and would be approximately equal to the largest estimates from cut fiber experiments in frog (180 mM/s with combined voltage and caffeine stimulation; Shirokova and Ríos, 1997; 200 mM/s with action potential stimulation; Pape et al., 1995). The present estimate is therefore generally consistent with the work with cell segments, under the assumption that it is possible to have all channels open in a maximally activated fiber.

Consequences for Interpretation of the Ca2+ Spark

Cheng et al. (1993) estimated the release current underlying a spark at 4 pA. Based on available measurements of unitary Ca2+ current, which at the time were ∼3 pA (Rousseau et al., 1987; Rousseau and Meissner, 1989), they suggested that a single Ca2+ spark could arise from the opening of individual SR Ca2+ release channels. As discussed above, the 3-pA value was obtained in the presence of high lumenal Ca2+ (50 mM) and in the absence of both monovalent cations and Mg2+. Here, we demonstrate that the unitary Ca2+ current through a single cardiac RyR in the cell is probably <0.5 pA. Given the estimate of 4 pA for the SR Ca2+ flux underlying a Ca2+ spark (Cheng et al. 1993; Blatter et al., 1997), ∼10 RyR channels with a unitary Ca2+ current of 0.35 pA would be required. Our single-channel data are, therefore, more consistent with the idea that individual Ca2+ sparks arise from the concerted opening of a cluster of RyR channels (Lipp and Niggli, 1996; Parker et al., 1996; Blatter et al., 1997). The agreement is not quantitative, however, because morphological studies indicate that cardiac RyRs are arranged in junctional arrays of several tens of channels (Sun et al., 1995; Franzini-Armstrong and Protasi, 1997).

A more quantitative agreement between spark amplitude and the morphology of channel clusters is found in skeletal muscle. Recent estimates place the current underlying large skeletal muscle sparks at between 12 and 15 pA (Ríos et al., 1998; Ríos, E., M.D. Stern, A. Gonzalez, G. Pizarro, and N. Shirokova, manuscript submitted for publication). Therefore, between 35 and 43 fully open channels of 0.35 pA would be required to generate such current. In skeletal muscle, the arrays of channels on either side of a junctional transverse tubule segment, or couplon, are 200–1,000-nm long and have between 20 and 70 channels. Our estimate of unitary current (extrapolated to skeletal muscle) is, therefore, consistent with the idea that the activation of all or some of the channels in such couplons constitutes a spark (Stern et al., 1997). Again, this is consistent with estimates of maximal flux density obtained in cut fiber experiments. Indeed, there should be two or three couplons per cubic micrometer, providing 20–50 pA release current/μm3, or ∼200 mM/s of Ca2+ flux density, when fully activated.

Abbreviations used in this paper

     
  • RyR

    ryanodine receptor

  •  
  • SR

    sarcoplasmic reticulum

appendix

Electrostatic Focussing of Ca2+ Diffusion

We modeled diffusional access of Ca2+ to the channel pore as spherically symmetrical diffusion converging to a radius r0 on the luminal side of the membrane, and diverging from r0 on the cytosolic side (Fig. 7). The [Ca2+] at r0 is assumed to be the same on both sides of the membrane; i.e., the resistance across the true pore is neglected. A uniform distribution of fixed negative charge is assumed to be present out to a radius r1. Within the sphere, the Ca2+ diffusion coefficient is Di, while in the outside it is D. The spherical sponge is assumed to be permeable to small ions. There will be a Donnan equilibrium potential difference across the boundary of the sponge; this causes a jump in [Ca2+] by a Nernst factor. Outside and within the sponge, [Ca2+] is assumed to diffuse in the absence of electric fields.

Donnan Equilibrium

The cytosol contains monovalent cations (activity k) and an equal concentration of mobile anions. The channel sponge has a concentration a of fixed negative charges. Inside the sponge, diffusible cations are enhanced by a Nernst factor q = exp(eV/kT) where V, the Donnan potential, is to be determined. Mobile anions are reduced by the same factor. Electroneutrality within the sponge requires:

\begin{equation*}kq=\frac{k}{q}+a,\end{equation*}
1

whose solution is:

\begin{equation*}q=\frac{\sqrt{4k^{2}+a^{2}+a}}{2k}.\end{equation*}
2

Inclusion of 2 mM divalent cations would make Eq. 1 a cubic equation, and reduce the Donnan factor by only 3%, so it has been omitted for simplicity.

Diffusion Calculation

In the cytosol, the diffusional free [Ca2+] produced by a source flux s is given by:

\begin{equation*}[Ca^{2+}]_{Cyto}=\frac{s}{2{\pi}D_{i}r}.\end{equation*}
3

Within the cytosolic hemisphere (CS) of the sponge, the [Ca2+] is:

\begin{equation*}[Ca^{2+}]_{CS}=\frac{s}{2{\pi}D_{i}r}+b_{1},\end{equation*}
4

where the constant b1 is to be determined by the boundary condition that [Ca2+] must jump by the factor q2 at the boundary of the sponge, r = r1. Solving for b1 and replacing it in the previous equation gives:

\begin{equation*}[Ca^{2+}]_{CS}=\frac{(D_{i}q^{2}-D)_{s}}{2{\pi}DD_{i}r_{1}}+\frac{s}{2{\pi}D_{i}r}.\end{equation*}
5

In the luminal hemisphere (LS) of the sponge, the solution of the diffusion equation is:

\begin{equation*}[Ca^{2+}]_{LS}=b_{2}- \left( \frac{s}{2{\pi}D_{i}r} \right) ,\end{equation*}
6

where the constant b2 is to be determined by requiring that the concentration at the true pore radius r0 be equal on both sides of the membrane (i.e., leaving out the diffusion resistance of the true pore). Solving for b2 then gives:

\begin{equation*}[Ca^{2+}]_{LS}=\frac{(Dr_{0}r_{1}-2Drr_{1}-D_{i}q^{2}rr_{0}+Drr_{0})_{s}}{2{\pi}DD_{i}rr_{0}r_{1}},\end{equation*}
7

while in the lumen the solution is given by:

\begin{equation*}[Ca^{2+}]_{lum}=b_{3}- \left( \frac{s}{2{\pi}Dr} \right) ,\end{equation*}
8

where the constant b3 is again determined by the Donnan factor boundary condition at r1. Solving for b3, replacing it, and taking the limit as r → infinity, we find the free Ca2+ in the SR lumen:

\begin{equation*}[Ca^{2+}]_{lum}=\frac{[D\;r_{1}+(D_{i}q^{2}-D)r_{0}]s}{{\pi}D\;D_{i}q^{2}r_{0}r_{1}}.\end{equation*}
9

Substituting the value of q from Eq. 2, and noting that the anion concentration is given by:

\begin{equation*}a=\frac{3n}{4{\pi}N_{a}r^{3}_{1}},\end{equation*}
10

where n is the number of negative charges, Na is Avogadro's number, and r1 is the radius of the sphere within which the charges are confined, and the fact that s = i/F, where i is the unitary current, gives:

\begin{equation*}[Ca^{2+}]_{lumen}=\;\frac{2i(3D_{i}nr_{0}\sqrt{64{\pi}^{2}k^{2}N^{2}_{a}r^{6}_{1}+9n^{2}}+32{\pi}^{2}Dk^{2}N^{2}_{a}r^{7}_{1}+\;}{{\pi}D\;D_{i}Fr_{0}r_{1}(\sqrt{64{\pi}^{2}k^{2}N^{2}_{a}r^{6}_{1}+9n^{2}}+3n)^{2}}\end{equation*}
\begin{equation*}\frac{32{\pi}^{2}D_{i}k^{2}N^{2}_{a}r_{0}r^{6}_{1}-32{\pi}^{2}Dk^{2}N^{2}_{a}r_{0}r^{6}_{1}+9D_{i}n^{2}r_{0})}{{\pi}D\;D_{i}Fr_{0}r_{1}(\sqrt{64{\pi}^{2}k^{2}N^{2}_{a}r^{6}_{1}+9n^{2}}+3n)^{2}}\end{equation*}
11

Eq. 11 has a minimum as a function of r1, located, in general, around 5–10 nm. Evaluating Eq. 11 at this optimum radius of the charge sphere gives a lower limit to the lumenal Ca2+ for a given unitary current. By assuming that all 2,768 acidic residues of the tetramer are ionized, r0 = 1 nm, and Di = D = 0.78 × 10−5 cm2/s, we obtain the very liberal estimate of the minimum lumenal free Ca2+ required to drive a unitary current of 3  pA at the zero transmembrane potential that was quoted in the text.

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Original version received 29 June 1998 and accepted version received 23 November 1998.

Author notes

Address correspondence to Dr. Michael Fill, Department of Physiology, Loyola University Chicago, 2160 S. First Ave., Maywood, IL 60153. Fax: 708-216-5158; E-mail: mfill@luc.edu