Ryanodine receptor (RyR) channels from mammalian cardiac and amphibian skeletal muscle were incorporated into planar lipid bilayers. Unitary Ca2+ currents in the SR lumen-to-cytosol direction were recorded at 0 mV in the presence of caffeine (to minimize gating fluctuations). Currents measured with 20 mM lumenal Ca2+ as exclusive charge carrier were 4.00 and 4.07 pA, respectively, and not significantly different. Currents recorded at 1–30 mM lumenal Ca2+ concentrations were attenuated by physiological [K+] (150 mM) and [Mg2+] (1 mM), in the same proportion (∼55%) in mammalian and amphibian channels. Two amplitudes, differing by ∼35%, were found in amphibian channel studies, probably corresponding to α and β RyR isoforms. In physiological [Mg2+], [K+], and lumenal [Ca2+] (1 mM), the Ca2+ current was just less than 0.5 pA. Comparison of this value with the Ca2+ flux underlying Ca2+ sparks suggests that sparks in mammalian cardiac and amphibian skeletal muscles are generated by opening of multiple RyR channels. Further, symmetric high concentrations of Mg2+ substantially reduced the current carried by 10 mM Ca2+ (∼40% at 10 mM Mg2+), suggesting that high Mg2+ may make sparks smaller by both inhibiting RyR gating and reducing unitary current.

## Introduction

The contractile proteins in skeletal muscle are activated by a sudden increase in cytosolic Ca2+ concentration. The cytosolic Ca2+ level is largely determined by the balance of Ca2+ uptake and release by the SR. Calcium is released from the SR through a specialized Ca2+ channel, the RyR. Functional, biochemical, and electron microscopic studies have recently called attention to striking differences between these channels in different taxonomic classes. Mammalian skeletal muscle predominantly contains the RyR1 channel isoform (McPherson and Campbell, 1993; Coronado et al., 1994; Ogawa, 1994). The RyR3 channel isoform is also expressed in mammalian striated muscles, but at relatively low levels (Sutko et al., 1991; Tarroni et al., 1997; Froemming et al., 2000). Amphibian skeletal muscle contains nearly equal amounts of the α- and β-RyR isoforms, which are homologues of mammalian RyR1 and RyR3, respectively (Lai et al., 1992; Airey et al., 1993; Oyamada et al., 1994; Sutko and Airey, 1996).

In skeletal muscle, some RyR channels are physically associated with dihydropyridine receptors (DHPRs) in the transverse (T-) tubule membrane. The DHPRs sense the T-tubule membrane depolarization and transmit this information to the RyR channel. This signal triggers the DHPR-linked RyR channels to open and release Ca2+ from the SR. At least in amphibians, it is proposed that this depolarization-induced Ca2+ release (DICR) activates nearby DHPR-free RyR channels through the Ca2+-induced Ca2+ release (CICR) mechanism. It is not known whether or not this duality of mechanisms translates to the existence of two additive components of Ca2+ release (as proposed in a model of Ríos and Pizarro, 1991). Whether and how different Ca2+ release activation mechanisms may correspond to the different types of RyR channels present is also uncertain.

A new dimension to this duality was recently added by Felder and Franzini-Armstrong (2002), who presented evidence that β isoforms occur in parajunctional arrays, while α-RyR1 isoforms constitute the T-tubule–facing, junctional arrays. It would be reasonable to expect different functional properties for channels that are not just molecular variants but are also arranged differentially in the terminal cisternae of the SR.

Spatially and temporally discrete Ca2+ release events called “Ca2+ sparks” were first observed in mammalian cardiac muscle cells (Cheng et al., 1993). Analogous events occur in amphibian skeletal muscle (Tsugorka et al., 1995; Klein et al., 1996; Kirsch et al., 2001). Additionally, spark-like events have also been recorded in mammalian skeletal muscle (Conklin et al., 1999; Kirsch et al., 2001; Zhou et al., 2003). The number of RyR channels that underlie an individual spark is still debated (e.g., Ríos and Brum, 2002; Schneider and Ward, 2002). Part of the debate stems from uncertainty concerning the amplitude of Ca2+ current carried by a single RyR channel in the cell. Although ingenious indirect estimates of unitary RyR Ca2+ current in situ have been produced (see Wang et al., 2001), its direct measurement requires that the channel be isolated from the cell and reconstituted into an artificial lipid bilayer (Smith et al., 1985; Fill and Coronado, 1988). However, most RyR channel studies in bilayers have been done under conditions designed to optimize the signal-to-noise characteristics, conditions that typically include high [Ca2+] and/or the use of nonphysiological concentrations of other ions.

Defining the attributes of the Ca2+ release channels in near-physiological conditions requires more than simply adjusting the Ca2+ concentrations. Indeed, the RyR channels are poorly selective Ca2+ channels, which do not discriminate well between divalent cations and discriminate only poorly between divalent and monovalent cations. Thus, several cations present in the cell (i.e., Ca2+, Mg2+, and K+) can permeate through an open RyR channel. This is important because the Mg2+ and K+ concentrations in the cytosol are large and the presence of these ions is known to reduce the unitary Ca2+ current.

Earlier work of our laboratories (Mejía-Alvarez et al., 1999) defined the unitary Ca2+ currents carried by single RyR channels isolated from mammalian heart in quasiphysiological salt solutions (150 mM Cs+, 1 mM Mg2+ with variable lumenal Ca2+ levels). The measured current was 0.35 pA when the lumenal Ca2+ concentration ([Ca2+]L) was 2 mM in the presence of 150 mM Cs+ symmetrical with no Mg2+ present. One shortcoming of these original measurements was the possibility that rapid closures and the limited bandwidth of bilayer recordings could have led to an underestimate of the current. Another was the presence of Cs+ as permeable monovalent cation. This may be important because this ion is substantially less permeant than K+ (pCs+/pK+ = 0.61; Williams et al., 2001). We now provide new measurements in an attempt to correct these limitations. A high caffeine concentration was used to prolong the open state (i.e., to reduce the potential impact of rapid closures) and the permeable monovalent cation was K+ (not Cs+). Additionally, we extended the measurements to include frog skeletal muscle channels, so that the results can also be applied to interpretation of sparks in amphibian skeletal muscle. Finally, in light of the interest in using Mg2+ as a modulator of Ca2+ spark frequency and morphology (González et al., 2000; Lamb, 2000; Lamb, 2002), we performed measurements of current in the presence of variable Mg2+ concentrations.

## Materials And Methods

Heavy SR microsomes were isolated from the leg muscles of the frog Rana pipiens or pig cardiac 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 formed across a 150-μm diameter hole in the wall of a Delrin cup. The cup was placed in a plastic block so that the bilayer separated two pools (cis and trans). Each pool was filled with a solution containing 20 mM HEPES-TRIS (pH 7.4) and 10 μM added free Ca2+. All other salts and pharmacological agents were added to this solution. All experiments were done in the presence of 5 or 10 mM symmetrical caffeine for cardiac or skeletal ryanodine receptors, respectively. In this study, TRIS was considered an impermeable cation. Although large cations can permeate through the RyR channel, to our knowledge there is no report of TRIS permeation through a RyR channel. Even if TRIS were permeable, the relatively low concentration used here makes it unlikely to substantially alter the interpretation of our results. In the frog studies, two current amplitudes were observed, believed to belong to two classes of channels. Unless specified otherwise, frog data and analysis were done on currents believed to correspond to the larger conductance class.

Bilayers were formed using a lipid mixture of phosphatydylethanolamine and phosphatydylcholine (7:3, 50 mg/ml decane; Avanti Polar Lipids, Inc.). Heavy SR microsomes were added to the cis pool. The trans pool was held at virtual ground. Small aliquots (2 μl) of a 4 M CsCH3SO3 solution were squirted (providing a brief period of high CsCH3SO3 concentration) at the cis side of the bilayer to facilitate RyR incorporation. In our experience, the use of CsCH3SO3 (compared with other salts) provided the best rate of single RyR channel incorporation. The total CsCH3SO3 added was always well below 1 mM. An equal amount of CsCH3SO3 was added to the trans chamber. Recording electrodes were carefully balanced and the transmembrane potential was held at 0 mV (unless otherwise stated). The polarity of RyR insertion was such that the channel's cytosolic side was always in the cis pool (Fill et al., 1990). The channels were positively identified by their sensitivity to ryanodine (unpublished data) and caffeine.

The Debye-Huckel equation was used to calculate the Ca2+ activity coefficient (γCa) in the different experimental solutions used in this study (control, 1 mM MgCl2, 150 mM KCl, 1 mM MgCl2 and 150 mM KCl; also see Fig. 7 A). The hydrated ionic radii of Mg2+, Ca2+, K+, and Cl were assumed to be 0.8, 0.6, 0.3, and 0.3 nm, respectively. The ionic strength in each experimental situation was determined with 1 to 5 mM CaCl2 present. The estimated range of γCa was 0.665–0.564 in the control and Mg-only studies. The range of γCa was substantially less (i.e., 0.350 to 0.341) in the KCl and KCl-Mg solutions. Thus, the γCa should be considered when interpreting and/or extrapolating the Ca2+ concentration data presented here.

Unitary currents were recorded using a conventional patch clamp amplifier (Axopatch 200B; Axon Instruments, Inc.). The current signal was digitized at 4 kHz with a 16-bit AD/DA converter (Digidata 1200; Axon Instruments, Inc.) and Bessel-filtered at 1 kHz. Unitary current amplitude measurements were made by either measuring the difference between mean open/closed currents from individual adjacent long open/closed events and/or by the difference between means of two Gaussian curves fit to all-points histograms. Data acquisition, unitary current measurement, statistical analysis, and data processing were performed using commercially available software packages (pClamp V6.0, Axon Instruments, Inc.; Origin, Microcal). The all-point histograms were generated from 1 to 4 min of recording using pClamp. The ordinates (unpublished data) represent the number of points. Abscissas in the histograms were shifted so that the closed current peak was at 0 pA. Data were plotted as mean ± SEM. Paired comparisons were statistically evaluated using a two-tailed Student's t test (Rosner, 1982).

### Model Simulations and Fitting

The four-barrier permeation model of Tinker et al. (1992) was used to calculate current at different ion concentrations, and implemented in a program kindly provided by Drs. Andrew Tinker (University College, London) and Alan L. Williams (Imperial College, London). The model is identical to that applied by Tinker et al. (1992). It describes permeation as a series of transitions obeying Eyring rate theory through a free energy profile consisting of 4 peaks and 3 wells. The electrical distances of the wells from the cytosolic edge were 0.1, 0.5 and 0.9. Predictions were done assuming a holding potential of 0 mV. The ion concentration of Ca2+, Mg2+, K+ were as stated in the text. The heights (in RT units) of the voltage- and concentration-independent local extremes of energy for Ca2+ were 3.00, 3.00, 3.00, 3.00, −2.35, −9.50, and −2.35 for peaks 1 through 4, and wells 1 through 3, respectively. The corresponding parameters for Mg2+ were 3.00, 3.00, 3.00, 3.00, −2.35, −9.80, and −2.35. For K+ they were 5.50, 5.50, 5.50, 5.50, −2.35, −3.25, and −2.35. Note that the energy profile for Mg2+ has a central well 0.3 RT deeper than that for Ca2+.

Additional fitting was performed with an extension of the Poisson-Nernst-Plank model of electrodiffusion (Chen et al., 1999, 2003). In this case each ion's diffusion is driven by the gradient of a chemical potential with a concentration term, an electrical term, and an excess potential (μ*) describing chemical interactions with the pore wall (Chen et al., 1999). The adjustable parameters include a diffusion coefficient and excess potential for each ion, as well as parameters of a simple geometry and charge profile for the channel. Geometry, charge profile, and parameters of monovalent ions are in Table 3 of Chen et al. (1999). The current versus [Ca2+] data were well fit with DCa = 8 × 10−8cm2/s, μ* = −91 mV, DMg = 5 × 10−8 cm2/s, μ* = −53 mV.

For visualization purposes, some datasets were fit by a single rectangular hyperbolic function of lumenal Ca concentration using the following equation:

$\mathrm{I}_{\mathrm{OBS}}=\mathrm{i}_{\mathrm{MAX}}{\times}\left\{{\left(\mathrm{B}{\times}\left[\mathrm{Ca}\right]_{\mathrm{L}}\right)}/{\left(\mathrm{1}+\left(\mathrm{B}{\times}\left[\mathrm{Ca}\right]_{\mathrm{L}}\right)\right)}\right\}\mathrm{.}$
(1)

Here, iOBS is the experimentally observed unitary current, iMAX is the maximum unitary current measured at high [Ca]L levels and B is the inverse concentration at half-maximal current.

## Results

The goal here was to measure unitary RyR channel currents carried by Ca2+ in the trans to cis (i.e., lumen to cytosol) direction. These measurements were done at 0 mV in the presence of a trans-to-cis Ca2+ gradient. Other permeant cations (i.e., K+ and Mg2+) were added symmetrically (i.e., to both sides of the bilayer) in some experiments. Net currents carried by these ions did not contribute to the unitary current at 0 mV because of the absence of driving force. To reduce open channel current measurement errors due to fast gating fluctuations, recordings were performed in the presence of symmetrical 10 or 5 mM caffeine to induce longer open events. In the first section below, the impact of 150 mM K+ and 1 mM Mg2+ on unitary Ca2+ current is explored. The second section presents a series of measurements at different [Ca2+]L, including those believed to apply physiologically.

### Unitary Currents in the Presence of Caffeine

In the presence of 10 mM caffeine, a substantial increase in the open probability (Po) of the RyR channel was noted upon addition of KCl (as reported by Meissner et al., 1997). The effect was greater in the cardiac than in the skeletal channel. The observed increase in Po made it difficult to measure current amplitude because closures were relatively infrequent. To circumvent this problem, cardiac channel studies were done at a lower caffeine concentration (5 mM). The current amplitude of the channel was identical at both caffeine concentrations. All data shown represent results in the presence of 5 mM caffeine (for cardiac preparations) or 10 mM caffeine (for skeletal muscle channels).

Representative records of a frog skeletal and a mammalian heart RyR channel are shown in Fig. 1, A and B. Single-channel activity was measured in the presence of 5 mM [Ca2+]L in the standard recording solutions (i.e., 20 mM Tris-HEPES, pH 7.4). The free Ca2+ concentration on the cytoplasmic side of the channel was ∼10 μM. No competing ions (K+ or Mg2+) were present. Single channel openings (current in trans to cis direction) are shown as downward deflections from the zero current level (filled arrowhead). The corresponding total amplitude (i.e., all-points) histograms are shown at the bottom. The unitary current was <3 pA in both cases.

The effect of other permeant ions on the unitary Ca2+ current carried by a mammalian cardiac RyR channel (RyR2) is shown in Fig. 2. In the absence of other permeant ions (Fig. 2 A), Ca2+ current at 0 mV was slightly larger than 2 pA when [Ca2+]L was 2 mM. Addition of 150 mM KCl (Fig. 2 B) or 1 mM Mg2+ (Fig. 2 C) symmetrically (i.e., to both sides of the channel) reduced the current to <2 pA. These data were collected from the same RyR2 channel.

The influence of K+ and Mg2+ on the unitary Ca2+ current of a frog RyR channel is demonstrated in Fig. 3. The Ca2+ current at 0 mV with 4 mM [Ca2+]L in the absence of other permeable ions was slightly larger than 3 pA (Fig. 3 A). The addition of 150 mM KCl and 1 mM Mg2+ (Fig. 3 B) to both chambers reduced it to nearly 1 pA. In summary, the presence of physiologically relevant concentrations of K+ and Mg2+ reduces substantially the unitary Ca2+ current of the mammalian and amphibian RyR channels.

The high K+ and Mg2+ permeability of the RyR channels is well documented (Smith et al., 1988; Lindsay et al., 1991; Tinker and Williams, 1992). The decrease in unitary Ca2+ current in the presence of these ions has been interpreted as a consequence of competition by K+ and Mg2+ for occupancy of sites in the RyR pore (Mejía-Alvarez et al., 1999). This interpretation is also buttressed by simulations using a barrier model of permeation (shown below).

### Accuracy of Solution Changes and Electrode Balancing

These studies involve measurement of relatively small unitary currents before and after addition of relatively large salt concentrations (K+ and/or Mg2+) to both sides of the bilayer. Relatively small errors in the salt addition and/or electrode balancing can affect the unitary current measurement. To evaluate these potential sources of error, current-voltage relationships of single amphibian RyR channels were measured after a series of symmetric KCl additions (50, 100, and 200 mM; Fig. 4). There was no Mg2+ present, the free Ca2+ concentration on each side of the channel was 10 μM, and caffeine was added symmetrically at 10 mM. Averaged results from six channels are represented in Fig. 4. All three current-voltage plots were Ohmic and reversed near 0 mV. The unitary current at 0 mV varied within a relatively small range (0.05 pA; see Fig. 4 inset). These data indicate that large symmetric salt additions could be made without introducing substantial error in the current measurements.

### Frog Unitary Currents Display Two Amplitudes

In the frog studies, multiple current levels were observed frequently, suggesting that multiple channels incorporated into the bilayers. In these records, different current amplitudes (or conductances) were frequently observed in the experimental conditions tested (43% of the cases). A sample multilevel record with different current amplitudes is shown in Fig. 5 (top). The corresponding all-points histogram (bottom) has peaks corresponding to the current amplitudes occurring individually, and both occurring simultaneously. The two individual amplitudes, defined in the histogram as the difference between the individual peaks and the baseline (see horizontal bars with numbers in panel B), differed by ∼35%. Both classes of openings were sensitive to ryanodine.

The characteristics of these events are examined further in Fig. 6. In panel A, histograms are presented of the individual amplitudes (determined as in Fig. 5) exclusively in bilayers that had two different amplitudes simultaneously. The individual distributions were well fitted by single Gaussian functions (fits depicted by continuous curves) and the average currents were significantly different (P < 0.001). The study in Fig. 6 B helps test whether these two amplitudes correspond to different channels. The dashed line represents the distribution of the larger current amplitudes in part A. The histogram (crosshatched bars) represents current amplitudes found in bilayers with only one clearly distinguishable level (and those with multiple but equal levels). The line is a fit using the sum of two Gaussian functions. The good fit suggests that there are two groups of individually appearing channels with unitary currents like those observed in the multilevel recordings. Hence, it can be reasonably concluded that the two amplitudes correspond to different channels, which insert individually, and sometimes together. The roughly similar number of bilayers with two different currents and two equal (high) currents is consistent with the possibility that the channels insert independently with roughly equal probability.

The α- and β-RyR channel isoforms are present in frog skeletal muscle in roughly equal amounts. Thus, it is possible that the two current amplitudes observed above correspond to these different RyR isoforms. There is no previously published evidence that these two isoforms have different conductance. In the mammal, however, Murayama et al. (1999) reported a significantly greater (∼16%) monovalent cation conductance of RyR3 over RyR1. Clearly, more experimentation is necessary before a solid interpretation concerning the two observed conductances here can be made. The frog RyR channel measurements that follow were done on channels in the larger conductance class.

### Lumenal Ca2+ Concentration Dependence of Unitary Current

The Ca2+ current carried by single mammalian or amphibian RyR channels was defined in four different experimental conditions over a wide range of [Ca2+]L. These conditions are illustrated in Fig. 7 A. In the first experimental condition (control; filled triangles), the only permeable ion present was Ca2+. In the second condition (open circles), 1 mM Mg2+ was added to each side of the channel so that there were two permeable cations present (Ca2+ and Mg2+). In the third condition (filled circles), 150 mM K+ was added symmetrically instead of the Mg2+ and the result was that there were two permeable cations present (Ca2+ and K+). In the final case (half-filled circles), 1 mM Mg2+ and 150 mM K+ were added symmetrically.

Several channels were studied in each condition. The summary data (means ± SEM; n = 5–22 channels per point) are plotted as a function of [Ca2+]L in Fig. 7 B for the mammalian RyR channel and in Fig. 7 C for the amphibian RyR channel. The lowest [Ca2+]L at which clearly resolved unitary currents could be measured was 1 mM. In every condition, unitary current at 0 mV increased less than proportionally with [Ca2+]L, tending toward saturation at high [Ca2+]L levels. Each set of data points was fit with a single rectangular hyperbolic function passing through the origin. For both mammalian and amphibian channels, the presence of competing ions attenuated unitary current at all [Ca2+]L tested. The attenuation induced by the presence of 1 mM Mg2+ was less than that induced by 150 mM K+. Current reduction was greatest when both K+ and Mg2+ were present.

The concentration of Ca2+ inside the SR is thought to be close to 1 mM in cardiac muscle and 1–5 mM in skeletal muscle (Hasselbach and Oetliker, 1983; Volpe and Simon, 1991; Inesi, 1994; Chen et al., 1996; Shannon and Bers, 1997). The membrane potential across the SR in situ is thought to be at or very close to 0 mV (Somlyo et al., 1981; Gilbert and Meissner, 1983; Best and Abramcheck, 1985; Tang et al., 1989). To better estimate unit Ca2+ current at such low Ca2+ levels, a small segment of the datasets shown in Fig. 7, B and C, are expanded and superimposed in Fig. 7 D. The mammalian and amphibian data nearly overlap (half-filled circles). These data indicate that the unit Ca2+ current carried by the mammalian or amphibian RyR channels in the presence of physiological Mg2+ and K+ concentrations is slightly less than 0.5 pA (red arrow in Fig. 7 D). The dashed line represents a previously published dataset (Mejía-Alvarez et al., 1999) collected on RyR2 channels with 150 mM symmetrical Cs+, no Mg2+, and no caffeine.

In Fig. 7 D, the experimental results are compared with predictions of the well-known 4-barrier Eyring rate model of Tinker et al. (1992), applied with the parameters outlined in the methods section. The open triangles represent values of current calculated at the Ca2+ concentrations in the abscissa, with Mg2+ and K+ included in the model at the levels used here. The model predicts currents generally greater than that experimentally observed, but reproduces well their tendency with increasing [Ca2+], as well as the changes observed in high [Mg2+].

### Unitary Currents in the Presence of High Mg2+ Concentrations

Recent studies have demonstrated that Ca2+ sparks in frog muscle fibers can still be recorded at high Mg2+ concentrations (as high as 7.5 mM), but with diminished amplitude and spatial width (González et al., 2000). Thus, it was of interest to evaluate unitary Ca2+ current at such high Mg2+ concentrations. Three sample channel records of a single amphibian RyR channel are shown in Fig. 8 A. These records were collected in the presence of 0, 5 (top), or 10 mM Mg2+ (added symmetrically). The solutions included 10 mM [Ca2+]L and the usual 10 mM caffeine. An obstacle for the accurate measurement of current attenuation was the clear decrease in Po (expected and observed) at elevated Mg2+ concentrations (even in the presence of caffeine). In Fig. 8 A, highly compressed records are shown to illustrate the decrease in Po. In spite of this complication, a few sufficiently long openings were recorded and adequate measurements of current amplitude were made at high Mg2+ levels.

Segments from each record (marked by the open bar) are shown expanded in Fig. 8 B. Summary unitary current data are presented in Fig. 8 C (filled squares). The nearly perfect prediction of the 4-barrier model (Tinker et al., 1992) using these same salt conditions is represented by the continuous curve. The filled circle represents the measured average current in the combined presence of 1 mM Mg2+ and 150 mM K+. The corresponding model prediction (in the combined presence of Mg2+ and K+) is represented by the open circle. In summary, 10 mM symmetrical Mg2+ reduced the unitary current carried by 10 mM Ca2+ to ∼40%.

## Discussion

Single RyR channel studies require that the channel be removed from the cell and reconstituted into an artificial membrane system. Consequently, many factors (known or unknown) that affect RyR channel operation will be absent. To maximize the signal-to-noise ratio and minimize the number of variables, most single RyR channel studies have been conducted in relatively simple experimental conditions, typically using a monovalent cation as charge carrier. In cases where Ca2+ is the carrier, very large [Ca2+]Ls are used and the current is enhanced by the absence of other permeant ions. The present studies were designed to more closely approach the salt conditions that exist in the cell. These include a substantially smaller Ca2+ gradient (down to 1 mM [Ca2+]L) and the presence of Mg2+ and K+.

The unitary Ca2+ current carried by a RyR channel in the presence of a large [Ca2+]L without competing permeant ions is well documented. Smith et al. (1988) reported 4.2 pA with 54 mM [Ca2+]L for rabbit skeletal channels. Tinker and Williams (1992) measured 5.5 pA with 210 mM [Ca2+]L for sheep cardiac channels. Here, unit Ca2+ current was measured both in the absence and presence of other permeant ions. The unit Ca2+ currents carried by the mammalian cardiac and amphibian skeletal RyR channels (at 0 mV) with 20 mM [Ca2+]L were not statistically different (P > 0.20, see Table I). The results confirm that physiologic concentrations of K+ and Mg2+ attenuate the unit Ca2+ current through both types of RyR channels tested. This head-to-head comparison under identical recording conditions also confirms the similar permeation properties of these RyR channels. We preliminarily reported a twofold difference in the unitary current carried by the frog and mammalian channels at 150 mM K, 1 mM Mg, and 1 mM lumenal Ca (Kettlun et al., 2000). The present results, obtained from more measurements, must supersede the previous report.

### Unitary Ca2+ Current Measurements

The free Ca2+ concentration inside the SR is thought to be near 1 mM in mammalian cardiac muscle (Shannon and Bers, 1997) and amphibian skeletal muscle (Volpe and Simon, 1991). Given the difficulties to directly measure current at such concentrations of the carrier, different theories have been used to predict the Ca2+ current through the RyR channel under those conditions. Tinker et al. (1992) used an Eyring-rate permeation model and unitary currents measured at higher than physiological [Ca2+]L (210 mM Ca2+) to predict that the mammalian RyR2 channel should carry a Ca2+ current of ∼1.4 pA. Mejía-Alvarez et al. (1999) directly measured Ca2+ currents carried by RyR2 channels at a very low [Ca2+]L in the presence of a competing monovalent cation (symmetrical 150 mM Cs+, absence of Mg2+ and with no transmembrane potential) and reported a unit Ca2+ current of 0.35 pA. We have extended these measurements here to include the amphibian RyR channel, and used caffeine to prolong open dwell times. The measurement conditions for the first time included a low [Ca2+]L in the simultaneous presence of Mg2+ and K+.

As shown in Fig. 7 and Table II, the current in the presence of 1 mM Mg2+ and 150 mM K+ with 1 mM [Ca2+]L as charge carrier was 0.48 pA for the amphibian channel. The unitary current of the mammalian cardiac channel was similar (0.49 pA). The value reported by Mejía-Alvarez et al. (1999) was ∼30% smaller. The most important reason that led to the greater current in the present experiments was probably the stabilization of the open state by caffeine.

### Unitary Ca2+ Current Predictions

To facilitate extrapolation to conditions that make measurement difficult, the present results were compared with model predictions. To stress these limited, nonmechanistic purposes, two permeation models with different physico-chemical underpinnings were used. One was the discrete state (4-barrier Eyring transition state) model of Tinker et al. (1992). Eyring's transition state theory does not apply to the physics of ion permeation (e.g., Andersen, 1999), in spite of which the model of Tinker et al. (1992) has become a standard descriptive tool in the work with ryanodine receptors. The unitary currents predicted with this model (at 1 mM Ca2+, Fig. 7 D) were ∼0.25 pA larger than those measured, but reproduced very well the changes with [Ca2+]L. Predicted Ca2+ currents at high Mg2+ concentrations (in the absence of KCl) were also compared with our measurements. The model currents in these simpler salt conditions at a higher [Ca2+]L (10 mM) were nearly identical to the measurements (Fig. 8). The good agreement between the discrete kinetic model predictions and our experiments supports the use of the model as a tool to estimate currents in vivo, in not easily reproducible conditions (for example, when concentrations are varying).

The flow of monovalent cations through RyR2 has also been modeled with an extension of the Poisson-Nernst-Planck or PNP model of electrodiffusion (Chen et al., 1999). Dr. Duan Chen kindly performed calculations with a version of the model modified to include divalents (Chenet al., 2003) using parameter values given in materials and methods, and found that he could fit well our I versus [Ca2+] data in the presence of K+ and Mg2+.

In summary, both models proved valuable for prediction and parametrization of RyR channel currents. Either one could be applied, for instance, to predict currents at lower [Ca2+]SR than used in the present measurements.

In the original description of the Ca2+ spark in mammalian cardiac muscle (Cheng et al., 1993), the possibility was put forward that these events may be generated by a single RyR channel. This suggestion assumed that the RyR channel had a unitary current of 3 pA (Rousseau and Meissner, 1989) and that the SR Ca2+ flux underlying the spark was 4 pA (Cheng et al., 1993). More recently, Soeller and Cannell (2002) concluded that the SR Ca2+ flux underlying the spark was 7–12 pA. Here, we show that the unitary current is probably near 0.5 pA with 1 mM [Ca2+]L present. 8–32 RyR channels with this current would have to open in concert to generate a spark. This is in reasonable agreement with noise analysis suggesting that ∼18 RyR channels may be involved in the generation of the spark of cardiac muscle (Bridge et al., 1999).

Other studies in cardiac myocytes, Wang et al. (2003) observed a quantal substructure in sparks, which combined with an internal calibration procedure (based on the observation of sparklets, associated with plasmalemmal L-type channel openings) led to an estimate of 1.2 pA per channel. Another estimate, this time for skeletal muscle, came from simulations that seek to reproduce long-lasting fluorescence events of low intensity, observed in intact frog skeletal muscle (González et al., 2000). Simulations of these events required a point source (presumably a single channel) of 0.4 pA.

These estimates (0.4–1.2 pA per channel) are relatively close given the differences in approach and conditions, and allow one to evaluate numbers of channels, within a factor of 3, when the collective current intensity is known.

Ca2+ sparks are commonly studied in amphibian skeletal muscle (Ríos and Brum, 2002; Schneider and Ward, 2002). In one study, elevated cytosolic Mg2+ concentrations (7 mM) greatly reduced the amplitude and spatial width of Ca2+ sparks elicited by depolarization in voltage-clamped frog skeletal muscle (González et al., 2000). One possible mechanism of this effect is that the added Mg2+ attenuates the unitary Ca2+ current, reducing spark width and amplitude, but not its rise time. To test this possibility, studies were performed here at a comparably high Mg2+ concentration (Fig. 8). The attenuation of unitary Ca2+ current was substantial (∼2.5-fold less than in 1 mM Mg2+). Thus, the reduction in Ca2+ spark amplitude observed at elevated cytosolic Mg2+ levels (González et al., 2000) may in part be due to an attenuation of unitary current. However, these very high Mg2+ levels also substantially reduce RyR channel open probability (see Fig. 8). Therefore, the reduced spark amplitude at elevated cytosolic Mg2+ levels must reflect a reduction in unitary Ca2+ current compounded by a reduction in the number of channels simultaneously open.

## Acknowledgments

We are grateful to Andrew Tinker (University College, London) and Alan L. Williams (Imperial College, London) for generously supplying a program that implements the 4-barrier permeation model. We also thank Le Xu and Gerhard Meissner (University of North Carolina at Chapel Hill) for help in implementation of the barrier model and discussions on the PNP model. We are indebted to Duan P. Chen (Rush University, Chicago) for fitting our data to an updated version of the PNP model. We are also grateful to D.M. Bers (Loyola University Chicago) for many discussions and suggestions.

This work was supported by National Institutes of Health grants HL57832 and HL64210 to M. Fill, and RA32808 to E. Rios. A. Gonzalez was the recipient of a Senior Fellowship of the American Heart Association of Metropolitan Chicago.

Olaf S. Andersen served as editor.

Abbreviations used in this paper: CICR, Ca2+-induced Ca2+ release; DHPR, dihydropyridine receptor; DICR, depolarization-induced Ca2+ release.

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