Effects of Tetracaine on Voltage-activated Calcium Sparks in Frog Intact Skeletal Muscle Fibers

The properties of Ca2+ sparks in frog intact skeletal muscle fibers depolarized with 13 mM [K+] Ringer's are well described by a computational model with a Ca2+ source flux of amplitude 2.5 pA (units of current) and duration 4.6 ms (18 °C; Model 2 of Baylor et al., 2002). This result, in combination with the values of single-channel Ca2+ current reported for ryanodine receptors (RyRs) in bilayers under physiological ion conditions, 0.5 pA (Kettlun et al., 2003) to 2 pA (Tinker et al., 1993), suggests that 1–5 RyR Ca2+ release channels open during a voltage-activated Ca2+ spark in an intact fiber. To distinguish between one and greater than one channel per spark, sparks were measured in 8 mM [K+] Ringer's in the absence and presence of tetracaine, an inhibitor of RyR channel openings in bilayers. The most prominent effect of 75–100 μM tetracaine was an approximately sixfold reduction in spark frequency. The remaining sparks showed significant reductions in the mean values of peak amplitude, decay time constant, full duration at half maximum (FDHM), full width at half maximum (FWHM), and mass, but not in the mean value of rise time. Spark properties in tetracaine were simulated with an updated spark model that differed in minor ways from our previous model. The simulations show that (a) the properties of sparks in tetracaine are those expected if tetracaine reduces the number of active RyR Ca2+ channels per spark, and (b) the single-channel Ca2+ current of an RyR channel is ≤1.2 pA under physiological conditions. The results support the conclusion that some normal voltage-activated sparks (i.e., in the absence of tetracaine) are produced by two or more active RyR Ca2+ channels. The question of how the activation of multiple RyRs is coordinated is discussed.

The properties of Ca 2+ sparks in frog intact skeletal muscle fi bers depolarized with 13 mM [K + ] Ringer's are well described by a computational model with a Ca 2+ source fl ux of amplitude 2.5 pA (units of current) and duration 4.6 ms (18 °C; Model 2 of Baylor et al., 2002). This result, in combination with the values of single-channel Ca 2+ current reported for ryanodine receptors (RyRs) in bilayers under physiological ion conditions, 0.5 pA (Kettlun et al., 2003) to 2 pA (Tinker et al., 1993), suggests that 1-5 RyR Ca 2+ release channels open during a voltage-activated Ca 2+ spark in an intact fi ber. To distinguish between one and greater than one channel per spark, sparks were measured in 8 mM [K + ] Ringer's in the absence and presence of tetracaine, an inhibitor of RyR channel openings in bilayers. The most prominent effect of 75-100 μM tetracaine was an approximately sixfold reduction in spark frequency. The remaining sparks showed signifi cant reductions in the mean values of peak amplitude, decay time constant, full duration at half maximum (FDHM), full width at half maximum (FWHM), and mass, but not in the mean value of rise time. Spark properties in tetracaine were simulated with an updated spark model that differed in minor ways from our previous model. The simulations show that (a) the properties of sparks in tetracaine are those expected if tetracaine reduces the number of active RyR Ca 2+ channels per spark, and (b) the single-channel Ca 2+ current of an RyR channel is ≤1.2 pA under physiological conditions. The results support the conclusion that some normal voltage-activated sparks (i.e., in the absence of tetracaine) are produced by two or more active RyR Ca 2+ channels. The question of how the activation of multiple RyRs is coordinated is discussed.

I N T R O D U C T I O N
Skeletal muscle is activated by the release of Ca 2+ from the sarcoplasmic reticulum (SR) into the myoplasm, where it can react with the Ca 2+ regulatory sites on troponin. This release takes place through Ca 2+ channels in the SR called ryanodine receptors (RyRs), which are under the control of voltage sensors in the membranes of the transverse tubular system. Small, brief, localized releases through one or more of these channels can occur either spontaneously or with small depolarizations. These microscopic events, which can be detected optically with Ca 2+ indicators, were fi rst observed in cardiac myocytes and called Ca 2+ sparks (Cheng et al., 1993). Because they are thought to represent the elementary event of SR Ca 2+ release, their study is expected to lead to useful information about the release process itself.
In frog intact twitch fi bers, a voltage-activated spark is thought to result from the fl ux of Ca 2+ through 1-5 active release channels (18°C; Baylor et al., 2002). A goal of the present experiments was to fi nd out whether a spark is produced by one or more than one release channel. This question was studied with tetracaine, a blocker of SR Ca 2+ release, which has been widely used in studies of excitation-contraction coupling. In single RyR channels in bilayers, tetracaine decreased open-channel probability of both skeletal (Xu et al., 1993;Csernoch et al., 1999) and cardiac (Gyorke et al., 1997) RyRs. The drug appears to block the channel by stabilizing a closed state of the channel without a change in single channel current. The reported values of the half-inhibitory concentration of tetracaine and of the Hill coeffi cient vary with preparation and recording conditions: 150 μM (mean; range 75-750 μM) and 2.5, respectively, for rabbit skeletal RyRs (Xu et al., 1993); 68 μM and 1.5 for rat skeletal RyRs (Csernoch et al., 1999); and 260-650 μM and 1.9-2.2 for rat cardiac RyRs (Gyorke et al., 1997).
Several studies show that tetracaine also affects the properties of Ca 2+ sparks. In rat ventricular myocytes, 100 μM tetracaine reduced spark frequency by a factor >5; the inhibition lasted 2-3 min after which spark frequency was approximately normal (Lukyanenko et al., 2001). This recovery was attributed to enhanced loading of the SR with Ca 2+ in tetracaine. Also in rat ventricular myocytes, 100 μM tetracaine reduced the average rate of rise of in-focus sparks by approximately threefold without altering the ‫2.1ف‬ pA quantal Ca 2+ fl ux attributed to a single active RyR Ca 2+ release channel (Wang et al., 2004). The latter result supports the idea that most cardiac sparks in the absence of tetracaine are produced by several simultaneously active channels.
In frog cut skeletal fi bers, 200 μM tetracaine eliminated voltage-activated Ca 2+ sparks elicited by a step depolarization from −90 to −58 mV (Shirokova and Rios, 1997) but spared a nonspark form of Ca 2+ release elicited by a smaller depolarization, from −90 to −72 mV. This form of release, termed "small-event" Ca 2+ release, is thought to arise from Ca 2+ fl uxes that are smaller than those that produce sparks. Shirokova and Rios (1997) hypothesized that, in the absence of tetracaine, smallevent release is a voltage-controlled source of Ca 2+ that, at larger depolarizations, is able to activate a cluster of RyRs via Ca 2+ -induced Ca 2+ release (CICR), thereby triggering a spark (see also Gonzalez et al., 2000).
In the present study, we have measured the effects of tetracaine on the properties of voltage-activated Ca 2+ sparks in frog intact skeletal muscle fi bers microinjected with fl uo-3 (Minta et al., 1989) and depolarized by 8 mM [K + ]. This value of [K + ] was chosen because it produces a substantial number of sparks while causing a minimal increase in resting fl uorescence. The concentration of tetracaine, 75-100 μM, was selected to block most sparks but leave enough for reliable measurements. The most obvious effect of 75-100 μM tetracaine was an approximately sixfold reduction in spark frequency. Although spark rise time was unchanged, tetracaine signifi cantly reduced the mean values of other spark morphological parameters: peak amplitude, decay time constant, FDHM, FWHM, and spark mass. These effects of tetracaine are well simulated by our spark model (updated in this study) under the assumption that tetracaine substantially reduces the amplitude of the Ca 2+ source fl ux without changing its duration. This suggests that normal sparks in intact frog fi bers are produced by more than one active SR Ca 2+ release channel. To our knowledge, this is the fi rst demonstration of a pharmacological agent other than Mg 2+ (Gonzalez et al., 2000) that is able to reduce but not eliminate the source fl ux of voltage-activated sparks in skeletal muscle fi bers.
In addition, in fi bers in 8 or 12.5 mM [K + ] Ringer's, 200 μM tetracaine essentially eliminated sparks and reduced the resting fl uorescence of fl uo-3 to values similar to that measured in normal Ringer's ([K + ] = 2.5 mM) without tetracaine. This result differs from that reported in frog cut fi bers, in which small depolarizations were found to elicit a nonspark form of SR Ca 2+ release, as assessed by an increase in fl uo-3 fl uorescence, that was not blocked by 200 μM tetracaine (Shirokova and Rios, 1997).
Preliminary versions of the results and of the updated model have been presented in abstract form (Hollingworth et al., 2005;Chandler et al., 2006).

Spark Experiments
The experimental methods were similar to those of Hollingworth et al. (2001). Microinjections of intact single fi bers of Rana pipiens were performed on an optical bench apparatus (Baylor and Oetliker, 1977) with a membrane-impermeant form of the fl uorescent Ca 2+ indicator fl uo-3 (K 5 fl uo-3; Molecular Probes Inc.). The spatially averaged fl uorescence signal from fl uo-3 was measured in this apparatus in response to an action potential (16°C). A fi ber was accepted for study if ∆F/F R , the change in the indicator's fl uorescence intensity divided by its resting fl uorescence intensity, was ≥15. For the seven fi bers that were used for the principal spark measurements of this study, the mean value of ∆F/F R was 27.7 ± 0.5 (mean ± SEM). The mean value measured at the end of the experiment was 16.1 ± 2.1.
To measure sparks, an injected fi ber was transferred to a recording chamber mounted on a home-built laser-scanning confocal microscope operating in line-scan mode (18°C). The sarcomere length of the fi ber was set to ‫0.3ف‬ μm (range, 2.8-3.1 μm, determined from confocal images). The values of FWHM of the microscope point-spread function (PSF), measured with 0.1 μm fl uorescent beads, are 0.21 μm in x and y and 0.51 μm in z. x-t fl uorescence intensity images (F(x,t)) were recorded from fi ber regions that contained ‫1.0ف‬ mM fl uo-3. The laser intensities used to excite fl uo-3 were about twice those used previously (Hollingworth et al., 2001). This increased the fl uorescence signal-noise ratio so that smaller sparks could be detected (see below). The values of F R , which were measured by a pair of photon-counting avalanche photodiodes, were typically 5-7 counts per μs in the present study compared with 2-4 counts per μs in the previous study. In those experiments, the standard deviation of ∆F/F R in the nonspark regions of the unsmoothed images was typically ‫,62.0ف‬ whereas in the present experiments, it was ‫.71.0ف‬ Three different solutions were used in most spark experiments. Recording began in normal Ringer's solution (NR), which contained (in mM) 120 NaCl, 2.5 KCl, 1.8 CaCl 2 , 5 PIPES (pH 7.1). This solution was then changed to an elevated [K + ] Ringer's (8-12.5 mM [K + ], made by the addition of K 2 SO 4 to NR); this depolarized the fi bers and stimulated sparks. The expected value of membrane potential in 8 mM [K + ] Ringer's (8K Ringer's) is about −70 mV and, in 12.5 mM [K + ] Ringer's (12.5K Ringer's), about −60 mV (Hodgkin and Horowicz, 1959). The solution was then changed to elevated [K + ] Ringer's containing tetracaine (made by addition of tetracaine hydrochloride; Sigma-Aldrich). In most experiments, [K + ] was 8 mM and the concentration of tetracaine was 75-100 μM. With this concentration of tetracaine, the frequency of sparks in 8K Ringer's was reduced but not eliminated, and a suffi cient number of sparks could be recorded in tetracaine to permit useful statistical comparisons between spark properties in the absence and presence of the drug. To bracket the effects of the solution changes, sparks were then measured in elevated [K + ] Ringer's without tetracaine and, fi nally, in NR. After each solution change, the fi ber was allowed to stabilize for 4 min before confocal recording was resumed. Typical times in the solutions were 10-15 min for each exposure to NR, 20-25 min for each exposure to elevated [K + ] Ringer's without tetracaine, and 30-60 min for exposure to elevated [K + ] Ringer's with tetracaine.

Optical Bench Experiments
Other experiments were performed in the optical bench apparatus to determine F R in different solutions (described in Figs. 7 and 8 in RESULTS). As in the spark experiments, an intact single fi ber was microinjected with fl uo-3, and the fi ber was accepted for study if ∆F/F R in response to an action potential was ≥15. Spatially averaged (nonconfocal) values of F R were measured from a 300 μm length of fi ber centered at the injection site using the methods described by Harkins et al. (1993). The measurements were performed with fi bers bathed in NR and in 8 and 12.5K Ringer's, both with and without tetracaine (16°C; sarcomere length = 3.24 ± 0.10 μm, n = 12). The optical bench experiments typically lasted 2-3 h, similar to the spark experiments on the confocal microscope. The mean ± SEM values of ∆F/F R in response to an action potential measured at the beginning and end of these experiments were 22.8 ± 1.4 and 20.1 ± 0.9, respectively (n = 12).

Analysis of Sparks
The raw F(x,t) images were converted to ∆F/F R images, in which F R here denotes the average intensity at any x of image pixels not containing sparks. Sparks were identifi ed in 3 × 3 smoothed ∆F/F R images by an automatic detection program. The increased laser intensities (see above) allowed the detection threshold of ∆F/F R to be set at 0.2, rather than 0.3 as used previously (Hollingworth et al., 2001), with the result that smaller sparks could be detected. Checks with the method described in Hollingworth et al. (2001) showed that, with a detection threshold of 0.2, false sparks were <1% of detected sparks in the present experiments. Similarly, false sparks were <1% in simulations performed to mimic these conditions (described below).
Prior to the selection of sparks with fi tted peak ≥ 0.5, the values of ∆F/F R in solutions other than NR were scaled (multiplied) by the ratio F T /F NR , in which F T and F NR denote values of F R in the test solution and NR, respectively. This scaling of amplitudes corrects for changes in F R caused by changes in resting [Ca 2+ ] ([Ca 2+ ] R ) associated with the solution changes. Thus, after scaling, spark amplitudes in the test solutions are referred to those expected in NR.
Two methods were used to estimate F T /F NR . In the fi rst method, F T /F NR was estimated in each spark experiment from the ratio of values of F R measured on the confocal microscope in closely adjacent fi ber regions shortly before and shortly after each solution change (Hollingworth et al., 2001). The second method used results from fi bers studied in the optical bench apparatus, with F T /F NR obtained from the average values of F R measured in different test solutions relative to that in NR. With the fi rst method, the mean values of F T /F NR and the number of fi bers (n) used for the measurements were 1.205 for 8K Ringer's without tetracaine (n = 8) and 1.064 for 8K Ringer's with 75-100 μM tetracaine (n = 7). With the second method, the values were 1.144 for 8K Ringer's without tetracaine (n = 12) and 1.023 for 8K Ringer's with 80 μM tetracaine (n = 3). Thus, both methods gave similar values of F T /F NR , which are not very different from 1.0. The second method was used for the F T /F NR corrections in RESULTS.
The effect of the F T /F NR correction factor was evaluated in two spark simulations with a Ca 2+ source fl ux of 1.7 pA for 4.2 ms (the same values used in column 6 of Table III). One had [Ca 2+ ] R = 50 nM to give F T /F NR = 1.0 and the other had [Ca 2+ ] R = 59.08 nM to give F T /F NR = 1.144, as was used in the experiments. For each simulation, 200,000 noisy sparks were generated and analyzed using the procedures described below except that the amplitude of the sparks with [Ca 2+ ] R = 59.08 nM was multiplied by 1.144. The corresponding mean values of the primary morphological factors (rise time, peak ∆F/F R , decay time constant, FDHM, and FWHM) differed by <1%; the derived morphological parameter spark mass (=1.206× peak ∆F/F R × FWHM 3 ; Hollingworth et al., 2001) differed by 6.5%. These differences are small compared with the effects of tetracaine on spark morphological properties described in RESULTS.

Spark Model 3
Ca 2+ sparks were modeled using the general procedures of Baylor et al. (2002). A spark is assumed to be driven by a brief fl ux of Ca 2+ that enters the myoplasm at a point source. Ca 2+ then spreads by diffusion while binding to both fl uo-3 and the intrinsic Ca 2+ buffers of myoplasm. The source fl ux is assumed to have a fi xed amplitude and duration. In most simulations, resting myoplasmic free [Ca 2+ ] ([Ca 2+ ] R ) was assumed to be 50 nM, consistent with estimates from intact fi bers of R. pipiens in NR (Hollingworth et al., 2001).
The set of reaction-diffusion equations and the values of the associated reaction rate constants and diffusion coeffi cients (collectively termed Model 3) differed in several ways from those used previously (Model 2; Baylor et al., 2002). As described below, spark simulations with both models were found to produce similar estimates of the amplitude and duration of the Ca 2+ source fl ux and of the mean values of the spark morphological parameters. Greater differences, however, were found in simulations of large SR Ca 2+ release events, such as that elicited by an action potential ( Fig. 2, described below). Model 3 is thought to represent myoplasmic conditions more accurately than Model 2 and was used for the spark simulations in this article. The differences between Models 2 and 3, and the reason for each modifi cation, are given below.

The Kinetics of the Ca 2+ -Troponin Reaction.
In spark Model 1 (Baylor et al., 2002), a simple one-step reaction was used to simulate the binding of Ca 2+ to each of the two regulatory sites on troponin; the same forward and reverse reaction rate constants were used for both sites (18°C; 1.017 × 10 8 M −1 s −1 and 132 s −1 , respectively; dissociation constant = 1.3 μM). With Model 1, the falling phase of simulated sparks failed to match that of measured sparks.
In Model 2, a two-step reaction was used for Ca 2+ binding to troponin ( Fig. 1 A; see also Baylor et al. 2002). The forward rate constant from Model 1 was used for each site but different values were used for the reverse rate constants. These were chosen rather arbitrarily as 20 × 132.1 = 2,642 s −1 and 132.1/20 = 6.6 s −1 , depending on whether troponin had one or two bound Ca 2+ ions, respectively. This multiplication and division by the same factor leaves the geometric mean of the two dissociation constants unchanged, 1.3 μM; hence the value of free [Ca 2+ ] at which half the regulatory sites are bound with Ca 2+ is unchanged, 1.3 μM. The properties of sparks simulated with Model 2 agreed well with the measured properties.
In Model 3, the same two-step reaction is used except that the values of k −1 and k −2 from Model 2 were divided and multiplied, respectively, by 1.49. This makes the rate constant of Ca 2+ dissociation from troponin agree with that measured experimentally, as described in the next paragraph. Values of troponin's rate constants in Model 3 are given in part A of Table I; the forward rate constant of the fi rst reaction and the reverse rate constant of the second reaction are twice those of each site because two Ca 2+ -free sites are available for the fi rst forward reaction and two Ca 2+bound sites are available for the second reverse reaction. Because the values of k +1 and k +2 are the same as those in Model 2, the values of the Ca 2+ dissociation constants (column 4 in part A of Table I) are 1.49-fold smaller and larger, respectively, than those in Model 2; the geometric mean of the dissociation constants is unchanged, 1.3 μM.

294
Effects of Tetracaine on Ca 2+ Sparks The selection of the new value of k −2 in Model 3 is based on the experimental fi ndings of Davis et al. (2004). These authors measured the apparent rate at which Ca 2+ dissociates from troponin on reconstituted thin fi laments of rabbit muscle; this rate is expected to essentially equal k −2 since k −1 >> k −2 . The measured value was 16 s −1 at 15°C; this corresponds to 19.7 s −1 at 18°C if a Q 10 of 2 is assumed. The value of k -2 was changed from 13.21 s −1 in Model 2 to 19.7 s −1 in Model 3 (=1.49 × 13.21 s −1 ) so that the apparent rate of Ca 2+ dissociation from troponin would match the value of Davis et al.; the value of k −1 was adjusted to keep the value of the geometric mean of the dissociation constants unchanged. Fig. 1 B shows the multistep reaction used in Model 3 to simulate the binding and transport of Ca 2+ by the SR Ca 2+ pump. The binding steps are taken from the ion binding scheme of Peinelt and Apell (2002); the Ca 2+ transport step (indicated by the arrow from ECa 2 to E, with rate constant k +9 ) was not included in Peinelt and Apell (2002) but is used here to describe the translocation of Ca 2+ into the SR lumen. Possible translocation of Mg 2+ and/or H + is not considered here. The binding steps involve competition among H + , Mg 2+ , and Ca 2+ for the transport sites. Because Peinelt and Apell (2002) gave only dissociation constants for the binding reactions (column 4 in Table I B), kinetic calculations require that either a forward or reverse rate constant be chosen for each reaction step. Forward rate constants were selected; the values for Ca 2+ and Mg 2+ are similar to those often used for reactions between these cations and proteins (10 8 M −1 s −1 for Ca 2+ ; 10 5 M −1 s −1 for Mg 2+ ; column 2 of Table I B). Each reverse rate constant (column 3) was then calculated from the product of the forward rate constant and the dissociation constant. Because the reactions of protein sites with H + are expected to be much more rapid than those with Ca 2+ and Mg 2+ , we assume that the reactions between H + and their binding sites are in equilibrium. The value of k +9 (4 s −1 ) was chosen to satisfy two criteria (Young et al., 2003): (1) R max , the steady-state turnover rate of the pump at saturating [Ca 2+ ], should be several per second at 18°C, and (2) Ca 1/2 , the value of free [Ca 2+ ] at which steady-state turnover equals half R max , should be in the low micromolar range. With k +9 = 4 s −1 (column 2 in Table I B), both conditions are satisfi ed: R max = 3.96 s −1 and Ca 1/2 = 3.41 μM. With a total enzyme concentration of 0.12 mM (Baylor et al., 1983(Baylor et al., , 2002, the maximal rate of Ca 2+ translocation is 0.95 mM Ca 2+ ions s −1 (= 3.96 s −1 × 0.12 mM × 2).

Ca 2+ Binding and Transport by the SR Ca 2+ Pump.
The reaction scheme for the Ca 2+ pump in Fig. 1 B has a major advantage over that used in spark Model 2 (Baylor et al., 2002); it requires only ?0.7 times as much Ca 2+ to be released from the SR to simulate the Ca 2+ transient elicited by an action potential. This advantage arises because the new scheme uses competitive binding of nontransportable ions, which decreases the number of pump sites immediately available to bind Ca 2+ . Otherwise, with similar concentrations of transport and troponin regulatory sites, as occurs in frog muscle, and similar forward rate constants for Ca 2+ binding, both types of sites would be expected to bind Ca 2+ at similar rates. is very similar in the two models, 232 and 230 μM, respectively.
In extreme cases, such as superfast twitch fi bers of the toadfi sh swimbladder, the concentration of Ca 2+ pump molecules appears to be several times that of the troponin regulatory sites (Appelt et al., 1991). In these fi bers, the Ca 2+ required to bind to the pump sites in the absence of competitive binding of nontransportable ions is calculated to be several times that required to bind to the troponin regulatory sites, and the advantage of competitive binding is expected to be even larger .

The Free Diffusion Coeffi cient of Fluo-3 in Myoplasm.
In Model 3, the value assumed for the free diffusion coeffi cient of fl uo-3 in myoplasm is slightly smaller than that in Model 2: 1.42 and 1.510 −6 cm 2 s −1 , respectively. This change was made to provide a more accurate temperature correction for fl uo-3′s diffusion coeffi cient at 18°C.

The Myoplasmic Concentration of Protein Sites that Are
Available To Bind Fluo-3. Most Ca 2+ indicators, including fl uo-3 (Harkins et al., 1993), bind strongly to relatively immobile TA B L E I Fig. 1  myoplasmic constituents such as soluble and structural proteins (Zhao et al., 1996). This property of fl uo-3 is incorporated into Model 2 with a reaction scheme in which both Ca 2+ -free and Ca 2+bound indicator can bind to immobile myoplasmic sites, denoted by Pr. In Model 2, the concentration of immobile sites, 3 mM, gave f = 0.88, where f is the fraction of fl uo-3 bound to Pr in a resting fiber. This value of f is consistent with the value of fl uo-3′s apparent diffusion coeffi cient, D app , measured previously in resting fi bers, 0.20 ± 0.02 × 10 −6 cm 2 s −1 (Harkins et al., 1993) and the assumption that D app and D, the free myoplasmic diffusion coeffi cient, are related by the equation: D app = D(1 − f) (Maylie et al., 1987). In Model 3, the value of [Pr] has been reduced from 3 to 1 mM. This reduces the fraction of fl uo-3 molecules bound to Pr and increases D app , consistent with our recent measurements. In these experiments, performed in the optical bench apparatus, the measured value of D app was 0.47 ± 0.04 × 10 −6 cm 2 s −1 (n = 4), which is 2-2.5 times larger than the previously reported value, 0.20 ± 0.02 × 10 −6 cm 2 s −1 . This larger value seems appropriate for modeling our Ca 2+ sparks because fi ber conditions were similar in the recent measurements of D app and in the spark experiments. Peak ∆F/F R of fl uo-3 in response to an action potential was 26.9 ± 1.4 at the start of the D app measurements and 22.2 ± 1.4 at the end (measured, on average, 126 min later). These values are similar to those measured in the spark experiments of this study, 27.7 ± 0.5 at the start and 16.1 ± 2.1 at the end (see above) as well as those in the spark experiments of Hollingworth et al. (2001). In contrast, peak ∆F/F R in the experiments of Harkins et al. (1993) was considerably smaller, 6.8 ± 0.5. This smaller value  Table I; the total myoplasmic concentration of both troponin and pump molecules is 120 μM. The reaction schemes and rate constants for the other myoplasmic constituents in the model (ATP, parvalbumin, fl uo-3, and protein) are the same as in Baylor et al. (2002).

Figure 2. Simulated changes in
Ca 2+ binding to the major myoplasmic Ca 2+ buffers elicited by an action potential. The reactions in Models 2 and 3 were used for A and B, respectively. In both panels, the bottom trace shows spatially averaged free ∆[Ca 2+ ] (from Fig. 4 of Baylor and Hollingworth, 1998) is thought to refl ect a larger value of [Ca 2+ ] R and consequently a larger value of F R (for a given concentration of indicator) in the fi bers of Harkins et al. (1993).
The likely explanation of the smaller D app in the earlier experiments is that the fl uo-3 injections in those experiments produced some minor damage; as a result, membrane depolarization near the injection site could slow the diffusion of fl uo-3, whose charge is −5, away from the injection site. The larger [Ca 2+ ] R estimated in those fi bers probably also refl ects minor damage. Interestingly, in one fi ber in our recent experiments, results similar to those found by Harkins et al. (1993) were obtained: ∆F/F R was 6.7 at the start of the experiment and 9.5 at the end (measured 125 min later), and the measured value of D app was 0.21 × 10 −6 cm 2 s −1 . Since this value of ∆F/F R is below our current criterion for acceptability, no other results are reported for this fi ber.
With [Pr] reduced to 1 mM in Model 3, the new value of f at [Ca 2+ ] R = 50 nM is 0.7, which is consistent with D app = 0.47 × 10 −6 cm 2 s −1 .

Simulation of Noisy Sparks and Estimation of their Morphological Parameters
The procedure for estimating the Ca 2+ fl ux that produces a spark was the same as that described by Baylor et al. (2002). The fi rst step was to make initial guesses of the fl ux amplitude and duration. Concentrations of free [Ca 2+ ] and its buffers were then calculated at different times after the onset of the Ca 2+ fl ux and at different distances from the point source of release. The fl uorescence of fl uo-3 was spatially fi ltered with a PSF that approximated that of the experimental apparatus to give ∆F/F R . A random number generator was used to simulate the main sources of noise and variability that contribute to the ∆F/F R measurements. These include instrumentation and photon noise (predominantly photon noise), random displacement of the scan line relative to the spark source, and random spark onset relative to the time of data sampling. The simulation of photon noise was changed slightly from that described by Baylor et al. (2002). In those simulations, random noise of mean zero and constant standard deviation (SD) was added to each pixel of the simulated ∆F/F R image. Because photon noise is expected to be proportional to √F, in this article the noise in each pixel was multiplied by √(1+∆F/F R ). The value of SD was set equal to the average standard deviation of the noise in the nonspark region of measured images. The smaller value of SD in the present measurements, 0.17 (vs. 0.26 in Hollingworth et al. 2001), refl ects the larger signal-noise ratio of ∆F/F R .
A large number of simulated noisy sparks (either 200,000 or suffi cient to give the same number as the experiment) were generated with their Ca 2+ source at the center of the y-z plane and with the scan line intersecting the plane randomly within a square 2.05 μm × 2.05 μm centered at the origin. These were analyzed exactly like measured sparks, including use of the same ∆F/F R threshold for spark detection and the same criteria for spark acceptance. The entire procedure was then repeated with new estimates of source fl ux amplitude and duration until the simulated mean values of spark rise time and peak ∆F/F R matched those of the measurements.

Spark Simulations with Model 3 Are Similar to Those with Model 2
The preceding three sections describe the changes in the methods of analysis and simulations used in this article. Table II shows properties of measured sparks and sparks simulated with the previous Model 2 and the new Model 3. Column 2 shows the mean ± SEM values of the principal morphological parameters of sparks in 12.5K Ringer's described by Hollingworth et al. (2001; also given in column 2 of Table V of Baylor et al., 2002). These were obtained from fi ts to 3,176 individual sparks that satisfi ed peak ∆F/F R ≥ 0.7. Column 3, which was taken from column 3 of Table V of Baylor et al. (2002), shows simulation results with Model 2 for the same number of sparks. These simulations used an SD for added noise of 0.26, a ∆F/F R detection threshold of 0.3, and a fi tted peak ∆F/F R criterion of ≥0.7. Column 4 shows analogous results with Model 3 with the same values of SD, detection threshold, and fi tted peak ∆F/F R criterion. The values of fl ux amplitude and duration estimated in the two simulations (Table II, top of columns 3 and 4) agree within 10%. Model 2 does a better job of simulating the measured FWHM, whereas Model 3 does a better job of simulating spark mass and a slightly better job of simulating FDHM. In both simulations, the parameter that is least well simulated is the decay time constant; Model 2 overestimates the value by 25% whereas Model 3 underestimates the value by 23%. On balance, both simulations appear to produce reasonable overall agreement with the measurements.

Statistics
The statistical significance of a difference between means was evaluated with Student's two-tailed t test; results were considered signifi cant if P < 0.01. t tests were performed with MLAB (Civilized Software, Inc.)

R E S U LT S
Effects of 75-100 μM Tetracaine on Ca 2+ Sparks   (Hollingworth et al., 2001). Columns 2-4 show mean ± SEM values of morphological parameters obtained from fi ts to 3,176 individual sparks that used ∆F/F R values of 0.3 for detection threshold and ≥0.7 for fi tted peak ∆F/F R (column 2, measured sparks; columns 3 and 4, sparks simulated with Models 2 and 3, respectively, with 0.26 for the standard deviation of the added noise). The differences between the simulations in columns 3 and 4 are described in the text. Row 1 gives the distance between the scan line and the spark source in the y-z plane, which is known in the simulations (distance = √(y 2 + z 2 )) but not in the measurements. The numbers at the top of columns 3 and 4 are the amplitude and duration of the Ca 2+ source fl ux used in the simulations. and 0.027 in 8K Ringer's with 80 μM tetracaine. Thus, in this experiment, 8K Ringer's increased spark frequency by a factor of ‫7ف‬ (relative to NR), and 80 μM tetracaine decreased spark frequency in 8K Ringer's by a factor of ‫.8ف‬ These frequencies are similar to those observed in the seven experiments of this type. The mean ± SEM values were (in sarcomere −1 s −1 ): 0.027 ± 0.009 in NR, 0.184 ± 0.041 in 8K Ringer's without tetracaine, and 0.032 ± 0.008 in 8K Ringer's with 75-100 μM tetracaine. The frequency of sparks remained fairly constant during exposure to tetracaine. In the seven experiments described above, the frequencies during the fi rst and last 10 min in tetracaine were 0.039 ± 0.012 and 0.024 ± 0.007 sarcomere −1 s −1 , respectively; these values are not signifi cantly different. This result in frog skeletal muscle contrasts with that in rat ventricular myocytes where spark frequency in tetracaine recovered after an initial inhibition (see DISCUSSION). Fig. 4 shows sample x-t images recorded while the fi ber was in 8K Ringer's (lefthand panels, without tetracaine; righthand panels, with tetracaine). The upper images are displayed in raw fl uorescence intensity units, whereas the lower images are in ∆F/F R units. Several sparks can be seen in each image. As expected, these sparks are centered on z-lines (see legend).
The top panels in Fig. 5 show zoomed ∆F/F R images of the two sparks marked by arrowheads in Fig. 4. The asterisks in the middle and bottom panels show the spark profi les in time and space, respectively; the curves show fi ts of the standard empirical functions. From the fi ts, estimates were obtained for the values of rise time, peak ∆F/F R , decay time constant, FDHM, FWHM, late baseline offset, and spark mass (see legend and values printed on fi gures).  Fluorescence images from a fi ber in 8K Ringer's exposed to 0 and 80 μM tetracaine (left and right panels, respectively). Top, raw x-t images. The sarcomere length of the fi ber, 3.1 μm, was calculated from the spatial periodicity in F, in which the thinner and thicker fl uorescent bands are centered on m-lines and z-lines, respectively (Hollingworth et al., 2001). Several Ca 2+ sparks are visible in each image; they occur at z-lines. Bottom, same data after conversion to ∆F/F R . See Fig. 5 for ∆F/F R calibrations. Same fi ber as in Fig. 3 Columns 2-5 of Table III give the number of sparks and the mean values (± SEM) of their frequency and morphological parameters determined in the seven tetracaine experiments described above. The second row gives frequency in absolute units; the third row gives frequency relative to that in 8K Ringer's without tetracaine. Columns 2 and 3 give values in 8K Ringer's before and after tetracaine, respectively; column 4 gives values from all images used for columns 2 and 3. Column 5 gives similar information for 8K Ringer's with 75-100 μM tetracaine. The reduction in frequency to 0.176 ± 0.022 times that in 8K Ringer's without tetracaine is significantly different from 1.0 (P < 0.01).
Columns 2 and 3 of Table III show that the values of the spark morphological parameters (last six rows) are similar for the fi rst and second exposures to 8K Ringer's. The only parameter that is signifi cantly different is spark rise time, 3.53 ± 0.06 and 3.82 ± 0.07 ms, respectively (P < 0.01); the percentage difference is small, however, 8%. Columns 4 and 5 show that all morphological parameters, with the exception of rise time, are reduced signifi cantly in tetracaine (P < 0.01). The mean percentage reductions are 11% for peak ∆F/F R , 19% for decay time constant, 11% for FDHM, 9% for FWHM, and 29% for spark mass. Thus, 75-100 μM tetracaine clearly alters the morphological parameters of sparks in 8K Ringer's. Since spark rise time closely tracks the duration of the underlying Ca 2+ source fl ux (e.g., Table VI of Baylor et al., 2002), especially at the Ca 2+ source, the constancy of rise time suggests that the duration of Ca 2+ release that produces a spark is similar with and without tetracaine. Consequently, the smaller values of peak ∆F/F R and other morphological parameters in tetracaine suggest that the mean amplitude of the underlying Ca 2+ source fl ux is reduced by tetracaine.
If a spark in 8K Ringer's without tetracaine is due to one active RyR Ca 2+ channel and tetracaine acts simply to stabilize a closed state of the channel (Xu et al., 1993;Gyorke et al., 1997;Csernoch et al., 1999), tetracaine would be expected to reduce the frequency of sparks without changing peak ∆F/F R or other morphological parameters. Since this is not the case, a normal voltageactivated spark in 8K Ringer's appears to require more than one active release channel. This is one of the main results of this study.

Comparison of Simulated and Measured Ca 2+ Sparks
Model 3 was used to simulate sparks in 8K Ringer's with and without 75-100 μM tetracaine. The approach  Fig. 4. In the middle panels, the asterisks show ∆F/F R profi les in time extracted at the spatial center of each spark (average of the three time lines at −0.2, 0, and +0.2 μm from the spark center); the curve is the fi t of Eq. 1 in Hollingworth et al. (2001). In the bottom panels, the asterisks show profi les in space extracted at the time of peak of each spark (average of two line scans, the ones just before and just after the fi tted time of peak); the curve is a fi t of a gaussian function (Eq. 2 of Hollingworth et al., 2001). The values of the morphological parameters not printed on the fi gure are 5.22 and 5.27 ms for FDHM (left and right, respectively) and 1.07 and 0.20 μm 3 for spark mass.
(MATERIALS AND METHODS) was to assume values of the amplitude and duration of the Ca 2+ source fl ux, simulate 200,000 randomly varied noisy sparks, and then calculate the simulated mean values of peak ∆F/F R and rise time; the large number of simulated sparks decreased the SEMs of the mean so that more accurate comparisons could be made between simulated and experimental means. The process was repeated with new values of fl ux amplitude and duration until the mean values of peak ∆F/F R and rise time matched those of the experiments. The resulting Ca 2+ source fl uxes were 1.7 pA and 4.2 ms, respectively, without tetracaine and 1.2 pA and 4.2 ms with tetracaine (columns 6 and 7 of Table III). Overall, the mean values of the morphological parameters of both sets of simulated sparks are in reasonable agreement with the corresponding experimental values (columns 4 and 5). The fl ux amplitude without tetracaine, 1.7 pA, is smaller than that estimated with Model 3 for sparks measured previously in frog intact fi bers, 2.4 pA (column 4 of Table II). Possible reasons for this difference are considered later in RESULTS.
The simulations in Table III indicate that the fl ux amplitude underlying a spark in tetracaine is ‫7.0ف‬ times that in its absence and suggest that the Ca 2+ fl ux through a single RyR Ca 2+ channel in an intact frog fi ber is ≤1.2 pA. The reductions in spark frequency and in the associated SR Ca 2+ effl ux by tetracaine might lead to increases in SR Ca 2+ content and, as a result, in single-channel Ca 2+ fl ux. In this case, the value of the Ca 2+ fl ux in tetracaine should be decreased before com-parison with control fl uxes, and the upper limit of 1.2 pA should be reduced accordingly. Thus, if SR Ca 2+ content is increased by tetracaine, some of the effects of tetracaine would appear to be more marked than those reported in this article.
Although the values of spark rise time are similar with and without tetracaine (3.67 ± 0.04 and 3.70 ± 0.09 ms, respectively, in columns 4 and 5 of Table III), it seemed important to consider the possibility that tetracaine slightly reduces the duration of SR Ca 2+ release during a spark, as might be the case in cardiac RyRs (Gyorke et al., 1997). To test this idea, spark simulations were used to determine the maximal and minimal durations of Ca 2+ source fl ux that are consistent with the rise times without and with tetracaine, respectively. The difference in these durations is <0.4 ms and suggests that any reduction in fl ux duration with tetracaine is expected to be <10%. The simulations also show that 1.2 pA remains a reasonable estimate of fl ux amplitude in tetracaine. (In these simulations, 3.79 ms was considered to be an upper limit of spark rise time without tetracaine, since a value >3.79 ms is not consistent [P < 0.01] with the observed value, 3.67 ± 0.04 ms [column 4 of Table III]. The Ca 2+ fl ux duration that gives a rise time of 3.79 ms and a peak ∆F/F R of 0.76 [also column 4 of Table III] is just less than 4.4 ms. With tetracaine, 3.47 ms was considered to be a lower limit of rise time, since a value <3.47 ms is not consistent [P < 0.01] with the observed value, 3.70 ± 0.09 ms [column 5 of Table III]. The Ca 2+ fl ux duration that gives a rise time of 3.47 ms and a peak ∆F/F R  of 0.68 [also column 5 of Table III] is just greater than 4.0 ms. The difference between these durations gives the inequality <0.4 ms reported above.) The overall conclusions from these simulations are that (a) tetracaine reduces the amplitude of the Ca 2+ fl ux underlying sparks to ‫7.0ف‬ times that in the absence of tetracaine (1.2 pA vs. 1.7 pA), and (b) the Ca 2+ fl ux through a single RyR Ca 2+ channel in an intact frog fi ber is likely to be ≤1.2 pA.

Effects of Tetracaine on the Frequency and Morphology of Measured and Simulated Ca
Although the effects of tetracaine on spark morphological properties are adequately described by the simulations in Table III, the effect on spark frequency is not. The ratio of spark frequency with and without tetracaine (row 3 of Table III) is signifi cantly different (larger) in the simulations, 0.618 (column 7), than in the measurements, 0.176 ± 0.022 (column 5) (P < 0.01). This indicates that the overall effect of tetracaine on sparks is not adequately simulated by a simple reduction in Ca 2+ fl ux through active SR Ca 2+ release channels. Nor would such a simple result be expected from bilayer experiments, where tetracaine's major action on the RyR Ca 2+ channel appears to be a stabilization of a closed state, not a reduction in current through the open channel (Xu et al., 1993;Gyorke et al., 1997;Csernoch et al., 1999).
Tetracaine's combined effects on spark frequency and morphology are further analyzed in Fig. 6. The symbols show the effect of 75-100 μM tetracaine on mean spark morphological parameters in the seven experiments of Table III; the panels show rise time (A), peak ∆F/F R (B), decay time constant (C), FDHM (D), FWHM (E), and spark mass (F). The values in tetracaine have been divided by those in the absence of tetracaine and plotted vs. frequency in tetracaine divided by that in the absence of tetracaine. These normalizations allow the data to be plotted without knowledge of the stoichiometry of tetracaine binding to the Ca 2+ release channels. The squares show normalized mean values from the seven individual experiments, and the asterisks show the mean of the seven normalized means. In these experiments, the frequency of sparks in 75-100 μM tetracaine was reduced to 0.11-0.33 times normal; the mean reduction is 0.176 (column 5 of Table III).
As mentioned above, if a spark in 8K Ringer's without tetracaine is due to one active RyR Ca 2+ channel and if tetracaine acts simply to stabilize a closed state of the channel, tetracaine would be expected to reduce spark frequency without a change in morphological parameters. This possibility is indicated by the horizontal line at 1.0 on the ordinate in the panels in Fig. 6. Although the normalized mean value of rise time (A) is not signifi cantly different from 1.0 (P = 0.33; n = 7), the normalized values of the other parameters (B-F) are noticeably different (smaller), and these decreases are all signifi cant (P < 0.01; n = 7). This analysis confi rms the conclusion from Table III that more than one release channel is likely to be in-volved in the generation of a normal voltage-activated spark in 8K Ringer's.
The four curved lines in each panel of Fig. 6 are drawn from theories that assume that either two or four RyR Ca 2+ channels are involved in normal spark generation. In each case, it is assumed that all RyR Ca 2+ channels, voltage-gated and otherwise, have the same amplitude and duration Ca 2+ fl ux and the same ability to bind tetracaine (and to bind it independently of the other channels). Derivation of the curves (described below) depends on binomial probabilities and the properties of sparks simulated with four different Ca 2+ source fl uxes (Table IV).
The last six rows of columns 2-5 of Table IV show that all simulated mean morphological parameter values are reduced progressively as the amplitude of the Ca 2+ source flux is reduced in steps of 0.425 pA. The reduction in mean values from 1.7 to 0.425 pA (column 5 vs. 2) is small for rise time, 7%, but larger for the other morphological parameters: 25% for peak ∆F/F R , 45% for decay time constant, 28% for FDHM, 29% for FWHM, and 63% for spark mass. Row 4 shows that the reduction in mean distance from the scan line to the spark source is also large, 54%. Row 3 gives the peak value of ∆F/F R of a noise-free spark with the scan line at the Ca 2+ source ± 0.2 μm. The value of ∆F/F R for 0.425 pA, 0.379 (column 5), does not satisfy peak ∆F/F R ≥ 0.5; thus, the 514 simulated sparks that were detected with 0.425 pA must have had their fitted peak ∆F/F R increased by random noise.
In Fig. 6, the simplest theory assumes that each release unit consists of two Ca 2+ channels that function independently. The uppermost continuous curve in each panel was generated from this theory, calculated as follows. Since a normal Ca 2+ spark in the present experiments is well simulated by a Ca 2+ fl ux of 1.7 pA for 4.2 ms, a single channel is assumed to have a Ca 2+ fl ux of 1.7/2 = 0.85 pA for 4.2 ms. If f denotes the fraction of release channels blocked by tetracaine (i.e., stabilized in the closed state), then (1 − f ) 2 , 2f(1 − f ), and f 2 are, respectively, the fraction of release units that have zero, one, and two channels blocked by tetracaine and, consequently, that can fl ux 1.7, 0.85, and 0 pA of Ca 2+ . As indicated in row 2 of Table IV, the relative frequency of accepted sparks with a fl ux of 1.7 and 0.85 pA, is 1.0 and 0.2667, respectively. Since release units with two blocked channels do not produce sparks, 1.0 × (1 − f ) 2 + 0.2667 × 2f(1 − f ) gives the frequency of sparks relative to that in the absence of tetracaine; this gives the abscissa value in each panel of Fig. 6 for a particular value of f. Similarly, the corresponding value on the ordinate in each panel in Fig. 6 is the weighted average of the mean parameter values in columns 2 and 4 of Table  IV, calculated with the relative weighting factors 1.0 × (1 − f ) 2 and 0.2667 × 2f (1 − f ). The theoretical curves were determined from such calculations with many values of f between 0 and 1.
The uppermost dashed curves in Fig. 6 were obtained with another two-channel model. One release channel, the controller channel, is required to be open (and therefore not be blocked by tetracaine) for the other channel, the follower, to fl ux Ca 2+ . In this case, (1 − f ) 2 , f(1 − f ), and f represent, respectively, the fraction of release units that can fl ux 1.7, 0.85, and 0 pA of Ca 2+ . Each curve was then calculated by the method described in the preceding paragraph.
The same approach was used to model release from four Ca 2+ channels, with fl uxes of 1.7, 1.275, 0.85, 0.425, and 0 pA and corresponding probability values. The lower continuous and dashed curves in each panel are analogous to the upper curves obtained for the twochannel models.
In Fig. 6, the curves from the four multichannel models reproduce the observed effects of tetracaine on spark frequency and morphological parameters. Because the curves are spaced closely together compared with the scatter in the data, none of these theories can be ruled out. The ability of these theories to adequately simulate tetracaine's effects on both spark frequency and morphological parameters contrasts with the results in column 7 of Table III, which adequately simulated the effects on morphological parameters but not on frequency.
Effect of the Peak ∆F/F R Criterion on the Simulated Ca 2+ Source Flux in the Absence of Tetracaine If the Ca 2+ source fl ux underlying normal sparks is stereotypical, for example, with an amplitude of 1.7 pA and a duration of 4.2 ms, the estimated fl ux should be independent of the value of the peak ∆F/F R criterion. To test this idea, the confocal images used for column 4 of Table III were analyzed with three different values of the peak ∆F/F R criterion: ≥0.5 (as in column 4 of Table III), ≥0.7, and ≥1.0. Columns 2, 4, and 6 of Figure 6. Effect of tetracaine on normalized spark properties. In each panel, the symbols show mean values of a particular morphological parameter with tetracaine relative to that without tetracaine plotted vs. the spark frequency with tetracaine relative to that without tetracaine (peak ∆F/F R criterion of ≥0.5). The open squares show the individual means from seven experiments; the asterisks show the mean value of these means. The horizontal lines show the predictions of the hypothesis that a normal spark is caused by a single active release channel. The curves show predictions from four hypotheses about the number of release channels per spark (two or four) and the way that these release channels are controlled, independent (continuous curves) or coupled (dashed curves), as described in RESULTS. For the average relative spark frequency of the measurements with tetracaine, 0.176 (column 5 of Table III), the different models predict the following values of f (=the probability that an individual channel is blocked by tetracaine) and of the mean number of pA per spark: 0.733 and 1.20 (two-channel independent), 0.659 and 1.41 (two-channel coupled), 0.648 and 1.09 (four-channel independent), 0.565 and 1.24 (four-channel coupled). Table V show the results. As expected, mean peak ∆F/ F R (row 5 of Table V) increases progressively with the peak ∆F/F R criterion; referred to the value in column 2, the values in columns 4 and 6 increase by 28% and 74%, respectively. Little change (<5%), however, is observed in the values of rise time, decay time constant, FDHM, and FWHM. As expected from the increases in peak ∆F/F R , spark mass also increases (by 12% in column 4 and 36% in column 6).
Columns 3, 5, and 7 of Table V show results of simulations with Model 3 using the peak ∆F/F R criteria from columns 2, 4, and 6, respectively. The fl ux duration for all three simulations was the same, 4.2 ms. For each value of the peak ∆F/F R criterion, the fl ux amplitude was adjusted, as usual, to make the mean peak ∆F/F R of the simulated sparks match that of the corresponding measurements. Interestingly, the estimated source fl ux amplitude increases progressively with the peak ∆F/F R criterion: 1.7, 1.9, and 2.5 pA, respectively. With each peak ∆F/F R criterion, reasonable overall agreement is observed between the mean parameter values of simulated and measured sparks. On the other hand, row 2 shows that the values of relative frequency do not match those of the measurements, similar to the situation observed with tetracaine in row 3 of Table III.
The fi nding that a larger Ca 2+ source fl ux is required for a larger peak ∆F/F R criterion suggests that multiple Ca 2+ fl ux amplitudes, rather than a single amplitude, underlie sparks in 8K Ringer's. This possibility is consistent with our earlier spark data, obtained in 12.5K Ringer's, in which measured sparks were found to have greater dispersion in their morphological properties than sparks simulated with a Ca 2+ source fl ux of fi xed amplitude and duration (Fig. 8 in Baylor et al., 2002).

Spark Simulations with Variable Amplitudes of Ca 2+ Source Flux
The observation that the estimated Ca 2+ source fl ux depends on the peak ∆F/F R criterion can be explained by a release unit with several RyRs; these might operate either independently or in a controller/follower confi guration, as in Fig. 6, but with their activation linked probabilistically through a "coupling coeffi cient." In the independent model, the coupling coeffi cient is the probability that any RyR in the release unit is activated; in the controller/follower model, it is the probability that a follower RyR is activated if the controller is activated.
Preliminary simulations show that this kind of model with 2, 3, 4, or 8 RyRs per release unit can explain the effect of peak ∆F/F criterion on both the estimate of the Ca 2+ source fl ux and the relative frequency of sparks. The SEMs of the mean values of peak ∆F/F R , however, are too large to determine the exact number of RyRs or the Ca 2+ fl ux through a single RyR. Related simulations show that the effect of tetracaine on spark properties can be explained by tetracaine fully blocking one or more channels in a release unit (i.e., as considered in the models in Fig. 6) without a change in coupling coeffi cient. Thus, the conclusions of the analysis in Fig. 6 are not limited to the special case that sparks in the absence of tetracaine are caused by a stereotypical Ca 2+ source fl ux of fi xed amplitude and duration. The values of fl ux amplitude and duration in column 4 of Table II, 2.4 pA and 5.0 ms (standard deviation of added noise, 0.26; detection threshold, 0.3; peak ∆F/F R criterion, ≥0.7; estimated membrane potential, −60 mV) are larger than those in column 5 of Sparks were simulated with Model 3 using a single source fl ux duration, 4.2 ms, as used for the simulations in Table III, and four different source fl ux amplitudes (indicated at the top of the columns); the fl ux amplitudes are in the ratio 1:0.75:0.5:0.25. In each simulation, 200,000 noisy sparks were generated as described in Table III. The second row gives the number of sparks relative to that in column 2. The third row gives the mean amplitude of each noise-free spark at the source ± 0.2 μm. The last six rows give mean ± SEM values of morphological parameters obtained from the usual fi ts. The mean parameter values were used to calculate the theoretical curves in Fig. 6, as described in the text.
4.2 ms (0.17, 0.2, ≥0.7, −70 mV). These differences could be due to the difference in the standard deviation of added noise, the detection threshold, or the difference in membrane potential. To determine the infl uence of detection threshold and of standard deviation of added noise, the present experiments were reanalyzed using a detection threshold of 0.3 and added noise levels in the simulations of 0.17 and 0.26. The fl ux amplitudes (2.1 and 2.0 pA, respectively) and durations (4.2 and 4.1 ms) are also smaller than those in column 4 of Table II, 2.4 pA and 5.0 ms. This indicates that the amplitude and duration of the Ca 2+ fl ux that generates voltage-activated sparks in intact fi bers may be larger at −60 mV than at −70 mV. This result about fl ux duration is consistent with the results of Hollingworth et al. (2001), who found that the mean rise time of sparks in 12.5K Ringer's was signifi cantly different from (larger than) that in NR: by 13% for R. pipiens and 17% for R. temporaria. A stronger effect of membrane potential on rise time was found in the experiments of Lacampagne et al. (2000) on frog cut fi bers, in which a step repolarization from +40 to −90 mV reduced the mean rise time of sparks initiated near the time of repolarization by up to 50%. It is possible that, in intact fi bers, an increase in external [K + ] produces a change in SR Ca 2+ content and that this leads to the increase in spark rise time observed. This possibility, however, would not explain the effect on rise time observed by Lacampagne et al. (2000), because they used the voltage-clamp technique.
The Effect of [K + ] and Tetracaine on F R Changes in fl uo-3′s resting fl uorescence, F R , caused by changes in [Ca 2+ ] R were determined in fi bers injected with fl uo-3 and studied in the optical bench apparatus. Fig. 7 A shows results from an experiment in which F R was measured 30-125 min after injection, when the fi ber was bathed in NR (open circles), 8K Ringer's (open squares), 8K Ringer's with 80 μM tetracaine (fi lled squares), and NR with 80 μM tetracaine (fi lled circles). The value of F R in NR (F NR ) declined during the experiment as fl uo-3 diffused along the fi ber axis away from the injection site. The curve shows an empirical function of time, given in the legend, that was fi tted to the values of F NR . This curve was used to estimate F NR throughout the experiment so that F R /F NR could be determined (Fig. 7 B). F T /F NR was taken to be the average value of F R /F NR during the second half of the period after a solution change, when F R / F NR appeared to reach a quasi-steady state. This was 1.176 for 8K Ringer's, 1.028 for 8K Ringer's with 80 μM tetracaine, and 0.944 for NR with 80 μM tetracaine. Fig. 8 A shows mean ± standard deviation (SD) values of F T /F NR from 12 experiments plotted vs. [K + ] at three different tetracaine concentrations (circles, 0 μM; X's, 80 μM; squares, 200 μM). In each experiment, measurements began with the fi ber in NR and were bracketed by one or more returns to NR (as in Fig. 7). The average values of F T /F NR are given in the legend; some of these were used as correction factors to refer spark amplitude in test solutions to that expected in NR (MA-TERIALS AND METHODS). In NR without tetracaine, the fi lled circle ([K + ] = 2.5 mM) lies, by defi nition, on the dashed horizontal line at 1.0. Tetracaine slightly reduced the value of F T /F NR in NR (see legend). The average value of F T /F NR in NR with ≥80 μM tetracaine, 0.97, is indicated by the dotted horizontal line in Fig.  8 A. These results suggest that (a) fi bers in NR continually release a small amount of Ca 2+ from the SR and/or have a resting infl ux of Ca 2+ from the external solution, which produces a slight elevation in [Ca 2+ ] R , and (b) this Ca 2+ entry into the myoplasm is blocked by tetracaine. Although an infl ux of Ca 2+ from the external solution cannot be ruled out, this is considered unlikely because, at the potentials expected in the solutions Columns 2 and 3 are the same as columns 4 and 6 of Table III. The recorded images used for column 2 were re-analyzed with peak ∆F/F R criterion of ≥0.7 (column 4) and ≥1.0 (column 6). Columns 5 and 7 are similar to column 3 except that the peak ∆F/F R criterion was ≥0.7 and ≥1.0, respectively. In all columns, the ∆F/F R detection threshold was 0.2; in columns 3, 5, and 7, the standard deviation of the added noise was 0.17. used in these experiments (−90 to −60 mV; [K + ] = 2.5 to 12.5 mM), Ca 2+ currents are not observed (Sanchez and Stefani, 1978;Almers and Palade, 1981). Confocal experiments show that fi bers in NR have a small but detectable frequency of sparks (0.027 ± 0.009 sarcomere −1 s −1 with a peak ∆F/F R criterion of ≥0.5, n = 7; fi rst section of RESULTS). This observation is consistent with the idea that resting SR Ca 2+ release occurs as sparks. This idea is supported by our results from three other fi bers, in which 75-100 μM tetracaine reduced the frequency of sparks in NR by an order of magnitude, from 0.039 ± 0.005 to 0.004 ± 0.000 sarcomere −1 s −1 .
A similar interpretation applies to the measurements of F T /F NR in elevated [K + ] Ringer's. 8K Ringer's without tetracaine appears to stimulate SR Ca 2+ release; this is indicated by an elevation of F T /F NR (Fig. 8 A) and by an increase in spark frequency of approximately sevenfold ( Fig. 3 and associated text). 80 μM tetracaine reduces but does not fully block this release (Fig. 8 A) and reduces the frequency of sparks without eliminating them (Table III and Fig. 6). 200 μM tetracaine reduces F T / F NR to near or below the value in NR (Fig. 8 A) and almost completely eliminates sparks. Similar results were found in 12.5K Ringer's with and without tetracaine.
Data in the different [K + ] Ringer's without tetracaine are plotted in Fig. 8 B. The value of F T /F NR minus 0.97 (ordinate) varies approximately linearly with the frequency of sparks (abscissa). This result is consistent with the idea that sparks account for most of the increases in F T /F NR above 0.97 observed with [K + ] = 2.5, 8, and 12.5 mM.

D I S C U S S I O N
The experiments described in this article show that 75-100 μM tetracaine has three main effects on voltageactivated Ca 2+ sparks in frog intact muscle fi bers depolarized by 8K Ringer's: (1) an approximately sixfold reduction in spark frequency; (2) little or no modifi cation of spark rise time; (3) 10-30% reductions in peak ∆F/F R , decay time constant, FDHM, FWHM, and mass.
To interpret these effects quantitatively, simulations of sparks were performed that included the main sources of noise and variability that are thought to contribute to the variability of measured sparks. The simulations show that the effects of 75-100 μM tetracaine are approximately those expected if tetracaine reduces the amplitude of the Ca 2+ source fl ux with little or no change in its duration. In 8K Ringer's without tetracaine, the estimated fl ux amplitude is 1.7 pA whereas, with 75-100 μM tetracaine, it is only 1.2 pA (columns 6 and 7 of Table III; peak ∆F/F R criterion of ≥0.5). The observed reduction in spark frequency with tetracaine (row 3 of Table III) cannot be explained, however, by a uniform reduction in source fl ux through all active RyR channels. This would predict a reduction in frequency of ‫%83ف‬ (column 7 of Table III), which is much smaller than that observed, ‫%28ف‬ (column 5). In addition, a uniform reduction in source fl ux would not be expected from bilayer studies (Xu et al., 1993;Gyorke et al., 1997;Csernoch et al., 1999). Rather, our results are consistent with the idea that (a) an average normal spark is generated by more than one active channel, (b) an average spark in 75-100 μM tetracaine is generated by fewer channels, and (c) 1.2 pA is an upper limit of the Ca 2+ fl ux through a single RyR channel under physiological conditions.
The upper limit of 1.2 pA is consistent with the results of Kettlun et al. (2003), who studied single RyR channels in bilayers. . Based on our estimate of 1.7 pA for the Ca 2+ source fl ux of a spark in 8K Ringer's without tetracaine, the single-channel values of Kettlun et al. (2003) suggest that some sparks of this type require two to four active RyR Ca 2+ channels. Unfortunately, our results do not indicate whether the two to four channels are contiguous or distributed within a small volume determined by the PSF of the confocal microscope. The solution bathing the fi ber was either NR (circles) or 8K Ringer's (squares) containing either 0 or 80 μM tetracaine (open and fi lled symbols, respectively). The curve is a plot of the empirical function F R (t) = k0 + k1/(t − t0) k2 , which was fi tted to the open circles (k0 = −131, k1 = 165.5, t0 = 15, and k2 = 0.0313). (B) Plot of F R data from part A after normalization by F NR , calculated with the empirical formula. The horizontal dashed line at 1.0 corresponds to no change in F R relative to that in NR. Fiber number, 050205.1; sarcomere length, 2.9 μm; 16°C.

Possible Mechanisms of RyR Coupling
The conclusion that some sparks require activation of two to four RyR channels leads to the question of how the opening of multiple RyRs is coordinated. Lacampagne et al. (1999) showed that RyR coupling must be very rapid. They studied voltage-activated sparks in frog cut fi bers with rapid (63 μs) data sampling and found that ∆F/F R rises abruptly from baseline and declines abruptly from peak, with the maximal rates of rise and decline reached shortly after the times of the respective transitions. Thus, the RyR Ca 2+ channels appear to open and close in near synchrony.
Two mechanisms have been suggested to explain the coordinated opening of a cluster of RyR channels: (1) local protein-protein interaction(s) between adjacent RyRs (e.g., "coupled gating;" Marx et al., 1998) and (2) diffusional activation of RyRs by Ca 2+ ions (Ca 2+ -induced Ca 2+ release; Endo et al., 1970;Ford and Podolsky, 1970;Rios and Pizarro, 1988). In either case, activation of the fi rst RyR in a cluster would be initiated by its voltage sensor in the T-tubular membrane.
The coordinated closing of the cluster probably depends on Ca 2+ inactivation of Ca 2+ release (Baylor et al., 1983;Schneider and Simon, 1988) and/or a change in the voltage sensor.
Block of Ca 2+ Release by Tetracaine As described in INTRODUCTION, Shirokova and Rios (1997) found that, in frog cut fi bers, 200 μM tetracaine blocked voltage-activated Ca 2+ sparks but spared a nonspark form of Ca 2+ release observed with small depolarizations ("small event" Ca 2+ release). We also found that tetracaine reduces the frequency of voltage-activated sparks (Table III and Fig. 6), although we failed to fi nd a tetracaine-insensitive form of Ca 2+ release. In both 8K Ringer's (estimated membrane potential, −70 mV) and in 12.5K Ringer's (estimated membrane potential, −60 mV), 200 μM tetracaine reduced F T /F NR to a value near that in NR (Fig. 8 A). The simplest hypothesis to explain these results is that in intact fi bers, there is one form of SR Ca 2+ release, with an elementary release event that can be detected as sparks, and that this release is blocked by tetracaine.

Comparison with Results in Cardiac Myocytes
In our experiments, sparks were measured for up to 1 h in 8K Ringer's with 75-100 μM tetracaine. During this time, spark frequency was about sixfold smaller than that in 8K Ringer's without tetracaine (0.032 vs. 0.184 sarcomere −1 s −1 ; Table III) and showed no sign of recovery ( Fig. 3 and fi rst section of RESULTS). This result differs markedly from that in rat cardiac myocytes, in which tetracaine's effect on spark frequency was transient (Lukyanenko et al., 2001): after a 1-min exposure to 100 μM tetracaine, spark frequency was about sixfold smaller than normal but during the next 2-4 min, it recovered fully. This recovery was attributed to an increase in SR luminal [Ca 2+ ] due to continued pumping of Ca 2+ by the SR Ca 2+ pump while RyR Ca 2+ channels were inhibited by tetracaine. Although tetracaine might also increase luminal [Ca 2+ ] in frog intact fi bers, our conclusion that a normal spark is due to more than one RyR Ca 2+ channel would not be altered since an elevation in luminal [Ca 2+ ] would be expected to increase the RyR single-channel Ca 2+ fl ux (e.g., Kettlun et al., 2003).
As noted in the fi rst section of DISCUSSION, the estimated single-channel RyR Ca 2+ fl ux is ≤1.2 pA in a frog skeletal fi ber exposed to 8K Ringer's with 75-100 μM For the measurements in which SD exceeded the symbol size, vertical wings extend one SD above and below the mean. The dashed line at 1.0 corresponds to no change with respect to NR. The dotted line at 0.97 corresponds to the expected value of F T /F NR in the absence of SR Ca 2+ release (see text). (B) Mean values of F T /F NR − 0.97 from part A plotted vs. spark frequency measured in the absence of tetracaine at the three values of [K + ]: 2.5 mM (F T /F NR = 1.0; number of sparks N = 79 from 7 fi bers), 8 mM (F T /F NR = 1.144; N = 1,061 from 7 fi bers), and 12.5 mM (F T /F NR = 1.616; N = 1,306 from 3 fi bers); peak ∆F/F R criterion of ≥0.5. The ordinate value of the fi lled circle (2.5 mM [K + ]) is, by defi nition, 0.03. The frequency of sparks in 12.5K Ringer's may be underestimated because of the relatively large value of F T /F NR in 12.5K Ringer's, 1.616, that was used to correct spark amplitudes. For the measurements in which SEM exceeded the symbol size, vertical and horizontal wings extend one SEM about the mean. The dashed curve is a least-squares fi t to the mean values of a straight line constrained to intersect the origin.