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(Circulation Research. 1996;78:166-171.)
© 1996 American Heart Association, Inc.

Articles

Relation Between the Sarcolemmal Ca²⁺ Current and Ca²⁺ Sparks and Local Control Theories for Cardiac Excitation-Contraction Coupling

L.F. Santana, H. Cheng, A.M. Gómez, M.B. Cannell, W.J. Lederer

From the Department of Physiology and the Medical Biotechnology Center (L.F.S., H.C., A.M.G., W.J.L.), University of Maryland at Baltimore School of Medicine, and the Department of Pharmacology and Clinical Pharmacology (M.B.C.), St George's Hospital Medical School, London, UK.

	Abstract

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Abstract Ca²⁺ sparks, the elementary events underlying excitation-contraction (E-C) coupling, occur when sarcoplasmic reticulum (SR) Ca²⁺ release channels open. They are activated locally by Ca²⁺ influx through sarcolemmal (SL) Ca²⁺ channels. By measuring the probability of spark occurrence under conditions in which their probability of occurrence is low, we address two important questions raised by our recent work: (1) When a Ca²⁺ spark is triggered, how many SL Ca²⁺ channels (at a minimum) contribute to its activation? (2) What is the relation between the subcellular local [Ca²⁺]_i produced by the opening of SL Ca²⁺ channels and the consequent SR Ca²⁺ release? By comparing the voltage dependence of Ca²⁺ sparks in rat ventricular myocytes with the Ca²⁺ current, we show that the opening of a single SL Ca²⁺ channel can trigger a Ca²⁺ spark. Furthermore, we deduce that the probability of SR Ca²⁺ release depends of the square of the local [Ca²⁺]_i produced by SL Ca²⁺ channel openings. These results are discussed with respect to the properties of Ca²⁺-induced Ca²⁺ release (CICR) and the local control theory of excitation-contraction coupling.

Key Words: intracellular Ca²⁺ • fluo 3 • nifedipine • Ca²⁺ current • excitation-contraction coupling

	Introduction

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During cardiac E-C coupling, Ca²⁺ release from the SR is due to the activation of the CICR mechanism.¹ The open probability of the SR Ca²⁺ release channels (identified as RyRs) depends on the [Ca²⁺]_i level (see Bers² for review). However, as pointed out by Cannell et al,³ it is difficult to explain how small changes in average [Ca²⁺]_i due to the Ca²⁺ current can regulate the large release of Ca²⁺ from the SR, since the [Ca²⁺]_i around the RyR should be dominated by the SR Ca²⁺ flux (see Stern⁴ for further analysis of this problem). Niggli and Lederer⁵ first suggested that "local control" of CICR might resolve this problem if SL Ca²⁺ channels were located next to SR Ca²⁺ release channels and if the RyRs were relatively insensitive to [Ca²⁺]_i.

Recently, microscopic elementary SR Ca²⁺ release events called "Ca²⁺ sparks" have been reported.⁶ A single Ca²⁺ spark occurs when an SR "release unit" is activated, resulting in a small flux of Ca²⁺ from the SR to the cytosol. The size of the flux suggests that the Ca²⁺ spark arises from the activation of one or a small number of SR Ca²⁺ release channels acting in concert.^{6 7} Ca²⁺ sparks can occur spontaneously in quiescent heart cells⁶ or can be evoked by activation of the SL Ca²⁺ current.^{6 7 8 9 10 11 12} Analysis of the properties of Ca²⁺ sparks can give valuable insight into the gating of RyR in intact cells.^{7 12}

A number of recent observations support the idea that it is the local [Ca²⁺]_i in the junctional space that determines P_s: (1) Application of inorganic⁷ or organic^{8 10 11 13} Ca²⁺ channel antagonists (which reduce the open probability of the L-type Ca²⁺ channel) greatly reduces P_s. (2) An undetectable (at the level of the light microscope) increase in [Ca²⁺]_i due to Ca²⁺ channel opening leads to a large increase in P_s.¹² (3) Under normal conditions, Ca²⁺ sparks are unable to activate additional Ca²⁺ sparks in adjacent regions⁶ despite the fact that the local [Ca²⁺]_i associated with a Ca²⁺ spark is much larger than the global increase in [Ca²⁺]_i produced by activation of the Ca²⁺ current.⁷ All of these observations can be explained by the fact that SR Ca²⁺ release channels are situated very close to the L-type Ca²⁺ channel, where they sense an 100-fold increase in local [Ca²⁺]_i when a nearby L-type Ca²⁺ channel opens.^{4 5 7 14}

Although the original proposal that Ca²⁺ sparks were elementary events underlying E-C coupling^{6 7 8} was challenged by the suggestion that Ca²⁺ spark amplitude was voltage dependent,⁹ it is now clear that Ca²⁺ spark amplitude is indeed independent of membrane potential.^{11 12} In addition, the idea that intrinsic RyR gating can provide CICR with stability⁴ is supported by the observation that the time course of the Ca²⁺ spark is not dependent on the duration of Ca²⁺ influx via SL Ca²⁺ channels.¹²

Despite these advances in our understanding of cardiac E-C coupling, several issues remain unclear: (1) When a Ca²⁺ spark is triggered, what is the minimal number of SL Ca²⁺ channels that contribute to its activation? (2) What is the relation between the local [Ca²⁺]_i and the probability of SR release unit activation and Ca²⁺ spark production (P_s)? We have therefore examined the relation between SL Ca²⁺ current and P_s in detail. Our results suggest that the opening of a single SL Ca²⁺ channel can activate a Ca²⁺ spark and that P_s depends on the square of the single SL Ca²⁺ channel current and the square of the local [Ca²⁺]_i.

	Materials and Methods

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Cells
Isolated rat heart ventricular myocytes were prepared as described earlier.^{6 7} Briefly, rat hearts were obtained from animals killed by lethal injection of pentobarbital (100 mg/kg). Langendorff perfusion of the rat heart was carried out by using a solution containing (mmol/L) NaCl 137, KCl 5, HEPES 20, MgCl₂ 1.2, glucose 15, and NaH₂PO₄ 1, with pH 7.4 at 37°C (solution A). After 2 minutes of perfusion, the perfusion solution was switched to a solution containing (mmol/L) NaCl 130, KCl 4.8, NaHCO₃ 25, MgCl₂ 1.2, glucose 12.5, and NaH₂PO₄ 1.2 (solution B) with the following additives: 1 mg/mL collagenase type 2 (Worthington), 0.04 mg/mL of pronase type IV (Sigma Chemical Co), and 1 mg/mL BSA for 20 minutes. Solution B without enzymes but with 100 µmol/L CaCl₂ and 1 mg/mL BSA was then used to perfuse the heart for several minutes (to wash away the enzyme solution). The heart was then minced and gently agitated to separate the cells. The cells harvested by this method were permitted to settle and then subjected to a gradually increasing [Ca²⁺] in solution A until the final solution contained 1 mmol/L Ca²⁺. These cells were stored in this solution at room temperature (20°C to 22°C) until used.

Pipettes and Solutions
Thin-wall glass capillaries (outer diameter, 1.5 mm; World Precision Instruments) were pulled to a nominal resistance of 0.5 to 1.5 M by using a Brown-Flaming–type puller (model 80P, Sutter Instruments). The pipette-filling solutions contained (mmol/L) CsCl 130, the Ca²⁺-sensitive fluorescent indicator fluo 3, 0.1, HEPES 10, MgCl₂ 0.33, tetraethylammonium chloride 20, and Mg-ATP 4, with pH 7.2.

During experiments, cells were continuously superfused with solution A containing 1 mmol/L CaCl₂. Once a gigaohm seal was formed and successful conversion to whole-cell patch-clamp configuration was achieved, cells were then superfused with a solution designed to isolate I_Ca ("recording solution"), which contained (mmol/L) NaCl 137, CsCl 5, CaCl₂ 1, NaH₂PO₄ 1, MgCl₂ 1.2, tetraethylammonium chloride 10, and 4-aminopyridine 4, with pH 7.4 at 20°C to 22°C. All solutions containing NaHCO₃ were continuously bubbled with 95% O₂/5% CO₂.

Voltage Clamp
Whole-cell currents were measured with an Axopatch 200A patch-clamp amplifier. Series resistance was continuously monitored, and experiments were carried out only when the series resistance was <2 M. Electronic series resistance compensation was used to reduce the effective series resistance to <1 M. Data were recorded by using PCLAMP 6.01 software (Axon Instruments) and on videotape (Neurodata).

Cells were held at -80 mV. Before a test depolarization, cells were depolarized to -50 mV by a slow (500-millisecond) voltage ramp and held at -50 mV for 50 milliseconds before test depolarizations were applied. After the test depolarization, the membrane potential was returned to -80 mV. That the SR Ca²⁺ load was normal is suggested by the absence of any spontaneous waves of CICR despite vigorous contractions (10% to 15% cell shortening) in response to large depolarizations.

Nifedipine
Nifedipine (1 µmol/L) was used in some experiments in the present study (see previous study from our laboratory⁸ ) because it significantly reduces the amplitude of I_Ca without changing the single-channel current amplitude and has little effect on the mean open time.¹⁵ To ensure a constant level of nifedipine block, a prepulse conditioning protocol was applied before every test depolarization; four depolarizations from the holding potential to 0 mV were applied for 10 milliseconds every 2 seconds before the test pulse.

Data Analysis
Voltage-clamp command signals were coordinated with the confocal microscope imaging system by electronics constructed by the authors.⁷ The imaging data were processed by using SOM and COMOS software (Biorad) and with IDL (Research Systems Inc). Data are presented as mean±SEM. Two-sample comparisons were performed by using the paired t test, and P<.05 was used as a measure of statistical significance. All electrophysiological signals were analyzed by using PCLAMP 6.01 (Axon Instruments).

Sparks were identified by thresholding as well as kinetic and spatial criteria. For an event to be counted as a spark, it had to meet the following criteria: The peak [Ca²⁺]_i of the spark had to be 50 nmol/L greater than [Ca²⁺]_i in the neighboring region, and time to peak of the Ca²⁺ spark had to be between 2 and 20 milliseconds, with a half-time of decay between 10 and 40 milliseconds. The spatial width (full width at half maximum) of the [Ca²⁺]_i signal at the peak of the Ca²⁺ spark had to be at least 0.5 µm but no more than 3 µm. To enable comparison of the probability of spark occurrence at different voltages and in different cells, we normalized the number of sparks occurring to the maximum number that occurred during the experiment: number of sparks/maximum number of sparks. The number obtained, P_s, is similar to the measures of spark occurrences used in other studies.^{11 12}

	Results

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Fig 1, top left, shows sample line-scan images and current records during 100-millisecond depolarizing pulses to various potentials in the presence of 1 µmol/L nifedipine. The images show that during the test pulse, the local elevations of [Ca²⁺]_i occur, which have been identified as Ca²⁺ sparks.^{6 7 10 12} The application of nifedipine in these experiments reduces I_Ca without significantly changing its voltage dependence, as shown in Fig 1, top right. The presence of nifedipine reduced the number of evoked sparks at all potentials and made it possible to quantify the number of Ca²⁺ sparks evoked at each test potential.

View larger version (28K): [in this window] [in a new window]   Figure 1. Voltage dependence of Ca2+ sparks and ICa in rat ventricular myocytes. Top left, Line-scan images of single heart muscle cells containing the fluorescent Ca2+ indicator fluo 3 at three representative potentials (-40, -10, and +40 mV) are shown, revealing three, five, and one Ca2+ spark, respectively. In each image, the position along the line scan is shown vertically; the time is shown horizontally. The cells were exposed to 1 µmol/L nifedipine. The top trace shows the voltage protocol to indicate the timing of a 100-millisecond depolarization. The bottom traces show ICa. Top right, Superimposed plots of the voltage dependence of ICa obtained under control conditions () and after the application of 1 µmol/L nifedipine () are shown (n=4). Vpulse indicates pulse voltage. Note that ICa has been reduced 16-fold by 1 µmol/L nifedipine. Bottom left, Superimposed plots of the voltage dependence of the normalized Ca2+ spark occurrence (Pspark) in nifedipine and [Ca2+]i in the absence of nifedipine (plotted as fluorescence ration [F/F0]). Peak Pspark in this panel corresponds to 20 Ca2+ sparks.

Fig 1, bottom left, shows that P_s first increases with voltage and then declines at more positive potentials. Pooled data from four similar experiments are shown. The figure shows the voltage dependence of normalized spark production, P_s, as well as (for comparison) the amplitude of the whole-cell intracellular Ca²⁺ transient recorded in the absence of nifedipine. The voltage dependence of the whole-cell intracellular Ca²⁺ transient is bell shaped, as reported previously,^{3 16} and it is notable that P_s has a similar voltage dependence. However, there is a clear deviation between the two data sets at positive potentials whose origin is uncertain. Although this difference could be related to the activity of the Na⁺-Ca²⁺ exchanger at positive potentials, a low [Na⁺]_i was used in these experiments to limit the contribution of the exchanger-mediated Ca²⁺ influx to the whole-cell transient. Nevertheless, a significant fraction of the changes in the amplitude of the intracellular Ca²⁺ transient can be explained by the changes in probability of recruiting Ca²⁺ sparks^{7 10 12} (see "Discussion").

Fig 1, top right, shows the voltage dependence of I_Ca under control conditions and in the presence of nifedipine, and it is clear that the main effect of nifedipine is to greatly decrease the amplitude of I_Ca at all potentials without altering its voltage dependence. However, comparison of the top right and bottom left panels of Fig 1 shows that the voltage dependence of P_s is shifted to more negative potentials along the voltage axis when compared with that for I_Ca.¹¹ The whole-cell I_Ca is related to the single-channel current by the following equation:

(1)

where n is the number of Ca²⁺ channels, i is the single-channel current, and P_o is the open probability of the Ca²⁺ channel. Since P_o generally increases with voltage, the reduction in the number of Ca²⁺ sparks evoked at more positive potentials (for any given whole-cell I_Ca) can be simply explained by the decrease in the magnitude of i with increasing depolarization.

Recent publications suggest two different possibilities for the relation between P_s and i. In a recent study, it was suggested that P_s followed the voltage dependence of i.¹¹ However, an earlier study suggested that P_s might depend on the square of the local [Ca²⁺],⁷ and since we expect the local [Ca²⁺] to be proportional to i (see "Discussion"), it would then follow that P_s should be proportional to the square of i. The probability of spark occurrence is given by the following equation:

(2)

where P_o is the probability that an SL Ca²⁺ channel is open and P_i is the probability that the current (i) through the open Ca²⁺ channel will activate a spark. From the above discussion, if

(3)

where k is a constant, then it follows from Equations 1, 2, and 3 that by dividing P_s by I_Ca, we can remove the voltage dependence of P_o and thus examine the relation between the single-channel current (i) and P_s:

(4)

So if P_s is proportional to i (x=1), then P_s/I_Ca should be constant, but if P_s is a steeper power function of i (x>1), then P_s/I_Ca will follow the voltage dependence of i raised to the power x-1.

Fig 2, top, shows the voltage dependence of P_s and I_Ca, and Fig 2, bottom, shows that P_s/I_Ca varies with membrane potential, decreasing with increasing depolarization. This result shows that P_s is not linearly related to i (x1). Although it is very difficult to measure single Ca²⁺ channel currents under physiological conditions, the voltage dependence of i should follow the Nernst-Planck equation for the voltage-dependent single-channel current (i)¹⁷ :

View larger version (13K): [in this window] [in a new window]   Figure 2. Relation between ICa and Ca2+ spark probability of occurrence (Psparks). Top, Voltage dependence of the normalized Psparks and ICa in the presence of 1 µmol/L nifedipine (data from Fig 1). Bottom, Psparks/ICa is plotted as a function of membrane potential (). The smooth curve shows the relative current from a single SL Ca2+ channel as a function of voltage predicted from the Nernst-Planck equation for electrodiffusion (see text) fitted by least squares (n=4; mean±SEM is reported).

(5)

where P_Ca is the permeability of Ca²⁺ through the membrane (adjusted to fit the data by least squares), V is the membrane potential, [Ca²⁺]_i is 100 nmol/L, [Ca²⁺]_o is 1 mmol/L, F is the Faraday constant, R is the gas constant, and T is the temperature.

Since our data are well described by this equation (line in Fig 2, bottom), P_s/I_Ca appears to be proportional to i, so x=2. In other words, our data suggest that P_s is proportional to the square of the single SL Ca²⁺ channel current.

It has been reported that the voltage dependence of spark rate around the threshold for the activation of I_Ca is exponential, changing e-fold in 7 mV.¹² However, in those experiments the voltage dependence of the Ca²⁺ current was not measured. In the present study, we examine the relation between I_Ca and spark production during voltage steps from -50 mV to between -48 and -32 mV. Fig 3, top, shows line-scan images and the measured I_Ca taken from a representative cell (out of 16 examined). As the voltage steps were increased above threshold, the number of evoked Ca²⁺ sparks increased. The voltage dependence of the normalized spark production, P_s, and the amplitude of I_Ca are shown in Fig 3, bottom, as circles and triangles, respectively. The voltage dependence of each is similar, showing an e-fold increase every 7.2 mV (solid line) (P_s, 7.12±0.16 mV per e-fold change [n=16]; I_Ca, 7.31±0.16 mV per e-fold change [n=16]). Unfortunately, the voltage range over which Ca²⁺ sparks can be counted is limited, because at positive potentials the large number of Ca²⁺ sparks leads to confusion in their identification (this was not a problem in the experiments described earlier, because nifedipine reduced P_s at all potentials). Over the voltage range examined, the increase in I_Ca with depolarization is determined primarily by the increase in P_o, from which we conclude that Ca²⁺ sparks (and thus functional Ca²⁺ release units) can be activated by the opening of a single SL Ca²⁺ channel (see "Discussion").

View larger version (13K): [in this window] [in a new window]   Figure 3. Voltage dependence of Ca2+ sparks and ICa during small depolarizations. Top, Three sample images of Ca2+ sparks at -42, -40, and -38 mV show two, four, and nine sparks, respectively. Above each image is shown the pulse protocol indicating the timing of 200-millisecond depolarizations from -50 mV. The simultaneously measured ICa is shown below each image. Scale bars=10 µm. Bottom, The voltage dependence of ICa and of normalized Ca2+ spark occurrence (Psparks) had similar voltage dependencies, changing e-fold in magnitude (k) every 7.31±0.16 and 7.12±0.16 mV, respectively. No significant statistical difference was detected between the two means (t test, n=16, P>> .05).

	Discussion

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The present study examines the relation between I_Ca and the elementary release of Ca²⁺ by the SR. SR Ca²⁺ release occurs when "functional Ca²⁺ release units" are activated and these units produce a local increase in [Ca²⁺]_i called a Ca²⁺ spark.^{6 7} Although others have called such limited increases in [Ca²⁺]_i "local Ca²⁺ transients," it is clear that there are no detectable differences in the time course of Ca²⁺ sparks whether they occur spontaneously or from the activation of L-type Ca²⁺ channels. In fact, the only difference between spontaneous Ca²⁺ sparks and those produced by activation of the Ca²⁺ current is their probability of occurrence.^{7 8 10 11 12} It may be that the use of the term "local Ca²⁺ transients" to describe Ca²⁺ sparks may have been based on the erroneous suggestion that Ca²⁺ sparks have different sizes at different potentials.⁹

The data presented here show that P_s is not proportional to the single SL Ca²⁺ channel current (i). By examining P_s/I_Ca we were able to remove the factor i·P_o from the voltage dependence of P_s. A major advantage of this approach is that it removes uncertainty about the voltage dependence of P_o, which is difficult to measure at very positive potentials. Since P_s/I_Ca followed the expected voltage dependence of Ca²⁺ permeation through a single Ca²⁺ channel, it follows that P_s must depend on the square of i (the single-channel current). Fick's first law of diffusion states that flux=D·A·d[Ca]/dx, where D is the effective diffusion coefficient and A is the area through which Ca²⁺ diffuses. The flux into the cell is proportional to the single-channel current [flux=i/(zF)], and this flux causes the local [Ca²⁺]_i to increase in the region where E-C coupling is sensed until the fluxes to and from that site are equal. It then follows that d[Ca]/dx should be proportional to i for any fixed geometry and D. Thus, the increment in local [Ca²⁺]_i at the site where E-C coupling is sensed will be proportional to the single-channel current as soon as a steady gradient across the junctional space is established (which should occur in a few microseconds, given the small distances involved). It should be noted that the terms D and A include all diffusional barriers in the junctional space, and we make the first-order assumption that there are no large changes in the effective value of D with i. From this simple analysis, it follows that since P_s is approximately proportional to the square of i, our data support the idea that P_s depends on the square of the local [Ca²⁺]_i, as suggested by Cannell et al,⁷ who deduced that the increase in the Ca²⁺ spark rate needed to explain the normal Ca²⁺ transient was so large that P_s could not be proportional to the local [Ca²⁺]_i. Further support for this view comes from reconstitution experiments, in which it has been shown that the instantaneous probability of SR Ca²⁺ release channel opening is much steeper than the steady state open probability.¹⁸ In fact, the data of Györke and Fill¹⁸ are reasonably well described by a Hill coefficient of 2, suggesting that the probability of SR release channel opening (and thus Ca²⁺ spark production) should be proportional to the square of the local [Ca²⁺]_i.

However, our data are at variance with the conclusion reached by López-López et al,¹¹ who stated ". . . [P_s] follows approximately the expected dependence on voltage of i." Their different result and conclusion may have arisen from a number of factors: (1) Spark occurrence is stochastic and follows Poisson statistics,¹² so that the small number of sparks (<16) in the experiment analyzed by López-López et al¹¹ would have resulted in a low signal-to-noise ratio. Thus, statistical fluctuations in the number of Ca²⁺ sparks at each potential could have obscured the true voltage dependence of spark production. (2) The analysis presented by López-López et al¹¹ is predicated on the voltage dependence of the activation curve of the L-type Ca²⁺ current, which was assumed to follow a simple Boltzmann distribution. This assumption may not be appropriate, since it ignores other factors that influence P_o (eg, Ca²⁺-dependent inactivation of Ca²⁺ channels and changes in gating behavior at high potentials).¹⁵ We avoided this problem by directly measuring I_Ca and examining the ratio of P_s to I_Ca. (3) There is also an implicit assumption that there is little change in mean open time with potential. In the present study, we used the dihydropyridine Ca²⁺ channel blocker nifedipine (see also other studies^{8 10 13} ) because its blockade largely prolongs closed times with little effect on open time (unlike the phenylalkylamine Ca²⁺ channel blockers; see McDonald and colleagues^{15 19} ). Thus, voltage-dependent drug effects on mean open time are less likely to be a problem with nifedipine,^{15 20} and by examining the ratio of P_s to I_Ca we completely avoid any effects on P_o (the ratio of the mean open time to the sum of the mean open and closed times), which will also help reduce any possible drug effects on the mean open time.

It may not be immediately obvious why the voltage dependence of Ca²⁺ spark production should match that of I_Ca near the foot of the I_Ca activation curve if P_s depends on the square of i and the square of the local [Ca²⁺]_i. The explanation for this observation resides in the relative change in P_o and the single-channel current around the foot of the I_Ca activation curve. At the foot of the activation curve, a 7-mV depolarization will result in an 270% increase in P_o and 7% reduction in the driving force (E_m-E_Ca) for Ca²⁺ entry. Thus, changes in P_s at the foot of the activation curve are dominated by changes in P_o rather than by changes in the single-channel current (and the local [Ca²⁺]_i associated with channel opening). If L-type Ca²⁺ channels gate independently, then the probability that n channels are open is P_oⁿ, and if n channels are required to activate a spark, then P_s=k·P_oⁿ, where k is a transmission factor that describes the strength of the coupling between L-type Ca²⁺ channel opening and Ca²⁺ spark production (and which depends on the single Ca²⁺ channel current). At the foot of the activation curve, P_o can be described by an equation of the form P_o=A·exp(B·V), where V is voltage and A and B are constants, so P_s=k·A·exp(n·B·V). Since the voltage change required to give an e-fold increase in P_o and P_s is (essentially) the same, it follows that n is 1 if k is approximately constant for small voltage changes (as argued above). Thus, the similar voltage dependence of P_o and P_s at the foot of the I_Ca activation can be explained by Ca²⁺ sparks being activated by the opening of a single Ca²⁺ channel. At more positive potentials, the fraction E_m/(E_m-E_Ca) becomes larger while P_o/E_m approaches zero, so the voltage dependence of P_s becomes dominated by the voltage dependence of the single-channel current (see above).

The decrease in the single-channel current (i) at positive potentials may explain the difference between the voltage dependence of P_s and the whole-cell intracellular Ca²⁺ transient (see Fig 1, bottom left). When i is small, the single-channel Ca²⁺ influx is less likely to activate an SR Ca²⁺ release unit. However, if more than one SL Ca²⁺ channel opens, the local [Ca²⁺]_i will be increased by the neighboring SL Ca²⁺ channels that open; thus, P_s will increase. To resolve individual Ca²⁺ sparks at positive potentials, we had to block the majority of the SL Ca²⁺ channels, which might then have precluded multiple SL Ca²⁺ channels from contributing to the activation of a functional release unit (an effect that would be more important at positive potentials, when i is small). An additional factor would be that the global increase in [Ca²⁺]_i will contribute to the increase in local [Ca²⁺ ]_i and slightly offset the decrease in local [Ca²⁺]_i produced by the decrease in i. (The size of this effect will depend on the amplitude of the intracellular Ca²⁺ transient outside the region where local [Ca²⁺]_i is sensed and would be much smaller when P_s is low.)

In summary, we have shown that Ca²⁺ sparks evoked by depolarization have the same voltage dependence as the triggering I_Ca, only near the foot of the activation curve of I_Ca. At more positive potentials, the voltage dependence of P_s shows that P_s also depends on the square of the single Ca²⁺ channel current and square of the local [Ca²⁺]_i. Therefore, these observations support our previous suggestions that the opening of a single SL Ca²⁺ channel is the minimum number needed to activate a "functional SR release unit," whose probability of activation depends on the square of the local [Ca²⁺]_i.^{5 7}

	Selected Abbreviations and Acronyms

 

CICR = Ca2+-induced Ca2+ release E-C = excitation-contraction ECa = Nernst potential for Ca2+ Em = membrane potential i = single-channel current ICa = Ca2+ current Po = open probability of the L-type Ca2+ channel Ps = probability of Ca2+ spark occurrence RyR = ryanodine receptor SL = sarcolemma SR = sarcoplasmic reticulum

	Acknowledgments

 
This study was supported by grants from the National Institutes of Health (HL-36974, HL-25675, and GM-14715), DRIF awards from the University of Maryland at Baltimore, the Medical Biotechnology Center, and the British Heart Foundation. Dr Gómez is supported by Ministerio de Educación y Ciencia (Ex94-03838550), Spain. Dr Cheng is a fellow of the Maryland Heart Association.

	Footnotes

 
Reprint requests to Dr W.J. Lederer, Department of Physiology and the Medical Biotechnology Center, University of Maryland at Baltimore School of Medicine, 660 W Redwood St, Baltimore, MD 21201. E-mail jlederer@umabnet.ab.umd.edu.

Received July 18, 1995; accepted October 25, 1995.

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