Relation Between the Sarcolemmal Ca2+ Current and Ca2+ Sparks and Local Control Theories for Cardiac Excitation-Contraction Coupling
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.
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 Ps: (1) Application of inorganic7 or organic8 10 11 13 Ca2+ channel antagonists (which reduce the open probability of the L-type Ca2+ channel) greatly reduces Ps. (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 Ps.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 coupling6 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 (Ps)? We have therefore examined the relation between SL Ca2+ current and Ps in detail. Our results suggest that the opening of a single SL Ca2+ channel can activate a Ca2+ spark and that Ps depends on the square of the single SL Ca2+ channel current and the square of the local [Ca2+]i.
Materials and Methods
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 MΩ 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 ICa (“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.
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 MΩ. Electronic series resistance compensation was used to reduce the effective series resistance to <1 MΩ. 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 (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 ICa 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.
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, Ps, is similar to the measures of spark occurrences used in other studies.11 12
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 ICa 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.
Fig 1⇑, bottom left, shows that Ps 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, Ps, 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 Ps 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+ sparks7 10 12 (see “Discussion”).
Fig 1⇑, top right, shows the voltage dependence of ICa 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 ICa 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 Ps is shifted to more negative potentials along the voltage axis when compared with that for ICa.11 The whole-cell ICa is related to the single-channel current by the following equation:
where n is the number of Ca2+ channels, i is the single-channel current, and Po is the open probability of the Ca2+ channel. Since Po generally increases with voltage, the reduction in the number of Ca2+ sparks evoked at more positive potentials (for any given whole-cell ICa) 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 Ps and i. In a recent study, it was suggested that Ps followed the voltage dependence of i.11 However, an earlier study suggested that Ps 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 Ps should be proportional to the square of i. The probability of spark occurrence is given by the following equation:
where Po is the probability that an SL Ca2+ channel is open and Pi is the probability that the current (i) through the open Ca2+ channel will activate a spark. From the above discussion, if
where k is a constant, then it follows from Equations 1, 2, and 3 that by dividing Ps by ICa, we can remove the voltage dependence of Po and thus examine the relation between the single-channel current (i) and Ps:
So if Ps is proportional to i (x=1), then Ps/ICa should be constant, but if Ps is a steeper power function of i (x>1), then Ps/ICa will follow the voltage dependence of i raised to the power x−1.
Fig 2⇓, top, shows the voltage dependence of Ps and ICa, and Fig 2⇓, bottom, shows that Ps/ICa varies with membrane potential, decreasing with increasing depolarization. This result shows that Ps is not linearly related to i (x≠1). 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 :
where PCa 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), Ps/ICa appears to be proportional to i, so x=2. In other words, our data suggest that Ps 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 ICa 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 ICa 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 ICa 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, Ps, and the amplitude of ICa 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) (Ps, 7.12±0.16 mV per e-fold change [n=16]; ICa, 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 Ps at all potentials). Over the voltage range examined, the increase in ICa with depolarization is determined primarily by the increase in Po, 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”).
The present study examines the relation between ICa 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 Ps is not proportional to the single SL Ca2+ channel current (i). By examining Ps/ICa we were able to remove the factor i·Po from the voltage dependence of Ps. A major advantage of this approach is that it removes uncertainty about the voltage dependence of Po, which is difficult to measure at very positive potentials. Since Ps/ICa followed the expected voltage dependence of Ca2+ permeation through a single Ca2+ channel, it follows that Ps 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 Ps is approximately proportional to the square of i, our data support the idea that Ps 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 Ps 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 “. . . [Ps] 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 Po (eg, Ca2+-dependent inactivation of Ca2+ channels and changes in gating behavior at high potentials).15 We avoided this problem by directly measuring ICa and examining the ratio of Ps to ICa. (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 studies8 10 13 ) because its blockade largely prolongs closed times with little effect on open time (unlike the phenylalkylamine Ca2+ channel blockers; see McDonald and colleagues15 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 Ps to ICa we completely avoid any effects on Po (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 ICa near the foot of the ICa activation curve if Ps 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 Po and the single-channel current around the foot of the ICa activation curve. At the foot of the activation curve, a 7-mV depolarization will result in an ≈270% increase in Po and ≈7% reduction in the driving force (Em−ECa) for Ca2+ entry. Thus, changes in Ps at the foot of the activation curve are dominated by changes in Po 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 Pon, and if n channels are required to activate a spark, then Ps=k·Pon, 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, Po can be described by an equation of the form Po=A·exp(B·V), where V is voltage and A and B are constants, so Ps=k·A·exp(n·B·V). Since the voltage change required to give an e-fold increase in Po and Ps 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 Po and Ps at the foot of the ICa activation can be explained by Ca2+ sparks being activated by the opening of a single Ca2+ channel. At more positive potentials, the fraction δEm/δ(Em−ECa) becomes larger while δPo/δEm approaches zero, so the voltage dependence of Ps 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 Ps 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, Ps 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 Ps is low.)
In summary, we have shown that Ca2+ sparks evoked by depolarization have the same voltage dependence as the triggering ICa, only near the foot of the activation curve of ICa. At more positive potentials, the voltage dependence of Ps shows that Ps 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|
|ECa||=||Nernst potential for Ca2+|
|Po||=||open probability of the L-type Ca2+ channel|
|Ps||=||probability of Ca2+ spark occurrence|
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 (E×94-03838550), Spain. Dr Cheng is a fellow of the Maryland Heart Association.
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 email@example.com.
- Received July 18, 1995.
- Accepted October 25, 1995.
- © 1996 American Heart Association, Inc.
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