| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
CELLULAR |
1 Institute of Molecular Physiology and Genetics, Slovak Academy of Sciences, Vlárska 5, Bratislava, Slovak Republic
 |
Abstract |
|---|
 Top Abstract IntroductionMethodsResultsDiscussionReferences |
|---|
(Received 21 July 2006;
accepted after revision 14 November 2006;
first published online 23 November 2006)
Corresponding author A. Zahradníková: Institute of Molecular Physiology and Genetics, Slovak Academy of Sciences, Vlárska 5, Bratislava, Slovak Republic. Email: alexandra.zahradnikova{at}savba.sk
|
Introduction |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionReferences |
|---|
The close temporal relationships between activation of calcium current, activation of calcium release, and calcium release-dependent inactivation of calcium current (Zahradníková et al. 2004) call for exact description of the kinetics of calcium spikes, in particular their latencies and spatiotemporal distribution. However, at the time resolution necessary for such studies, the signal-to-noise ratio of these signals is very low. Instead of filtration of calcium signals to improve their quality, it would be advantageous to approximate their time course by a fitting function. This was successfully performed for calcium sparks in skeletal muscle (Lacampagne et al. 1999), but not for cardiac calcium sparks or for calcium spikes. Additionally, the fitted function may provide parameters that could serve for comparison of calcium spike features under different experimental conditions. If the fitted function was based on mechanisms of underlying calcium release, the functional parameters could even provide insight into changes in the calcium release mechanism.
The aim of this work was to characterize the kinetics of calcium signals measured by the fast indicator Oregon Green 488 BAPTA-5N (OG-5N) and by fluo-3 and fluo-4 in the presence of EGTA. To this end, we developed an appropriate fitting function that reflected activation of RyRs by multiple calcium ions and termination of RyR activity by an activation-dependent inactivation mechanism. The function provided very good approximations for calcium spikes measured with various fluorescent calcium indicators (OG-5N, fluo-3 or fluo-4) in the presence of EGTA. All indicators reported faithfully the occurrence and latency of calcium spikes, but fluo dyes were too slow to trace the calcium spike kinetics. Analysis of correlations between the amplitude and time course of calcium spikes supported the concept of steep calcium-dependent activation and fateful inactivation of calcium release flux.
|
Methods |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionReferences |
|---|
Cell isolation
Cardiac myocytes were enzymatically isolated from the left ventricle of young adult male Wistar rats (200–250 g) as previously described (Zahradník & Palade, 1993). Heparinized rats (5000 u kg–1 I.P.) were deeply anaesthetized with sodium pentobarbital (100 mg kg–1 I.P.). The heart was rapidly excised and mounted on a Langendorff apparatus. All anaesthetic and surgical procedures were approved by the State veterinary and food administration of the Slovak Republic.
Hearts were retrogradely perfused through the aorta with Tyrode solution (mM: 135 NaCl, 5.4 KCl, 5.0 MgCl2, 1 CaCl2, 0.33 NaH2PO4, 10 Hepes, pH 7.2) for 5 min, then with Ca2+-free Tyrode solution for 5 min and finally with collagenase (liberase) solution (mM: 135 NaCl, 5.4 KCl, 5.0 MgCl2, 0.02 CaCl2, 0.33 NaH2PO4, 10 Hepes, 0.19 u ml–1 liberase, pH 7.3). All solutions were oxygenated and heated to 37°C. After 5 min of enzyme perfusion, the left ventricle and septum were dissected and further incubated in the enzyme for up to 5 min. The tissue was then triturated in 4 ml of the stopping medium (mM: 106 CH3SO3H, 106 KOH, 3.9 KCl, 2.4 MgSO4, 8 K2HPO4, 1 EGTA, 22 taurine, 22 glucose, pH 7.3). The cell suspension was filtered through a nylon mesh and sedimented at 25 g for 5 min. The cells were washed twice with 4 ml of stopping medium and stored in cell culture dishes at room temperature for use within 1–6 h after isolation.
Chemicals and solutions
Liberase (Liberase Blendzyme 2) was from Roche Diagnostics (Basel, Switzerland), TTX was from Alomone Laboratories (Jerusalem, Israel), fluo-3, fluo-4, Oregon Green 488 BAPTA-5N and 100 mM standard solutions of EGTA and CaEGTA were from Molecular Probes (Eugene, OR, USA), all other chemicals were of analytical grade from Sigma-Aldrich Chemie GmbH (Taufkirchen, Germany). The osmolarity of all solutions was adjusted to 300 mosmol kg–1.
The external solution contained (mM): 135 NaCl, 5.4 CsCl, 10 Hepes, 5 MgCl2, 0.33 NaH2PO4, and 1 CaCl2, pH 7.3. For experiments with OG-5N, patch pipettes were filled with the internal solution containing (mM): 135 CsCH3SO3, 10 CsCl, 10 Hepes, 2 EGTA, 2 CaEGTA, 3 MgSO4, 3 ATPNa2, and 1 mM OG-5N, pH 7.3. Free calcium was adjusted to 100 nM, using a calcium ion-selective electrode (Orion, USA), by adding the necessary amounts of 100 mM EGTA or 100 mM CaEGTA solutions. For experiments with fluo-3 and fluo-4, the internal solution contained (mM) 135 CsCH3SO3, 10 CsCl, 10 Hepes, 1 EGTA, 3 MgSO4, 3 ATPNa2, and 60 or 100 µM fluorescent calcium indicator, pH 7.3. For recording calcium sparks, EGTA was omitted from the internal solution and fluo-3 concentration was 60 µM. To record isolated calcium currents, K+ currents were blocked by replacement of potassium by caesium, and Na+ currents were inhibited by the use of TTX (20 µM) and a holding potential of –50 mV. Calcium channels were kept in the phosphorylated state by the use of cAMP (50 µM) in the internal solution and of the membrane-permeant phosphodiesterase inhibitor IBMX (10 µM) in the external solution.
Electrophysiological measurements
The cells were patch clamped in whole-cell configuration with pipettes pulled by the P-97 Flaming/Brown Micropipette Puller (Sutter Instruments Co, USA) from borosilicate glass capillaries (no. BF150-110-10, Sutter Instruments). Pipettes of resistance in the range of 1.3–2.0 M
were used. Patch-clamp amplifier (Axopatch 200B, Axon Instruments, USA) with A/D converter (Digidata 1320A, Axon Instruments, USA) and pClamp software (Axon Instruments, USA) were used to voltage clamp the cells and record ionic currents. Cell capacitance and series resistance were both passively and actively compensated to 50–70%, and the leak was electronically subtracted. Single, 50 mV, 70 ms step voltage test pulses (from –50 mV holding potential to 0 mV) were used to activate calcium currents and calcium release. The experimental protocol consisted of single stimuli following an at least 30 s sojourn at the holding potential. For recording of calcium sparks, no voltage pulses were given and the cells were held at –40 mV. All experiments were performed at room temperature. A custom-made synchronizer was used for triggering the patch-clamp protocol at the desired time of the confocal scanning progress. The data obtained by the pClamp software were further analysed using Origin Pro v.7 SR4 (OriginLab Corporation, USA).
Confocal measurements
Calcium release from the sarcoplasmic reticulum was measured by means of a Leica TCS SP2 AOBS confocal microscope (Leica Microsystems, Germany). Fluorescent calcium indicators (fluo-3, fluo-4 or OG-5N) dialysed into the cell were excited at 488 nm. The fluorescent emission was recorded at the wavelength range of 493–600 nm through a PlanApochromat 63x/1.32 NA oil immersion objective and a pinhole set to 2.5 Airy units, providing a 
980 nm-thick optical section. For the recording of confocal images, the Leica confocal software (Leica Microsystems, Germany) was used. A line segment parallel to the longitudinal axis of the cell was scanned in bidirectional x–t scanning mode with a frequency of 2000 Hz. The scanning speed required the use of a 4x zoom factor; the resulting images therefore had a spatial resolution of 116 nm pixel–1. Individual release sites were identified in images recorded by the confocal microscope. Temporal profiles of fluorescence intensity from 7 pixels (0.8 µm width) centred at the release sites were obtained using Scion Image software (Scion Corporation, USA). The resulting data were further analysed using Origin Pro v.7 SR4 (OriginLab Corporation, USA).
Fitting the time course of the calcium signals
First we have approximated the time course of calcium spikes with the function composed of two sequential exponentials, which has been introduced by Lacampagne et al. (1999; their eqn (2)) for analysing skeletal muscle calcium sparks, which we will further refer to as the sequential model. The function was slightly rearranged for description of the incomplete return of fluorescence to the baseline level:
|
| (1) |
|
| (2) |
|
| (3) |
is the observed normalized fluorescence increase, FM is the maximal normalized fluorescence increase in the absence of spike termination, FT is the fraction of fluorescence increase that returns to the baseline level after termination of the spike, t0 and t1 are the times of the start and the peak of calcium spike, respectively, and 
A and T are the time constants of spike activation and termination, respectively. This function has two time points, t0 and t1, where the rate of change of fluorescence is discontinuous, i.e. times of abrupt commencement and cessation of calcium release flux. Because this function is phenomenological, there is no relationship between the parameter FT and the remaining parameters of the curve. Derivation of the fitting equation for cardiac calcium spike
In the derivation we have assumed that the increase in calcium release flux follows higher-order kinetics of activation, analogous to those of the extended minimal gating model of the ryanodine receptor (RyR) (Zahradníková
et al. 1999), consistent with the multiple calcium-binding sites of the RyR channel that have to be occupied before channel opening. We have also assumed that the termination of calcium flux is coupled to activation, i.e. the flux can terminate only upon and after being activated; therefore the rate of calcium release flux termination increases with the extent of calcium release flux activation. The relationship between calcium release flux and fluorescence was expressed according to Song et al. (1998):
|
| (4) |
is the proportionality factor (which is a function of the dissociation constant and the off-rate of EGTA, and of the initial calcium concentration; see Song et al. 1998) for the contribution of the steady-state increase in fluorescence to total fluorescence. From now on we will refer to this model as the coupled model.
The theoretical time course of the calcium release flux JCa was derived as the product of the calcium release flux in the absence of release termination, JCa,max, the probability of its being activated, PA(t), and the probability of its not being terminated, 1 –
PT(t):
|
| (5) |
|
| (6) |
A is the time constant of calcium release flux activation.
Since the process of release termination is sequential to the process of release flux activation, the time course of the probability of release flux termination, PT(t), was derived as the time integral of the convolution of the probability density of calcium release flux activation, pdfA(t), with the probability density of calcium flux termination given that release flux is activated, pdfT(t) (see Colquhoun & Hawkes 1983). The probability densities pdfA(t) and pdfT(t) are defined as
|
| (7) |
|
| (8) |
T is the time constant of calcium release termination. Then,
|
| (9) |
|
| (10) |
The convolution was carried out using Laplace transforms in the program Mathematica (Ver. 5.2, Wolfram Research, USA). The time course of the calcium spike was then expressed as
|
| (11) |
Analysis of amplitude histograms
The visibility function, characterizing the proportion of undetected calcium spikes at low event amplitudes, was analysed according to Izu et al. (1998) with minor modifications. Their eqn (31) was modified to take into account that amplitudes were measured in units of 
F/F0
= 1 –
F/F0:
|
| (12) |
|
| (13) |
|
| (14) |
Simulation of local calcium release events
Simulations of individual calcium release events were performed assuming spherical symmetry and a radius of the calcium release of 50 nm. The kinetic and diffusion parameters of chemical species considered in the model are summarized in Table 1. The time course of calcium flux was assumed to be (a) a square step lasting 10 ms; (b) an exponentially decaying time course with a time constant of 3.67 ms; or (c) flux corresponding to the coupled model with a time constants of activation (A) and termination (T) of 2.5 and 3.67 ms, respectively. The maximal amplitude of calcium release current was fixed to 10 pA. Calculations were performed using the CalC program (Ver. 5.5.9; Matveev et al. 2004) on a non-uniform grid with 600 grid points and with simulation radius of 3 µm. Simulation time was 200 ms in all cases.
|
|
| (15) |
|
| (16) |
All symbolic calculations were performed in Mathematica (Ver. 5.2, Wolfram Research, USA). All numerical calculations, data fitting and statistical analysis were performed in the program Origin (Ver. 7.0 SR4, OriginLab, USA). The errors are shown as S.E.M. Multiple comparisons were performed with one-way ANOVA or two-way ANOVA with Bonferroni correction for post hoc tests.
|
Results |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionReferences |
|---|
|
We collected 144 temporal profiles of calcium spikes from nine images from five animals, recorded with OG-5N in response to voltage stimuli such as shown in Fig. 1A. Their time courses were fitted first with the sequential model (eqn (1)) – a function containing the sequence of two exponentials – that has been previously used by Lacampagne et al. (1999) to describe the time course of calcium sparks in skeletal muscle. Approximation of a typical calcium spike by the sequential model is shown in Fig. 1E (green line). From the visual comparison of the data with the theoretical curve the fit seems to be adequate. However, it is not clear whether the discontinuous rate of fluorescence change at the start of calcium release and at the time of the peak, predicted by the model, is genuine. Therefore, the quality of the fit of the function to the data was tested by averaging the residuals of fits to data records, aligned with respect to either the latency (t0) or the time to peak (tmax), parameters that were obtained from the fits of individual records, as in Lacampagne et al. (1999). It can be seen (Fig. 2A and B) that if the records were aligned with respect to latency, the residuals did not show any systematic deviation. On the other hand, if the records were aligned with respect to the time to peak, a clear artefact emerged at t
=
tmax. Because alignment of the sequential model with respect to the time to peak produced a systematic deviation of the residuals from zero, it appears that the rate of change of the calcium signal at the time when calcium release flux starts to decrease is not discontinuous as defined by eqn (1). Additionally, despite good convergence and adequate fit, the sequential model provided values of the parameters FM and A that were not distributed normally. About 10% of analysed spikes showed unrealistically high values (up to 106 times the median value) of FM and A (not shown; see Table 2 for parameter statistics). The dependency between the maximum of fluorescence (FM) and the activation time constant (A) is depicted in Fig. 3A. There was a strong positive correlation between these two parameters. Systematic errors in residuals as well as the unrealistic parameter estimates suggest that the sequence of two exponentials is not usable for description of calcium spikes. Moreover, fitting of the calcium spikes by a product of two exponentials did not satisfactorily describe the data either (not shown), similarly to the findings reported by Lacampagne et al. (1999) for calcium sparks.
|
|
|
A that were all within 0.3–3 x the median value (Fig. 3A and Table 2). The average characteristics of calcium spikes for the above data sets are presented in Table 2. Although the visual appearance of fits by the coupled model and those by the sequential model was similar, all parameters of the coupled model were substantially different from the respective parameters determined by the sequential model (Table 2). Properties of calcium spikes measured with OG-5N
The observed amplitudes of spikes reflect the intensity of fluorescence at the source of release flux (i.e. full event amplitude) as well as the distance of the source from the confocal plane (Izu et al. 1998; Cheng et al. 1999; Rios et al. 2001). However, events far away from the confocal plane cannot be identified because of their low amplitude. Fitting the low-amplitude part of the histogram (a < 0.9) with eqn (11) provided parameters of the visibility function, K = 0.55 ± 0.01 and n = 15.0 ± 3.0. The value of the parameter K was approximately equal to two times the standard deviation of noise (dotted line in Fig. 3C). The large steepness of the visibility function (Fig. 3C, solid line, right axis) indicates that all events with a > 0.7 were recorded, while the probability of recording events with a < 0.4 was extremely small. The distribution of full amplitudes (Fig. 3D) was obtained using the method of Rios et al. (2001) from the high-amplitude bins of the amplitude histogram (a > 0.7), which were not distorted by imperfect visibility of low-amplitude events. The distribution could be fitted by a Gaussian function with mean of 0.97 ± 0.01 and standard deviation of 0.10 ± 0.01.
Next, we have explored the relationships between the kinetic and amplitude parameters of calcium spikes. The strong positive correlation between the time constant of activation and the time to peak (Fig. 4A) and the weak negative correlation between the time constant of termination and the time to peak (Fig. 4B) suggest that the time to peak is controlled predominantly by the activation kinetics of calcium release. The time to peak and the time constant of activation were both negatively correlated to the spike amplitude (Fig. 4C and D). While the latter correlation was the weaker of the two, it was still statistically highly significant. We have found no correlation between the amplitude of calcium spikes and their time constant of termination (Fig. 4E).
|
To clarify whether calcium signals recorded with fluo indicators in the presence of EGTA represent calcium spikes, i.e. whether they are a measure of calcium release flux, we have compared the time course of calcium signals obtained with the OG-5N protocol (Song et al. 1998), characterized in the previous section, and those obtained with the fluo-3 protocol (Inoue & Bridge, 2005). All recorded signals could be well approximated by the function given in eqn (9). The average parameters at two concentrations of the indicator (60 and 100 µM) for data recorded with the indicators fluo-3 and fluo-4 are given in Table 2. The time courses of the averaged signals, aligned with respect to their latencies, recorded with 1 mM OG-5N or with 60 or 100 µM fluo-3 are compared after normalization in Fig. 5. It can be seen that the rising phase of the signals measured with fluo-3 is somewhat slower than that of calcium spikes measured with OG-5N. The time constant of activation was larger for fluo-3 and fluo-4 than for OG-5N and significantly larger for fluo-4 than for fluo-3 (Table 2). It suggests that the time course of the rising phase of the spike is distorted by the kinetics of calcium binding to fluo indicators. The difference in the rate of the declining phase of the OG-5N and fluo signals was even higher. The time constant of release flux termination was substantially and significantly longer in both fluo indicators under all tested conditions, and the prolongation increased with increasing concentration of the indicator (Table 2). The larger value of T also affected the time to peak, which was significantly prolonged. The higher values of T suggest that both fluo-3 and fluo-4 distort the decaying phase of the spike. Therefore, these indicators are not suitable for determination of the kinetic properties of calcium release flux.
|
Time course of calcium sparks
To compare the time course of calcium sparks with that of calcium spikes, both measured with fluo-3, we collected calcium sparks in cells held at –40 mV. Typical line-scan images of calcium sparks, recorded using solutions identical to those used for collecting calcium spikes, but in the absence of EGTA, are shown in Fig. 6A. The corresponding fluorescence profiles are presented in Fig. 6B. It is apparent that the spatial spread of fluorescence increase is much larger in the absence than in the presence of EGTA (compare to Fig. 1C), thus many of the observed calcium sparks should be out of focus. Therefore, we have selected the largest sparks for analysis to maximize the fraction of in-focus sparks in the dataset. The results of fitting the fluorescence profiles with the sequential and the coupled model are given in Table 3. Interestingly, both models provided comparable approximations of the fluorescence time course. Neither the kinetic parameters of the fit (A, T) nor the derived parameters – amplitude, time to peak and FDHM – differed significantly between models. In contrast to the signals obtained in the presence of EGTA, calcium sparks could be fitted reliably by the sequential model, and the estimated parameters FM and A attained realistic values (Fig. 3B). The rising as well as falling phases of the fluorescence signals were remarkably slower in the absence of EGTA, and the parameters A and T, extracted from the models, were larger by 50% and 250%, respectively, for calcium sparks than for calcium spikes measured with fluo-3 (cf. Table 2 and Table 3). The increased values of the parameters A and T of calcium sparks with respect to those determined for calcium spikes indicate that the fluorescent signal of calcium sparks contains components other than those proportional to calcium release flux and its time integral, since the time course of calcium release flux is not supposed to be altered by the absence of EGTA (Rios & Brum, 2002). Therefore, in the case of calcium sparks, the parameters A and T of the coupled model do not represent correct estimates of calcium release flux.
|
|
To clarify the extent to which the fluorescence signal reflects the time course of calcium release flux, we simulated fluorescent signals using three models of calcium release flux: (a) instantaneous activation followed after 10 ms of constant flux by instantaneous termination (rectangular time course); (b) instantaneous activation followed by monoexponential termination (exponential time course); and (c) activation and termination according to the coupled model of release flux. The release fluxes and the simulated fluorescence signals in response to these release fluxes are presented in Fig. 7A. In the case of OG-5N the theoretical time courses of release fluxes are reproduced almost exactly, because under these conditions the fluorescence signal decreases very steeply with the distance from the release site (Fig. 7B). The largest distortion can be observed for the model of release flux that activates and terminates instantaneously. In this case, only 50% of the fluorescence change can be considered ‘instantaneous’ at experimentally achievable temporal resolution. The model of instantaneous release activation followed by its exponential termination displayed much less distortion, but the observed decay of the simulated optical signal was perceptibly slower than the decay of the release flux. The best correspondence between the release flux and the optical signal was achieved for the coupled model.
|
The goodness of description of the simulated calcium signals by the two kinetic models is analysed in the Supplemental data. The coupled model provided excellent description of the time course of calcium spikes, if the time course of release flux was governed by the coupled model but not if the release flux was a rectangular pulse. In the latter case, the sequential model was superior to the coupled model. For the description of the time course of calcium sparks, the sequential model was superior to the coupled model, independent of the actual time course of release flux.
|
Discussion |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionReferences |
|---|
In this work, we have for the first time described the time course of a calcium spike, using a model based on a RyR gating model (Zahradníková et al. 1999). For successful description of calcium spikes and to obtain reliable parameters of calcium release flux, it was necessary that calcium release flux had the following properties: (a) activation proceeds with higher-order kinetics; and (b) termination is not temporally separated from activation, but is consequent to activation. In other words (a) models, in which activation was a first-order exponential process, provided unrealistic parameter values characterizing the time constant of activation and the maximum fluorescence increase, and (b) models, in which release termination was a single exponential process independent of activation, either starting concurrently with activation, or after a constant delay, showed a systematic deviation from the observed time course of fluorescence.
The full amplitude of calcium spikes had a Gaussian distribution, indicating that individual calcium release events differed in their peak calcium release flux. We have observed a negative correlation between the observed amplitude and the activation time constant of calcium spikes, confirming the assumption on calcium dependence of activation, and suggesting that individual couplons may differ in the number of activated RyR channels (due to differences in the number of channels in the cluster and/or in the ability of RyR to activate), or in the single-channel amplitudes of their calcium current (e.g. due to the regional differences in luminal calcium concentration). How is it possible that the kinetics of release flux activation can be described by a kinetic scheme derived for constant calcium concentration, when increasing number of RyRs should increase calcium in the dyadic space explosively? In the absence of specific experiments we can only hypothesize, in line with out recent theoretical estimates (Valent et al. 2006), that calcium concentration in the dyadic space rapidly attains constant values, and calcium release flux is then dominated by the activation kinetics of RyRs and the ability of calcium to leave into the cytosol. If this assumption holds, the most probable reasons for the variation of the activation time constant with the amplitude of release flux could be in regional differences in luminal calcium and in differences in the perimeter/area ratio of individual release sites.
The coupled model implies that the cluster of ryanodine receptors that is activated during a calcium spike has an inherent tendency for termination of its activity. We have observed no correlation between the amplitude of calcium spikes and their time constant of termination. An absence of correlation between these two parameters of calcium release flux was also observed in the reconstructions of calcium release fluxes by Soeller & Cannell (2002). If OG-5N tracks the time course of calcium release flux faithfully, as shown by Song et al. (1998) and by the presented simulations (Fig. 7), then this finding suggests that the rate of calcium release termination is independent of calcium release flux. In that case, luminal regulation of calcium release flux, either at the level of single-channel calcium current, or at the level of channel gating, should not contribute substantially to calcium release termination. Furthermore, larger calcium release flux – whether due to an increased number of ryanodine receptors in the cluster, their higher open probability, or higher single-channel calcium current – should be associated with increased calcium concentration in the dyadic space. The absence of correlation between the amplitude and the termination rate of calcium spikes indicates that calcium-dependent inactivation is not a major determinant of release termination, leaving activation-dependent (fateful) inactivation (Zahradníková & Zahradník, 1996; Stern et al. 1999) as a possible mechanism. These conclusions are subject to the caveat that the time constant of termination might be artificially prolonged by unbinding of calcium from the OG-5N dye; this we consider unlikely, as unbinding of calcium from this indicator (DiGregorio et al. 1999) as well as from two other closely related indicators, Calcium Orange-5N and Rhod-5N (Escobar et al. 1997; Zahradníková et al. 2003) occurs at a submillisecond time scale.
These data complement and extend the observations of Soeller & Cannell (2002), which were based on reconstruction of calcium release flux from a limited number of averaged calcium sparks. The time constant of activation and the time to peak were slightly slower in our experiments, while the time constant of termination was similar to that observed by Soeller & Cannell (2002). On the other hand, our data are in contrast to those of Lukyanenko et al. (1998), who observed an increase in the rate of calcium release termination with increased calcium release flux amplitude. At present we do not know the reason for this discrepancy. While in the work of Soeller and Cannell and in our study the overall calcium load of the myocytes was constant, Lukyanenko et al. (1998) varied the amplitude of calcium release fluxes in cells by varying their calcium load. If this were the reason for the differences in their observed release flux duration, it would suggest that in our experiments the regional differences in calcium load did not account for the differences in the amplitude of calcium spikes, meaning that calcium load at different loci is mostly homogeneous. These findings call for further investigation of the kinetics of calcium spikes under different conditions.
Accuracy of the time course of release flux reported by OG-5N
Calcium released via the ryanodine receptors, before entering the cytosol, has to diffuse across the dyadic space, a narrow gap between the membranes of the t-tubule and of the sarcoplasmic reticulum. Moreover, it can be detected only after having bound to the indicator. Do these processes, preceding detection, alter the observed kinetics of fluorescence change? We have recently shown (Valent et al. 2006) that upon instantaneous opening of a cluster of RyRs, the calcium concentration in the dyadic space reaches hundreds of micromolar within 100 µs. Due to the minute volume of the dyadic space, the fraction of released calcium that binds to dyadic buffers is small. Therefore calcium flux out of the dyadic space into the cytosol closely follows calcium release flux, with a delay that is undetectable with available technologies. Simulations of the response of OG-5N to instantaneous activation of calcium release from a source of size comparable to the couplon have shown that this fast indicator tracks the kinetics of release flux quite faithfully (Fig. 7A). Under the conditions of the experiment, binding of calcium to OG-5N is limited to a small volume of cytosol in the immediate vicinity of the release site (Fig. 7B). Therefore the distortions induced by blurring of the fluorescence signal with the point spread function of the imaging apparatus are only minor, and they do not appreciably change the kinetics of the optical response. The simulated time course of fluorescence was not appreciably changed even if the kinetics or the diffusion of OG-5N were slowed down by one order of magnitude (data not shown). Altogether our results and simulations indicate that the coupled model provides a reliable description of the time course of calcium release flux in calcium spikes recorded with OG-5N in the presence of EGTA.
Kinetic limitations of the dyes affect monitoring of calcium spikes
Comparison of the signals recorded with the fast indicator OG-5N and with the higher-affinity, but slower indicators fluo-3 and fluo-4 has shown that the time courses of their termination are significantly slower than that of OG-5N, pointing to the slower kinetics of these dyes. The value of T in fluo indicators was within the range reported previously for the decay time constant of calcium release flux derived from the time course of calcium sparks (Lukyanenko et al. 1998). Moreover, the duration of calcium signals measured with these indicators was still much shorter than the duration of calcium sparks (25–40 ms, Cheng et al. 1993; Cannell et al. 1995; Lopez-Lopez et al. 1995; Lukyanenko et al. 1998; Soeller & Cannell, 2002). Therefore we suppose that this prolongation was caused by the slower unbinding of calcium from fluo-3 and fluo-4 (while unbinding of calcium did not alter the measured time course substantially with OG-5N, which is a very fast indicator). These findings are supported by our simulations of calcium spikes under the conditions used for the experiment. The simulations showed, however, that abrupt changes in fluorescence, caused by instantaneous activation and/or termination of release flux, should be detectable with fluo-3 if the signal-to-noise ratio was sufficiently high. We conclude that the signals detected by fluo-3 and fluo-4 in the presence of EGTA do not correspond exactly to the time course of calcium release flux, most likely due to the contribution of binding/unbinding reactions between calcium and fluo indicators (Escobar et al. 1997) to the time course of the fluorescence signal. Therefore fluo indicators are not suitable for estimations of the kinetics of calcium release flux during calcium spikes. On the other hand, OG-5N and fluo indicators provided latencies that were undistinguishable, and therefore fluo indicators may be safely used for detection of calcium spikes and for determination of their latency by the coupled model.
Comparison of calcium spikes and calcium sparks
The time course of calcium spikes is dominated by the time course of calcium release flux with only a minor component (<5%) of the integral of calcium release flux, while the time course of calcium sparks is dominated by the integral of calcium release flux and by diffusion of Ca2+ ions away from the source. As a result, the time course of both, the rising phase and the decaying phase of the calcium spark is slower than that of the calcium spike. Simulations have shown that the prominent differences between the time courses of these two local calcium release signals arise due to the differences in the apparent diffusion distance (longer in the absence of EGTA) and rate of removal of Ca2+ ions (slower in the absence of EGTA), and can be reproduced if the kinetics of release flux are identical under both conditions. Because of the contribution of the diffusion of the Ca2+:dye complex to the time course of the optical signal, the basic assumptions of the coupled model do not hold in the absence of EGTA, and this model provides only phenomenological description of calcium sparks with parameters not directly related to the kinetics of release flux during calcium sparks. Although the coupled model and the sequential model approximate the time course of experimental calcium sparks with similar quality, the simulations suggest that the sequential model (Lacampagne et al. 1999) is more suitable for phenomenological description of calcium spark kinetics.
It would be quite convenient if the temporal characteristics of calcium sparks and calcium spikes could be meaningfully compared without the distortion introduced into the signal by the processes of calcium diffusion and binding. We suggest that the duration of release flux could serve as such a temporal characteristic. For calcium sparks, time to peak (tmax) has been widely used as a measure of release duration (see, e.g. Rios et al. 2001), and our simulations show that it is indeed equal to release duration if the time course of calcium release flux is rectangular. If release flux does not terminate abruptly, its decrease to 50% of maximum may be considered to mark the end-point of release duration, and therefore release duration in terms of calcium spike parameters may be characterized as RD = t50 + FDHM (where t50 is the time to 50% amplitude). Therefore we have compared the values of RD of calcium spikes with the values of tmax of calcium sparks in our experimental data as well as in the three simulations with different shapes of release flux. We obtained comparable values (RD = 13.9 ± 0.3; tmax = 14.8 ± 0.7 ms, respectively; not significantly different) for these two parameters of experimental calcium signals. The corresponding values of RD and tmax for simulated signals were also close to each other (10.3 and 10.0 ms for rectangular time course of release flux; 6.0 and 7.4 ms for exponentially decaying release flux, and 12.9 and 12.8 ms for release flux governed by the coupled model). Altogether these comparisons suggest that the rise time of calcium sparks is a good characteristic of release flux duration, no matter what the underlying release flux time course.
Implications of the kinetics of calcium spikes
Despite intense efforts, the time course of calcium release flux during local calcium release events in cardiac as well as in skeletal muscle remains poorly understood. The large number of assumptions necessary for determination of the release flux from the optical signals of fluorescent calcium indicators (see Rios & Brum, 2002 for review) lead to wide variations of estimates of the duration, amplitude, and time course of fluxes. Specifically, release flux was assumed or estimated to commence and terminate abruptly (Blatter et al. 1997; Izu et al. 1998; Smith et al. 1998; Wang et al. 2004), or to have a more-or-less abrupt start followed by exponential kinetics of termination (Lukyanenko et al. 1998, 2000). In this regard, analysis of our data shows that in cardiac muscle, neither activation nor termination of calcium release flux is abrupt, i.e. the opening and closure of RyR channels in the couplon does not appear to be fully coupled. However, our findings do not rule out cooperativity in activation of RyRs in the couplon, which might for instance transpire as a decrease in the time constant of activation with increased numbers of interacting RyRs. Similarly, although the time constant of release termination in our model is a property of each RyR, it may be speeded up by interaction of RyRs. These conclusions cannot be directly extended to skeletal muscle, as there the structure of the couplon and the mechanism of RyR activation are different (Rios & Stern, 1997). It is often assumed that local calcium release events in skeletal muscle result from concerted, almost synchronous opening and closure of RyR channels (see Rios & Brum, 2002 for review). Our results show that studying calcium spikes in skeletal muscle has the potential to verify this assumption.
The picture that emerges from this study suggests that the gradual character of recruitment and termination of RyR activity might constitute a basis for regulatory mechanisms controlling the efficiency of excitation–contraction in cardiac couplons under physiological conditions. The mechanisms compromised due to RyR dysfunction in cardiac disease may now be identified and quantified.
|
References |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionReferences |
|---|
Cannell MB, Cheng H & Lederer WJ (1994). Spatial non-uniformities in [Ca2+]i during excitation–contraction coupling in cardiac myocytes. Biophys J 67, 1942–1956.
Cannell MB, Cheng H & Lederer WJ (1995). The control of calcium release in heart muscle. Science 268, 1045–1049.
Cheng H, Lederer WJ & Cannell MB (1993). Calcium sparks: elementary events underlying excitation–contraction coupling in heart muscle. Science 262, 740–744.
Cheng H, Song LS, Shirokova N, Gonzalez A, Lakatta EG, Rios E & Stern MD (1999). Amplitude distribution of calcium sparks in confocal images: theory and studies with an automatic detection method. Biophys J 76, 606–617.
Cleemann L, Wang W & Morad M (1998). Two-dimensional confocal images of organization, density, and gating of focal Ca2+ release sites in rat cardiac myocytes. Proc Natl Acad Sci U S A 95, 10984–10989.
Colquhoun D & Hawkes AG (1983). The principles of the stochastic interpretation of ion-channel mechanisms. In: Single-Channel Recording, Sakmann B & Neher E (ed.) pp. 135–175. Plenum, New York.
DiGregorio DA, Peskoff A & Vergara JL (1999). Characterization of the calcium release domains during excitation-contraction coupling in skeletal muscle fibers. Pflugers Arch 443, 508–519.[CrossRef]
Escobar AL, Velez P, Kim AM, Cifuentes F, Fill M & Vergara JL (1997). Kinetic properties of DM-nitrophen and calcium indicators: rapid transient response to flash photolysis. Pflugers Arch 434, 615–631.[CrossRef][Medline]
Inoue M & Bridge JH (2003). Ca2+ sparks in rabbit ventricular myocytes evoked by action potentials: involvement of clusters of L-type Ca2+ channels. Circ Res 92, 532–538.
Inoue M & Bridge JH (2005). Variability in couplon size in rabbit ventricular myocytes. Biophys J 89, 3102–3110.
Izu LT, Wier WG & Balke CW (1998). Theoretical analysis of the Ca2+ spark amplitude distribution. Biophys J 75, 1144–1162.
Lacampagne A, Ward CW, Klein MG & Schneider MF (1999). Time course of individual Ca2+ sparks in frog skeletal muscle recorded at high time resolution. J Gen Physiol 113, 187–198.
Lopez-Lopez JR, Shacklock PS, Balke CW & Wier WG (1995). Local calcium transients triggered by single L-type calcium channel currents in cardiac cells. Science 268, 1042–1045.
Lukyanenko V, Györke I, Subramanian S, Smirnov A, Wiesner TF & Györke S (2000). Inhibition of Ca2+ sparks by ruthenium red in permeabilized rat ventricular myocytes. Biophys J 79, 1273–1284.
Lukyanenko V, Wiesner TF & Györke S (1998). Termination of Ca2+ release during Ca2+ sparks in rat ventricular myocytes. J Physiol 507, 667–677.
Matveev V, Zucker RS & Sherman A (2004). Facilitation through buffer saturation: constraints on endogenous buffering properties. Biophys J 86, 2691–2709.
Nagerl UV, Novo D, Mody I & Vergara JL (2000). Binding kinetics of calbindin-D(28k) determined by flash photolysis of caged Ca2+. Biophys J 79, 3009–3018.
Rios E & Brum G (2002). Ca2+ release flux underlying Ca2+ transients and Ca2+ sparks in skeletal muscle. Front Biosci 7, d1195–d1211.[Medline]
Rios E, Shirokova N, Kirsch WG, Pizarro G, Stern MD, Cheng H & Gonzalez A (2001). A preferred amplitude of calcium sparks in skeletal muscle. Biophys J 80, 169–183.
Rios E & Stern MD (1997). Calcium in close quarters: microdomain feedback in excitation–contraction coupling and other cell biological phenomena. Annu Rev Biophys Biomol Struct 26, 47–82.[CrossRef][Medline]
Sham JS, Song LS, Chen Y, Deng LH, Stern MD, Lakatta EG & Cheng H (1998). Termination of Ca2+ release by a local inactivation of ryanodine receptors in cardiac myocytes. Proc Natl Acad Sci U S A 95, 15096–15101.
Smith GD, Keizer JE, Stern MD, Lederer WJ, Cheng H (1998). A simple numerical model of calcium spark formation and detection in cardiac myocytes. Biophys J 75, 15–32.
Soeller C & Cannell MB (2002). Estimation of the sarcoplasmic reticulum Ca2+ release flux underlying Ca2+ sparks. Biophys J 82, 2396–2414.
Song LS, Sham JS, Stern MD, Lakatta EG & Cheng H (1998). Direct measurement of SR release flux by tracking ‘Ca2+ spikes’ in rat cardiac myocytes. J Physiol 512, 677–691.
Stern MD, Song LS, Cheng H, Sham JS, Yang HT, Boheler KR & Rios E (1999). Local control models of cardiac excitation-contraction coupling. A possible role for allosteric interactions between ryanodine receptors. J Gen Physiol 113, 469–489.
Valent I, Zahradníková A, Pavelková J & Zahradník I (2007). Spatial and temporal Ca2+, Mg2+, and ATP2– dynamics in cardiac dyads during calcium release. Biochim Biophys Acta 1768, 155–166.[Medline]
Wang SQ, Stern MD, Rios E & Cheng H (2004). The quantal nature of Ca2+ sparks and in situ operation of the ryanodine receptor array in cardiac cells. Proc Natl Acad Sci U S A 101, 3979–3984.
Zahradník I & Palade P (1993). Multiple effects of caffeine on calcium current in rat ventricular myocytes. Pflugers Arch 424, 129–136.[CrossRef][Medline]
Zahradníková A, Dura M, Györke I, Escobar AL, Zahradník I & Györke S (2003). Regulation of dynamic behavior of cardiac ryanodine receptor by Mg2+ under simulated physiological conditions. Am J Physiol Cell Physiol 285, C1059–C1070.
Zahradníková A, Kubalová Z, Pavelková J, Györke S & Zahradník I (2004). Activation of calcium release assessed by calcium release-induced inactivation of calcium current in rat cardiac myocytes. Am J Physiol Cell Physiol 286, C330–C341.
Zahradníková A & Zahradník I (1996). A minimal gating model for the cardiac calcium release channel. Biophys J 71, 2996–3012.
; grey line) according to the coupled model. The time course of calcium release flux (PJ
=
PA
x
PT) and the integral of the fraction of calcium release flux that contributes to the fluorescence signal (PInt) are shown as solid and dashed green lines, respectively. Normalized theoretical fluorescence signal (PJ
+
PInt) is shown as a red line.
, line shows the correlation with R
= 0.94, P < 0.0001) and the coupled model (
). B, the relationship between the spark amplitude (FM) and activation time constant (
