Calcium spike variability in cardiac myocytes results from activation of small cohorts of ryanodine receptor 2 channels

Abstract

In mammalian cardiac myocytes, the elementary calcium releases triggered by step voltage stimuli manifest either as solitary or as twin spikes that vary widely in kinetics and amplitude for unknown reasons. Here we examined the variability of calcium spikes measured using line-scanning confocal microscopy in patch-clamped rat ventricular myocytes. Amplitude distributions of the single and of the first of twin spikes were broader than those of the second spikes. All could be best approximated by a sum of a few elementary Gaussian probability distribution functions. The latency distributions of the single and the first spikes were identical, much shorter and less variable than those of the second spikes. The multimodal distribution of spike amplitudes and the probability of occurrence of twin spikes were stochastically congruent with activation of only a few of the many RyR2 channels present in the release site cluster. The occurrence of twin release events was rare due to refractoriness of release, induced with a probability proportional to the number of RyR2s activated in the primary release event. We conclude that the variability of the elementary calcium release events supports a calcium signalling mechanism that arises from stochastics of RyR2 gating and from inactivation of local origin.

Key points

• Cardiac myocytes contract due to the upsurge in intracellular calcium concentration resulting from the activation of ryanodine receptor (RyR) channels residing at calcium releasing sites.

• Calcium release can be observed as local calcium spikes that vary in amplitude, time course and frequency of occurrence due to reasons that are not well understood.

• In this study we quantify the characteristics of calcium spikes in isolated myocytes, typify them by stochastic analysis and interpret them by mathematical modelling.

• We show that the observable properties of calcium spikes are compatible with gating properties, calcium/magnesium sensitivity and distribution of RyR channels, if only a few out of the many RyRs clustered at the release sites activate at a single release event.

• The proposed mechanism of stimulated calcium release clarifies the concepts of the structure and function of calcium releasing sites and of plasticity and dynamics of calcium signalling in cardiac development and disease.

Introduction

Recent progress in cardiac Ca²⁺ signalling gravitates to molecular mechanisms of stochastic nature that are difficult to reconcile with the extraordinary stability of cardiac excitation–contraction coupling. At the subcellular level, calcium signalling operates at contact sites of sarcolemmal t-tubules and terminal cisternae of the sarcoplasmic reticulum, known as dyads, couplons, calcium release sites or calcium release units (Sun et al. 1995; Franzini-Armstrong et al. 1999; Stern et al. 1999). At the molecular level, these sites consist of small groups of voltage-dependent dihydropyridine receptor (DHPR) calcium channels and of clusters of densely packed RyR2 calcium-releasing channels (Franzini-Armstrong et al. 1999; Baddeley et al. 2009; Hayashi et al. 2009; Scriven et al. 2010), communicating with each other by calcium ions across the narrow gap of the tubulo-reticular junction. The released calcium ions diffuse to the surrounding cytosol and give rise to local calcium signals observed by confocal microscopy as calcium sparks (Cheng et al. 1993) or as calcium spikes (Song et al. 1998). It was shown that these calcium signals activate independently from each other (Cheng et al. 1993; Cannell et al. 1994). The activation mechanism of calcium release is better understood than the mechanism of its termination, but debates still continue regarding the details of molecular mechanisms (Prosser et al. 2010; Xie et al. 2010; Zahradnikova et al. 2010a).

It has been shown that calcium sparks generated by the peripheral dyads, localized at the outer surface of the sarcolemma, have quantal character due to activation of a small number of RyR2s (Wang et al. 2004); more specifically, of about 1–7 RyR2s (Wang et al. 2001, 2004) out of the 25–150 RyR2s constituting an average surface dyad (Franzini-Armstrong et al. 1999; Baddeley et al. 2009). Peripheral release sites (Baddeley et al. 2009) have less complex morphology and smaller size than intracellular sites (Hayashi et al. 2009), which are composed of 40–270 RyR2s (Franzini-Armstrong et al. 1999; Chen-Izu et al. 2006; Soeller et al. 2007; Hayashi et al. 2009). Nevertheless, the observed small number of quantal levels (Wang et al. 2004) was unexpected, since it was in apparent contradiction with the calcium sensitivity of RyR2s in vitro (Gyorke & Gyorke, 1998; Xu & Meissner, 1998; Zahradnikova et al. 2003) as well as in situ (Cannell et al. 1994; Lukyanenko & Gyorke, 1999), considering that free calcium concentration in the dyadic gap was estimated to reach hundreds of micromoles during calcium release (Cannell & Soeller, 1997; Valent et al. 2007).

Recently, however, it was shown that magnesium ions bind to the activation site of RyR2 with a K_D of about ∼100 μm (Zahradnikova et al. 2003, 2010b; Gusev & Niggli, 2008; Tencerova et al. 2012) that provides about 97% occupancy of RyR2 activation sites at a physiological Mg²⁺ concentration in the cytosol. Unbinding of Mg²⁺ from RyR2 was shown to proceed rather slowly and was proposed to limit recruitment of RyR2s during the typical 10–15 ms lasting calcium release flux (Zahradnikova et al. 2003, 2010b). Another RyR2 inhibitory Mg²⁺ binding site (Meissner & Henderson, 1987; Laver et al. 1997; Zahradnikova et al. 2003), although of lower affinity, contributes to lower RyR2 availability as well.

If the recruitment of RyR2s during calcium release is low, it should drive the stochastics of the variability of local calcium release events (Bridge et al. 1999). Therefore, the objective of this work was to characterize the variability of elementary calcium release events and relate it to activation of RyR2s. To this end, we collected a large set of calcium spikes evoked by identical stimuli and analysed the distributions of their parameters on stochastic grounds. We show that the calcium spikes are composed of a low number of elementary quanta and that each calcium spike may induce a refractoriness of its release site. The small range of quantum size variance across release sites and the stochastics of recruitment of elementary release quanta suggest that they reflect openings of individual RyR2 channels.

Methods

Whole-cell patch-clamp and laser scanning confocal microscopy were employed simultaneously and synchronously on isolated left ventricular myocytes. Room temperature was held at 23°C.

Ethical approval

The study conforms to the ethical standards set by The Journal of Physiology (Drummond, 2009). The housing and treatment of animals complied with the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health (USA). All anaesthetic and surgical procedures were approved by the State Veterinary and Food Administration of the Slovak Republic and by the Ethical committee of the Institute of Molecular Physiology and Genetics, Slovak Academy of Sciences.

Cell isolation

Cardiac myocytes were isolated from the left ventricle of young adult (12 weeks old) male Wistar rats (n = 18, 200–240 g, Dobra Voda, Slovakia) as previously described (Zahradnik & Palade, 1993). In brief, heparinized rats (5000 U kg⁻¹ i.p.) were deeply anaesthetized with sodium pentobarbital (100 mg kg⁻¹ i.p.). Killing of the rats was performed under full anaesthesia, the heart was rapidly excised, mounted by the aorta on a Langendorff apparatus and retrogradely perfused with Tyrode solution (in 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 a collagenase-containing solution (in mm: 135 NaCl, 5.4 KCl, 5.0 MgCl₂, 0.02 CaCl₂, 0.33 NaH₂PO₄, 10 Hepes, 0.1–0.2 mg ml⁻¹ collagenase, 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 triturated in 4 ml of the stopping medium (in mm: 106 CH₃SO₃H, 106 KOH, 3.9 KCl, 2.4 MgSO₄, 8 K₂HPO₄, 1 EGTA, 22 taurine, 22 glucose, pH 7.3). The myocyte suspension was filtered through a nylon mesh, washed twice with the stopping medium and stored in cell culture dishes at room temperature for use within 1–6 h of isolation.

Chemicals and solutions

Collagenase was from Sevapharma, Czech Republic (Collagenasa cruda) or Roche, France (Liberase TM), tetrodotoxin (TTX) was from Alomone Labs (Jerusalem, Israel), the calcium indicator Fluo-3 was from Molecular Probes (Eugene, OR, USA), isobutylmethylxantin (IBMX), EGTA and all other chemicals were of analytical grade from Sigma-Aldrich Chemie GmbH (Taufkirchen, Germany). All solutions were adjusted to pH 7.3 and osmolality of 300 mosmol kg⁻¹.

The external bath solution contained (in mm): 135 NaCl, 5.4 CsCl, 10 Hepes, 5 MgCl₂, 0.33 NaH₂PO₄, 1 CaCl₂, 0.01 IBMX and 0.02 TTX. Patch pipettes were filled with the internal solution containing (in mm): 135 CsCH₃SO₃, 10 CsCl, 10 Hepes, 3 MgSO₄, 3 ATPNa₂, 0.05 cAMP, 1 EGTA and 100 μm Fluo-3. The myocytes were kept in a phosphorylated state by the use of ATP and cAMP in the internal solution and of the membrane-permeable phosphodiesterase inhibitor IBMX in the external solution (Zahradnik & Palade, 1993).

Electrophysiological measurements

Myocytes were whole-cell patch clamped using patch-pipettes of 1.1–1.8 MΩ and Axopatch 200B (Axon Instruments, USA) or VE-2 (Alembic Instruments, Canada) amplifiers, a Digidata 1320A A/D converter, and pCLAMP software (all from Axon Instruments, USA). Cell capacitance and series resistance were both passively and actively compensated to 50–85%. A small leak current was electronically subtracted. Cells with a large leak current were discarded. Calcium currents were elicited by single 80 ms step voltage pulses from a −50 mV holding potential to 0 mV or −35 mV and low-pass filtered at 10 kHz. Voltage stimulation and digitization of current response was synchronized with acquisition of fluorescence signal.

Laser scanning confocal microscopy

Calcium spikes were recorded using the calcium indicator Fluo-3, which provides a better signal-to-noise ratio than low-affinity indicators (Zahradnikova et al. 2007). Line-scan confocal images were recorded with a Leica TCS SP2 AOBS laser scanning confocal microscope (Leica Microsystems, Germany) in the bidirectional x–t scanning mode at a line frequency of 2 kHz after stabilization of the amplitude and kinetics of the triggering calcium current, which indicated completed equilibration of the pipette solution with the cell cytosol. The indicator was excited at 488 nm, and the emission at 493–600 nm was collected by a PlanApochromat 63×/1.32 NA oil-immersion objective and a pinhole set to 2 Airy units, providing a 980 nm thick optical section focused typically to 5 μm into the cell. The scanning line was oriented along the myocyte longitudinal axis. The scanning speed required the use of a 4× zoom factor. The resulting images had a resolution of 116 nm per pixel along the scanning line and of 0.5 ms per pixel between the scanning lines. No filtering was applied to the recorded line scan images.

Only cell sites that provided well-localized calcium spikes were used for analysis. Temporal profiles of fluorescence intensity at individual release sites were obtained by averaging 7-pixel wide bands (0.8 μm) centred at the release sites using Scion Image software (Scion Corporation, USA).

Data analysis and curve fitting

Statistical analysis and data fitting were performed with Origin Pro (version 7.5 and 8, OriginLab Corporation, USA) and Mathematica (version 8, Wolfram Research, USA). The statistical significance of differences was tested with Kruskal–Wallis ANOVA. Means are given with the SEM, if not indicated otherwise.

Parameters of calcium spikes

The parameters of single calcium spikes were determined by fitting their time course with the theoretical function (Zahradnikova et al. 2007)

(1)

where F_Spike is the theoretical time course of the spike, t is the time elapsed from the start of the voltage stimulus, t₀ is the latency of the calcium spike. F_M is the maximal normalized fluorescence increase in the absence of release termination, α is a proportionality factor, and τ_A and τ_T are the time constants of spike activation and termination, respectively.

When two release events were detectable in the same fluorescence profile, we used eqn (2) obtained as a simple sum of two theoretical functions:

(2)

where the parameters corresponding to the first and the second spike are denoted by the indexes 1 and 2, respectively. The best fit with the compound eqn (2) was accepted only if it provided a better goodness of fit than the fit with eqn (1).

We have observed and analysed four characteristic parameters of calcium spikes – amplitude, latency, time to peak and full-duration at half-maximum. Since Fluo-3, used in this study for its best signal-to-noise ratio, is not sufficiently fast (Zahradnikova et al. 2007), the fitted time constants τ_A and τ_T of spike activation and termination were not considered here to characterize calcium spikes. On the other hand, the latency that was shown to be independent of the calcium binding kinetics of the indicator (Zahradnikova et al. 2007) was used as a spike parameter. The amplitude of calcium spikes, A, estimated as the peak of the fitted trace, was used as a measure of calcium release flux (Song et al. 1998; Zahradnikova et al. 2007). The time to peak of spikes, TTP, estimated as the time of the peak amplitude relative to the latency, was used as a measure of the rate of calcium release activation. The full-duration at half-maximum, FDHM, estimated as the corresponding interval of the fitted traces, was used as a measure of calcium release duration.

Fitting of amplitude distributions

Amplitude distributions of collections of calcium spikes were fitted by a sum of scaled Gaussian probability distribution functions by the maximum likelihood method in Mathematica (version 8.0, Wolfram Research, USA), using the original (unbinned) data:

(3)

where is the log-likelihood of the model, m is the number of analysed spikes, n_Max is the maximum number of amplitudes in the tested model, A_j is the observed amplitude of the jth spike, F_i is the fraction of spikes consisting of the ith amplitude, A_i is the ith amplitude, and σ_i is the standard deviation of this amplitude. When A_i and σ_i were assumed to be independent, the number of optimized parameters in each model was n_Par = 3n_Max– 1. When quantal amplitudes were treated as integer multiples of the first amplitude, A_i = iA_q, and their standard deviation was assumed to be identical, σ_i = σ, the number of optimized parameters was n_Par = n_Max+ 1.

Model comparison was performed according to Burnham & Anderson (2002): the Akaike information criterion (AIC) of the ith model was calculated as

(4)

where all parameters and variables have been defined previously. The relative weights of the models were calculated as

(5)

where N is the number of the tested models and MinAIC is the AIC value of the best model.

Quantal content of calcium spikes

The quantal content (n_q) of individual spikes was assigned as the number i of quanta that maximized the probability of their occurrence, p_i, in a spike with the observed amplitude A:

(6)

where all parameters have been defined previously. The values of p_i were calculated for i = 〈 1, n_max〉.

The probability of occurrence of spikes of quantal content n_q in the experimental dataset, p(n_q), was determined as the fraction of these spikes in the whole dataset of single and first (primary) spikes.

The statistical distribution of calcium spikes according to their quantal content was optimized by fitting the probabilities of occurrence of spikes with different quantal content by the binomial distribution:

(7)

where p_A is the activation probability of additional quanta during spikes after activation of the first quantum and N_q is the total number of quanta per average calcium release site (the pool size). Equation (7) was fitted to the distribution of quantal content of spikes by the method of maximal likelihood. For each given N_q varied in the interval of 4–200, the fitting provided the respective optimal activation probability, p_A. To correct for differences in the degrees of freedom for various values of N_q, goodness of fit was calculated for all N_q using the method of Landau and Páez (1997) as described previously (Zahradnikova et al. 1999; Zahradnik et al. 2005). In brief, the χ² values for each N_q were calculated from the respective sum of squares and from the experimental variance, estimated using N_q and p_A that provided the lowest minimal sum of squares. This set of χ² values was tested by the χ² test (Press et al. 1992) to find the subset of N_q values that pass the significance level (P = 0.05).

Probability of second spikes

The probability of occurrence of second spikes p_2nd was expressed as the probability that despite the occurrence of a primary calcium release with quantal content n_q, refractoriness of the release site is not induced:

(8)

where p_refr is the probability that calcium release with quantal content n_q = 1 will induce refractoriness.

Simulation of the indicator response during calcium release flux

Binding of calcium to the indicator Fluo-3 during the flow of calcium release current was simulated as described previously (Zahradnikova et al. 2007) with the program CalcC (version 6.0.5, Matveev et al. 2002), assuming spherical symmetry and using parameters listed in Zahradnikova et al. (2007). The time course of calcium release current was described by the equation

(9)

corresponding to the time course of calcium release flux used for analysis of calcium spikes (Zahradnikova et al. 2007), where I_max is a scaling factor, and the values of time constants were set to τ_A = 3 ms and τ_T = 5 ms. The peak value of I_Ca with these parameters was 0.5 I_max.

Results

Primary analysis

Typical recordings of calcium spikes elicited by repeated voltage stimuli to 0 mV are shown in Fig. 1. The corresponding calcium currents and line scan images are shown in panels B and C. As illustrated, the fluorescent signals varied widely, despite the stable amplitude and time course of the triggering calcium currents. The variability occurred at each single release site in sequential records as well as between different release sites within a single record. This is more obvious from the extracted time courses of calcium spikes shown in Fig. 1D. The time course of individual spikes was fitted with the theoretical function (eqns (1) or (2)) to eliminate the problem of estimation of spike properties caused by the relatively high level of noise present in the data. The average signal-to-noise ratio (SNR) at 0 mV was 10.4 ± 0.3 and ranged from 1.3 to 33.9, with less than 1% of spikes having SNR < 2.0. All spike characteristics presented below were estimated from such noise-free fitted data traces.

Figure 1. Typical calcium currents, line scan images and calcium spikes.

Recordings from the same position were made at 15 s intervals. A, voltage stimuli to 0 mV. B, whole-cell calcium currents. C, x–t line-scan fluorescence images. The numbered arrowheads point to the positions of the release sites generating calcium spikes and their width corresponds to the width of analysed fluorescence profiles. D, fluorescence profiles of the spikes indicated in C. Red lines are the best fits of spikes by eqns (2) (single spikes) or (3) (twin spikes, asterisks). The time coordinate is identical in all panels.

The peak calcium current in response to a depolarization to 0 mV was 0.84 ± 0.06 nA. Each release site responded to this trigger current randomly either by a single spike, by a set of two spikes (twins), or it did not respond (<10% occurrence). When the stimulation was carried out periodically for several minutes or when its frequency was increased, a significant decline in spike amplitudes was observed (not shown). Therefore, to avoid eventual systematic errors due to a time-dependent variation in spike characteristics, calcium spikes were recorded in response to only a single voltage stimulus at each preselected scanning position. One to three positions per myocyte were probed after equilibration of the dye in the cytosol, typically about 8 min after breaking into the cell and establishing whole-cell configuration. Under these conditions, we have collected a set of 305 calcium spikes from 30 line scan images made in 18 myocytes of 13 hearts.

A large majority (86.6%) of calcium release events occurring during the voltage stimuli to 0 mV consisted of single calcium spikes, while 13.4% of the calcium release events consisted of two subsequent (twin) spikes (traces marked by asterisks in Fig. 1D). We did not observe three subsequent spikes in response to a single stimulus. The spikes occurring in response to membrane repolarization as well as cells showing spontaneous spike activity during recording were not included into the analysis.

An interesting insight into spike behaviour was obtained from the amplitude–latency relationship of all calcium spikes (Fig. 2). It revealed that single spikes and the first of the twin spikes (i.e. the primary spikes) occurred with similar short latencies. However, the amplitudes of the single spikes were highly variable and often large, while the amplitudes of the first spikes were significantly smaller and less variable than those of the single spikes. The second of the twin spikes had mostly small and only slightly variable amplitudes but large and highly variable latencies.

Figure 2. The estimated latencies and amplitudes of all calcium spikes recorded at voltage stimuli to 0 mV.

The single, first and second spikes are indicated in white, green and red symbols, respectively.

The amplitudes of calcium spikes that occurred as a single spike, as the first, or as the second of the twin spikes are compared in Fig. 3. The amplitudes of both the first and the second of the twin spikes were smaller than those of the single spikes, but their sum was not different from the amplitude of single spikes. These results are statistically highly significant (P < 0.001, Kruskal–Wallis ANOVA). Considering that single and twin spikes were alternately observed at the same position, and considering the high (>90%) probability of spike occurrence, it can be supposed that the first and the second spikes arise from the same release site, not from two independent unresolved nearby sites. In other words, from a statistical point of view, all calcium spike-generating release sites belong to the same group. In spite of this, the amplitude of the second spike did not correlate with the amplitude (R = 0.20, P = 0.21) or the latency of the first spike (R = 0.01, P = 0.92) as might be the case when both arise from the same source. Notably, the occurrence of second spikes increased when the amplitude of the first spike was smaller (see below).

Figure 3. Statistics of amplitudes of calcium spikes.

The same data set as in Fig. 2. Box plots show 25, 50 and 75 percentiles of amplitude distributions of the single, first and second spikes, and of the combined amplitudes of the first and the second spikes. Data points (filled circles) with similar values are laterally offset. Statistically significant differences at P = 0.05 are displayed as horizontal lines.

The statistics of latencies of spikes grouped according to their type (Fig. 4A) indicated no difference between latencies of the single and the first spikes but a substantial difference of both from latencies of the second spikes. The same relationships hold for their cumulative histograms (Fig. 4B). The intervals between the first and the second spikes displayed high variability. Their distribution (Fig. 4C) showed a maximum at around 14 ms, followed by a more slowly decaying tail at >30 ms. Twin spikes with intervals shorter than 3 ms were not observed. This can be attributed in part to the slow kinetics of Fluo-3, the excess noise and the insensitivity of the fitting routine, although we could reliably resolve even very short spike latencies. The intervals between the first and the second spikes did not correlate with the amplitude (R = 0.04, P = 0.78) or latency of the first spike (R = 0.22, P = 0.16), indicating an independent triggering process. To conclude, the distributions of intervals and latencies show that the single and the first spikes (primary spikes) have a similar probability to be evoked at the same latency interval, while the second spikes are significantly delayed and have a reduced probability of occurrence.

Figure 4. Analysis of the latencies of calcium spikes.

The same data set as in Fig. 2. A, statistics of latencies of the calcium spikes. Box plots show 25, 50 and 75 percentiles of the latency distribution of single, first and second spikes. Statistically significant differences at P = 0.05 are displayed as horizontal lines. Data points (filled circles) with similar values are laterally offset. B, the normalized cumulative latency distribution of single, first and second spikes (continuous, dashed and thin continuous lines, respectively). C, the distribution of intervals between the onsets of the first and of the second spike in twin spikes. The median is 21.0 ms, the minimum 3.3 ms and maximum 62.8 ms.

The times to peak (TTP, Fig. 5A) and durations (FDHM, Fig. 5B) of the single and the first spikes did not differ, while both TTP and FDHM of the second spikes were significantly shorter (P < 0.001, Kruskal–Wallis ANOVA). Since both TTP and FDHM are measures of RyR2 gating, their equivalence in primary spikes suggests that the properties of RyR2 channels at the time of occurrence of single and first events were not different. On the other hand, different TTP and FDHM of the second spikes point to changes in RyR2 channel behaviour at the time of occurrence of the second spikes, namely, faster activation and shorter open time duration. There was no correlation between the TTP of the second spikes and the interval of their activation after the first spike (R = 0.19, P = 0.23).

Figure 5. Kinetic properties of calcium spikes.

The same data set as in Fig. 2. A, statistics of the time to peak (TTP) of single, first and second spikes. B, statistics of the full duration at half-maximum (FDHM) of single, first and second spikes. Data points (filled circles) with similar values are laterally offset. Box plots show 25, 50 and 75 percentiles of the distributions

Secondary analysis

How can it be that the single and the first spikes differ so much in their amplitude, while they are equivalent in other respects? It turned out to be instrumental to compare their amplitude distributions (Fig. 6A). For the first spike amplitudes, 90% of the events had amplitude less than 3.5 ΔF/F₀ units, and their amplitude distribution could be described by a single Gaussian probability density function with an amplitude mode A₁ = 1.81 with a standard deviation σ₁ = 0.66. Nevertheless, 10% of the first events still had much larger amplitudes, which were not consistent with the dominant distribution (P = 0.0054). This suggests that the majority of the first spikes might, in fact, represent minimal events of calcium release and might be attributed to the elementary quantum of release as described by Wang et al. (2004). At the same time, single spikes displayed a broad amplitude distribution (Fig. 6A).

Figure 6. Amplitude distribution of the single, first and second spikes.

The same data set as in Fig. 2. A, amplitude histograms of single (open) and first spikes (black). B, amplitude histogram of all primary spikes. Filled black columns show the theoretical distribution for 4 equidistant amplitude levels (see Table 2). C, amplitude histogram of the second spikes (open). Black columns show the theoretical distribution for second spikes with a maximum of 2 open RyR2 channels (see Results).

Considering the evidence that the first and the single spikes (primary spikes) originate from the same population (see above), it may be hypothesized that the differences in their mean amplitudes are caused primarily by a random difference in the fraction of calcium spikes with different amplitude modes. Therefore, we analysed the amplitude distribution of primary spikes (Fig. 6B) by the maximum likelihood method, assuming Gaussian distribution for individual amplitude levels (Tables 1 and 2). Fitting the distribution by a sum of independent scaled Gaussian probability distribution functions (eqn (3)) provided four amplitude modes that were close to integer multiples of each other (Table 1), with widths that did not change systematically with the amplitude of the mode. Therefore, fitting was performed with additional models that assumed equidistant modes of identical widths, representing the number of elementary quanta (n_max of 2 to 5). The model with a single Gaussian mode was also included in the analysis.

Table 1.

Parameters of maximum likelihood fit of the amplitude distribution of primary spikes by four independent scaled Gaussian modes

i	Ai	Ai/ i	σi
1	1.98	1.98	0.59
2	3.84	1.92	0.65
3	5.48	1.83	0.48
4	6.88	1.72	0.80

i number of the mode; A_i, amplitude of the mode; A_i/i, amplitude per mode; σ_i, standard deviation of amplitude.

Table 2.

Comparison of maximum likelihood fits of the amplitude distribution of primary spikes by different models

Model	Aq	σq	F1	F2	F3	F4	F5	Lik	AIC	wi
Independent	n/a	n/a	0.39	0.44	0.11	0.06	N/A	−558	1141	0.028
n = 1	3.70	1.65	1	n/a	n/a	n/a	n/a	−577	1161	1.4 × 10−6
n = 2	2.66	1.08	0.62	0.38	n/a	n/a	n/a	−570	1149	0.0005
n = 3	2.28	0.86	0.46	0.46	0.08	n/a	n/a	−567	1143	0.009
n = 4	1.87	0.61	0.34	0.39	0.23	0.04	n/a	−561	1134	0.96
n = 5	1.41	0.61	0.18	0.30	0.29	0.18	0.05	−570	1154	3.8 × 10−5

n, quantal content; A_q, quantal amplitude; σ_q, standard deviation of quantal amplitude; F₁–F₅, fraction of spikes with quantal content of n; Lik, log-likelihood; AIC, Akaike information criterion; w_i, statistical weight of the model. The maximal value of Lik and w_i and the minimal value of the AIC are shown in bold.

Out of the six tested models, the model with four independent modes provided the maximum value of likelihood. However, the model with four equidistant modes provided a significantly better value of the AIC (Table 2). In the optimal fit, the amplitude of the elementary quantum was A_q = 1.87 with a standard deviation σ_q = 0.61 (Table 2, Fig. 6B, black bars).

Maximum likelihood analysis of the amplitude distribution of the second spikes was performed in analogy to that of the primary spikes. Models with 1, 2 and 3 amplitude levels had relative weights of 0.27, 0.51 and 0.08. It means that the optimal description of the amplitude distribution of the second spikes (Fig. 6C) required two Gaussian distributions with average amplitude A_q,2nd = 1.31 and a standard deviation w_2nd = 0.43. This elementary quantum amplitude of the second spikes is 70% of that of the primary spikes. The reduced elementary quantum amplitude indicates a lower calcium flux during the second spikes that could be attributed to a reduced calcium concentration gradient between the SR lumen and the cytosol.

Knowing the amplitude of the elementary quantum allowed determining the distribution of spikes according to their quantal content using eqn (6). The resulting frequency of occurrence of quantal contents for primary spikes is shown in Fig. 7A. It could be approximated by a binomial distribution (eqn (7)), assuming independent recruitment of additional quanta from their pools at calcium release sites. The N_q and p_A values yielding the lowest minimal sum of squares were 11 and 0.099, respectively. Interestingly, however, a large interval of pool sizes, N_q, provided a good description of the frequency of occurrence of spikes of certain quantal content after correction for the degrees of freedom. The goodness of fit was fulfilled for N_q≥ 47 for the estimated experimental error of 3.6% (Fig. 7C). The probability of activation of individual quanta, p_A, was inversely proportional to the pool size, but remained low for the whole range of acceptable pool sizes, specifically, 0.023 for N_q = 47 and 0.006 for N_q = 200.

Figure 7. Testing the quantal character of the single, first and second spikes recorded at voltage stimuli to 0 mV.

A, a histogram of the relative occurrence of primary spikes (white) with different quantal contents. The best fit of the data with eqn (7) (n_q = 182, p_A = 0.0060) is shown by black columns. B, the histogram of relative occurrences of second spikes with different quantal contents (white). The best fit of the data with eqn (7) (n_q = 182, p_A = 0.003) is shown as black bars. In B and C, a similar fit could be obtained for n_q = 47–200. C, the goodness of fit, expressed as χ²/df, for description of the amplitude distribution of single/first (filled symbols) and second spikes (open symbols). The lines show the value of n_q at which the fits are accepted by the χ² test at P = 0.05 (continuous and dashed for primary and second spikes, respectively). D, the fraction of primary spikes of the respective quantal content that were followed by a second spike. The best fit with eqn (8) (p_refr = 0.70) is shown by black bars.

The frequency of occurrence of quantal contents of second spikes is shown in Fig. 7B. Again, it was well approximated by a binomial distribution (eqn (7)), assuming independent recruitment of additional quanta in the whole pool of quanta. The estimated experimental error of 4.0% (Fig. 7C) provided χ² values that passed the χ² test at P = 0.05 for N_q≥ 47. The levels of probability of activation of individual quanta, p_A, were 0.012 for N_q = 47, and 0.003 for N_q = 200, the p_A values of about one-half of those estimated for the primary spikes.

The relationship between the quantal content and the fraction of twin spikes is examined in Fig. 7D. This plot clearly indicates a strong dependence between the quantal content of the primary spike and the probability of second spike activation. This relationship could be the result of a release-dependent release inactivation of the activated release site. To verify this supposition, we have tested the hypothesis that each activated quantum contributes independently to the refractoriness of the site due to an inactivation process. Under this scenario, the more quanta are activated during a release event, the higher is the probability of release-dependent release inactivation and transition of the release site to a refractory state. If the release site was not in the refractory state after the primary release, a second spike occurred at a random interval after the first spike. The probability that the site is not refractory after a spike may then be calculated using eqn (8) for each quantal contents of the primary spike. Fitting of eqn (8) to the dependence of the fraction of calcium release sites that gave rise to second spikes on the quantal content of the primary spike (Fig. 7D) provided a probability value of 0.70 ± 0.02 that a local calcium release of a single quantum will induce refractoriness. The probability that two, three or four elementary quanta induce refractoriness was 0.91 ± 0.01, 0.97 ± 0.003 and 0.99 ± 0.001, respectively. This translated to a predicted probability of occurrence of second spikes of 0.30 ± 0.02, 0.09 ± 0.01, 0.03 ± 0.003 and 0.01 ± 0.001 after spikes with quantal content of 1, 2, 3 and 4, respectively (Fig. 7D).

Calcium spikes in response to threshold stimuli

Previously it has been demonstrated that the amplitude of calcium spikes in response to threshold stimuli is smaller than that in response to maximum stimuli (Song et al. 2001). If the quantal hypothesis is relevant we should observe reasonable changes in the quantal characteristics of spikes activated by threshold voltage stimuli. For this purpose we have collected a set of 135 calcium spikes (19 cells from 5 hearts) evoked by depolarization to −35 mV that did not activate a measurable calcium current. Under these conditions, only 12.2 ± 0.9% of release sites that produced spikes at 0 mV were activated and of these, 3.0% gave rise to twin spikes. The estimated amplitudes and latencies of each observed spike are shown in Fig. 8A. When compared to primary spikes evoked by pulses to 0 mV, the mean amplitude of primary spikes at –35 mV was significantly smaller (2.42 ± 0.09 vs. 3.70 ± 0.10; P < 0.001), the mean latency was substantially longer (42.8 ± 1.7 ms vs. 5.7 ± 0.3 ms; P < 0.001), the mean time to peak was not different (8.7 ± 0.3 ms vs. 9.0 ± 0.2 ms; P = 0.27), while the mean FDHM was significantly shorter (15.5 ± 0.4 ms vs. 19.1 ± 0.3 ms; P < 0.001). The probability of observing a spike at a release site within a time interval corresponding to the time to peak reached 0.015 at 20 ms and stayed constant to the end of the voltage pulse. Due to the low frequency of occurrence and long latency of spikes at −35 mV, the number of acquired twin spikes was too small for their further analysis.

Figure 8. Properties of calcium spikes evoked by threshold stimuli.

A, the estimated latencies and amplitudes of all calcium spikes evoked by depolarisation to −35 mV. The single, first and second spikes are indicated in white, green and red symbols, respectively. B, white columns represent the amplitude distribution of the primary spikes evoked by depolarization to –35 mV. Black bars show the best theoretical amplitude distribution with 3 equidistant amplitude levels (see Results).

Analysis of the amplitude distribution of the primary spikes (Fig. 8B) by maximum likelihood (eqn (3)) using the Akaike information criterion gave relative weights of 4.3 × 10⁻⁸, 0.116 and 0.8836 to models employing 1, 2 or 3 equidistant quantal amplitudes, respectively. The models with 4 or 5 quantal amplitudes produced a fit identical to that for 3 amplitudes but with zero fractions of quantal amplitudes 4 and 5. The best fit of the amplitude distribution (eqn (3)) for n_max = 3 provided the amplitude of the elementary quantum, A_q = 1.89 and the standard deviation σ_q = 0.52 (Fig. 8B, black columns), which were not different from those of spikes at 0 mV (1.87 and 0.61, respectively). At −35 mV, the spikes consisting of a single quantum, of two quanta and of three quanta amounted to 74%, 25% and 2% of the observed spikes, respectively, providing a substantially lower mean number of activated quanta than spikes at 0 mV (1.3 vs. 2.0). This is compatible with a 3.4-fold reduction in the probability of activation of individual quanta, p_A, relative to that observed at 0 mV. In line with the quantal hypothesis, the lower amplitude of calcium spikes evoked by threshold stimuli resulted solely from a reduced number of activated quanta, and not from changes in the amplitude of a single quantum.

Discussion

In this work we addressed the problem of recruitment of RyR2 channels during calcium release in mammalian cardiomyocytes. We characterized the variability of local calcium release, specifically the variability in the occurrence, size and kinetics of calcium spikes. It turned out that all observations can be explained on the basis of the recently emerging picture of calcium releasing sites as spatially constrained clusters of DHPR and RyR2 channels (Franzini-Armstrong et al. 1999; Soeller et al. 2007; Baddeley et al. 2009; Hayashi et al. 2009; Scriven et al. 2010) functionally linked through local calcium concentration (Rios & Stern, 1997; Cannell & Kong, 2012). We show that the calcium release events observed at intracellular release sites have quantal character. This could be brought about by stochastic activation of a small number of elementary releasing units from their large pool at each release site.

A central observation for the interpretation of the release flux as consisting of independent quanta was the consistent occurrence of twin spikes in response to pulses to 0 mV. Activation of twin calcium spikes had been shown previously (Song et al. 1998, 2001); however, their origin was not studied. The differences between the first and the second spikes revealed here opened the question of their origin. Our analysis of the amplitude and latency distributions confirmed that the first spikes originate from the same pool as the single spikes and that both result from activation of elementary units of the same group type, since their temporal characteristics are indistinguishable. However, the second spikes displayed significantly different amplitude and kinetic characteristics. Still, we could conclude that they originate from the same pool of release units, because their amplitude was complementary to the amplitude of the first spikes. In addition, the probability of their occurrence was inversely related to the preceding activity at their release site due to refractoriness of the release site resulting from inactivation of local origin (eqn (8)). These arguments, together with the observations of random activation of each type of calcium spikes at the same release site (Fig. 1), confirm that we deal with a complex but consistent phenomena of common origin.

The origin of quantal release flux

The elementary units of calcium release flux could be identified with individual RyR2 channels, in line with the conclusions of Wang et al. (2004). The reasons are as follows. Local calcium release events were typically brought about by 1–4 elementary units from their average pool larger than 47 units (Fig. 7C). These units apparently share their general characteristics with single RyR2 channels and behave as expected for RyR2s. Specifically, the elementary units: (i) are localized in pools/clusters spatially separated as are the clusters of RyR2 (Cheng et al. 1993; Lopez-Lopez et al. 1994; Chen-Izu et al. 2006); (ii) are activated by calcium current (Cannell et al. 1995; Lopez-Lopez et al. 1995; Wang et al. 2001); (iii) are recruited independently of each other (Cannell et al. 1994); (iv) activate with low probability (Zahradnikova et al. 1999, 2003, 2010b); and (v) display similar lifetimes (Wang et al. 2004; Gaburjakova & Gaburjakova, 2006; Zahradnikova et al. 2007) and release flux amplitudes (see below). Taken together, it seems reasonable to conclude that the elementary units giving rise to intracellular calcium spikes are, in fact, single RyR2 channels.

The complex structure of release sites (Baddeley et al. 2009; Hayashi et al. 2009) poses the question of whether the quanta of release flux originate from a single RyR cluster or of several ones that form a single release site. As has been pointed out for the case of calcium sparks (Zahradnikova & Zahradnik, 2012), the observed binomial distribution of quantal sizes can be quantitatively explained if each quantum corresponds to opening of a single RyR from the set of RyRs assembled either in a single cluster or in several clusters forming the release site that behave as one calcium release unit; in other words, when all RyRs of the release site share the same local cytosolic and luminal environments. In this case, only activation of the first RyR depends on DHPR activation, while the quantal behaviour resulting from recruitment of the remaining RyRs depends solely on their stochastic activation (Zahradnikova et al. 2010b).

If the clusters forming the release site have their own local cytosolic and luminal space, that is, if each of them is independent, activation of calcium release in each cluster has to be triggered independently by calcium influx through DHPR openings. The observed local calcium release signal should then represent activation of several independent sub-spikes within an interval corresponding to the time to peak. This scenario is difficult to reconcile with the 25% probability of observing two quanta per spike at threshold stimulation to –35 mV, since the probability of observing activation of an additional spike within the time to peak of the first spike was only 0.015 (see Results). Moreover, an increase of TTP and FDHM with the quantal content due to the imperfect synchronization of an increasing number of clusters should be observed. In real experiments, negative correlations were observed between the quantal content of the spark and the spark rise time (Wang et al. 2004), and between the quantal content and both TTP and FDHM (R = −0.11 and −0.12, P = 0.047 and 0.043, respectively) in our dataset (not shown). These negative correlations have been proposed to arise from the inhibitory feedback of the Ca²⁺ increase in the dyadic gap (Wang et al. 2004). A contribution from the reduction of release duration due to the Ca²⁺ decrease in the SR lumen (Terentyev et al. 2002) should be considered as well.

Probability of RyR activation during calcium spikes

The wide amplitude distribution of primary calcium spikes at 0 mV was best described by four equidistant quantal levels. The quantal content of individual calcium spikes had a binomial distribution, which suggests that the recruitment of individual RyR2 channels after the first RyR2 opening in the spike occurred with a constant probability, that is, as if the effect of the Ca²⁺ concentration increase in the dyadic gap due to RyR2 openings were independent of the number of open RyRs. This is in apparent contradiction with a simple calcium activation mechanism. We propose that the reason is in the steady-state inhibition of RyR2s by the high Mg²⁺ concentration in the cytosol (Zahradnikova et al. 2003, 2010b). Therefore, Ca²⁺ ions can bind to, and activate, RyR2s only after unbinding of Mg²⁺ from the RyR2 activation sites, a process that is independent of Ca²⁺ concentration. The same mechanism could explain the recruitment of RyRs in calcium sparks as well (Zahradnikova et al. 2010b).

The average number of quanta observed in our experiments at 0 mV was 2.0. Previously, a similar estimate (2.7) has been made for the calcium release flux of calcium sparks evoked under similar conditions (cell-attached loose patch clamp, +70 mV stimulus relative to the myocyte resting potential) from peripheral dyads, and the quanta of calcium release flux were interpreted as openings of individual RyRs (Wang et al. 2004). Our data therefore suggest that local calcium release in intracellular dyads is mechanistically similar to that of peripheral dyads. The lower average number of activated RyRs per dyad estimated in this work may have been caused by a lower probability of RyR2 activation during the spike, since the high concentrations of calcium buffers (EGTA and Fluo-3) present under our conditions in the cytosol may inhibit calcium release to some extent (Neco et al. 2010). An alternative explanation, i.e. a smaller number of RyR2s per cluster in our experiments, is less plausible, since the number of RyR2s seems to be larger in intracellular dyads (Hayashi et al. 2009) than that in peripheral dyads (Baddeley et al. 2009; Hayashi et al. 2009), although the construction of release units is not known in detail.

The lower average quantal content of spikes evoked by threshold depolarizations (1.3) can be tentatively explained by the difference in the mode of their activation. The frequency of DHPR opening increases, while the amplitude of their single channel current decreases with increasing depolarization. Since the coupling fidelity between DHPR and RyR opening is low (Zhou et al. 1999; Polakova et al. 2008), many DHPR openings precede the activation of the first RyR at the calcium release site (Zahradnikova et al. 2004; Polakova et al. 2008). Frequent DHPR openings at 0 mV may increase calcium concentration in the dyadic gap much more than the rare, albeit larger, DHPR openings at −35 mV. This gives rise to modulation of calcium release activation by the recent history of calcium influx within the dyad (Zahradnikova et al. 2004). It originates from saturation of the calcium buffering capacity in the dyadic space and from shifting the fraction of Mg²⁺ and Ca²⁺ ions bound to the RyR in favour of Ca²⁺ (Zahradnikova et al. 2004). However, full understanding of this phenomenon needs further experiments.

The estimates of the number of RyRs per release site translate to estimates of the probability of RyR recruitment during the elementary calcium release event. At 0 mV, the earlier estimate of n_RyR = 182 (Soeller et al. 2007) corresponds to p_A = 0.006 for the probability that additional RyRs are recruited. In the lowest limit of n_RyR = 14 (Baddeley et al. 2009), the average quantal content of calcium spikes at 0 mV would correspond to p_A = 0.078. Thus, even for the smallest estimates of the cluster size, the resulting probabilities of RyR2 recruitment during spikes remain low.

Refractoriness of calcium release

It was shown that a calcium spark induces a decrease of the coupling fidelity between DHPR and RyR channels (Wang et al. 2001), and that activation of a calcium spike induces refractoriness of the release site (Sham et al. 1998). Recovery of release was shown to be dependent on luminal Ca²⁺ (Terentyev et al. 2002) but to proceed slower than refilling of the calcium store (Sobie et al. 2005). Our data collected at 0 mV point to a strong propensity of dyads to refractoriness after any release event. While 30% of calcium spikes consisting of a single quantum were followed by a second spike, a second spike was observed in only ∼3% of spikes consisting of three quanta. The steep decrease in frequency of second spikes with increasing quantal size of the primary spike suggests that each quantum of release flux increases the probability of release refractoriness by 70%. The refractoriness of the release sites may have been induced either by the refractoriness of the trigger, i.e. by inactivation of the DHPR channels by calcium ions released by the first calcium spike (Lacampagne et al. 1996; Sham, 1997; Zahradnikova et al. 2004) or by diminished propensity for calcium release, i.e. by deactivation of RyRs that could develop due to the depletion of the SR (Terentyev et al. 2002; Sobie et al. 2005) or by their fateful inactivation (Sham et al. 1998; Zahradnikova et al. 2007). The probability of all aforementioned processes increases with increased calcium release flux, in line with the observations presented here.

Molecular implications

The observed distribution of quantal content provided a range of acceptable values of p_A for recruitment of RyRs in the release site, ranging from 0.006 to 0.084. These probabilities translate into rates of Mg²⁺ dissociation of 33–130 s⁻¹ (Zahradnikova & Zahradnik 2012). These rates are quite plausible, since they are comparable with or higher than the rates of dissociation of Mg²⁺ from the Mg²⁺–parvalbumin complex (4–33 s⁻¹, Permyakov et al. 1987) or from its complex with troponin-C or with the C-terminal fragment of troponin-C (5 and 0.7 s⁻¹, Rosenfeld & Taylor, 1985), and comparable or lower than the rates of Mg²⁺ dissociation from ATP (150 s⁻¹, Baylor & Hollingworth, 1998).

The amplitude of calcium release current corresponding to a quantum of release flux can be estimated using the data published by Song et al. (1998) and Zahradnikova et al. (2007). Calcium current corresponding to calcium spikes has been previously estimated to be 10.5 nA per cell with a membrane capacitance of 111 pF (Song et al. 1998), i.e. with a volume of 20 pl (Satoh et al. 1996). For a cell with approximately one release site per μm³ (Chen-Izu et al. 2006; Soeller et al. 2007) this translates to 0.51 pA per spike, i.e. 0.26 pA per quantum of release flux. Assuming the same calibration (41.7 nA per 20 pl cell per unit of ΔF/F₀ with OG-5N as an indicator; Song et al. 1998), and noting that the amplitude of spikes measured with OG-5N is 12.3% of that of spikes measured with Fluo-3 (Zahradnikova et al. 2007), we obtain a value of 0.40 pA for a quantal amplitude of 1.87 ΔF/F₀ units observed in this study with the Fluo-3 indicator. Both estimates are quite consistent with the single-channel amplitude of RyR currents of ≤0.5 pA estimated for physiological conditions (Mejia-Alvarez et al. 1999; Kettlun et al. 2003). However, they are lower than the published quantal amplitude of calcium sparks (1.2 pA; Wang et al. 2004). This difference may have been caused by the uncertainties in both types of calibration used (Song et al. 1998; Wang et al. 2004).

Physiological implications

The quantal character of calcium sparks (Wang et al. 2004) and of calcium spikes (this study) allows to endorse the single-channel principle to cardiac E–C coupling. For a density of one release site per μm³ (Chen-Izu et al. 2006; Soeller et al. 2007), 95% probability of release site activation (Song et al. 2001; Polakova et al. 2008), and average cell volume of 24 pl, estimated according to Satoh et al. (1996) from the average membrane capacitance of 159 pF of our cells, the estimates of the single-channel amplitude (0.26–0.40 pA) and the number of open RyR2s per release site (2.0), obtained in this work, yield overall calcium release flux per cell of about 10–19 nA. With the average voltage-dependent calcium current amplitude of 0.84 nA in our experiments, and 0.92 nA in the experiments of Song et al. (1998), this overall calcium release current translates to a release flux providing 92–96% of total calcium flux, in agreement with previous estimates of 90% (Bers, 2002). Thus, the opening of two RyR2s per release site on average is able to provide the expected amount of calcium for contraction.

It is not easy to accept an idea that single molecules, albeit in clusters, bear the responsibility to carry out a life-supporting function. On the other hand, considering the contractile space supported by a single release site, together with the costs of calcium cycling, this principle may, in fact, mean that a finer control of contractile output can be achieved through gating of single molecules rather than through concerted gating of tens of channels. A practical consequence is that it might be easier for the myocyte to keep the release sites fully functional and easy to refurbish according to the ever changing demands of the organism.

Dispersion of the local calcium release events into intense early and minor delayed ones may have implications for other calcium-dependent cell functions. For instance, the resulting slower and protracted calcium transient will limit inactivation of DHPR calcium channels and so shape the action potential, the time course of contraction and the cellular calcium homeostasis.

Experimental limitations

Indicator saturation

In this work the high-affinity indicator Fluo-3 was preferred over the low-affinity indicators such as Oregon Green BAPTA-5N, since Fluo-3 provides a much better signal-to-noise ratio (Zahradnikova et al. 2007). However, the higher affinity of Fluo-3 (1.13 μm, Smith et al. 1998) might lead to its saturation during high release fluxes that increase the local calcium up to ∼5 μm (Rios & Brum, 2002). The linearity of the indicator could be tested by simulations employing the CalcC program for reaction–diffusion modelling of calcium dynamics (Matveev et al. 2002). The parameters of simulations were identical to those described in Zahradnikova et al. (2007). The time course of calcium release flux was described by eqn (9) with t_A = 3.0 and t_T = 5.0 ms, respectively. Saturation of Fluo-3 increased from the value of 8% in the absence of calcium flux to 12% at the maximum response to calcium release flux with peak amplitude of 1 pA. The response to peak currents up to 4 pA, twice the maximal estimate for calcium spikes in this study calibrated according to Song et al. (1998), deviated from linearity by less than 5%.

Resolution of release sites

The density of calcium release sites has been estimated to be 1 μm⁻³, with the average distance to the surrounding neighbours of 1.02 ± 0.03 μm (Soeller et al. 2007). These short distances imply the possibility of unresolved recording of two events from separate release sites as a single calcium spike based on the limited spatial resolution of the confocal microscope (see Methods). Previously we have estimated that 36 release sites can be observed per 100 μm longitudinal scanning line (Zahradnikova et al. 2010b). The accuracy of this estimate was verified here by counting the number of in-focus spikes and measuring the length of the scanned line in the analysed dataset. Although the 1.8 μm average longitudinal distance between release sites (Soeller et al. 2007) would point to the occurrence of 56 release sites per 100 μm, the obtained maximal longitudinal density was 37 release sites per 100 μm, suggesting that release sites that are only slightly displaced from the scanning line and/or focal plane do not give rise to resolvable calcium spikes. The observed longitudinal density of release sites corresponds to a recorded area of ∼0.37 μm² perpendicular to the scanning line, about 60% of the local area served by one release site, which has been estimated as 0.59 μm² (Soeller et al. 2007). This number is in accordance with the estimate of 0.39 μm² based on the microscope resolution of 0.98 μm in the vertical and 0.40 μm in the horizontal direction. Thus, it is most likely that individual release sites were well resolved in this study and that the recorded spikes were not considerably distorted by calcium release form the neighbouring release sites.

Detection limits of calcium spikes

To test the detection limits of our analysis, we have performed simulated experiments using computer generated spikes with a variable signal-to-noise ratio (SNR). These have shown that the fitting procedure identified correctly 86% of spikes with SNR = 2.0 and 96% of spikes with SNR = 3.0 (data not shown). Since only 0.8% of recorded spikes had SNR < 2, and 2.3% had SNR between 2 and 3 (data not shown), it is evident that the amplitude distributions described in this study are not considerably distorted by the presence of spikes below the detection limit.

Conclusions

Calcium spikes evoked in isolated myocytes by membrane depolarization bear the stochastic signature of a random process congruent with the molecular properties of RyR channels and with their distribution in calcium release sites. We show that the stochastic properties of calcium spikes can be interpreted considering activation of only a few out of the many RyRs clustered at the release sites. This helps to unify views on structure and function of calcium releasing sites and to understand the related aspects of plasticity and dynamics of calcium signalling in development and disease of myocardium.

Glossary

RyR

ryanodine receptor

DHPR

dihydropyridine receptor

SNR

signal-to-noise ratio

TTP

time to peak

FDHM

full duration at half-maximum

Author's present address

Eva Poláková: Department of Pharmacology and Systems Therapeutics, Mount Sinai School of Medicine, New York, NY, USA.

Author contributions

A.Z.Jr., I.Z. and A.Z. designed experiments. A.Z.Jr. R.J. and E.P. performed all experiments. R.J., A.Z.Jr., E.P. and J.P. performed primary data analysis. A.Z. and I.Z. provided the theoretical framework for secondary analysis. R.J., A.Z.Jr., I.Z. and A.Z. performed secondary data analysis. J.P., R.J. and A.Z. performed computer simulations. All authors participated in drafting the manuscript. I.Z. and A.Z. revised it critically for important intellectual content. All authors approved the final version. All experiments were conducted at the laboratory in Bratislava, Slovakia.