βAR stimulation increases RyR density and cluster size and shortens nearest neighbor distances

We measured and analyzed 14 SANCs, from one rabbit heart, comprising 6 cells in the basal state and 8 cells under βAR stimulation. RyRs form clusters of various sizes, with the mean density of RyRs of 67.7 ± 13.2 RyR/μm² (mean±SEM) in SANCs in the basal state. βAR stimulation significantly increased the RyR density to 119.1 ± 22.6 RyR/μm² and created more superclusters. As summarized in S1 Table, βAR stimulation induced significant changes in the RyR network. RyR density increased by 76.1% (p = 0.04262). Mean cluster size increased by 30.2% (from 17.40 to 22.66 RyR/cluster, p = 0.04262). The 95th percentile of cluster size also increased significantly (p = 0.04262), indicating the emergence of more superclusters. Concurrently, the network became more compact, with the mean nearest neighbor distance between clusters decreasing by 34.5% (from 180.15 nm to 118.02 nm, p = 0.00799). These comparisons are visualized in the box plots in Fig 1. All metrics showed statistically significant differences between the basal and βAR groups (two-sided Mann-Whitney U test, p ≤ 0.05).

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Fig 1. Box-plot comparisons of RyR density, spacing, and cluster size between basal andβAR stimulation. Presented are per-cell metrics from S1 Table derived from DBSCAN-labeled localizations. A–C. Box plots show RyR density (RyR/μm²), mean nearest neighbor distance (NND, nm) and mean cluster size (RyR/cluster). Box plots display the median (solid horizontal line), interquartile range (box), whiskers extending to 1.5 × the interquartile range. Cross shows mean values. P-values above each panel are from two-sided Mann–Whitney U tests; all comparisons shown are significant (p ≤ 0.05). Together, panels A–C indicate significantly increased density and larger clusters with shorter cluster spacing under βAR stimulation. Cells were treated with 0.3 µM isoproterenol for 5 min at 37 °C; control cells received vehicle only.

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βAR stimulation increases RyR supercluster number and sizes

We further examined the increase in cluster size by analyzing the cluster size distributions (Fig 2). In a representative cell in the basal state (Cell 6, Fig 2A), the distribution is highly skewed, with a rapid decay from the smallest cluster sizes. In contrast, the βAR-stimulated cell (Cell 12, Fig 2C) exhibits a right-shifted and heavier tail, indicating a significantly higher population of large aggregates. Panels B and D in Fig 2 show examples of RyR distributions in cell regions in basal state and in the presence of βAR stimulation that clearly visualize the change. While under the basal state, cells contained large clusters (e.g., 71 and 41 RyR), the βAR-stimulated cells featured “superclusters” that were not prevalent in the basal state, reaching sizes up to 414 RyR. This indicates that βAR stimulation promotes the formation of markedly larger RyR aggregates. During βAR stimulation, the 95th percentile of cluster size significantly (p = 0.04262) increased by 52.4%, from 54.09 to 82.43 RyR/cluster (see inset in Fig 2C).

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Fig 2. RyR cluster-size distributions and exemplary large clusters underβAR stimulation. Presented are DBSCAN-derived cluster sizes (RyR per cluster) and representative regions from basal and βAR cells. A, C. Histograms of cluster size for a basal cell (Cell 6) and a βAR-stimulated cell (Cell 12) show more clusters overall and a right-shifted, heavier tail under βAR, indicating larger aggregates. Double headed arrows show superclusters with sizes >76 RyRs as defined in the text. B, D. Examples of the largest clusters in each condition overlaid on a smoothed density map (blue glow); red polygons mark cluster boundaries, numbers indicate RyR per cluster. The basal field contains large clusters (e.g., 71 and 41 RyR), whereas βAR exhibits superclusters reaching 414 RyR. The numbers of clusters and cluster sizes increased during βAR stimulation. Inset in Panel C shows the effect of βAR stimulation on cluster-size within 95th percentile (RyR/cluster) in a box plot. P-value (0.0426) is from two-sided Mann–Whitney U test (see numerical values in S1 Table).

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βAR stimulation changes spatial organization within RyR clusters

RyR clusters were categorized into size groups based on the pooled distribution of cluster sizes across all cells and conditions. We first identified all clusters from 14 cells (6 basal, 8 βAR-stimulated) at the 5-minute timepoint and ranked them by the number of RyRs per cluster. Size categories were defined using percentile cutoffs from this combined distribution:

• Small: ≤ 6 RyRs (≤25th percentile)
• Medium-Small: 7–10 RyRs (25th-50th percentile)
• Medium-Large: 11–21 RyRs (50th-75th percentile)
• Large: 22–76 RyRs (75th-95th percentile)
• Supercluster: > 76 RyRs (>95th percentile), see examples shown by double-headed arrows in Fig 2A and 2C.

This percentile-based approach provides biophysically meaningful categories (as we show below in our SANC model simulations) that capture the natural distribution of cluster sizes while maintaining sufficient sample sizes for statistical analysis.

If superclusters form through coalescence of adjacent smaller clusters under βAR stimulation; as suggested by the visual evidence in Fig 2, their internal RyR distribution should become less uniform, with the original clusters appearing as dense cores separated by relatively sparse boundary regions at merger sites. To test this prediction, we quantified the coefficient of variation (CV) of local RyR density within each cluster, where higher CV indicates more uneven internal spacing (Fig 3; mathematical details in Methods). Cell-level analysis (n = 6 basal, n = 8 βAR-stimulated cells) revealed that βAR stimulation significantly increased overall density heterogeneity (CV: 0.324 vs. 0.306, p = 0.020, Mann-Whitney U), with the effect being size-dependent (Fig 3A and 3B). Superclusters (>76 RyRs) showed the largest effect, with a 9.8% increase in CV (p = 0.043, Mann-Whitney U), while large clusters (22–76 RyRs) showed a consistent trend (+5.0%, p = 0.108). Smaller cluster categories showed no significant change. This size-dependent pattern is consistent with superclusters forming through coalescence of adjacent clusters under βAR stimulation, as visualized in Fig 2D, creating internal heterogeneity with dense RyR-rich cores separated by relatively sparse regions.

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Fig 3. Density heterogeneity analysis reveals size-dependent changes in internal RyR organization followingβ-adrenergic stimulation. A. Box plots showing density heterogeneity (coefficient of variation of local RyR density) for clusters grouped by size category under basal (orange) and βAR-stimulated (blue) conditions. Each data point represents a cell-level mean (n = 6 basal, n = 8 βAR-stimulated cells). Horizontal brackets with asterisks indicate statistically significant differences between basal and βAR groups (Mann-Whitney U test on cell-level means; p ≤ 0.05). Higher CV indicates more uneven internal RyR spacing, consistent with dense cores and sparse boundary regions expected from cluster coalescence. B. Percent change in density heterogeneity following βAR stimulation for each cluster size category, showing a size-dependent gradient with the largest effect in superclusters (+9.8%).

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The increasing density heterogeneity with cluster size is consistent with the functional requirement for different cluster sizes to serve distinct roles in cardiac pacemaking, with larger coalesced clusters developing internal sub-domains that may coordinate Ca release across numerous RyRs while avoiding the metastability known for larger fully packed clusters without voids [28].

Structure-function relationship of RyR network revealed by numerical model simulations

To further interpret our experimental findings and obtain functional insights into how the RyR network regulates pacemaker function, we performed numerical model simulations. We simulated SANC function for eight scenarios representing all possible combinations of 2 densities (normal and high), 2 RyR clustering (normal clustering and superclustering) and 2 coupled-clock parameter sets, i.e. P_up (SR Ca pump), I_CaL, I_Kr and I_f for basal state and βAR stimulation. Normal (low) RyR density was set to 67.65 RyR/μm², the average density in the basal state and high density was set to 119.07 RyR/μm², the average density during βAR stimulation (S1 Table). Normal clustering was set as measured in Cell 6 (basal state) and superclustering was set as measured in Cell 12 (βAR stimulation). Results of the simulations are presented in Fig 4. Representative examples of submembrane Ca dynamics together with functional state of each CRU (color coded) are shown in S1-S8 Videos in S1 File for each scenario.

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Fig 4. Synergistic effect of RyR density and superclustering on AP firing cycle length duringβAR stimulation revealed by numerical model simulations. Shown are simulations for 8 different scenarios (shown by respective numbers at the individual plots and labels) performed for combinations of i) two different RyR densities found at the basal state (in scenarios labeled “normal density” of 67.65 RyR/μm²) and during βAR stimulation (labeled “high density” of 119.07 RyR/μm²); ii) two cluster-size distributions found in the basal state (labeled “Normal clustering” taken from Cell 6, Fig 2A) and during βAR stimulation (labeled “superclustering” taken from Cell 12; Fig 2C); and iii) for basal state or βAR stimulation (labeled “Basal” or “βAR”, respectively). A. APCL versus time in all 8 scenarios; solid curves show respective polynomial fits. B. Bar plots summarize the steady-state APCL (mean±SD) across all 8 simulation conditions (two densities × two cluster distributions × two coupled-clock states), each run for 5 independent realizations to account for stochastic variability (40 total simulations). See also S1-S8 Videos. C. Snapshots of S1-S8 Videos showing submembrane local Ca dynamics and CRUs at −45 mV near ICaL activation threshold for each simulation scenario labeled by numbers at the snapshots. [Ca] was coded by red shades from black (0.15 μM) to pure red (>10 μM). Refractory CRUs are shown in blue shades; CRUs ready to release are in green; and CRUs releasing Ca are in grey shades. Both blue shades and grey shades reflect JSR Ca changes, with a saturation level set at 0.3 mM. Scale bar: 10 µm. D. Dynamics of Ca concentration in free SR (CaFSR, left panel) and junctional SR (CaJSR, right panel) in scenarios 1, 2 and 8. In the right panel, the time was shifted to illustrate and compare different rates of junctional SR refilling with Ca from the nadir (t = 0). Horizontal dashed line shows the Ca spark activation threshold (300 μM) in our model.

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Simulations revealed that increasing RyR density alone prolonged the AP cycle length (APCL) in the basal state firing but shortened APCL during βAR stimulation, a dichotomy explained by differential SR Ca load dynamics (see Discussion). However, introducing superclustering alone shortened APCL under both basal and during βAR-stimulated conditions. The combination of high density and superclustering, representing the full βAR phenotype that we found experimentally, resulted in a synergistic effect that yielded the shortest APCL of all conditions (231.9 ms, magenta color in Fig 4). The critical moment in clock coupling happens close to the threshold of I_CaL, near the AP ignition onset when LCR activity increases [9]. To get insights into the coupling process, for each scenario we provide snapshots here (Fig 4C) of S1-S8 Videos in S1 File showing submembrane Ca dynamics (coded in red shades) at -45 mV, reflecting LCR activity and their self-organization at that critical moment (Fig 4C). The LCR abundance in the snapshots was inversely linked to APCL: the lowest LCR activity was linked to the longest APCL (slowest AP firing) in basal state with high RyR density and normal clustering (scenario 2), whereas the highest LCR activity was linked to the shortest APCL (fastest AP firing) during βAR stimulation with high RyR density and superclustering (scenario 8). The LCR activity in scenario 8 was self-organized into large and abundant propagating events (S8 Video in S1 File).

Further insights into different LCR activity in different RyR networks were obtained by examining dynamics of Ca concentration in free SR (CaFSR) and junctional SR (CaJSR). Both systolic and diastolic CaFSR levels substantially decreased in scenario 2 with increased RyR density (vs. scenario 1) but substantially increased in scenario 8 with the shortest APCL (Fig 4D, left panel). The CaFSR level decreased in denser RyR network in the basal state, because overall larger junctional SR (accommodating larger RyR numbers) with more connections to free SR shifts source-to-sink balance towards sink. The lower Ca loading of the free SR, in turn, resulted in slower refilling of junctional SR and therefore delayed LCR occurrence during diastolic depolarization as reflected in rare small LCRs in scenario 2 (Fig 4C, right panel).

To learn more about functional importance of different size clusters, we collected statistics on cluster firing averaged across all 5 realizations for each of the 8 scenarios in each size category with respect to membrane potential at which they fire (Fig 5). Histograms of firing events at each potential showed that in the basal state (left panels) a large fraction of smaller clusters began firing at the rapid AP upstroke, i.e., at Vm > -20 mV. Thus, this fraction of smaller clusters stays in reserve and does not contribute to diastolic depolarization. In contrast, a major fraction of larger clusters (Medium-large, Large, and Superclusters) fired during diastolic depolarization (from -65 to -40 mV). Superclusters, being infrequent (>95th percentile), rigorously recruited (via CICR) their neighbors within a 1 μm neighborhood to fire as shown by orange histograms in each size category which were significantly shifted towards lower potentials (almost coinciding with the distribution of superclusters). During βAR stimulation (right panels) firing of all clusters substantially shifted towards diastolic depolarization, indicating that those clusters that were in reserve during basal state now contribute to pacemaker function, representing a new mechanism of βAR stimulation.

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Fig 5. A new mechanism of βAR stimulation via CRU reserve and superclustering revealed by numerical model simulations of SANC function.

Shown are results of statistical analysis of numerical simulations of SANC function in basal state (left panels) and during βAR stimulation (right panels) in each CRU size category with respect to membrane potential at which CRUs fire. The analysis was performed separately for CRUs located close to superclusters (with 1 μm neighborhood, orange histograms) and far from the superclusters (dark blue histograms, overlapped). The orange histograms for CRUs near superclusters were shifted to lower membrane potentials (towards diastolic depolarization range) indicating their strong recruitment by superclusters. During βAR stimulation all histograms shifted towards diastolic depolarization range and percentage of CRUs close to superclusters (shown in each histogram) increased resulting in a stronger recruitment of CRUs by the superclusters especially at the very early stage of diastolic depolarization close to maximum diastolic potential near -65 mV.

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How do superclusters participate in this mechanism? First, the network density increases during βAR stimulation, and therefore more clusters fall into the 1 µm neighborhood of the superclusters (67–71% during stimulation vs 16–18% in basal state, Fig 5). Next, Ca releases from clusters become stronger (with higher pumping rate, P_up), especially in superclusters having more RyRs. Thus, overall recruitment capability of superclusters via CICR substantially increases. This results in a strong recruitment of neighboring RyRs to fire during early diastolic depolarization, creating a pronounced increase in the orange histogram near maximum diastolic potential (MDP, near -65 mV). Other clusters (far from superclusters) fire stronger but at later stages of diastolic depolarization and during AP upstroke.

We further explored the isolated effect of RyR density while fixing the cluster-size distribution of the basal cell (Cell 6, Fig 2A). Under basal conditions, increasing density notably prolonged APCL (from ~375 ms to 429 ms). Conversely, during βAR-stimulation, increasing density shortened APCL (from ~276 ms to 240 ms), accelerating the AP firing rate. This demonstrates that denser CRU networks work synergistically with upregulated Ca cycling, including SR pumping rate and increased membrane currents (βAR state) to shorten diastolic depolarization and increase the AP firing rate (Fig 6).

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Fig 6. Dependence of AP cycle length on RyR surface density revealed by our numerical model simulations.

Shown are steady-state AP cycle lengths (ms) simulated at basal (red) and βAR (blue) settings while varying RyR density from 10 to 160 RyR/μm² with a cluster-size distribution assigned for both βAR stimulation and basal state (Fig 2A).

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To evaluate whether our model conclusions are sensitive to the choice of DBSCAN clustering parameter, we repeated all eight simulation scenarios using cluster-size distributions derived with ε multipliers of 3.5 and 4.5 in addition to the default value of 4.0 (S4 Table). S4 Table reports a single representative realization per scenario at each ε value; note that the five-realization means at ε = 4.0 reported in Fig 4B differ slightly due to stochastic variability between runs. Across all three ε values, scenario 8 (βAR stimulation with high density and superclustering) consistently produced the shortest APCL (230.2, 238.0, and 229.1 ms for ε = 4.0, 3.5, and 4.5, respectively; mean 232.5 ± 4.0 ms, CV = 1.7%), while scenario 2 (basal state with high density and normal clustering) consistently produced the longest APCL (446.5, 483.8, and 425.7 ms; mean 452.0 ± 24.0 ms, CV = 5.3%). The rank order of APCL across all eight scenarios was nearly perfectly preserved, with only a minor swap between two closely matched βAR scenarios (scenarios 6 and 7, differing by less than 4% in mean APCL: 266.5 vs 269.5 ms) at ε = 3.5. Across all scenarios, the coefficient of variation of APCL ranged from 1.1% to 5.5%, confirming that our conclusions regarding the synergistic effects of RyR density and superclustering on pacemaker rate are robust to moderate variation in the clustering parameter. Importantly, the key finding, that the full βAR phenotype (high density + superclustering + enhanced Ca cycling and membrane currents) produces the fastest firing rate, was invariant across all ε values.

Limitations and future studies

As noted above, our dSTORM analysis captures structural snapshots at a single timepoint and cannot resolve the dynamics of RyR reorganization. Our absolute RyR counts depend on several assumptions inherent to single molecule localization microscopy, including incomplete antibody labeling (which would underestimate counts), residual over-counting from imperfect merging of fluorophore blinking events despite our grouping and stability filters (see Methods), and the possibility of multiple localizations per RyR homotetramer due to secondary antibody amplification. These factors affect absolute values of NRyR and derived densities. However, because identical labeling, imaging, and analysis protocols were applied to both basal and βAR-stimulated cells, the relative comparisons between conditions, which form the basis of our main conclusions, remain valid despite systematic uncertainty in absolute channel count. This robustness is further supported by our ε sensitivity analysis (S4 Table), which demonstrated that varying the DBSCAN clustering parameter preserved the rank order of all simulation outcomes.

The findings are based on rabbit SANCs. While rabbit is a common model in cardiac pacemaker research, species differences in ion channel expression could differ substantially. Comparative studies in other species, including human SANCs, are needed to establish the generality of these findings. All cells were obtained from a single rabbit heart; inter-animal variability cannot be assessed from the present dataset and will require future studies with multiple animals.

All localizations in our dataset were acquired in TIRF mode, which selectively excites fluorophores within approximately 100 nm of the coverslip-attached cell surface (see Methods). Because the coverslip-attached surface represents the plasma membrane, all detected RyR clusters are by definition located within this thin sub-membrane layer, with no meaningful axial distance variation within our dataset.

We examined only the RyR network beneath the cell membrane. These sub-membrane RyRs are the population most directly relevant to pacemaker function, as they reside at peripheral couplings where junctional SR opposes the surface membrane and L-type Ca channels (primarily Cav1.3 in SANCs [8]) are co-localized. Accordingly, our computational model places all CRUs directly beneath the cell membrane, with each CRU coupled to LTCCs across a 20 nm dyadic space [51]. In contrast to LTCCs, NCX is uniformly distributed in the cell membrane; thus, RyRs interact with NCX locally, but these interactions are not limited to the dyadic cleft. A recent study by Lang et al. [52] reported the subsarcolemmal cleft in SAN cells to be 15 ± 1 nm, close to the value used in our model. Our model assumes tight functional coupling between each CRU and its local complement of membrane ion channels. However, our imaging visualized only RyRs, and whether superclusters maintain the same spatial relationship with L-type Ca channels as smaller clusters remains unresolved. Co-localization studies using dual-color dSTORM to simultaneously map RyR2 and Cav1.3 would clarify whether superclusters recruit additional L-type Ca channels or extend beyond the footprint of existing membrane channel clusters.

Any computational cell model is a simplification of biological reality. Our model incorporated the experimentally measured distributions of cluster sizes, but it does not capture all possible interactions of RyRs within CRUs and with other molecules in time and space. For example, while our CRU agent-based model of SANC can examine effects of RyR densities and cluster sizes, it does not simulate stochastic gating of individual RyR channels or their cooperative interactions within a cluster (e.g., coupled gating, allosteric activation by neighboring channels, or modulation by accessory proteins such as CASQ2 and FKBP). Instead, each CRU is treated as a unitary release element whose Ca spark amplitude scales with cluster size. Therefore, our speculation about the importance of less organized clusters of larger sizes to avoid metastability will need further numerical validation using a more detailed model of CRUs (such as in [28,34]) that includes interactions of individual RyRs within the cluster. Future studies will address the question of how βAR stimulation affects RyRs in the cell interior and whether these changes are different from (or linked to) RyR distribution/density at the cell periphery. Our data analysis suggests that superclusters are likely formed by smaller cluster merger events. However, how specifically the clusters move, coalesce, expand, and join together in periphery regions remains to be investigated. Finally, further studies will clarify regional heterogeneity of supercluster distribution within cells that might relate to pacemaker site localization within SAN tissue.

Clinical relevance

Our finding that RyR superclusters are particularly important for achieving the highest possible heart rates during β-adrenergic stimulation is clinically relevant. Dysfunctional RyR gating and altered Ca handling are implicated in sinoatrial node dysfunction (SND) and arrhythmias, including sick sinus syndrome [41]. Cardiac aging is associated with a decline in pacemaker function and increased incidence of SND [42]. Our results suggest that disruptions or alterations in the nanoscale organization of RyR network (such as changes in cluster size distribution or density) could be an underappreciated mechanism contributing to SND. Our results suggest that alterations leading to less synchronized Ca release by a RyR network with fewer large clusters or excessive number of small, disorganized clusters could contribute to bradycardia, and in severe cases, sinus arrest. Investigating how RyR cluster architecture changes with age using super-resolution microscopy could provide new insights into age-related SND.

Impaired β-adrenergic responsiveness is common in aging and heart failure. Our data suggest that structural alterations in the RyR network might contribute to this blunted chronotropic response. Therapeutic strategies aimed at preserving or restoring optimal RyR clustering could potentially improve heart rate regulation. For example, age-associated overexpression of BIN1 emerges alongside dysregulated endosomal recycling and disrupted trafficking of RyRs, whereas BIN1 knockdown restores the nanoscale distribution and clustering plasticity of cardiac RyRs [36].

Our results may also have implications for sports physiology. It was shown that the training-induced bradycardia involves intrinsic sinoatrial node remodeling including downregulation of HCN4 channels [43]. The present study raises the possibility that RyR network remodeling could also contribute the bradycardia. Indeed, our results in Figs 4 and 6 demonstrate that increase in RyR density could lead to lower pacemaker rates at rest.

Understanding the importance of RyR clustering might open new therapeutic avenues. While directly manipulating nanoscale protein organization is challenging, strategies aimed at modulating factors that influence RyR clustering or stabilizing functional cluster sizes could potentially be explored for treating SND or improving heart rate control. Further research correlating RyR nanoscale structure with functional readouts in relevant clinical models (e.g., aging animals, models of heart failure) is needed to fully explore these implications.

Ethics statement

The present study conformed to the Guide for the Care and Use of Laboratory Animals,

published by the US National Institutes of Health. The experimental protocols were approved

by the Animal Care and Use Committee of the National Institutes of Health (protocol # 457-LCS-2024). A New Zealand White rabbit (Charles River Laboratories, USA) weighing 2.8-

3.2 Kg was deeply anesthetized with sodium pentobarbital (50–90 mg/kg) injected to the central ear vein. The adequacy of anesthesia was monitored in the rabbit until reflexes to ear and tale pinch and jaw tone were lost.

Enzymatic isolation of individual SANC

SANCs were isolated from a male rabbit, as previously described [44]. The heart was removed quickly and placed in solution containing (in mM): 130 NaCl, 24 NaHCO₃, 1.2 NaH₂PO₄, 1.0 MgCl₂, 1.8 CaCl₂, 4.0 KCl, and 5.6 glucose equilibrated with 95% O₂/5% CO₂ (pH 7.4 at 35 °C). The sinoatrial node region was cut into small strips (~1.0 mm wide) perpendicular to the crista terminalis and excised. The final sinoatrial node preparation, which consisted of sinoatrial node strips attached to the small portion of crista terminalis, was washed twice in nominally Ca-free solution containing (in mM) 140 NaCl, 5.4 KCl, 0.5 MgCl2, 0.33 NaH₂PO₄, 5 HEPES, and 5.5 glucose (pH = 6.9) and incubated on a shaker at 35 °C for 30 min in the same solution with the addition of elastase type IV (0.6 mg/mL; Sigma, Chemical Co.), collagenase type 2 (0.8 mg/mL; Worthington, NJ, USA), Protease XIV (0.12 mg/mL; Sigma, Chemical Co.), and 0.1% bovine serum albumin (Sigma, Chemical Co.). The sinoatrial preparation was next placed in modified “Kraftbruhe” solution, containing (in mM) 70 potassium glutamate, 30 KCl, 10 KH₂PO₄, 1 MgCl₂, 20 taurine, 10 glucose, 0.3 EGTA, and 10 HEPES (titrated to pH 7.4 with KOH), and kept at 4 °C for 1 h in the Kraftbruhe solution containing 50 mg/mL polyvinylpyrrolidone (Sigma, Chemical Co.). Finally, cells were dispersed from the sinoatrial node preparation by gentle pipetting in the “Kraftbruhe” solution and stored at 4 °C.

Staining and mounting

Isolated rabbit SANCs were plated on #1 glass, 14-mm glass-bottom MatTek dishes pre-coated with laminin (~40 µg/mL) in phosphate-buffered saline (PBS) with 1% penicillin/streptomycin. Cells were rinsed twice with PBS, fixed in 2–4% paraformaldehyde for 10 min at room temperature, rinsed, quenched in 100 µM glycine for 10 min, rinsed again, permeabilized with 1% Triton X-100 in PBS for 15 min, and rinsed twice with 0.1% Triton/PBS. Samples were then blocked in PBS containing 2% IgG-free BSA, 5% normal goat serum, 0.02% sodium azide, and 0.1% Triton X-100 for 60 min to 4 h. Our primary antibody was RyR2 monoclonal antibody (clone C3-33, Thermo Fisher Scientific cat# MA3–916). The primary antibody was diluted (1:100) in blocking buffer and applied for 60 min at room temperature or overnight at 4 °C, followed by four 5–10 min washes in 0.1% Triton/PBS. Then cross-adsorbed secondary antibody F(ab’)2-Goat anti-mouse IgG (H + L), Alexa Fluor 647 (Thermo Fisher Scientific cat# A-21237) diluted 1:200 was applied to cells and incubated for 60 min at room temperature or overnight at 4 °C in the dark, followed by four 5–10 min washes in 0.1% Triton/PBS in the dark and two final PBS rinses. Then the Alexa Fluor 647-labeled SANCs were submerged in an imaging buffer containing 20% VectaShield (H-1000, Vector Laboratories) diluted in Tris-glycerol (5% v/v TRIS 1 M pH 8 in glycerol, Sigma-Aldrich). For experiments involving acute βAR stimulation, before fixation, SANCs were equilibrated 15–20 min at 37 °C in physiological solution containing 1.8 mM Ca² ⁺ , then treated with 0.3 µM isoproterenol for 5 min at 37 °C; control cells received vehicle only.

Single-molecule detection

The prepared and mounted SANC samples were imaged using ZEISS Elyra 7 super-resolution microscope, equipped with dSTORM single molecule localization microscopy module (SMLM). Fluorophore emission light was collected via an alpha Plan-Apochromat 100 × objective lens and Immersol 518 F fluorescence-free immersion oil (NE = 1.518 at 23°C). The laser beam was adjusted to TIRF incidence to selectively excite fluorophores on the cell surface within approximately 100 nm of the coverslip. Blinks were collected across a 512 × 512 pixel field of view (51.2 × 51.2 μm at 100 nm/pixel) on the cell surface. All original dSTORM data in the form of Raw SMLM Molecule Tables are available online at Harvard Dataverse https://doi.org/10.7910/DVN/T0REJ3.

Single-molecule detections were performed using ZEN Black 3.0 software throughout each acquisition. The peak mask size was set to 9 pixels, defining the window around each candidate molecule that was isolated for fitting. A peak intensity-to-noise ratio threshold of 6 was applied, so that only peaks at least sixfold above the local background were accepted as genuine detections. Each isolated peak was then fit with the software’s point-spread-function model to obtain subpixel coordinates, and positions were stored as floating-point values (rounded to the nearest nanometer for downstream analysis). Subsequent quality filters and analyses were applied as described in the following sections.

Image analysis

Our Super-Resolution Single-Molecule Localization Microscopy (SMLM) processing pipeline, depicted in the flowchart in Fig 7 used ZEN Black 3.0 software application supplemented with our Python and MATLAB code (available at GitHub: https://github.com/valventura/dSTORM). The pipeline performs precise filtering, cell region delineation, clustering, and statistical analysis of RyR localizations in SANCs. Our analysis is divided into two major stages: (1) pre-processing and filtering of the Raw SMLM Molecule Table generated by the ZEN Black software and (2) clustering and statistical analysis of this final particle table.

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Fig 7. Flowchart of the dSTORM-based RyR cluster analysis algorithm.

Presented is our Single-Molecule Localization Microscopy (SMLM) processing pipeline for precise filtering, delineation, clustering, and statistics of RyR localizations in SANCs. Raw detections are drift-corrected, grouped, and spatially filtered, then gated by localization precision (1–30 nm), photon count (1,000–6,000), PSF half-width (6.42–250 nm), χ² (0–2), and background (≤ mean + 1.5·SD), with a ≥ 6 blinks-per-site rule. Cell region is defined by a periphery mask with nuclear-void removal (if applicable) to compute the final area. The post-processed particles are clustered by DBSCAN using an adaptive nearest-neighbor ε; from the labels we derive nearest neighbor distances (NNDs), cluster-size metrics (mean, SD, 95th percentile), and RyR density, and compare groups by two-sided Mann–Whitney U tests.

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SMLM localization filtering and delineation

Raw SMLM detections were subjected to a multi-stage filtering process to remove low-quality localizations. An example of filtering within cell area and related histograms are shown in Figs 8 and 9, respectively.

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Fig 8. Filtering of RyR dSTORM localizations in a SANC.

Shown is a representative cell before and after the filtering pipeline. A. Unfiltered localizations (cyan). B. Retained localizations (cyan) after applying the periphery mask (red polygon) together with automated windows on localization quality and spatial context. Colors/symbols: cyan dots are RyR events; red polygon is the cell periphery; the red header reports the periphery perimeter (l = 135.96 µm) and area (A = 286.97 µm²). Filters applied: precision 1–30 nm, photons 1,000–6,000, PSF half-width 6.42–250 nm, χ² 0–2, background < mean + 1.5 SD; and a blinks-per-site rule (≥6 molecular blinks within 50 nm). Together, panels A–B demonstrate removal of extra-cellular and low-quality detections while preserving the in-cell high-quality RyR localization detections.

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Fig 9. Distributions of dSTORM localization parameters and their filtered values.

Density histograms (blue) of the raw localization parameters (calculated for cell 6); green dashed lines mark the acceptance limits used in the filtering pipeline. A–E. Filter gates are applied to all detections: localization precision 1–30 nm, number of photons 1,000–6,000, PSF half width 6.42–250 nm, χ² 0–2, and background capped by a dynamic limit of mean + 1.5·SD (0–1902.84 in this dataset). These windows are indicated by the dashed vertical lines in each panel. F. Distribution of blinks-per-site computed in a 50 nm neighborhood; the dashed line marks the ≥ 6 blinks threshold used to define stable RyR sites. Together, the figure summarizes the criteria that remove low-precision, low-photon, poorly fit, or high-background events while preserving high-quality in-cell detections; across this cell, 111,307 original localizations were reduced to 13,894 after all gates including the ≥ 6 blinks rule (12.5% retained).

https://doi.org/10.1371/journal.pcbi.1014267.g009

1. 1. Nearest-Neighbor Density Filter

Each localization was evaluated within a circular search area, and if the number of neighboring peaks was below the position threshold, that localization is considered an outlier and removed from the SMLM image and molecule list. For each localization, the number of neighboring molecules within a radius of 100 nm was counted; localizations with fewer than two neighbors were excluded. Single or pairs of isolated RyRs likely represent either non-functional receptors, RyRs not yet incorporated into functional release sites, or artifacts from antibody labeling and imaging.

1. 2. Drift Correction

Sample drift was corrected with the Model‑based method in ZEN Black 3.0. In this approach, the software estimates a linear drift directly from the sample structures. For each segment of the acquisition, a correction vector is computed from the average alignment of all structures. We set Correction Type = Model‑based and enabled segmentation with Segments = Automatic while limiting the max to 4. In automatic mode, the algorithm chose the number of segments but never exceeded the user‑defined maximum. The drift was first corrected within each segment and then residual offsets between segments were corrected.

1. 3. SMLM Grouping

The localization data were grouped in ZEN Black 3.0 using the SMLM-Grouping tool to merge repeated detections of the same molecule over consecutive frames. Grouping parameters were chosen Max On Time = 5 frames, Off Gap = 10 frames, and Capture Radius = 1.0 pixels.

The algorithm identifies peaks that fall within the defined capture radius across successive frames and assigns them to a single molecule if the temporal constraints are met.

• Max On Time limits the maximum number of consecutive frames in which a fluorophore can appear while still being treated as one molecule. Peaks persisting longer than this are discarded to prevent false merging of overlapping emitters.
• Off Gap specifies how many frames the fluorophore may temporarily disappear while still being linked to the same molecule. If this limit is exceeded, the peaks are separated into distinct molecules.
• Capture Radius defines the spatial tolerance [set to 1.0 pixel (x, y)] within which peaks are considered part of the same molecule based on the rendered localization precision.

After applying these parameters, the Group function was executed to merge localizations meeting the criteria. This procedure reduced redundant detections from fluorophore blinking, yielding a refined SMLM molecule table with fewer but more accurately positioned molecular localizations.

1. 4. Localization Feature Filters: We applied a series of acceptance windows based on the localization fit parameters, as summarized in S2 Table. These gates included:

• Localization Precision: 1.0–30.0 nm
• Photon Count: 1,000–6,000 photons
• PSF Half Width: 6.42–250.0 nm
• Chi Square : 0.0–2.0
• Background Variance: A dynamic threshold was applied, retaining localizations with background variance of the cell’s total background distribution.

1. 5. Cell Region Delineation: We analyzed data only within the cell perimeter, i.e., falling inside the periphery polygon (Fig 8). In some images, depending on proximity to the cell surface, nuclei clearly influenced RyR detection, and their respective regions were also excluded from analysis (“Cell Area - Nucleus Area”).
2. 6. Site Stability Filter: To ensure that retained localizations represent stable RyR sites, we combined a spatial neighborhood check with a blink-based stability criterion. First, using a k-d tree, we counted for each localization the number of neighboring localizations within a 50 nm radius. We then computed the number of detected blinks (blinks_per_site) for each site as the total count of temporally linked events assigned to that position. Sites exhibiting fewer than six blinks were excluded from further analysis, an empirically determined threshold indicative of stable fluorophore behavior [45]. A similar filtering algorithm (≥5 neighbors within 60 nm) was used previously in [46]. This two-step filter removed low-confidence, transient detections and retained reproducible RyR localizations (Fig 9).

The set of localizations passing all features, stability, and spatial gates constituted the Post-processed SMLM Molecule Table, which was used for all subsequent clustering.

Clustering analysis

The RyR localizations from the Post-processed SMLM Molecule Table were clustered using the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm to identify RyR clusters. The two key parameters for DBSCAN, min_samples and ε, were determined based on the biophysical characteristics of RyR clusters and the properties of SMLM data.

We defined cluster cores using a min_samples of 3. Given that functional RyR clusters (CRUs) can be small, this value was selected as the minimal robust definition of a dense region (a point and two neighbors). This low threshold provided the necessary sensitivity to detect the smallest biologically relevant RyR aggregates, which may consist of only a few RyR molecules. A higher threshold (e.g., 5 or 10) would risk misclassifying these small but significant nascent clusters as noise, thereby skewing the resulting size and density distributions.

Our calculation of clustering radius (ε) in our DBSCAN algorithm is as follows:

1. For a given cell with localizations, the distance to the 3rd nearest neighbor (i.e., corresponding to min_samples = 3) was computed for each point .
2. From the resulting set of distances } we identified all positive distances and computed their 5^th percentile .
3. The clustering radius is defined as

The multiplier 4.0 is dimensionless and was chosen so that ε functions as an interaction envelope: large enough to preserve intra-cluster cohesion across density gradients, yet small enough to maintain inter-cluster separation.. An example result of DBSCAN clustering is shown in Fig 10.

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Fig 10. DBSCAN clustering (red outlines) of RyR dSTORM localizations in a basal SANC.

A representative example (Cell 6) showing adaptive DBSCAN labels on retained localizations. A smoothed “blue-glow” density map forms the backdrop, lime dots mark RyR events, and red polygons trace convex-hull boundaries of individual clusters. Colors/overlays derive from the plotting routine (blue gradient heatmap + lime points; red hulls). DBSCAN used the min-samples-th nearest-neighbor ε rule (ε = 4.0 × 5th percentile of positive min_samples-th NN distances) with min_samples = 3; points labeled as noise are omitted from the display.

https://doi.org/10.1371/journal.pcbi.1014267.g010

To assess the sensitivity of our results to the clustering parameter ε, we performed additional simulations using cluster-size distributions derived from DBSCAN with ε multipliers of 3.5 and 4.5 (in addition to the default 4.0). These bracketing values were chosen to test whether moderate variation in the clustering radius would alter the functional conclusions of our numerical model.

Cluster geometry and spacing analysis

Following DBSCAN, we quantified the geometry and spatial relationships of all resulting clusters.

1. Cluster Size and Density: Cluster size was defined as the total number of localizations (RyR) assigned to that cluster label. We computed the mean, standard deviation (SD), and 95th percentile of cluster sizes on a per-cell basis. RyR Density (RyR/μm²) was calculated as the total number of clustered localizations divided by the final area.
2. To determine cluster spacing (nearest neighbor distance), we first computed the 2D convex hull for every individual cluster. A global k-d tree was then constructed from all vertices of all hulls in the cell. For each cluster we found the shortest Euclidean distance from any of its hull vertices to a vertex belonging to any other cluster. This shortest inter-hull distance was recorded, and the per-cell Mean and SD of nearest neighbor distance were calculated from this set of inter-cluster distances. Our measured nearest edge-to-edge distances have physiological relevance as RyR clusters interact via CICR mechanism activated when released Ca from one cluster reaches RyRs at the border of a neighboring cluster.
3. Statistical Analysis: Comparisons between basal and βAR-stimulated groups for all derived metrics were performed using a two-sided Mann-Whitney U test.

Density heterogeneity calculation

To quantify the internal spatial organization of RyRs within individual clusters, we computed the coefficient of variation (CV) of local RyR density across each cluster. For each cluster, local density was estimated at every RyR position using k-nearest neighbor distances: for each RyR, the mean Euclidean distance to its k = 5 nearest neighbors within the same cluster was calculated, and local density was defined as the reciprocal of this mean distance. Clusters containing fewer than 10 RyRs were excluded from this analysis, as reliable estimation of local density variation requires a sufficient number of internal neighbors. The CV of local density across all RyRs within a cluster was then computed as the standard deviation divided by the mean:

where represents the local density values across all RyRs in the cluster. Higher CV indicates more uneven internal density, as expected when previously separate clusters coalesce to form larger structures with dense cores and sparse boundaries. A CV of zero would indicate perfectly uniform spacing. To respect the nested data structure (multiple clusters within each cell), per-cluster CV values were averaged within each cell to obtain a single cell-level estimate. Statistical comparisons between basal (n = 6 cells) and βAR-stimulated (n = 8 cells) groups were performed using two-sided Mann-Whitney U tests on these cell-level means, both across all clusters and within each size category separately. All cells were obtained from a single rabbit heart.

Numerical model simulations

Numerical simulations were performed using a refined SANC model featuring a functional network of individual RyRs. We developed this model based on our previous agent-based model in which interacting agents were CRUs [14]. The CRU dynamics in that model were tuned against the Stern et al. Ca spark model [28], which resolves individual RyR channels within a cluster interacting via CICR, and validated against experimental data. Due to voxel size limitations CRU sizes in that model were constructed as multiples of 16 RyRs. In the present study, we overcame this limitation by constructing CRU sizes (and their reciprocal junctional SR sizes and Ca releases) with single-RyR precision, closely reproducing the realistic RyR cluster distributions obtained by our dSTORM imaging. Each CRU functions as an autonomous agent that transitions among three functional states: ready to release, releasing (open), and refractory. A CRU can transition from ready to open only when its local junctional SR Ca concentration exceeds a threshold (300 μM), with the transition probability governed by local Ca²⁺ in the dyadic space. The resulting Ca spark amplitude scales with the number of RyRs in the cluster. Released Ca diffuses to neighboring CRUs, enabling CICR-mediated recruitment. Each CRU is functionally coupled to its local complement of membrane ion channels (I_CaL, I_NCX) and the SR Ca pump, and the ensemble of all CRUs drives the global membrane potential via a coupled-clock formulation [4,14].

The modified model code is provided at GitHub: https://github.com/victoramaltsev/RyR-network-SANC-model. The CRUs were randomly rotated and (uniformly) randomly distributed under cell membrane. To minimize effect of randomness on the simulation results, we simulated data for five different random realizations for each simulation scenario of 8 (total 40 simulation runs of 16 s duration) with average data presented in Fig 4B. In each simulation run, APCL data were analyzed for the last 10 s, when the system achieved a steady firing pattern. All model equations, parameters, and their experimental sources are detailed in Appendix A of Maltsev et al. 2024 [14]. βAR stimulation was simulated in the model by modifying four key parameters following: the maximum SR Ca pumping rate P_up was increased ×2.0 (from 0.012 to 0.024 mM/ms); the whole-cell maximum I_CaL conductance g_CaL was increased ×1.75 (from 0.464 to 0.812 nS/pF); the maximum I_Kr conductance g_Kr was increased ×1.5 (from 0.057 to 0.085 nS/pF); and the midpoint of I_f activation (V_1/2) was shifted +7.8 mV (from −64.0 to −56.2 mV), while I_f conductance g_f remained unchanged at 0.105 nS/pF (S3 Table). Under basal conditions with realistic CRU distributions, the model produces steady-state AP firing rates of approximately 160 bpm, consistent with experimentally measured rates in isolated rabbit SANCs [14].