Figure 5. Mathematical modeling linking changes in ryanodine receptor (RyR) configuration and function during β-adrenergic stimulation.

(a) 3D computational volumetric meshes built from correlative imaging of the t-tubular network (confocal microscopy) and RyRs (3D dSTORM). Constructed geometries consisted of 10 × 10 × 10 nm voxels and a 1 × 1 × 1 µm volume. The four geometries were chosen to represent the range of cluster dispersion seen in imaging (see Supplementary file 1 for details). (Top row) Reconstructed t-tubular structures (blue) are illustrated with superimposed thresholded RyR signals (green). (Bottom row) Corresponding computational geometries, with indicated RyR channel pores (orange) and cleft space (red) defined by morphological dilation around the RyRs. The four geometries were selected to represent the range of RyR dispersion observed in experiments, ranging from solid to majorly fragmented Ca²⁺ release units (CRUs) (see ‘Materials and methods’). (b) In total, 400 stochastic spark simulations were performed in each geometry with baseline model parameters, and another 400 were conducted with the regulatory effects of β-adrenergic receptor (β-AR) stimulation added (RyR sensitization and increased sarcoplasmic reticulum [SR] content). The ΔF/F₀ time course is shown for each spark. The maximal amplitude used to define the release as an experimentally observable spark event (ΔF/F₀ ≥ 0.3), a sub-spark quark event (ΔF/F₀ ≥ 0.1), or a failed spark (ΔF/F₀ < 0.1). (c, d) The classification of release into spark and non-spark events was used to estimate spark fidelity and the ratio of leak that is ‘silent’ (i.e., sub-spark release) in each simulation case. (e, f) Average amplitude and time to peak (TTP) measurements for observable sparks. Unshaded and shaded bars in (c–f) denote baseline and sensitized (simulated β-AR activation) RyR conditions, respectively. Error bars in (e) and (f) show SEM, while the bars in (c) indicate the 95% Agresti–Coull confidence interval.

Figure 5—figure supplement 1. Comparison of experimentally measured and simulated Ca²⁺ sparks.

Amplitude and time to peak (TTP) values for experimentally measured Ca²⁺ sparks are plotted under control conditions and the three time points of isoproterenol stimulation (10, 30, and 60 min). Comparison is made with simulated sparks generated by the four modeled Ca²⁺ release unit (CRU) geometries under baseline conditions, and under simulated isoproterenol conditions including increased ryanodine receptor (RyR) release flux and Ca²⁺ sensitivity. Note that the simulated sparks shown are identical in the three latter plots. Crosses indicate population means, and circles show the covariance ellipse at 1 SD.

Figure 5—figure supplement 2. Model behavior at different sarcoplasmic reticulum (SR) loads.

To test model behavior, we perturbed the SR load parameter in the isoproterenol model while maintaining ryanodine receptor (RyR) Ca²⁺ sensitivity. We compared the standard isoproterenol model (i.e., SR load = 1300 µM, see Figure 4—figure supplement 1) with SR content reduced to 1100 µM (left panel, ‘Iso^a’), or increased to 1500 µM (right panel, ‘Iso^b’). These perturbations had little effect on spark time to peak (TTP), with similar trends observed across the modeled Ca²⁺ release unit (CRU) geometries. Spark amplitude, on the other hand, was observed to be markedly sensitive to SR load perturbation. Results are plotted alongside experimental data recorded at 10 min or 60 min following isoproterenol treatment (left and right panels, respectively).