Disorder in Ca2+ release unit locations confers robustness but cuts flexibility of heart pacemaking

Figures

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  Figure 1.. Schematic illustration of approximation of local Ca dynamics in our updated CRU-based SAN cell model. (A) CRUs are placed under the cell membrane. (B and C) Three layers of voxels approximate intracellular Ca dynamics (shown not in scale): in cross-section (B) and longitudinal section (C). For more details, see Appendix.

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  Figure S1.. Representative Ca sparks generated by our CRU model. Sparks were simulatied and compared at initial JSR Ca loading 1 mM (A) and 0.3 mM (B). Left: Overlapped time series of [Ca] in dyadic cleft (blue line) and [Ca] in JSR (red line). Right: Respective line-scan images of the sparks. The spark at 0.3 mM of JSR Ca loading had a lower amplitude and duration. To better illustrate Ca spread, the color map in line-scan images is saturated at [Ca]cleft = 1 µM. CRU positions for square lattice configuration are shown by blue lines. The spark was generated by CRU3 and the images show that its outskirt could reach neighboring CRUs (CRU2 and CRU4) at 1 mM JSR Ca loading, but not at 0.3 mM (i.e., at the [Ca]JSR threshold of spark activation). The membrane potential was −60 mV.

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  Figure 2.. Effect of Poisson clumping: Clusterization of CRUs and emergence of voids as disorder in CRU locations increases. Left: The cell cylinder surfaces unwrapping to squares with examples of distributions of RyR clusters under the cell membrane with varying degrees of disorder used in our simulations of SAN cell function. 555 CRUs are distributed in each case. SD values of normal distributions used to perturb CRU locations from their perfect square lattice positions are shown in respective labels above each image. Right: Histograms of the respective distributions of nearest neighbor distances with their mean and SD values (in μm).

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  Figure 3.. Disorder in CRU position shortens CL (i.e., increases AP firing rate). (A) CL intervalograms for SAN cell models with various degrees of disorder in CRU positions. Inset shows that CL correlates with the average nearest neighbor distance, that is, shortens as disorder increases. (B) Respective examples of simulated spontaneous APs.

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  Figure 4.. Perturbing CRU positions around their original square lattice positions increases synchronization and recruitment of CRU to release Ca via locally propagating CICR, resulting in earlier activation of INCX and shorter AP firing cycle. (A–D) Shown are representative examples of simulations of Vm (A), number of open CRUs at a given time (B), INCX (C), and ICaL (D). The traces are synchronized at the MDP to clearly see difference in time course during diastolic depolarization.

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  Figure 5.. Disorder in CRU positions accelerates synchronization of CRU firing and AP ignition process. (A and B) Shown are representative cycles of AP firing (Vm, blue curves) for 500 ms simulation time beginning from the MDP (time = 0) for two CRU distributions: uniformly random (A) and square lattice (B). The ignition process in both cases is characterized by simultaneous activation of CRUs firing (black), INCX (red), and ICaL (green, truncated) during diastolic depolarization. However, the activation kinetics is faster in the uniformly random case so its diastolic depolarization is about twice shorter.

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  Figure 6.. Sizes of LCRs increase during diastolic depolarization via propagating CICR as disorder in CRU positions increases from square lattice to uniformly random (from top to bottom). Shown are instant distributions of local [Ca]sub ([Ca] under cell membrane) at the same membrane potential of −45 mV, i.e., close to the ICaL activation threshold. [Ca]sub is coded by a color scheme shown at the bottom from 0.15 to 10 μM; open CRUs are shown by white dots. Closed CRUs in refractory period are shown by blue dots; closed reactivated CRUs (available to fire) are shown by green dots. JSR Ca level is coded by respective shade (white, blue, or green) with a saturation level set at 0.3 mM. See respective Videos 1, 2, 3, 4, and 5.

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  Figure 7.. Results of sensitivity analysis demonstrating failure of pacemaker function (AP firing ceased) in cell models with square lattice positions of CRUs, but not with uniformly random CRU distribution at lower, albeit physiological, ICaL densities. (A) Bridging experimentally measured ICaL densities (green circles) and our model parameter gCaL describing maximum ICaL conductance (magenta). The data points for ICaL experimental data were replotted from Monfredi et al. (2018). Magenta band shows range of gCaL in our sensitivity analysis. (B) Results of sensitivity analyses for cell models with uniformly random CRU distribution (red) and square lattice distribution (blue). Data points are average CLs evaluated between 5 and 16.5 s after simulation onset. Red shade square shows the gCaL margin where square lattice models failed, but uniformly random model continued generating spontaneous APs. (C) An example of AP firing failure in a square lattice model, but rhythmic AP firing in uniformly random model when in both cases gCaL reduced to 70% of its basal value. See original simulation data in Fig. S2.

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  Figure S2.. SAN cell with uniformly random distribution of CRUs features more robust spontaneous AP firing (right) versus that with a square lattice distribution of CRUs (left). Shown are simulated AP traces in our gCaL sensitivity analysis in which gCaL gradually decreased from 100 to 55% of its basal state value of 0.464 nS/pF. Specific gCaL values are shown at the top of each panel. Red shade shows the AP safety margin (functional reserve) that a SAN cell can utilize to increase its robust function via redistribution of its CRU locations to increase the presence of noise (i.e., natural CRU clustering).

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  Figure 8.. New insights for dormant cell signaling. (A) Despite both models with uniformly random and square lattice models failed at a very low gCaL of 0.2552 nS/pF, subthreshold Vm oscillations continue in both cases. However, oscillations in uniformly random distribution had much larger amplitude (shown in inset). (B) The oscillations were not only much more powerful but occurred at a faster frequency as revealed by the power spectra of both Vm signals computed for time after AP failure (from 0.5 to 16.5 s).

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  Figure 9.. Disorder in CRU positions shortens the CL, but simultaneously decreases the effect of βAR. (A) Bar graph of respective AP firing lengths (for numerical data, see Table 1). (B) An example of simulations of βAR stimulation effects for extreme cases of CRU distributions: uniformly random (top) versus square lattice (bottom). (C) CL changes correlate with basal CL (before βAR stimulation), βAR stimulation synchronizes AP firing towards a common AP firing CL. See original simulation data in Fig. S3.

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  Figure S3.. Effect of βAR stimulation wanes as disorder in CRU positions increases. Shown are CL intervalograms for simulations of AP firing in basal state (blue plots) and in the presence of βAR stimulation (red plots). Note: βAR stimulation shortens the CLs towards about the same level within a narrow range of 291–266 ms, i.e., βAR stimulation unifies spontaneous AP firing towards a higher common rate. All simulations started from the identical initial conditions.