Recruiting RyRs to Open in a Ca2+ Release Unit: Single-RyR Gating Properties Make RyR Group Dynamics

Blink nadir measurements of sarcoplasmic reticulum are consistent with strong local Ca2+ depletion

Ca2+ blinks measure the exit of Ca2+ from the junctional sarcoplasmic reticulum (JSR) in a cardiac myocyte during a Ca2+ spark. Here, the relationship between experimental blink fluorescence measurements and the [Ca2+] in the JSR is explored using long 3D simulations of diastolic Ca2+ release. For a fast intra-SR Ca2+-activated fluorophore such as Fluo-5N, we show that a simple mathematical formula relates the two for an ideal blink (i.e., when fluorescence signals come only from the JSR). The formula shows that normalized JSR [Ca2+] is much lower than the normalized fluorescence and that JSR Ca2+ depletes ∼40-50% more than previously inferred from blink fluorescence measurements. In addition, we show that stray fluorescence signals (e.g., from other parts of the sarcoplasmic reticulum network) can mask even deeper Ca2+ depletion. Overall, the simulations show that strong JSR Ca2+ depletion such as that seen in many simulations is consistent with the relatively moderate fluorescence changes seen in experiments.

Image-Driven Modeling of Nanoscopic Cardiac Function: Where Have We Come From, and Where Are We Going?

Complementary developments in microscopy and mathematical modeling have been critical to our understanding of cardiac excitation-contraction coupling. Historically, limitations imposed by the spatial or temporal resolution of imaging methods have been addressed through careful mathematical interrogation. Similarly, limitations imposed by computational power have been addressed by imaging macroscopic function in large subcellular domains or in whole myocytes. As both imaging resolution and computational tractability have improved, the two approaches have nearly merged in terms of the scales that they can each be used to interrogate. With this review we will provide an overview of these advances and their contribution to understanding ventricular myocyte function, including exciting developments over the last decade. We specifically focus on experimental methods that have pushed back limits of either spatial or temporal resolution of nanoscale imaging (e.g., DNA-PAINT), or have permitted high resolution imaging on large cellular volumes (e.g., serial scanning electron microscopy). We also review the progression of computational approaches used to integrate and interrogate these new experimental data sources, and comment on near-term advances that may unify understanding of the underlying biology. Finally, we comment on several outstanding questions in cardiac physiology that stand to benefit from a concerted and complementary application of these new experimental and computational methods.

In silico simulations reveal that RYR distribution affects the dynamics of calcium release in cardiac myocytes

The dyads of cardiac myocytes contain ryanodine receptors (RYRs) that generate calcium sparks upon activation. To test how geometric factors of RYR distribution contribute to the formation of calcium sparks, which cannot be addressed experimentally, we performed in silico simulations on a large set of models of calcium release sites (CRSs). Our models covered the observed range of RYR number, density, and spatial arrangement. The calcium release function of CRSs was modeled by RYR openings, with an open probability dependent on concentrations of free Ca2+ and Mg2+ ions, in a rapidly buffered system, with a constant open RYR calcium current. We found that simulations of spontaneous sparks by repeatedly opening one of the RYRs in a CRS produced three different types of calcium release events (CREs) in any of the models. Transformation of simulated CREs into fluorescence signals yielded calcium sparks with characteristics close to the observed ones. CRE occurrence varied broadly with the spatial distribution of RYRs in the CRS but did not consistently correlate with RYR number, surface density, or calcium current. However, it correlated with RYR coupling strength, defined as the weighted product of RYR vicinity and calcium current, so that CRE characteristics of all models followed the same state-response function. This finding revealed the synergy between structure and function of CRSs in shaping dyad function. Lastly, rearrangements of RYRs simulating hypothetical experiments on splitting and compaction of a dyad revealed an increased propensity to generate spontaneous sparks and an overall increase in calcium release in smaller and more compact dyads, thus underlying the importance and physiological role of RYR arrangement in cardiac myocytes.

Simulating cardiac Ca2+ release units: effects of RyR cluster size and Ca2+ buffers on diastolic Ca2+ leak

Leak of Ca²⁺ out of the cardiac sarcoplasmic reticulum (SR) via ryanodine receptors (RyRs) during diastole is vital to regulate SR Ca²⁺ levels. This leak can become deleterious when large spontaneous RyR-mediated Ca²⁺ release events evoke proarrhythmic Ca²⁺ waves that can lead to delayed after-depolarizations. Here, we model diastolic SR Ca²⁺ leak at individual SR Ca²⁺ release sites using computer simulations of RyR arrays like those in the dyadic cleft. The results show that RyR arrays size has a significant effect on SR Ca²⁺ leak, with bigger arrays producing larger and more frequent Ca²⁺ release events. Moreover, big RyR arrays are more susceptible to small changes in the levels of dyadic Ca²⁺ buffers. Such changes in buffering shift Ca²⁺ leak from small Ca²⁺ release events (involving few open RyRs) to larger events (with many open RyRs). Moreover, by analyzing a large parameter space of possible buffering and SR Ca²⁺ loads, we find further evidence for the hypothesis that SR Ca²⁺ leak by RyR arrays can undergo a sudden phase transition.

Simulating diffusion from a cluster of point sources using propagation integrals

A computational methodology to simulate the diffusion of ions from point sources (e.g., ion channels) is described. The outlined approach computes the ion concentration from a cluster of many ion channels at pre-specified locations as a function of time using the theory of propagation integrals. How the channels' open/closed states evolve in time does not need to be known at the start of the simulation, but can be updated on-the-fly as the simulation goes along. The technique uses analytic formulas for the solutions of the diffusion equation for three common geometries: (1) ions diffusing from a membrane (planar symmetry); (2) ions diffusing into a narrow cleft for effective two-dimensional diffusion (cylindrical symmetry); and (3) ions diffusing into open space like the cytosol (spherical symmetry). Because these formulas are exact solutions valid for arbitrarily long timesteps, no spatial or time discretizations are necessary. The only discrete locations are where the ion concentration is computed, and the only discrete timesteps are when the channels' open/closed states are updated. Beyond pure diffusion, the technique is generalized to the Excess Buffer Approximation of ion chelation to give an analytic solution of this approximation of the full reaction/diffusion system. Both the pure diffusion and the diffusion/buffering algorithms scale linearly with the number of channels and the number of ion concentration locations.