The ryanodine receptor patchwork: knitting calcium spark dynamics.

Ca2+ sparks are microscopic (1–2 μm), probabilistic events that reflect release of Ca2+ from clusters of release channels, known as ryanodine receptors (RyRs), in the sarcoplasmic reticulum (SR) membrane. Although sparks have been observed in skeletal and smooth muscle, they have been most intensively studied in heart cells. Each cardiac Ca2+ spark reflects the stochastic gating of a cluster containing a relatively small number (10–100) of RyRs, and a typical ventricular myocyte may contain 10,000–20,000 of such RyR clusters, also known as Ca2+ release units (CRUs). In the 21 years since sparks were first discovered (1), these events have received considerable attention from the research community. Part of the appeal of Ca2+ sparks is the fact that they are a link between the molecular and cellular scales. Measurements of sparks allow one to make inferences about the gating of individual RyRs, and, in turn, spark behavior determines the characteristics of cellular-level events such as Ca2+ leak from the SR in quiescent myocytes and Ca2+ transients triggered by membrane depolarization. Sparks are also the fundamental basis of regenerative, propagating Ca2+ waves that can potentially initiate arrhythmias, so these events form a bridge between intracellular Ca2+ handling and pathological electrical signaling. Because of the complexity involved in understanding SR Ca2+ release across multiple spatial scales, mathematical modeling has frequently been employed as a tool for developing quantitative predictions. Simulation of cardiac Ca2+ sparks, a research area with a relatively long history, has produced some notable examples in which mathematical modeling produced a conceptual advance that was ahead of the existing state of experimental recordings, and this allowed the simulations to inspire subsequent experimental work. In the most celebrated case, Stern (2) developed the “local control” theory in 1992 on the basis of the observation that simple deterministic mathematical models could not reproduce experimental observations. This was essentially a prediction for the existence of elementary events, a hypothesis that was confirmed the following year when recordings of Ca2+ sparks were first reported (1). Similarly, in 2002, Sobie et al. (3) published a stochastic mathematical model of the cardiac Ca2+ spark and proposed that strong local depletion of SR [Ca2+] was essential to ensure the reliable termination of these events. Subsequent experiments confirmed that local depletion occurs and provided compelling evidence that it is indeed critical for spark termination. In both this case and the local control theory mentioned above, the modeling predictions were valuable in part because they established a conceptual framework for the interpretation of later experimental data. This allowed investigators to interpret data as either consistent with or inconsistent with modeling predictions, thereby achieving consensus, rather than arguing endlessly about confusing experimental results. In this issue of the Biophysical Journal, Walker et al. (4) present a cardiac Ca2+ spark model that may potentially have a similar long-term impact. As described below, the article generates interesting predictions about how the molecular-level structure of the CRU influences Ca2+ spark properties, and the results are certain to prove useful for interpreting new data as they are obtained. An additional aspect of spark modeling history helps to place the results of Walker et al. in context. Simulations of microscopic cardiac Ca2+ signaling have generally proceeded along one of two different tracks (5). In one category, many studies have used Monte Carlo methods to simulate gating of RyR clusters and explore the probabilistic aspects of spark triggering and termination (2, 3, 6, 7). However, these models have usually greatly simplified the geometrical details of the Ca2+ release unit. In the other category, studies have explored how the details of the geometry within the CRU influence the temporal evolution of Ca2+ concentrations during release events. Over the course of many important studies, progressively more geometrically complex models have been developed. For instance, a 2012 study (8) builds the Ca2+ release unit model directly from electron micrographs, allowing the model to capture nanometer-scale details of the cytosolic and SR compartments. With only a couple of exceptions (9, 10), however, models in this category usually greatly simplify RyR gating. The study by Walker et al. (4) is notable, in part, because these authors bring together the two traditions of modeling at the Ca2+ spark level. Similar to another recent model (9), Walker et al. simulate the fine geometrical details of the Ca2+ release unit and also incorporate a model of RyR gating that is consistent with contemporary experimental data, including the fact that no role has yet been demonstrated for Ca2+-dependent inactivation of this channel. The simulations presented by Walker et al. (4) make a couple of important contributions: First, they propose a reasonable role for the known regulation of RyR gating by SR [Ca2+], so-called luminal regulation. Changes in SR [Ca2+] have been shown in many studies to affect RyR gating, and the simulations predict potential physiological consequences of this regulation. Although older Ca2+ spark models emphasized the importance of SR [Ca2+] regulation in determining spark dynamics (3), recent simulations indicate that this regulation is not strictly required for robust termination (9, 11), and the results shown in Walker et al. (4) confirm this. However, by performing simulations both with and without luminal regulation, Walker et al. propose that luminal regulation is critical for cellular Ca2+ leak to depend nonlinearly on SR [Ca2+]. This is a potentially testable hypothesis that may help to delineate a clear role for regulation of the RyR by SR [Ca2+]. The second important contribution by Walker et al. (4) is a prediction of how irregularity in the distribution of RyRs in the cluster influences Ca2+ spark triggering. Most early spark models assumed that RyR clusters formed a regular array, but recent imaging data indicate that these clusters may form more complex shapes. The authors incorporated into their simulations structures of RyR clusters obtained using super-resolution microscopy, and they performed stochastic simulations using many RyR clusters with randomly-generated structures. Importantly, they introduced a metric, derived from graph theory, that essentially quantifies how strongly RyRs within the cluster are connected to one another. Simulations indicate that interconnected RyR clusters are more likely to produce Ca2+ sparks whereas disconnected clusters will generate more RyR openings that fail to initiate sparks, or so-called “invisible leak”. The simulation results thereby provide insight into how the “patchwork” of the irregular RyR array affects Ca2+ spark dynamics. Although this result is arguably what one would intuitively expect, the quantitative rigor of the prediction will undoubtedly prove valuable when interpreting future simulation and experimental results. A reader outside the cardiac Ca2+ signaling field may well ask: why bother with such fine structural detail? After all, the purpose of a model is not to represent reality in all its infuriating complexity, but instead to represent a reasonable approximation of reality. Given that premise, perhaps the geometrical detail included in the study (4) is unnecessary or even counterproductive. However, this potential criticism has an important rejoinder, which is that these structural details will be necessary to understand alterations seen in disease. As recently reviewed (12), disease states, particularly heart failure, can be associated with modified CRU geometry, including changes in RyR cluster size, alterations in the distance between the cellular and SR membranes, and changes in local SR volumes. Disease may also be associated with alterations to the regularity of RyR clusters, although this has not yet been explored thoroughly using super-resolution techniques. As new data are obtained, mathematical models such as the one presented by Walker et al. (4) will therefore provide an essential tool for linking structural experimental data with physiological results, and for predicting how the structural changes influence function. The discussion of disease suggests additional ways in which future research can build off the study by Walker et al. (4). It will be important for future studies to move beyond the Ca2+ spark level by incorporating multiple, spatially specified CRUs within the same model. In this way such a model could predict how irregularity in the RyR cluster influences the likelihood that local Ca2+ sparks may initiate regenerative, potentially arrhythmogenic Ca2+ waves. Despite this limitation, which will certainly be addressed going forward, the interesting study presented in this issue (4) provides an excellent example of how mathematical modeling can be used both as a tool for synthesizing existing experimental data and as a means of predicting experiments that have not yet been performed. Experimental data are always required to build and constrain models, but when models are constructed thoughtfully, they can enable better interpretation of new data.