Spontaneous Ca²⁺ sparks and Ca²⁺ homeostasis in a minimal model of permeabilized ventricular myocytes

Abstract

] in the myoplasm or SR can influence the frequency, amplitude, and kinetics of local events. In ventricular myocytes, for instance, propagating Ca 2ϩ waves emerge when spontaneous Ca 2ϩ sparks trigger additional sparks in a regenerative fashion (5). Similarly, changes in channel gating at the level of individual RyRs can immediately affect the production of local events and, over time, influence bulk myoplasmic and SR [Ca 2ϩ ]. An increase in RyR opening will cause a gradual decrease in SR [Ca 2ϩ ] (46), whereas inhibition of RyR opening, over time, will lead to elevated SR [Ca 2ϩ ] (21). This principle has been elegantly demonstrated by Lukyanenko and coworkers (35) in quiescent rat ventricular myocytes treated with caffeine (to sensitize RyRs) or tetracaine (to inhibit RyRs).In heart cells, changes in Ca 2ϩ signaling due to altered RyR activity are currently receiving considerable attention because of close links to disease (13, 48). In particular, catecholaminergic polymorphic ventricular tachycardia (CPVT), an inherited disorder associated with a dramatic increase in arrhythmia risk, results from mutations in either RyRs or calsequestrin, a SR Ca 2ϩ buffer protein that associates with and modulates RyRs (20,33). Experiments in vitro have shown that CPVT-causing mutations usually increase the open probability of the RyR, resulting in a hyperactive or "leaky" channel (12,28,31). Studies (1, 36) have also suggested that leaky RyRs are characteristic of several experimental heart failure models. Thus, a quantitative understanding of how changes in RyR gating influence local and global Ca 2ϩ responses can provide insights into disease pathophysiology and can potentially suggest novel therapies.The difference in spatial scales between local and global Ca 2ϩ signals, however, creates significant challenges for the development of mechanistic mathematical models. In particular, gating of RyRs depends on both myoplasmic and SR [Ca 2ϩ ] (30), and concentrations within clusters during local events can be dramatically different from the bulk concentrations. In addition, because of the relatively small number of RyRs responsible for Ca 2ϩ sparks (6), the stochastic gating of these channels must be considered when simulating local events. Previous studies (9,27,42,44) have used Monte Carlo simulation methods to investigate the stochastic triggering of Ca 2ϩ sparks, but these have generally treated myoplasmic and bulk SR [Ca 2ϩ ] as fixed boundary conditions. Conversely, modeling studies (4, 10, 40) focusing on cellular Ca 2ϩ transients have usually used representations of SR Ca 2ϩ release that do not account for the stochastic nature of the local events. Attempting to simulate Ca 2ϩ signaling at both spatial scales simultaneously is a daunting prospect because the stochastic behavior of thousands of local events must be considered to determine the effects on the bulk concentrations. As a result, only a few studies (16, 17, 49, 50) have attempted to capture both phenomena.

Discrete-State Stochastic Models of Calcium-Regulated Calcium Influx and Subspace Dynamics Are Not Well-Approximated by ODEs That Neglect Concentration Fluctuations

“…Williams et al demonstrated that a population of subspace domains can be represented by a probability density approach and can be utilized to simulate global calcium dynamics [45]. Hartman et al utilized a model of a small number of coupled calcium activated channels to predict the global calcium release dynamics in response to pharmacological modification of single channel kinetics [46]. However, this study is the first to compare a model of calcium channel regulation accounting for the finite subspace volume (and using a discrete representation of the number of subspace calcium ions) with the corresponding ODE formulation that assumes a large system size (and uses a continuous representation of calcium concentration).…”

How Does Stochastic Ryanodine Receptor-Mediated Ca Leak Fail to Initiate a Ca Spark?

“…S3 qualified as Ca sparks). As the detection threshold increases, nonspark leak is increased (25). If we reduce our detection threshold to D[Ca] I ¼ 0.05 mM, more Ca sparks are seen ( Fig.…”

Decoding myocardial Ca2+ signals across multiple spatial scales: A role for sensitivity analysis

“…The first study to simulate both stochastic spark triggering and cellular action potentials (APs) was published by Greenstein and Winslow in 2002 [62]. Several studies published more recently have used either elegant algorithms [63-68], or improvements in computational power [69-74], to develop new models. The biological questions that can be asked with these models, however, are somewhat different from those that can be addressed with the lumped models.…”

“…In these newer models, however, SR Ca 2+ leak via stochastic gating of RyRs is simulated explicitly. Several studies published in the past few years have computed leak in a resting myocyte as a function of SR [Ca 2+ ] and have used the simulations to quantify the relative importance of visible leak in the form of Ca 2+ sparks, versus “invisible” leak that would be difficult to detect with standard recording techniques [68, 70, 73, 74]. Sensitivity analyses with these newer models can therefore consider additional model outputs, such as the resting spark rate or the number of Ca 2+ sparks triggered by specific voltage-clamp depolarizations.…”