Parameter sensitivity analysis of stochastic models provides insights into cardiac calcium sparks.

We present a parameter sensitivity analysis method that is appropriate for stochastic models, and we demonstrate how this analysis generates experimentally testable predictions about the factors that influence local Ca(2+) release in heart cells. The method involves randomly varying all parameters, running a single simulation with each set of parameters, running simulations with hundreds of model variants, then statistically relating the parameters to the simulation results using regression methods. We tested this method on a stochastic model, containing 18 parameters, of the cardiac Ca(2+) spark. Results show that multivariable linear regression can successfully relate parameters to continuous model outputs such as Ca(2+) spark amplitude and duration, and multivariable logistic regression can provide insight into how parameters affect Ca(2+) spark triggering (a probabilistic process that is all-or-none in a single simulation). Benchmark studies demonstrate that this method is less computationally intensive than standard methods by a factor of 16. Importantly, predictions were tested experimentally by measuring Ca(2+) sparks in mice with knockout of the sarcoplasmic reticulum protein triadin. These mice exhibit multiple changes in Ca(2+) release unit structures, and the regression model both accurately predicts changes in Ca(2+) spark amplitude (30% decrease in model, 29% decrease in experiments) and provides an intuitive and quantitative understanding of how much each alteration contributes to the result. This approach is therefore an effective, efficient, and predictive method for analyzing stochastic mathematical models to gain biological insight.

Decoding myocardial Ca²âº signals across multiple spatial scales: a role for sensitivity analysis.

Numerous studies have employed mathematical modeling to quantitatively understand release of Ca(2+) from the sarcoplasmic reticulum (SR) in the heart. Models have been used to investigate physiologically important phenomena such as triggering of SR Ca(2+) release by Ca(2+) entry across the cell membrane and spontaneous leak of Ca(2+) from the SR in quiescent heart cells. In this review we summarize studies that have modeled myocardial Ca(2+) at different spatial scales: the sub-cellular level, the cellular level, and the multicellular level. We discuss each category of models from the standpoint of parameter sensitivity analysis, a common simulation procedure that can generate quantitative, comprehensive predictions about how changes in conditions influence model output. We propose that this is a useful perspective for conceptualizing models, in part because a sensitivity analysis requires the investigator to define the relevant parameters and model outputs. This procedure therefore helps to illustrate the capabilities and limitations of each model. We further suggest that in future studies, sensitivity analyses will aid in simplifying complex models and in suggesting experiments to differentiate between competing models built with different assumptions. We conclude with a discussion of unresolved questions that are likely to be addressed over the next several years.

Recovery of cardiac calcium release is controlled by sarcoplasmic reticulum refilling and ryanodine receptor sensitivity.

AIMS: In heart cells, the mechanisms underlying refractoriness of the elementary units of sarcoplasmic reticulum (SR) Ca(2+) release, Ca(2+) sparks, remain unclear. We investigated local recovery of SR Ca(2+) release using experimental measurements and mathematical modelling. METHODS AND RESULTS: Repeated Ca(2+) sparks were induced from individual clusters of ryanodine receptors (RyRs) in quiescent rat ventricular myocytes, and we examined how changes in RyR gating influenced the time-dependent recovery of Ca(2+) spark amplitude and triggering probability. Repeated Ca(2+) sparks from individual sites were analysed in the presence of 50 nM ryanodine with: (i) no additional agents (control); (ii) 50 µM caffeine to sensitize RyRs; (iii) 50 µM tetracaine to inhibit RyRs; or (iv) 100 nM isoproterenol to activate ß-adrenergic receptors. Sensitization and inhibition of RyR clusters shortened and lengthened, respectively, the median interval between consecutive Ca(2+) sparks (caffeine 239 ms; control 280 ms; tetracaine 453 ms). Recovery of Ca(2+) spark amplitude, however, was exponential with a time constant of ∼100 ms in all cases. Isoproterenol both accelerated the recovery of Ca(2+) spark amplitude (τ = 58 ms) and shortened the median interval between Ca(2+) sparks (192 ms). The results were recapitulated by a mathematical model in which SR [Ca(2+)] depletion terminates Ca(2+) sparks, but not by an alternative model based on limited depletion and Ca(2+)-dependent inactivation of RyRs. CONCLUSION: Together, the results strongly suggest that: (i) local SR refilling controls Ca(2+) spark amplitude recovery; (ii) Ca(2+) spark triggering depends on both refilling and RyR sensitivity; and (iii) ß-adrenergic stimulation influences both processes.