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

Abstract

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.