Parameter Sensitivity Analysis of a Stochastic Ca2+ Spark Model using Novel Computational Methods

Abstract

Parameter sensitivity analysis is useful for identifying how changes in model parameters affect measurable model outputs. Stochastic models, however, require multiple simulations with each parameter change, which can make a comprehensive analysis extremely time-consuming. We developed a novel parameter sensitivity analysis method for stochastic models that involves randomly varying all parameters, running a single simulation with each set of parameters, and then statistically relating the random parameters to the simulation results using regression methods. We tested this method using an established stochastic Ca2+ spark model with 18 parameters. Results show that standard linear regression can successfully relate parameters to continuous model outputs such as spark amplitude and duration, and logistic regression can provide insight into how parameters affect Ca2+ spark triggering (a probabilistic process that is all-or-none in a single simulation). Benchmark studies demonstrate that the new method is less computationally intensive than standard methods by a factor of 6.6. Importantly, we tested model predictions with measurements of Ca2+ sparks in mice with knockout of the sarcoplasmic reticulum (SR) protein triadin. These mice exhibit a decrease in the number of RyRs per Ca2+ release unit, a decrease in junctional SR volume, and an increase in diastolic SR [Ca2+]. The regression model predicts that these changes cause a 30% decrease in Ca2+ spark amplitude, almost exactly matching the 29% decrease observed experimentally. Additionally, this analysis provides an intuitive and quantitative understanding of how much each alteration in the triadin knockout mouse contributes to the observed change in spark amplitude. This approach is therefore an effective, efficient and predictive method for analyzing stochastic mathematical models to gain biological insight.