Parameter Sensitivity Analysis of Stochastic Models Provides Insights into Cardiac Calcium Sparks

• Published in: Biophysical journal Vol. 104; no. 5; pp. 1142 - 1150
• Main Authors: Lee, Young-Seon, Liu, Ona Z, Hwang, Hyun Seok, Knollmann, Bjorn C, Sobie, Eric A
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 05.03.2013; Biophysical Society; The Biophysical Society
• Subjects: Animals; Calcium; Calcium - metabolism; Calcium Signaling; Carrier Proteins - genetics; Computer Simulation; heart; linear models; Logistic Models; Mathematical models; Mice; Mice, Knockout; Models, Cardiovascular; Multivariate Analysis; Muscle Proteins - genetics; Myocardium - metabolism; prediction; Proteins; Regression analysis; sarcoplasmic reticulum; Simulation; Stochastic models; Stochastic Processes; Systems Biophysics
• ISSN: 0006-3495; 1542-0086
• DOI: 10.1016/j.bpj.2012.12.055

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 Ca²⁺ 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 Ca²⁺ spark. Results show that multivariable linear regression can successfully relate parameters to continuous model outputs such as Ca²⁺ spark amplitude and duration, and multivariable 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 this method is less computationally intensive than standard methods by a factor of 16. Importantly, predictions were tested experimentally by measuring Ca²⁺ sparks in mice with knockout of the sarcoplasmic reticulum protein triadin. These mice exhibit multiple changes in Ca²⁺ release unit structures, and the regression model both accurately predicts changes in Ca²⁺ 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.