Quantitative performance metrics for robustness in circadian rhythms

Motivation: Sensitivity analysis provides key measures that aid in unraveling the design principles responsible for the robust performance of biological networks. Such metrics allow researchers to investigate comprehensively model performance, to develop more realistic models, and to design informative experiments. However, sensitivity analysis of oscillatory systems focuses on period and amplitude characteristics, while biologically relevant effects on phase are neglected. Results: Here, we introduce a novel set of phase-based sensitivity metrics for performance: period, phase, corrected phase and relative phase. Both state- and phase-based tools are applied to free-running Drosophila melanogaster and Mus musculus circadian models. Each metric produces unique sensitivity values used to rank parameters from least to most sensitive. Similarities among the resulting rank distributions strongly suggest a conservation of sensitivity with respect to parameter function and type. A consistent result, for instance, is that model performance of biological oscillators is more sensitive to global parameters than local (i.e. circadian specific) parameters. Discrepancies among these distributions highlight the individual metrics' definition of performance as specific parametric sensitivity values depend on the defined metric, or output.