Distribution-based sensitivity metric for highly variable biochemical systems

Classical sensitivity analysis is routinely used to identify points of fragility or robustness in biochemical networks. However, intracellular systems often contain components that number in the thousands to tens or less and consequently motivate a stochastic treatment. Although methodologies exist to quantify sensitivities in stochastic models, they differ substantially from those used in deterministic regimes. Therefore it is not possible to tell whether observed differences in sensitivity measured in deterministic and stochastic elaborations of the same network are the result of methodology or model form. The authors introduce here a distribution-based methodology to measure sensitivity that is equally applicable in both regimes, and demonstrate its use and applicability on a sophisticated mathematical model of the mouse circadian clock that is available in both deterministic and stochastic variants. The authors use the method to produce sensitivity measurements on both variants. They note that the rank-order sensitivity of the clock to parametric perturbations is extremely well conserved across several orders of magnitude. The data show that the clock is fragile to perturbations in parameters common to the cellular machinery ('global' parameters) and robust to perturbations in parameters that are clock-specific ('local' parameters). The sensitivity measure can be used to reduce the model from its original 73 ordinary differential equations (ODEs) to 18 ODEs and to predict the degree to which parametric perturbation can distort the phase response curve of the clock. Finally, the method is employed to evaluate the effect of transcriptional and translational noise on clock function. [Includes supplementary material].