Quantifying robustness of biochemical network models

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Abstract
Robustness of mathematical models of biochemical networks is important for validation purposes and can be used as a means of selecting between different competing models. Tools for quantifying parametric robustness are needed. Two techniques for describing quantitatively the robustness of an oscillatory model were presented and contrasted. Single-parameter bifurcation analysis was used to evaluate the stability robustness of the limit cycle oscillation as well as the frequency and amplitude of oscillations. A tool from control engineering – the structural singular value (SSV) – was used to quantify robust stability of the limit cycle. Using SSV analysis, we find very poor robustness when the model's parameters are allowed to vary. The results show the usefulness of incorporating SSV analysis to single parameter sensitivity analysis to quantify robustness.