On Parametric Sensitivity and Structural Robustness of Cellular Functions -- the Oscillatory Metabolism of Activated Neutrophils

Robustness of cellular functions is a key property of living organisms. Modelling and analysis of the genetic and biochemical networks underlying specific functions will enable quantification of the robustness as well as identification of the specific mechanisms providing robustness. Studies on cellular robustness has so far largely focused on parametric sensitivities, i.e., robustness of functions (behavior) with respect to changes in model parameters. In this paper we argue that robustness analysis of cellular models also should encompass structural robustness, i.e., robustness with respect to perturbations in the model structure. This is important not only to quantify the robustness of the cell functions themselves, but equally important, to gain knowledge about the quality of the model as such. In particular, if the model displays poor robustness against structural perturbations this serves as an indication of a potentially highly uncertain model and hence care must be exercised when interpreting the obtained parametric sensitivities. We here propose a simple method for analysing structural robustness of functions related to bistability and periodic oscillations in intracellular networks. The method is applied to a model of the oscillatory metabolism of activated neutrophils (white blood cells) recently proposed in Olsen et al., Biophys J., 84:69-81, 2003. The model is found to be highly robust against parametric uncertainties, but is shown to display poor structural robustness. Indeed, attempting to divide the model into compartments, with the aim of emulating spatial distributions that exist in vivo, results in a qualitatively different model prediction.