BMC Systems Biology

Background: Quantifying the robustness of biochemical models is important both for determining the validity of a natural system model and for designing reliable and robust synthetic biochemical networks. Several tools have been proposed in the literature. Unfortunately, multiparameter robustness analysis suffers from computational limitations. Results: A novel method for quantifying the robustness of oscillatory behavior to parameter perturbations is presented in this paper. This method relies on the combination of Hopf bifurcation and Routh-Hurwitz stability criterion, which is widely applied in control system design. The proposed method is employed to calculate the robustness of two oscillating biochemical network models previously analyzed in the literature. The robustness bounds here obtained are tighter than what was previously obtained in the literature for both models. Conclusion: The method here proposed for quantifying the robustness of biochemical oscillator models is computationally less demanding than similar multiparamter variation techniques available in the literature. It also provides tighter bounds on two models previously analyzed in the literature. Background It is well acknowledged that characteristics of biochemical systems, such as oscillatory behavior, are preserved under significantly different environmental conditions, i.e., the systems are robust. Some biological systems have been experimentally proven to be robust [1-3]. Since biological systems are robust, the mathematical models developed to represent their characteristics must also reflect this property. In addition, since it is not possible to precisely determine the parameters in the modeling process, biochemical system models must maintain basic properties, such as oscillatory behavior, in the presence of parameter perturbations [4]. Therefore, robustness is considered as an important measure of the validity of mathematical models. Determining the robustness of the oscillatory behavior of a bio-molecular model has also relevance in design problems. In fact, by determining the region in parameter space where oscillations persist, one can provide guidelines (see [5,6] for example) for designing the components of synthetic oscillators such as those of [7,8]. Parametric robustness of biochemical oscillator networks has been the subject of several studies [4,9]. In