Robustness analysis, prediction and estimation for uncertain biochemical networks

Mathematical models of biochemical reaction networks are important tools in systems biology and systems medicine to understand the reasons for diseases like cancer, and to make predictions for the development of effective treatments. In synthetic biology, for instance, models are used for the design of circuits to reliably perform specialized tasks. For analysis and predictions, plausible and reliable models are required, i.e., models must reflect the properties of interest of the considered biochemical networks. One remarkable property of biochemical networks is robust functioning over a wide range of perturbations and environmental conditions. Plausible mathematical models of such robust networks should also be robust. However, capturing, describing, and analyzing robustness in biochemical reaction networks is challenging. First, including uncertainty in the structures, parameters, and perturbations into the model is not straightforward due to different types of uncertainties encountered. Second, robustness as well as system and thus model properties are often itself inherently uncertain, such as qualitative (i.e., nonquantitative) descriptions. Finally, analyzing nonlinear models subject to different uncertainties and with respect to quantitative and qualitative properties is still in its infancy. In the first part of this perspective article, network functions and behaviors of interest are formally defined. Furthermore, different classes of uncertainties and perturbations in the data and model are consistently described. In the second part, we review frequently used approaches and present our own recent developments for robustness analysis, estimation, and model-based prediction. We illustrate their capabilities to deal with the different types of uncertainties and robustness requirements.