Computing enclosures for uncertain biochemical systems

In this study, the authors present a novel method that provides enclosures for state trajectories of a non-linear dynamical system with uncertainties in initial conditions and parameter values. It is based on solving positivity conditions by means of semi-definite programmes and sum of squares decompositions. The method accounts for the indeterminacy of kinetic parameters, measurement uncertainties and fluctuations in the reaction rates because of extrinsic noise. This is particularly useful in the field of systems biology when one seeks to determine model behaviour quantitatively or, if this is not possible, semi-quantitatively. The authors also demonstrate the significance of the proposed method to model selection in biology. The authors illustrate the applicability of their method on the mitogen-activated protein kinase signalling pathway, which is an important and reoccurring network motif that apparently also plays a crucial role in the development of cancer.