Kinetic perturbations as robustness analysis tool for biochemical reaction networks

Abstract

Models of biochemical reaction networks can be decomposed into a stoichiometric part and a kinetic part. The stoichiometric part describes the structural mass flows while the kinetic part describes how the flow rates vary with substrate concentrations and regulatory interactions. Herein a method for analyzing the robustness of biochemical networks with respect to perturbations of the kinetic part is proposed. In particular, we consider a class of perturbations that modify the local kinetic slopes while leaving the reaction flow rates in steady state unchanged. A method for computing the associated robustness radii for perturbations of single or multiple kinetic slopes is devised. The corresponding non-robust perturbations can be implemented in the original nonlinear model through specific parameter variations described by the perturbation class. The proposed method is illustrated through application to the Huang-Ferrell model of MAPK signaling cascades. In particular, we compute the smallest kinetic perturbations that translate the nominal utltrasensitive response into a bistable and oscillatory response, respectively. The results are highly relevant since MAPK cascades are conserved pathways known to produce bistability as well as sustained oscillations depending on the context in which they operate.