Robustification as a tool in modeling biochemical reaction networks

Biological functions have evolved to become robust against a multitude of perturbations such as gene mutations, intracellular noise and changes in the physical and chemical environment. This robustness should be reflected in models of the underlying biochemical networks, and robustness analysis has consequently been established as an important tool for model validation in systems biology. However, while robustness analysis can be used to invalidate a given model, it does not support the postulation of model modifications that can serve to improve the robustness. Herein we propose a method for this purpose, based on computing the sensitivity of the robustness with respect to generic dynamic perturbations applied to the individual network edges. To quantify robustness we compute the smallest simultaneous change in the activity of the network nodes that induces a bifurcation in the network, resulting in a qualitative change in the network behavior. The proposed method can be used to identify network interactions with the most significant impact on the overall robustness of a given function. By considering the impact of adding new nodes and edges, the method can also be used to postulate the presence of important unmodeled components and interactions. The focus here is on biological functions related to bistable switches and sustained oscillations, and the proposed methodology is demonstrated through application to metabolic oscillations in white blood cells and bistable switching in MAPK signal transduction. The classical Goodwin model of oscillations in a simple gene regulatory network is used for illustration throughout the paper.

► A method for identifying network modifications with the most significant impact on the robustness of a biological function is proposed.
► The focus is on biological functions related to sustained oscillations and bistable switches and robustness is quantified by computing the smallest perturbation of the network node actitvities that induces a qualitative change in the system behavior.
► The proposed method considers modifications of network interactions included in the model as well as addition of new nodes and edges.
► We demonstrate the applicability and strengths of the method by application to a simple model of a gene transcriptional loop underlying circadian oscillations, a model of the metabolic oscillations in activated white blood cells and, finally, the bistable switch in MAPK signal transduction pathways.