Structural analysis in biology: A control-theoretic approach

Despite their complexity, biological systems are able to endure huge parameter fluctuations and survive in the most diverse environmental conditions. Mathematical tools from graph theory and systems and control theory are naturally well-suited to understand the functioning of biological systems and reveal that their tremendous robustness is often rooted in their peculiar interconnection structure. This survey considers a wide class of ordinary-differential-equation biological models, including chemical reaction networks, and provides an overview of structural approaches proposed in the literature to assess whether a system structure enjoys fundamental qualitative properties, yielding specific types of dynamic or steady-state behaviours, regardless of the precise parameter values.