Steady-State Differential Dose Response in Biological Systems

In pharmacology and systems biology, it is a fundamental problem to determine how biological systems change their dose-response behavior upon perturbations. In particular, it is unclear how topologies, reactions, and parameters (differentially) affect the dose response. Because parameters are often unknown, systematic approaches should directly relate network structure and function. Here, we outline a procedure to compare general non-monotone dose-response curves and subsequently develop a comprehensive theory for differential dose responses of biochemical networks captured by non-equilibrium steady-state linear framework models. Although these models are amenable to analytical derivations of non-equilibrium steady states in principle, their size frequently increases (super) exponentially with model size. We extract general principles of differential responses based on a model's graph structure and thereby alleviate the combinatorial explosion. This allows us, for example, to determine reactions that affect differential responses, to identify classes of networks with equivalent differential, and to reject hypothetical models reliably without needing to know parameter values. We exemplify such applications for models of insulin signaling.