Pairwise approximation of interaction between perturbations on complex networks

Recent work has shown that the effects of drug combinations, such as antibiotics, can be predicted from the effects of the drugs in pairs. Unfortunately, little is known about why these pairwise approximations work so well. Interactions between drugs are typically not purely chemical, but instead arise from the ways that different drugs impact cell physiology. Therefore, drug interactions more closely resemble generalized perturbations to complex networks than the molecular-level behavior governing similar approximations in statistical physics. Here we investigate how combinations of perturbations impact behavior of three types of dynamical systems: coupled biochemical reactions, large-scale models of bacterial metabolism, and networks of coupled phase oscillators. We find that the “macroscopic” effects of combined perturbations—for example, the net flux through a reaction network—can often be predicted from the effects of pairwise perturbations, but pairwise effects are rarely predictable from single-perturbation effects. We also highlight exceptions to these trends and propose network-level properties that may facilitate these pairwise approximations. Our results show that pairwise approximations may help predict the effects of combined perturbations in a wide range of systems.