Biological version of Braess' paradox arising from perturbed homeostasis

Abstract

Braess' paradox is an observation in traffic networks in which changes to the structure of the network---such as the addition of a road---which are intended to enhance flow can often instead have the paradoxical effect of reducing flow through the network. Versions of Braess' paradox have subsequently been observed in many other network types. Homeostasis is a seemingly unrelated biological concept in which interacting regulatory mechanisms work in concert to regulate a particular system output such that it is relatively insensitive to changes in input. A classic example is the broad range of ambient temperatures (input) over which mammalian body temperature (output) is close to constant. In this work, we propose a connection between these concepts using the mathematical formulation of infinitesimal homeostasis and argue that perturbations of homeostatic systems in disease may often lead to observations of paradoxical behavior via the universal unfoldings of infinitesimal homeostasis. We illustrate the concept with an example system drawn from the study of the pathophysiology and treatment of asthma; as a network flow model, this exhibits a form of paradoxical behavior akin to Braess' paradox which we argue arises from perturbation of homeostasis due to disease.