Robustness of networked systems to unintended interactions with application to engineered genetic circuits

TL;DR

This paper establishes conditions under which networked systems, including engineered genetic circuits, are robust to unintended interactions, emphasizing the importance of subsystem properties and interaction map structure.

Contribution

It provides new sufficient conditions for robustness of networked systems to unintended interactions, applicable to engineered genetic circuits and other complex networks.

Findings

Subsystems must attenuate constant disturbances

Interaction maps should be monotone and feedback-free

Results guide robust genetic circuit design

Abstract

A networked dynamical system is composed of subsystems interconnected through prescribed interactions. In many engineering applications, however, one subsystem can also affect others through "unintended" interactions that can significantly hamper the intended network's behavior. Although unintended interactions can be modeled as disturbance inputs to the subsystems, these disturbances depend on the network's states. As a consequence, a disturbance attenuation property of each isolated subsystem is, alone, insufficient to ensure that the network behavior is robust to unintended interactions. In this paper, we provide sufficient conditions on subsystem dynamics and interaction maps, such that the network's behavior is robust to unintended interactions. These conditions require that each subsystem attenuates constant external disturbances, is monotone or "near-monotone", the unintended interaction map is monotone, and the prescribed interaction map does not contain feedback loops. We employ this result to guide the design of resource-limited genetic circuits. More generally, our result provide conditions under which robustness of constituent subsystems is sufficient to guarantee robustness of the network to unintended interactions.