Fundamental trade-offs in the robustness of biological systems with feedback regulation

Natural biological systems use a complex network of feedback regulation to effectively respond to their changing environment. Even though in engineered systems we understand how accurate feedback can be depending on the electronic or mechanical parts that it is implemented with, we largely lack a similar theoretical framework to study biological feedback. Specifically, it is not fully understood or quantified how accurate or robust the implementation of biological feedback actually is. In this paper, we study the sensitivity of biological feedback to variations in biochemical parameters using five example circuits: positive autoregulation, negative autoregulation, double-positive feedback, positive-negative feedback and double-negative feedback (the toggle switch). We find that of these examples of biological feedback are subjected to fundamental trade-offs, and we propose multi-objective optimisation as a framework to study them. The impact of this work is to improve robust circuit design for synthetic biology and to improve our understanding of systems biology.