Fundamental Trade-Offs in the Robustness of Biological Systems with Feedback Regulation

Natural biological systems use feedback regulation to effectively respond and adapt 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 feedback regulation in biological systems. 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 some of these examples of biological feedback are subjected to fundamental performance trade-offs, and we propose multi-objective optimization as a framework to study their properties. The impact of this work is to improve robust circuit design for synthetic biology and to improve our understanding of feedback for systems biology.