Highlights d Feedback control is an essential component of biomolecular systems d The design of feedback systems necessarily imposes performance tradeoffs d We use control theory to study an important class of molecular feedback motifs d Our work provides a map between biochemical parameters and circuit performance

A common feature of both biological and man-made systems is the use of feedback to control their behavior. In this paper, we explore a particular model of biomolecular feedback implemented using a sequestration mechanism. This has been demonstrated to implement robust perfect adaption, often referred to as integral control in engineering. Our work generalizes a previous model of the sequestration feedback system and develops an analytical framework for understanding the hard limits, performance tradeoffs, and architectural properties of a simple model of biological control. We find that many of the classical tools from control theory and dynamical systems can be applied to understand both deterministic and stochastic models of the system. Our work finds that there are simple expressions that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and noise. These findings yield a holistic picture of the general behavior of sequestration feedback, and will hopefully contribute to a more general theory of biological control systems.

Summary As we begin to design increasingly complex synthetic biomolecular systems, it is essential to develop rational design methodologies that yield predictable circuit performance. Here we apply mathematical tools from the theory of control and dynamical systems to yield practical insights into the architecture and function of a particular class of biological feedback circuit. Specifically, we show that it is possible to analytically characterize both the operating regime and performance tradeoffs of an antithetic integral feedback circuit architecture. Furthermore, we demonstrate how these principles can be applied to inform the design process of a particular synthetic feedback circuit.