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.
Integral feedback control is commonly used in mechanical and electrical systems to achieve zero steady-state error following an external disturbance. Equivalently, in biological systems, a property known as robust perfect adaptation guarantees robustness to environmental perturbations and return to the pre-disturbance state. Previously, Briat et al proposed a biomolecular design for integral feedback control (robust perfect adaptation) called the antithetic feedback motif. The antithetic feedback controller uses the sequestration binding reaction of two biochemical species to record the integral of the error between the current and the desired output of the network it controls. The antithetic feedback motif has been successfully built using synthetic components in vivo in Escherichia coli and Saccharomyces cerevisiae cells. However, these previous synthetic implementations of antithetic feedback have not produced perfect integral feedback control due to the degradation and dilution of the two controller species. Furthermore, previous theoretical results have cautioned that integral control can only be achieved under stability conditions that not all antithetic feedback motifs necessarily fulfill. In this paper, we study how to design antithetic feedback motifs that simultaneously achieve good stability and small steady-state error properties, even as the controller species are degraded and diluted. We provide simple tuning guidelines to achieve flexible and practical synthetic biological implementations of antithetic feedback control. We use several tools and metrics from control theory to design antithetic feedback networks, paving the path for the systematic design of synthetic biological controllers.
Integral control is commonly used in mechanical and electrical systems to ensure perfect adaptation. A proposed design of integral control for synthetic biological systems employs the sequestration of two biochemical controller species. The unbound amount of controller species captures the integral of the error between the current and the desired state of the system. However, implementing integral control inside bacterial cells using sequestration feedback has been challenging due to the controller molecules being degraded and diluted. Furthermore, integral control can only 10 be achieved under stability conditions that not all sequestration feedback networks fulfill. In this work, we give guidelines for ensuring stability and good performance (small steady-state error) in sequestration feedback networks. Our guidelines provide simple tuning options to obtain a flexible and practical biological implementation of sequestration feedback control. Using tools and metrics from control theory, we pave the path for the systematic design of synthetic biological circuits.
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