Anti-Windup Protection Circuits for Biomolecular Integral Controllers

Robust Perfect Adaptation (RPA) is a desired property of biological systems wherein a systems output perfectly adapts to a steady state, irrespective of a broad class of perturbations. Achieving RPA typically requires the deployment of integral controllers, which continually adjust the systems output based on the cumulative error over time. However, the action of these integral controllers can lead to a phenomenon known as "windup". Windup occurs when an actuator in the system is unable to respond to the controllers commands, often due to physical constraints, causing the integral error to accumulate significantly. In biomolecular control systems, this phenomenon is especially pronounced due to the positivity of molecular concentrations, inevitable promoter saturation and resource limitations. To protect against such performance deterioration or even instability, we present three biomolecular anti-windup topologies. The underlying architectures of these topologies are then linked to classical control-theoretic anti-windup strategies. This link is made possible due the development of a general model reduction result for chemical reaction networks with fast sequestration reactions that is valid in both the deterministic and stochastic settings. The topologies are realized as chemical reaction networks for which genetic designs, harnessing the flexibility of inteins, are proposed. To validate the efficacy of our designs in mitigating windup effects, we perform simulations across a range of biological systems, including a complex model of Type I diabetic patients and advanced biomolecular proportional-integral-derivative (PID) controllers. This work lays a foundation for developing robust and reliable biomolecular control systems, providing necessary safety and protection against windup-induced instability.