Anti-windup strategies for biomolecular control systems facilitated by model reduction theory for sequestration networks

Robust perfect adaptation, a system property whereby a variable adapts to persistent perturbations at steady state, has been recently realized in living cells using genetic integral controllers. In certain scenarios, such controllers may lead to "integral windup," an adverse condition caused by saturating control elements, which manifests as error accumulation, poor dynamic performance, or instabilities. To mitigate this effect, we here introduce several biomolecular anti-windup topologies and link them to control-theoretic anti-windup strategies. This is achieved using a novel model reduction theory that we develop for reaction networks with fast sequestration reactions. We then show how the anti-windup topologies can be realized as reaction networks and propose intein-based genetic designs for their implementation. We validate our designs through simulations on various biological systems, including models of patients with type I diabetes and advanced biomolecular proportional-integral-derivative (PID) controllers, demonstrating their efficacy in mitigating windup effects and ensuring safety.