Feed-forward loop improves the transient dynamics of an antithetic biological controller

Integral controller is widely used in industry for its capability of endowing perfect adaptation to disturbances. To harness such capability for precise gene expression regulation, synthetic biologists have endeavoured in building biomolecular (quasi-)integral controllers, such as the antithetic integral controller. Despite demonstrated successes, challenges remain with designing the controller for improved transient dynamics and adaptation. Here, we explore and investigate the design principles of alternative RNA-based biological controllers, by modifying an antithetic integral controller with prevalently found natural feed-forward loops (FFL), to improve its transient dynamics and adaptation performance. With model-based analysis, we demonstrate that while the base antithetic controller shows excellent responsiveness and adaptation to system disturbances, incorporating the type-1 incoherent FFL into the base antithetic controller could attenuate the transient dynamics caused by changes in the stimuli, especially in mitigating the undesired overshoot in the output gene expression. Further analysis on the kinetic parameters reveals similar findings to previous studies that the degradation and transcription rates of the circuit RNA species would dominate in shaping the performance of the controllers.