Exploiting the Nonlinear Structure of the Antithetic Integral Controller to Enhance Dynamic Performance

The design of biomolecular feedback controllers has been identified as an important goal across a broad range of biological applications spanning synthetic biology, cell therapy, metabolic engineering, etc. This originates from the need to regulate various cellular processes in a robust and timely fashion. Recently, antithetic integral controllers found their way into synthetic biology due to the Robust Perfect Adaptation (RPA) property they endow - the biological analogue of robust steady-state tracking. The antithetic integral motif hinges on a sequestration reaction between two molecules that annihilates their function. Here, we demonstrate that the complex resulting from the nonlinear sequestration reaction can be leveraged as an inhibitor to enhance the dynamic performance while maintaining the RPA property. We establish that this additional inhibition by the sequestration complex gives rise to a filtered Proportional-Integral (PI) controller thus offering more flexibility in shaping the dynamic response and reducing cell-to-cell variability. Furthermore, we explore the effect of various biological inhibitory mechanisms on the overall performance. The various analyses in the paper are carried out using analytical tools and are supported by numerical simulations. Finally, an experimental validation is performed using the cyberloop - a hybrid platform where the controller is implemented in silico to control a genetic circuit in vivo.