Analysis and design of antithetic proportional-integral-derivative biocontrol-systems with species dilution

The nonlinearity and non-separability of the antithetic PID (aPID) controller have provided greater flexibility in the design of biochemical reaction networks (BCRNs), resulting in significant impacts on biocontrol-systems. Nevertheless, the dilution of control species is disregarded in designs of aPID controllers, which would lead to the failure of inhibition mechanism in the controller and loss of robust perfect adaptation (RPA)-the biological counterpart of robust steady-state tracking. Here, the impact of dilution processes on the structure of aPID is investigated in this study. It is discovered that the proportional and low-pass filters are altered when the dilution processes is present in control species, which increases the coupling between the controller parameters. Moreover, additional integrations for the reference signal and control output generated by control species dilution further leads to the loss of RPA. Subsequently, a novel aPID controller represented by BCRNs, termed quasi-aPID, has been designed to eliminate the detrimental effects of the dilution processes. In an effort to ameliorate the interdependencies among controller parameters, a degradation inhibition mechanism is employed within this controller. Furthermore, this work establishes the limiting relationship between the controller's reaction rates in order to guarantee RPA, while abstaining from the introduction of supplementary species and biochemical reactions. By using the quasi-aPID controller in both the Escherichia coli gene expression model and the whole-body cholesterol metabolism model, its effectiveness is confirmed. Simulation results demonstrate that, the quasi-aPID exhibits a smaller absolute steady-state error in both models and guarantees the RPA property.