Synthetic Biology-Inspired Robust-Perfect-Adaptation-Achieving Control Systems: Model Reduction and Stability Analysis

Abstract

In addition to perfectly steering the output concentration of a process network to an exogenous set-point, a desired synthetically implemented biological controller should be able to robustly maintain this regulated output in the face of the extrinsic disturbances and inherent uncertainties due to an ever-varying environment besides the imprecise modeling. Such an ability, which is called robust perfect adaptation (RPA), can be achieved by integral feedback control (IFC). Answering how IFC is (biochemically) constructible in generally unknown synthetic networks has been a research focus in the community. One of these answers, which has been well investigated previously, is to utilize a simple (Hill-type) integral negative feedback controller. Another effective solution, which has made significant progress, is the increasingly being used antithetic integral feedback controller. In this article, by applying these two RPA-achieving controllers in control of an uncertain process network with an arbitrary number of species, the behavior of the resulting closed-loop systems, in which the effect of molecular dilution is also considered, is analyzed. Through this analysis, by assuming that the stability is preserved, it is shown that the latter controller can be approximately reduced to the former (simpler) one by individually increasing one of its parameters (the annihilation rate). Furthermore, to address the stability assumption, exact parametric conditions are derived to guarantee the stability of the control systems. These findings can lead us to gain a deeper insight into and to simplify the robust design, performance analysis, and implementation of such living circuits. Simulation results accompany this article's analytical elaborations.