Multi-time-scale biomolecular ‘quasi-integral’ controllers for set-point regulation and trajectory tracking

Abstract

Recent trends in synthetic biology to move from prototypes to applications have triggered higher expectations on the robustness, predictability and responsiveness of biomolecular circuits. Therefore, a systematic approach to designing biomolecular controllers for regulating gene expression is needed. Although a number of integral control motifs (ICMs) have been proposed for set-point regulation, their performance in vivo is challenged by integration leakiness due to dilution, which cannot be neglected in growing cells. In this paper, we study a class of quasi-integral controllers designed based on existing ICMs and multiple time-scale separations. We demonstrate that by engineering all controller reactions to be much faster than dilution, set-point regulation can be achieved even in the presence of a leaky integrator. Furthermore, by engineering controller parameters for a second layer of time-scale separation, arbitrarily small tracking error can be achieved under certain technical conditions. We demonstrate a realization of our design principle through a small RNA feedback circuit.