Toward single-cell control: noise-robust perfect adaptation in biomolecular systems.

Robust perfect adaptation (RPA), whereby a consistent output level is maintained even after a disturbance, is a highly desired feature in biological systems. This property can be achieved at the population average level by combining the well-known antithetic integral feedback (AIF) loop into the target network. However, the AIF controller amplifies the noise of the output level, disrupting the single-cell level regulation of the system output and compromising the conceptual goal of stable output level control. To address this, we introduce a regulation motif, the noise controller, which is inspired by the AIF loop but differs by sensing the output levels through the dimerization of output species. Combining this noise controller with the AIF controller successfully maintained system output noise as well as mean at their original level, even after the perturbation, thereby achieving noise RPA. Furthermore, our noise controller could reduce the output noise to a desired target value, achieving a Fano factor as small as 1, the commonly recognized lower bound of intrinsic noise in biological systems. Notably, our controller remains effective as long as the combined system is ergodic, making it applicable to a broad range of networks. We demonstrate its utility by combining the noise controller with the DNA repair system of Escherichia coli, which reduced the proportion of cells failing to initiate the DNA damage response. These findings enhance the precision of existing biological controllers, marking a key step toward achieving single-cell level regulation.