Time‑varying performance of quasi‑integral feedback control in cells

Determine the tracking and disturbance‑rejection performance of the phosphorylation‑cycle‑based quasi‑integral feedback controller for gene expression (the quasi‑integral control system defined in equation (phoQIC)) when disturbances and/or reference inputs are time‑varying, including scenarios that require trajectory tracking in living cells.

Background

The paper develops a quasi‑integral feedback (QIC) architecture implemented via a fast covalent modification (phosphorylation) cycle to achieve robust adaptation of a genetic module’s output in mammalian cells. Analysis and experiments address constant (step) disturbances and constant references.

The authors note that many applications involve time‑varying references and perturbations, e.g., trajectory tracking under varying cellular conditions, but the performance of the closed‑loop QIC system in these time‑varying scenarios has not yet been established.