How to suppress stochastic fluctuations while achieving adaptation with biologically realistic integral controllers

A key challenge in biology is identifying biochemical modules with network-independent properties. Antithetic integral feedback (AIF) is a recently proposed module in which two species perfectly annihilate each other's biological activity. The AIF module ensures the steady-state average level of any cellular component remains constant under sustained perturbations, regardless of that component's uncontrolled dynamics. However, recent work has suggested that such robustness comes at the expense of increased stochastic fluctuations. We present theoretical results that support and quantify this trade-off for the commonly analyzed AIF variant in the non-biological limit with perfect annihilation. However, we find that this trade-off is a singular behaviour of the idealized module: even minute deviations from perfect adaptation permit significant noise suppression. While our results highlight the energetic cost of simultaneously achieving robust averages and reducing stochastic fluctuations, they show that there is no fundamental trade-off between the two. This is further supported by data for other variants of the AIF module that can reduce noise even in the idealized case, which highlights that some realizations of the AIF module have preferrable noise properties for synthetic biology applications.