High rates of fuel consumption are not required by insulating motifs to suppress retroactivity in biochemical circuits

Retroactivity arises when the coupling of a molecular network U to a downstream network D results in signal propagation back from D to U . The phenomenon represents a breakdown in modularity of biochemical circuits and hampers the rational design of complex functional networks. Considering simple models of signal-transduction architectures, we demonstrate the strong dependence of retroactivity on the properties of the upstream system, and explore the cost and efficacy of fuel-consuming insulating motifs that can mitigate retroactive effects. We find that simple insulating motifs can suppress retroactivity at a low fuel cost by coupling only weakly to the upstream system U . However, this design approach reduces the signalling network’s robustness to perturbations from leak reactions, and potentially compromises its ability to respond to rapidly-varying signals.