  Retroactivity arises when the coupling of a molecular network $\mathcal{U}$
to a downstream network $\mathcal{D}$ results in signal propagation back from
$\mathcal{D}$ to $\mathcal{U}$. 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 $\mathcal{U}$. 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.
