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Abstract
Many signaling systems show adaptation-the ability to reset themselves after responding
to a stimulus. We computationally searched all possible three-node enzyme network
topologies to identify those that could perform adaptation. Only two major core topologies
emerge as robust solutions: a negative feedback loop with a buffering node and an
incoherent feedforward loop with a proportioner node. Minimal circuits containing
these topologies are, within proper regions of parameter space, sufficient to achieve
adaptation. More complex circuits that robustly perform adaptation all contain at
least one of these topologies at their core. This analysis yields a design table highlighting
a finite set of adaptive circuits. Despite the diversity of possible biochemical networks,
it may be common to find that only a finite set of core topologies can execute a particular
function. These design rules provide a framework for functionally classifying complex
natural networks and a manual for engineering networks. For a video summary of this
article, see the PaperFlick file with the Supplemental Data available online.