Universal structures for adaptation in biochemical reaction networks

At the molecular level, the evolution of life is driven by the generation and diversification of adaptation mechanisms. A universal description of adaptation-capable chemical reaction network (CRN) structures has remained elusive until now, since currently-known criteria for adaptation apply only to a tiny subset of possible CRNs. Here we identify the definitive structural requirements that characterize all adaptation-capable collections of interacting molecules, however large or complex. We show that these network structures implement a form of integral control in which multiple independent integrals can collaborate to confer the capacity for adaptation on specific molecules. Using an algebraic algorithm informed by these findings, we demonstrate the existence of embedded integrals in a variety of biologically important CRNs that have eluded previous methods, and for which adaptation has been observed experimentally. This definitive picture of biological adaptation at the level of intermolecular interactions represents a blueprint for adaptation-capable signaling networks across all domains of life, and for the design of synthetic biosystems.