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Biochemical systems that express certain chemical species of interest at thesame level at any positive equilibrium are called "absolute concentrationrobust" (ACR). These species behave in a stable, predictable way, in the sensethat their expression is robust with respect to sudden changes in the speciesconcentration, regardless the new positive equilibrium reached by the system.Such a property has been proven to be fundamentally important in certain generegulatory networks and signaling systems. In the present paper, wemathematically prove that a well-known class of ACR systems studied by Shinarand Feinberg in 2010 hides an internal integral structure. This structureconfers these systems with a higher degree of robustness that what waspreviously unknown. In particular, disturbances much more general than suddenchanges in the species concentrations can be rejected, and robust perfectadaptation is achieved. Significantly, we show that these properties aremaintained when the system is interconnected with other chemical reactionnetworks. This key feature enables design of insulator devices that are able tobuffer the loading effect from downstream systems - a crucial requirement formodular circuit design in synthetic biology.

A hidden integral structure endows Absolute Concentration Robust systems with resilience to dynamical concentration disturbances