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

TL;DR

This paper reveals a hidden integral structure in ACR biochemical systems that enhances their robustness, allowing them to withstand a broader range of disturbances and maintain stable concentrations, which is crucial for synthetic biology applications.

Contribution

The paper proves the existence of a hidden integral structure in ACR systems, increasing their robustness and enabling better modular design in synthetic biology.

Findings

Hidden integral structure in ACR systems identified

Enhanced robustness against general disturbances demonstrated

Robust perfect adaptation maintained under network interconnection

Abstract

Biochemical systems that express certain chemical species of interest at the same level at any positive equilibrium are called "absolute concentration robust" (ACR). These species behave in a stable, predictable way, in the sense that their expression is robust with respect to sudden changes in the species concentration, regardless the new positive equilibrium reached by the system. Such a property has been proven to be fundamentally important in certain gene regulatory networks and signaling systems. In the present paper, we mathematically prove that a well-known class of ACR systems studied by Shinar and Feinberg in 2010 hides an internal integral structure. This structure confers these systems with a higher degree of robustness that what was previously unknown. In particular, disturbances much more general than sudden changes in the species concentrations can be rejected, and robust perfect adaptation is achieved. Significantly, we show that these properties are maintained when the system is interconnected with other chemical reaction networks. This key feature enables design of insulator devices that are able to buffer the loading effect from downstream systems - a crucial requirement for modular circuit design in synthetic biology.