A hidden integral structure endows absolute concentration robust systems with resilience to dynamical concentration disturbances

Abstract

Biochemical systems that express certain chemical species of interest at the same level at any positive steady state 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, provided that the system reaches a (potentially new) positive steady state. Such a property has been proven to be of importance 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 than was previously known. 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 the 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. We further note that while the best performance of the insulators are achieved when these act at a faster timescale than the upstream module (as typically required), it is not necessary for them to act on a faster timescale than the downstream module in our construction.

RNA Compensation: A Positive Feedback Insulation Strategy for RNA-Based Transcription Networks

“…Under cellular conditions, the phosphorated OmpR (OmpR-P) is insensitive to both variations in OmpR and EnvZ, meaning ACR of OmpR-P is achieved. 38 This is implemented catalytically through the bifunctional enzymes acting as both kinase and phosphatase. Other examples of ACR found in nature include the glyoxylate bypass regulation system that is also implemented through the action of catalytic biomolecules.…”

“…In this system, EnvZ serves to phosphorylate and desphorylate the response regulator OmpR. Under cellular conditions, the phosphorated OmpR (OmpR-P) is insensitive to both variations in OmpR and EnvZ, meaning ACR of OmpR-P is achieved . This is implemented catalytically through the bifunctional enzymes acting as both kinase and phosphatase.…”

Absolutely robust controllers for chemical reaction networks

“…For the simple mass-action ACR system which is a nonlinear integral feedback relation. Such types of integral feedback loops appear in many different biochemical systems [7,9,33,46,47].…”

Protein–protein complexes can undermine ultrasensitivity-dependent biological adaptation

“…There also exist a number of other studies which use simple feedback structures to create RPA (and approximate RPA) capable networks, but these are also predicated on the use of Michaelis-Menten kinetics [10,49,[51][52][53][57][58][59]61]. In addition, there are a range of analytical and semi-analytical methods, based on time-scale separation [43], control theoretic approaches [53,58,61] and chemical reaction network theory (CRNT) [30,[69][70][71][72], which have successfully been used in the literature to identify RPA capacity (including the capacity for approximate (imperfect) RPA, as well as the special case of RPA known as absolute concentration robustness (ACR)) in a range of signalling networks. While these methods may prove useful for identifying parameter conditions that promote RPA, comparing biologically important functionalities, such as the range of inputs for which RPA obtains, elude these approaches.…”