Absolutely Robust Controllers for Chemical Reaction Networks

TL;DR

This paper introduces a novel class of controllers for chemical reaction networks that leverage absolute concentration robustness to achieve robust regulation of a target species in both deterministic and stochastic settings.

Contribution

It develops a new control framework using ACR properties, applicable to complex biochemical systems, and demonstrates its effectiveness through theoretical analysis and practical examples.

Findings

Controllers achieve robust regulation of target species.

Target species distribution approximates a Poisson with desired mean.

ACR controllers enable perfect adaptation and complement existing methods.

Abstract

In this work, we design a type of controller that consists of adding a specific set of reactions to an existing mass-action chemical reaction network in order to control a target species. This set of reactions is effective for both deterministic and stochastic networks, in the latter case controlling the mean as well as the variance of the target species. We employ a type of network property called absolute concentration robustness (ACR). We provide applications to the control of a multisite phosphorylation model as well as a receptor-ligand signaling system. For this framework, we use the so-called deficiency zero theorem from chemical reaction network theory as well as multiscaling model reduction methods. We show that the target species has approximately Poisson distribution with the desired mean. We further show that ACR controllers can bring robust perfect adaptation to a target species and are complementary to a recently introduced antithetic feedback controller used for stochastic chemical reactions.