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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.
Autocatalysis underlies the ability of chemical and biochemical systems to replicate. Recently, Blokhuis et al. gave a stoechiometric definition of autocatalysis for reaction networks, stating the existence of a combination of reactions such that the
The Bond Graph approach and the Chemical Reaction Network approach to modelling biomolecular systems developed independently. This paper brings together the two approaches by providing a bond graph interpretation of the chemical reaction network conc
The use of mathematical models has helped to shed light on countless phenomena in chemistry and biology. Often, though, one finds that systems of interest in these fields are dauntingly complex. In this paper, we attempt to synthesize and expand upon
Chemical reaction networks (CRNs) are fundamental computational models used to study the behavior of chemical reactions in well-mixed solutions. They have been used extensively to model a broad range of biological systems, and are primarily used when
A decomposition of a chemical reaction network (CRN) is produced by partitioning its set of reactions. The partition induces networks, called subnetworks, that are smaller than the given CRN which, at this point, can be called parent network. A compl