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Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous-time Markov processes. In this manuscript, the identifiability of the underlying network structure with a given stochastic system dynamics is studied. It is shown that some data types related to the associated stochastic dynamics can uniquely identify the underlying network structure as well as the system parameters. The accuracy of the presented network inference is investigated when given dynamical data are obtained via stochastic simulations. 

In all higher organisms, life begins with a single cell. During the early stages of development, this single cell grows and divides multiple times to develop into the many different kinds of cells that make up an organism. This is a highly regulated process during which cells receive instructions telling them what kind of cell to become. These instructions are relayed via genes, and a particular combination of activated genes determines the cell’s fate. Specific pieces of DNA, known as enhancers, act as switches that control when and where genes are active, while so-called shadow enhancers are found in groups and work together to turn on the same gene in a similar way. Shadow enhancers are often active during the early stages of life to direct the formation of specialized cells in different parts of the body. But so far, it has been unclear why it is beneficial to the divide the role of activating genes across several shadow enhancers rather than a single one. Here, Waymack et al. examined shadow enhancers around a gene called Kruppel in embryos of the fruit fly Drosophila melanogaster . Manipulating the shadow enhancers showed that they help to make gene activity more resistant to changes. Factors such as fluctuations in temperature have different effects on each shadow enhancer. Having several shadow enhancers working together ensures that, whatever happens, the right genes still get activated. For genes like Kruppel , which are key for healthy development, the ability to withstand unexpected changes is a valuable evolutionary benefit. The study of Waymack et al. reveals why shadow enhancers are involved in the regulation of many genes, which may help to better understand developmental defects. Many conditions caused by such defects are influenced by both genetics and the environment. Genetic illnesses can vary in severity, which may be related to the roles of shadow enhancers. As such, studying shadow enhancers could lead to new approaches for treating genetic diseases. 

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 signalling 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.