CRNs

CRNs is an acronym that can refer to several terms; in science the most common usage is chemical reaction networks, a formal representation of chemical reactions among molecular species. A CRN consists of a set of chemical species, a set of reactions, and stoichiometric coefficients describing how species are consumed and produced. Reactions can be represented by directed edges between complexes, and there are two common graph forms: the complex graph, whose nodes are formal sums of species (complexes) and whose edges are reactions, and the reaction graph, where nodes are individual reactions.

In a deterministic setting, CRNs are modeled with mass-action kinetics; the state is a vector of species concentrations, and the evolution is described by ordinary differential equations derived from stoichiometry and rate constants. In stochastic settings, particularly at small copy numbers, CRNs are modeled as continuous-time Markov chains or via the chemical master equation, capturing random discrete events of reaction occurrences.

Reaction network theory studies properties such as persistence, multistationarity, and stability. Key results include the deficiency zero and deficiency one theorems, which give conditions for the existence and uniqueness of equilibria and, in some cases, their stability. Network structure, such as reversibility and the presence of conservation laws, strongly influences dynamics and long-term behavior.

Applications span modelling metabolic pathways, gene regulatory and signaling networks, and the design of synthetic biochemical circuits in systems and synthetic biology, as well as chemical engineering. The acronym also refers to the Clinical Research Network in the United Kingdom, which coordinates clinical trials and supports research infrastructure.