Characterisation of conserved and reacting moieties in chemical reaction networks

A detailed understanding of biochemical networks at the molecular level is essential for studying complex cellular processes. In this paper, we provide a structural description of biochemical networks by considering individual atoms and chemical bonds. To address combinatorial complexity, we introduce a well-established approach to group similar types of information within biochemical networks. A conserved moiety is a set of atoms whose association is invariant across all reactions in a network and arises from the decomposition of the reaction network. A reacting moiety is a set of bonds that are either broken, formed, or undergo a change in bond order in at least one reaction in the network and arises from the decomposition of the molecular network. By mathematically identifying these moieties, and by developing the link between these two decompositions, we establish the biological significance of conserved and reacting moieties according to the mathematical properties of the stoichiometric matrix. We also present a novel decomposition of the stoichiometric matrix based on conserved moieties. This approach establishes a clear connection between graph theory, linear algebra, and biological interpretation, thus offering new perspectives for the study of chemical reaction networks.