Conserved and reacting moieties of metabolic networks

A biochemical reaction network is generally represented as a stoichiometric hypergraph, where each vertex corresponds to a metabolite and each hyperedge represents a reaction. While this representation provides an accurate algebraic and graphical description of metabolic networks, it lacks essential graph-theoretic structures, such as cycles and spanning trees, which are central to topological and structural analysis. Each metabolite can also be represented as a molecular graph, where each vertex corresponds to an atom and each edge represents a chemical bond. This molecular representation at the level of atoms and bonds enables the identifica tion of conserved and reacting structures. A conserved moiety is defined as a group of atoms whose association remains invariant across all reactions in the network. A reacting moiety is a group of bonds that are broken, formed, or change order in at least one reaction. This thesis bridges these two levels of representation by introducing a new method to identify conserved and reacting moieties, enabling a mathematically and biologically meaningful representation of biochemical systems. First, we introduce and develop a well-established mathematical method to identify con served and reacting moieties. This framework enables the representation of a biochemical network at three interrelated levels: the established metabolite–reaction level, an atom–bond resolution level, and a newly defined conserved–reacting moiety level. The method enhances structural resolution and biological interpretability by bridging these scales. Second, we relate the stoichiometric hypergraph to a set of graph incidence matrices, where each graph corresponds to a moiety transition graph associated with one species of conserved moiety. This representation provides a graph-theoretical interpretation of the four fundamental subspaces of the stoichiometric matrix and establishes a direct link between the algebraic structure of metabolic models and the topological features of moiety-based graphs, offering new analytical tools for interpreting network structure and modularity. Finally, we develop a preprocessing method for splitting lumped reactions in metabolic networks using sparse flux analysis. This approach improves chemical granularity by replacing lumped reactions with stoichiometrically equivalent elementary steps, enabling more accurate structural interpretation. This preprocessing step prepares the network for the application of our mathematical framework for conserved and reacting moieties to a real-world genome-scale model. As an illustrative case, we focus on a segment of mitochondrial β-oxidation, showing how this procedure reduces combinatorial complexity and enhances interpretability in a biologically relevant setting. Overall, this work introduces a multiscale modelling framework that connects chemical structures to the algebraic foundations of constraint-based models. By integrating moiety level representations, the thesis enhances the interpretability, modularity, and scalability of biochemical network analysis. While not demonstrating all possible applications, this approach provides a foundation with potential relevance for systems biology, metabolic engineering, and data-driven model refinement.

Publisher

University of Galway

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CC BY-NC-ND

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University of Galway Theses (PhD Theses)