Structural conserved moiety splitting of a stoichiometric matrix

• Published in: Journal of theoretical biology 2020-08, Vol.499 (C), p.110276-110276, Article 110276
• Main Authors: Ghaderi, Susan, Haraldsdóttir, Hulda S., Ahookhosh, Masoud, Arreckx, Sylvain, Fleming, Ronan M.T.
• Format: Article
• Language: English
• Subjects: BASIC BIOLOGICAL SCIENCES; Conserved moiety; Hypergraph; life sciences & biomedicine; mathematical & computational biology; Mathematical modelling; Moiety matrix splitting; moitey matrix splitting; Reaction network; Stoichiometric matrix
• ISSN: 0022-5193; 1095-8541
• DOI: 10.1016/j.jtbi.2020.110276

•Biochemical networks are a special class of hypergraph.•A stoichiometric matrix is an incidence matrix for a hypergraph.•A stoichiometric matrix is not an arbitrary rectangular matrix.•It is the sum of a set of conserved moiety subnetwork incidence matrices. Characterising biochemical reaction network structure in mathematical terms enables the inference of functional biochemical consequences from network structure with existing mathematical techniques and spurs the development of new mathematics that exploits the peculiarities of biochemical network structure. The structure of a biochemical network may be specified by reaction stoichiometry, that is, the relative quantities of each molecule produced and consumed in each reaction of the network. A biochemical network may also be specified at a higher level of resolution in terms of the internal structure of each molecule and how molecular structures are transformed by each reaction in a network. The stoichiometry for a set of reactions can be compiled into a stoichiometric matrix N∈Zm×n, where each row corresponds to a molecule and each column corresponds to a reaction. We demonstrate that a stoichiometric matrix may be split into the sum of m−rank(N) moiety transition matrices, each of which corresponds to a subnetwork accessible to a structurally identifiable conserved moiety. The existence of this moiety matrix splitting is a property that distinguishes a stoichiometric matrix from an arbitrary rectangular matrix.