Structural conserved moiety splitting of a stoichiometric matrix

Journal of Theoretical Biology, vol. 499, pp. 110276

Abstract

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.

Authors 5

1. Susan Ghaderi

   University of Luxembourg · Luxembourg Centre for Systems Biomedicine

   Affiliation as printed

   Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue du Swing, Belvaux L-4362, Luxembourg

2. Hulda S. Haraldsdóttir

   University of Luxembourg · Luxembourg Centre for Systems Biomedicine

   Affiliation as printed

   Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue du Swing, Belvaux L-4362, Luxembourg

3. Masoud Ahookhosh

   KU Leuven · University of Luxembourg · Luxembourg Centre for Systems Biomedicine

   Affiliation as printed

   Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue du Swing, Belvaux L-4362, Luxembourg; Department of Electrical Engineering (ESAT-STADIUS)- KU Leuven, Kasteelpark Arenberg 10, Leuven 3001, Belgium

   Department of Electrical Engineering (ESAT-STADIUS)- KU Leuven, Kasteelpark Arenberg 10, Leuven 3001, Belgium

   Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue du Swing, Belvaux L-4362, Luxembourg

4. Sylvain Arreckx

   University of Luxembourg · Luxembourg Centre for Systems Biomedicine

   Affiliation as printed

   Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue du Swing, Belvaux L-4362, Luxembourg

5. Ronan M. T. Fleming corresponding Aachen Analytical Biosciences Division of Systems Biomedicine and Pharmacology Leiden Academic Centre for Drug Research

   Leiden University · University of Luxembourg · Luxembourg Centre for Systems Biomedicine

   Affiliation as printed

   Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue du Swing, Belvaux L-4362, Luxembourg; Analytical Biosciences, Division of Systems Biomedicine and Pharmacology, Leiden Academic Centre for Drug Research, Leiden University, Leiden, the Netherlands. Electronic address: ronan.mt.fleming@gmail.com

   Analytical Biosciences, Division of Systems Biomedicine and Pharmacology, Leiden Academic Centre for Drug Research, Leiden University, Leiden, the Netherlands

   Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue du Swing, Belvaux L-4362, Luxembourg