Analysis of the pathway structure of metabolic networks

Metabolic networks comprise a multitude of enzymatic reactions carrying out various functions related to cell growth and product formation. Although such reactions are occasionally organized into biochemical pathways, a formal procedure is desired to identify the independent pathways in a bioreaction network and the degree of engagement of each individual reaction in these pathways. We present a procedure for the identification of the independent pathways of bioreaction networks of any size and complexity. The method makes use of the steady-state internal metabolite stoichiometry matrix and defines the independent pathways through the reaction membership of its kernel matrix. Examples from the aromatic amino acid biosynthetic pathway and central carbon metabolism of cells in culture are provided to illustrate the method. Applications to the analysis of the control structure of bioreaction networks are also discussed.