To reconstruct metabolic pathways from biochemical and/or genome sequence data, the stoichiometric and thermodynamic feasibility of the pathways has to be tested. This is achieved by characterizing the admissible region of flux distributions in steady state. This region is spanned by what can be called a convex basis. The concept of elementary flux modes provides a mathematical tool to define all metabolic routes that are feasible in a given metabolic network. In addition, we define enzyme subsets to be groups of enzymes that operate together in fixed flux proportions in all steady states of the system.