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We give a concise development of some of the major algebraic properties of extreme pathways (pathways that cannot be the result of combining other pathways) of metabolic networks, contrasting them to those of elementary flux modes (pathways involving a minimal set of reactions). In particular, we show that an extreme pathway can be recognized by a rank test… (More)

Elementary mode analysis is a useful metabolic pathway analysis tool in understanding and analyzing cellular metabolism, since elementary modes can represent metabolic pathways with unique and minimal sets of enzyme-catalyzed reactions of a metabolic network under steady state conditions. However, computation of the elementary modes of a genome- scale… (More)

Elementary flux modes are an important class of metabolic pathways used to characterize the functioning and behavior of metabolic networks of biochemical reactions in a biological cell. The computation of the elementary flux modes is accomplished by using the so-called Nullspace Algorithm whose high computational cost and memory requirements still limit the… (More)

Background: Metabolic pathway analysis is a powerful tool to study the metabolic structure of a cellular metabolism that comprises an intricate network for transforming metabolites through enzyme-catalyzed reactions. The approach is based on convex analysis to solve a homogeneous system of linear equations and inequality constraints derived from the steady… (More)

Elementary flux modes give a mathematical representation of metabolic pathways in metabolic networks satisfying the constraint of non-decomposability. The large cost of their computation shifts attention to computing a minimal generating set which is a conically independent subset of elementary flux modes. When a metabolic network has reversible reactions… (More)

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