326 NATURE BIOTECHNOLOGY VOL 18 MARCH 2000 http://biotech.nature.com RESEARCH ARTICLES Cellular metabolism is often much more plastic than the set of path- ways defined in biochemistry textbooks 1,2 . It is not always straight- forward to determine the metabolic route that leads from a particu- lar starting material to (a) given product(s), or to decide whether a particular enzyme is essential in the process. These issues have attracted increased interest with the growth of functional genomics 3-8 . For example, DNA arrays allow study of comprehensive patterns of gene expression 6 . Will it be possible to interpret these data in terms of how the metabolic phenotype is changing? Currently, three different but related approaches are advocated for mapping biochemical networks without preconceptions. Each of these benefits from not requiring kinetic information. First, methods were developed for constructing transformation routes leading from a given substrate to a given product by successive addition of reaction steps 9,10 . Second, it was suggested to use a set of linearly independent basis vectors in flux space 5,11,12 . In other words, such a set contains flux distributions (regarded geometri- cally as vectors in a space) from which, by adding or substracting multiples of them, all admissible flux distributions can be obtained. However, the choice of the basis vectors to describe this space is not unique. Finally, building on the stoichiometric net- work analysis of Clarke 13 and earlier work on futile cycles 14 , the concept of ‘elementary flux modes’ 15-17 was introduced. An ele- mentary mode is a minimal set of enzymes that could operate at steady state, with the enzymes weighted by the relative flux they need to carry for the mode to function (Figs 1, 2). ‘Minimal’ means that if only the enzymes belonging to this set were operating, com- plete inhibition of one of these would lead to cessation of any steady-state flux in the system. This allows detection of the full set of nondecomposable steady-state flows that the network can sup- port, including cyclic flows. Any steady-state flux pattern can be expressed as a non-negative linear combination of these modes (in a sense, a mixture of pure states) to form a unique set. For a com- parison of the three methods, see also ref. 18. For reasons to be explained later, information on kinetics and regulatory interactions is not needed to define the modes. Thus, it can easily be determined whether a stoichiometrically balanced path exists between a particular set of substrates and products, capturing the essential network character of biochemical transfor- mations. Note that it would not suffice to construct linear paths by following the successive conversions of metabolite molecules, because by-products that cannot be excreted by the cell have to be balanced by additional reactions, which produce further by-prod- ucts, and so on. We make a distinction between reversible and irreversible reac- tions. Irreversibility here means that the net flux always has the same sign under physiological conditions (Fig. 1). Any elementary mode has to use the irreversible reactions in the appropriate direction. In contrast to other approaches 5,9,13 , it is unnecessary to split reversible reactions into two oppositely directed irreversible steps, which would increase the number of the fluxes to be computed and require a time- consuming elimination of spurious cycles within reversible reactions. On the other hand, one often not only obtains modes situated on the boundary (“extreme currents” in Clarke’s terminology 13 ) of the admissible flux region (i.e. defined by flux combinations that corre- spond to valid steady states of the metabolic network), but also modes interior of this region, that are not independant of the extreme currents in a mathmatical sense, but are also elementary in the sense of not being decomposable 15,16 . The latter are elementary as well in the sense of not being decomposable into simpler modes. Metabolites are classified as internal or external according to whether or not they are to fulfill the quasi-steady-state condition. In other words, the total rate of production of each internal metabolite equals the total rate of its consumption. In contrast, external metabolites (which are alternatively called pool metabolites, or sources and sinks, and need not be extracellular) do not fulfill this condition because they participate in additional reactions that are not involved in the system under study. A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks Stefan Schuster 1 , David A. Fell 2 , and Thomas Dandekar 1,3 1 Department of Bioinformatics, Max Delbrück Center for Molecular Medicine, D-13092 Berlin-Buch, Germany. 2 School of Biological and Molecular Sciences, Oxford Brookes University, Oxford OX3 0BP, England. 3 Biocomputing and Structures Program, EMBL, D-69012 Heidelberg, Germany. Received 30 October 1998; accepted 21 December 1999 A set of linear pathways often does not capture the full range of behaviors of a metabolic network. The concept of ‘elementary flux modes’ provides a mathematical tool to define and comprehensively describe all metabolic routes that are both stoichiometrically and thermodynamically feasible for a group of enzymes. We have used this concept to analyze the interplay between the pentose phosphate pathway (PPP) and glycolysis. The set of elementary modes for this system involves conventional glycolysis, a futile cycle, all the modes of PPP function described in biochemistry textbooks, and additional modes that are a priori equally entitled to pathway status. Applications include maximizing product yield in amino acid and antibiotic synthesis, reconstruction and consistency checks of metabolism from genome data, analysis of enzyme deficiencies, and drug target identification in metabolic networks. Keywords: elementary modes, metabolic networks, functional genomics, stochiometric network analysis © 2000 Nature America Inc. • http://biotech.nature.com © 2000 Nature America Inc. • http://biotech.nature.com