A new method for the mathematical analysis of large metabolic networks is presented. Based on the fact that the occurrence of a metabolic reaction generally requires the existence of other reactions providing its substrates, series of metabolic networks are constructed. In each step of the corresponding expansion process those reactions are incorporated whose substrates are made available by the networks of the previous generations. The method is applied to the set of all metabolic reactions included in the KEGG database. Starting with one or more seed compounds, the expansion results in a final network whose compounds define the scope of the seed. Scopes of all metabolic compounds are calculated and it is shown that large parts of cellular metabolism can be considered as the combined scope of simple building blocks. Analyses of various expansion processes reveal crucial metabolites whose incorporation allows for the increase in network complexity. Among these metabolites are common cofactors such as NAD+, ATP, and coenzyme A. We demonstrate that the outcome of network expansion is in general very robust against elimination of single or few reactions. There exist, however, crucial reactions whose elimination results in a dramatic reduction of scope sizes. It is hypothesized that the expansion process displays characteristics of the evolution of metabolism such as the temporal order of the emergence of metabolic pathways.
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Dandekar T, Moldenhauer F, Bulik S, Bertram H, Schuster S (2003) A method for classifying metabolites in topological pathway analyses based on minimization of pathway number. BioSystems 70:255–270 CrossRefPubMedGoogle Scholar
Ebenhöh O, Heinrich R (2003) Stoichiometric design of metabolic networks: multi-functionality, clusters, optimization, weak and strong robustness. Bull Math Biol 65:323–357 CrossRefPubMedGoogle Scholar
Ebenhöh O, Handorf T, Heinrich R (2004) Structural analysis of expanding metabolic networks. Genome Informatics 15:35–45 Google Scholar
Heinrich R, Schuster S (1996) The regulation of cellular systems. Chapman and Hall, New York Google Scholar
Heinrich R, Schuster S, Holzhütter HG (1991) Mathematical analysis of enzymic reaction systems using optimization principles. Eur J Biochem 201:1−21 CrossRefPubMedGoogle Scholar
Horowitz NH (1945) On the evolution of biochemical syntheses. Proc Natl Acad Sci 31:153–157 Google Scholar
Jeong H, Tombor B, Albert R, Oltvai ZN, Barab’asi AL (2000) The large−scale organization of metabolic networks. Nature 407:651–654 CrossRefPubMedGoogle Scholar
Martin W, Russell MJ (2003) On the origins of cells: a hypothesis for the evolutionary transitions from abiotic geochemistry to chemoautotrophic prokaryotes, and from prokaryotes to nucleated cells. Phil Trans R Soc Lond B 358:59−85 CrossRefGoogle Scholar
Milo R, Shen−Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U (2002) Network motifs: simple building blocks of complex metabolic networks. Science 298:824–827 CrossRefPubMedGoogle Scholar
Papin JA, Price ND, Wiback SJ, Fell DA, Palsson BO (2003) Metabolic pathways in the post−genome era. TIBS 28:250–258 PubMedGoogle Scholar
Schomburg I, Chang A, Schomburg D (2002) BRENDA, enzyme data and metabolic information. Nucleic Acids Res 30:47–49 CrossRefPubMedGoogle Scholar
Schuster S, Hilgetag C (1994) On elementary flux modes in biochemical reaction systems at steady state. J Biol Syst 2:165–182 CrossRefGoogle Scholar
Schuster S, Fell DA, Dandekar T (2000) A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nature Biotechnol 18:326–332CrossRefGoogle Scholar
Wagner A, Fell DA (2001) The small world inside large metabolic networks. Proc R Soc Lond B 268:1803–1810 CrossRefGoogle Scholar