Topology of Plant Metabolic Networks

  • Eva Grafahrend-Belau
  • Björn H. Junker
  • Christian Klukas
  • Dirk Koschützki
  • Falk Schreiber
  • Henning Schwöbbermeyer

Metabolic networks can be modeled as graphs, i.e., mathematical structures consisting of vertices (representing objects such as metabolites) and edges/hyper-edges (representing the connection between objects such as reactions). An example of a very simple metabolic network is shown in Fig. 7.1. Often the term network refers to an informal concept describing a structure composed of objects and connections, whereas the term graph refers to an abstract mathematical structure formed by a set of vertices and a set of edges. For simplicity, we will consider both terms equivalent in the following.


Metabolic Network Average Path Length Network Motif Closeness Centrality Target Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Albert I, Albert R (2004) Conserved network motifs allow protein-protein interaction prediction. Bioinformatics 20:3346–3352.PubMedCrossRefGoogle Scholar
  2. 2.
    Arita M (2004) The metabolic world of Escherichia coli is not small. Proc Natl Acad Sci USA 101:1543–1547.PubMedCrossRefGoogle Scholar
  3. 3.
    Artzy-Randrup Y, Fleishman SJ, Ben-Tal N, Stone L (2004) Comment on “Network motifs: simple building blocks of complex networks” and “Superfamilies of evolved and designed networks”. Science 305:1107c.CrossRefGoogle Scholar
  4. 4.
    Backhaus K, Erichson B, Plinke W, Weiber R (2003) Multivariate Analysis Methods. An Application-Oriented Introduction, 10th ed., Springer, Berlin.Google Scholar
  5. 5.
    Barabási AL, Oltvai ZN (2004) Network biology: understanding the cell’s functional organization. Nat Rev Genet 5:101–113.PubMedCrossRefGoogle Scholar
  6. 6.
    Batagelj V, Mrvar A (2004) Pajek – Analysis and visualization of large networks. In: Jünger M, Mutzel P (eds) Graph Drawing Software (Mathematics and Visualization). Springer, Berlin/Heidelberg, pp. 77–103.Google Scholar
  7. 7.
    Becker MY, Rojas I (2001) A graph layout algorithm for drawing metabolic pathways. Bioinformatics 17:461–467.PubMedCrossRefGoogle Scholar
  8. 8.
    Berg JM, Tymoczko JL, Stryer L (2002) Biochemistry. W H Freeman, New York.Google Scholar
  9. 9.
    Borisjuk L, Hajirezaei MR, Klukas C, Rolletschek H, Schreiber F (2005) Integrating data from biological experiments into metabolic networks with the DBE information system. In Silico Biology 5:93–102.PubMedGoogle Scholar
  10. 10.
    Brandenburg FJ, Forster M, Pick A, Raitner M, Schreiber F (2004) BioPath – exploration and visualization of biochemical pathways. In: Jünger M, Mutzel P (eds) Graph Drawing Software (Mathematics and Visualization). Springer, Berlin/Heidelberg, pp. 215–236.Google Scholar
  11. 11.
    Brandenburg FJ, Jünger M, Mutzel P (1997) Algorithmen zum automatischen Zeichnen von Graphen. Informatik Spektrum 20:199–207.CrossRefGoogle Scholar
  12. 12.
    Brandes U, Wagner D (2004) Visone – analysis and visualization of social networks. In: Jünger M, Mutzel P (eds) Graph Drawing Software (Mathematics and Visualization). Springer, Berlin/Heidelberg, pp. 321–340.Google Scholar
  13. 13.
    Breitkreutz BJ, Stark C, Tyers M (2003) Osprey: a network visualization system. Genome Biology 4: R22.PubMedCrossRefGoogle Scholar
  14. 14.
    Card SK, Mackinlay JD, Shneiderman B (1999) Readings in Information Visualization: Using Vision to Think. Morgan Kaufmann Publ. Inc., San Francisco, CA.Google Scholar
  15. 15.
  16. 16.
    Chung HJ, Kim M, Park CH, Kim J, Kim JH (2004) ArrayXPath: mapping and visualizing microarray gene-expression data with integrated biological pathway resources using scalable vector graphics. Nucleic Acids Res 32(Web-Server-Issue):460–464.CrossRefGoogle Scholar
  17. 17.
    Colantuoni C, Henry G, Zeger S, Pevsner J (2002) SNOMAD (standardization and normalization of microarray data): web-accessible gene expression data analysis. Bioinformatics 18:1540–1541.PubMedCrossRefGoogle Scholar
  18. 18.
    Demir E, Babur, O Dogrusoz U, Gursoy A, Nisanci G, Cetin-Atalay R, Ozturk M (2002) PATIKA: an integrated visual environment for collaborative construction and analysis of cellular pathways. Bioinformatics 18:996–1003.PubMedCrossRefGoogle Scholar
  19. 19.
    Di Battista G, Eades P, Tamassia R, Tollis IG (1994) Annotated bibliography on graph drawing algorithms. Comput Geom-Theor Appl 4:235–282.Google Scholar
  20. 20.
    Di Battista G, Eades P, Tammasia R, Tollis IG (1999) Graph drawing: algorithms for the visualization of graphs. Prentice Hall, New Jersey.Google Scholar
  21. 21.
    Dobrin R, Beg QK, Barabási AL, Oltvai ZN (2004) Aggregation of topological motifs in the Escherichia coli transcriptional regulatory network. BMC Bioinformatics 5:10.PubMedCrossRefGoogle Scholar
  22. 22.
    Dogrusoz U, Giral E, Cetintas A, Civril A, Demir E (2004) A compound graph layout algorithm for biological pathways. In: Pach J (ed.) Graph Drawing. Springer, Berlin/Heidelberg, pp. 442–447.Google Scholar
  23. 23.
    van Dongen SM (2000) Graph Clustering by Flow Simulation. Center for Mathematics and Computer Science, Amsterdam.Google Scholar
  24. 24.
    Dysvik B, Jonassen I (2001) J-Express: exploring gene expression data using Java. Bioinformatics 17:369–370.PubMedCrossRefGoogle Scholar
  25. 25.
    Eades P (1984) A heuristic for graph drawing. Congr Numer 41:149–160.Google Scholar
  26. 26.
    Eades P, Sugiyama K (1990) How to draw a directed graph. J Inform Proc 13:424–437.Google Scholar
  27. 27.
    Ederer M, Sauter T, Bullinger E, Gilles ED, Allgöwer F (2003) An approach for dividing models of biological reaction networks into functional units. Simulation 79:703–716.CrossRefGoogle Scholar
  28. 28.
    Eom YH, Lee S, Jeong H (2006) Exploring local structural organization of metabolic networks using subgraph patterns. J Theor Biol 241:823–829.PubMedGoogle Scholar
  29. 29.
    Everitt BS, Landau S, Leese M (2001) Cluster analysis. Oxford University Press Inc., New York.Google Scholar
  30. 30.
  31. 31.
    Fellenberg M, Mewes HW (1999) Interpreting clusters of gene expression profiles in terms of metabolic pathways. In: Giegerich R, Hofestädt R, Lengauer T, Mewes W, Schomburg D, Vingron M, Wingender E (eds) German Conference on Bioinformatics, Springer. pp. 185–187.Google Scholar
  32. 32.
    Fiehn O, Kopka J, Dörmann P, Altmann T, Trethewey R, Willmitzer L (2000) Metabolite profiling for plant functional genomics. Nature Biotechnol 18:1157–1161.CrossRefGoogle Scholar
  33. 33.
  34. 34.
    Fruchterman TMJ, Reingold EM (1991) Graph drawing by force-directed placement. Software Practice and Experience 21:1129–1164.CrossRefGoogle Scholar
  35. 35.
    Gagneur J, Jackson DB, Casari G (2003) Hierarchical analysis of dependency in metabolic networks. Bioinformatics 19:1027–1034.PubMedCrossRefGoogle Scholar
  36. 36.
    Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci USA 99:7821–7826.PubMedCrossRefGoogle Scholar
  37. 37.
    Girvan M, Newman MEJ (2004) Finding and evaluating community structure in networks. Phys Rev E 69(026113).Google Scholar
  38. 38.
    Guimerà R, Nunes Amaral LA (2005) Functional cartography of complex metabolic networks. Nature 443:895–900.CrossRefGoogle Scholar
  39. 39.
    Han J, Kamber M (2001) Data Mining, Concepts and Techniques. Morgan Kaufmann Publishers, USA.Google Scholar
  40. 40.
  41. 41.
    Holme P, Huss M, Jeong H (2003) Subnetwork hierarchies of biochemical pathways. Bioinformatics 19:532–538.PubMedCrossRefGoogle Scholar
  42. 42.
    Hood L, Perlmutter RM (2004) The impact of systems approaches on biological problems in drug discovery. Nature Biotechnol 22:1215–1217.CrossRefGoogle Scholar
  43. 43.
    Hu Z, Mellor J, Wu J, Yamada T, Holloway D, DeLisi C (2005) VisANT: data-integrating visual framework for biological networks and modules. Nucl Acids Res 33(Web Server issue):W352–W3577.PubMedCrossRefGoogle Scholar
  44. 44.
    Hu Z, Mellor JC, Wu J, DeLisi C (2004) VisANT: an online visualization and analysis tool for biological interaction data. BMC Bioinformatics 5:17.PubMedCrossRefGoogle Scholar
  45. 45.
    Ingram PJ, Stumpf MP, Stark J (2006) Network motifs: structure does not determine function. BMC Genomics 7:108.PubMedCrossRefGoogle Scholar
  46. 46.
    Ishihara S, Fujimoto K, Shibata T (2005) Cross talking of network motifs in gene regulation that generates temporal pulses and spatial stripes. Genes to Cells 10:1025–1038.PubMedCrossRefGoogle Scholar
  47. 47.
    Jain AK, Dubes RC (1988) Algorithms for Clustering Data. Prentice Hall, New York.Google Scholar
  48. 48.
    Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. ACM Computing Surveys 31:264–323.CrossRefGoogle Scholar
  49. 49.
    Jeong H, Tombor B, Albert R, Oltvai ZN, Barabási AL (2000) The large-scale organization of metabolic networks. Nature 407:651–654.PubMedCrossRefGoogle Scholar
  50. 50.
    Junker BH, Klukas C, Schreiber F (2006) VANTED: A system for advanced data analysis and visualization in the context of biological networks. BMC Bioinformatics 7:109.PubMedCrossRefGoogle Scholar
  51. 51.
    Junker BH, Koschützki D, Schreiber F (2006) Exploration of biological network centralities with CentiBiN. BMC Bioinformatics 7:219.PubMedCrossRefGoogle Scholar
  52. 52.
    Kanehisa M, Goto S, Hattori M, Aoki-Kinoshita KF, Itoh M, Kawashima S, Katayama T, Araki M, Hirakawa M (2006) From genomics to chemical genomics: new developments in KEGG. Nucleic Acids Res 34:D354–D358.PubMedCrossRefGoogle Scholar
  53. 53.
    Karp PD, Ouzounis CA, Moore-Kochlacs C (2005) Expansion of the BioCyc collection of pathway/genome databases to 160 genomes. Nucleic Acids Research 33:6083–6089.PubMedCrossRefGoogle Scholar
  54. 54.
    Karp PD, Paley S (1994) Automated drawing of metabolic pathways. In: Hunter L, Searls D, Shavlik J (eds) Proc. 3rd International Conference on Bioinformatics and Genome Research, AAAI Press, New Jersey, pp. 207–215.Google Scholar
  55. 55.
    Karp PD, Paley SM (1993) Representation of metabolic knowledge: pathways. In: Altman R, Brutlag D, Karp PD, Lathrop R, Searls D (eds) Proc. 2nd International Conference on Intelligent Systems for Molecular Biology. AAAI Press, Menlo Park, California, pp. 225–238.Google Scholar
  56. 56.
    Karp PD, Riley M, Paley SM, Pellegrini-Toole A, Krummenacker M (1999) EcoCyc: encyclopedia of Escherichia coli genes and metabolism. Nucleic Acids Res 27:55–58.PubMedCrossRefGoogle Scholar
  57. 57.
    Karp PD, Riley M, Paley SM, Pellegrini-Toole A, Krummenacker M (2000) The EcoCyc and MetaCyc databases. Nucleic Acids Res 28:56–59.PubMedCrossRefGoogle Scholar
  58. 58.
    Kashtan N, Itzkovitz S, Milo R, Alon U (2002) Mfinder Tool Guide. Tech. Rep. Department of Molecular Cell Biology and Computer Science & Applied Mathematics, Weizman Institute of Science, Rehovot, Israel.Google Scholar
  59. 59.
    Kashtan N, Itzkovitz S, Milo R, Alon U (2004) Topological generalizations of network motifs. Physical Review E 70:031909.CrossRefGoogle Scholar
  60. 60.
    Kitano H (2004) Biological robustness. Nat Rev Genet 5:826–837.PubMedCrossRefGoogle Scholar
  61. 61.
    Kitano H, Funahashi A, Matsuoka Y, Oda K (2005) Using process diagrams for the graphical representation of biological networks. Nature Biotechnol 23:961–966.CrossRefGoogle Scholar
  62. 62.
    Koch I, Junker BH, Heiner M (2005) Application of Petri net theory for modelling and validation of the sucrose breakdown pathway in the potato tuber. Bioinformatics 21: 1219–1226.PubMedCrossRefGoogle Scholar
  63. 63.
    Koschützki D, Lehmann KA, Peeters L, Richter S, Tenfelde-Podehl D, Zlotowski O (2005) Centrality indices. In: Brandes U, Erlebach T (eds) Network Analysis: Methodological Foundations. Vol. 3418 of Lecture Notes in Computer Science (LNCS) Tutorial. Springer-Verlag, Springer Berlin/Heidelberg, pp. 16–61.Google Scholar
  64. 64.
    Kose F, Weckwerth W, Linke T, Fiehn, O (2001) Visualizing plant metabolomic correlation networks using clique-metabolite matrices. Bioinformatics 17:1198–1208.PubMedCrossRefGoogle Scholar
  65. 65.
    Krause AE, Frank KA, Mason DM, Ulanowicz RE, Taylor WW (2003) Compartments revealed in food-web structure. Nature 426:282–285.PubMedCrossRefGoogle Scholar
  66. 66.
    Krieger CJ, Zhang P, Müller LA, Wang A, Paley S, Arnaud M, Pick J, Rhee SY, Karp PD (2004) MetaCyc: a multiorganism data-base of metabolic pathways and enzymes. Nucleic Acids Res 32:438–442.CrossRefGoogle Scholar
  67. 67.
    Lee TI, Rinaldi NJ, Robert F, Odom DT, Bar-Joseph Z, Gerber GK, Hannett NM, Harbison CT, Thompson CM, Simon I, Zeitlinger J, Jennings EG, Murray HL, Gordon DB, Ren B, Wyrick JJ, Tagne JB, Volkert TL, Fraenkel E, Giord DK, Young RA (2002) Transcriptional regulatory networks in Saccharomyces cerevisiae. Science 298: 799–804.PubMedCrossRefGoogle Scholar
  68. 68.
    Lemke N, Herédia F, Barcellos CK, dos Reis AN, Mombach JCM (2004) Essentiality and damage in metabolic networks. Bioinformatics 20(1): 115–119.PubMedCrossRefGoogle Scholar
  69. 69.
    Ma HW, Zeng AP (2003) The connectivity structure, giant strong component and centrality of metabolic networks. Bioinformatics 19: 1423–1430.PubMedCrossRefGoogle Scholar
  70. 70.
    Ma HW, Zeng AP (2003) Reconstruction of metabolic networks from genome data and analysis of their global structure for various organisms. Bioinformatics 19:270–277.PubMedCrossRefGoogle Scholar
  71. 71.
    Ma HW, Zhao XM, Yuan YJ, Zeng AP (2004) Decomposition of metabolic network into functional modules based on the global connectivity structure of reaction graph. Bioinformatics 20:1870–1876.PubMedCrossRefGoogle Scholar
  72. 72.
    Mangan S, Itzkovitz S, Zaslaver A, Alon U (2006) The incoherent feed-forward loop accelerates the response-time of the gal system of Escherichia coli. J Mol Biol 356: 1073–1081.PubMedCrossRefGoogle Scholar
  73. 73.
    Mangan S, Zaslaver A, Alon U (2003) The coherent feed-forward loop serves as a sign-sensitive delay element in transcription networks. J Mol Biol 334:197–204.PubMedCrossRefGoogle Scholar
  74. 74.
  75. 75.
  76. 76.
    Michal G (1999) Biochemical Pathways. Spektrum Akademischer Verlag, Heidelberg.Google Scholar
  77. 77.
    Middendorf M, Ziv E, Wiggins CH (2005) Inferring network mechanisms: The Drosophila melanogaster protein interaction network. Proc Natl Acad Sci USA 102:3192–3197.PubMedCrossRefGoogle Scholar
  78. 78.
    Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheer M, Alon U (2004) Superfamilies of evolved and designed networks. Science 303:1538–1542.PubMedCrossRefGoogle Scholar
  79. 79.
    Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U (2002) Network motifs: simple building blocks of complex networks. Science 298:824–827.PubMedCrossRefGoogle Scholar
  80. 80.
    Mlecnik B, Scheideler M, Hackl H, Hartler J, Sanchez-Cabo F, Trajanoski Z (2005) PathwayExplorer: web service for visualizing high-throughput expression data on biological pathways. Nucleic Acids Research 33:W633–W637.PubMedCrossRefGoogle Scholar
  81. 81.
    Moreno JL (1934) Who Shall Survive?: A New Approach to the Problem of Human Interrelations. Nervous and Mental Disease Publishing Company, Washington.CrossRefGoogle Scholar
  82. 82.
    Müller LA, Zhang P, Rhee SY (2003) AraCyc: A biochemical pathway database for Arabidopsis. Plant Physiol 132:453–460.CrossRefGoogle Scholar
  83. 83.
    Nakao M, Bono H, Kawashima S, Kamiya T, Sato K, Goto S, Kanehisa M (1999) Genome-scale gene expression analysis and pathway reconstruction in KEGG. Genome Informatics 10:94–103.PubMedGoogle Scholar
  84. 84.
    Nicholson, DE (1997) Metabolic Pathways Map (Poster). Sigma Chemical Co., St. Louis, St. Louis, MO.Google Scholar
  85. 85.
    Oltvai ZN, Barabási AL (2002) Systems biology: life’s complexity pyramid. Science 298:763–764.PubMedCrossRefGoogle Scholar
  86. 86.
    Pan D, Sun N, Cheung KH, Guan Z, Ma L, Holford M, Deng X, Zhao H (2003) PathMAPA: a tool for displaying gene expression and performing statistical tests on metabolic pathways at multiple levels for Arabidopsis. BMC Bioinformatics 4:56.PubMedCrossRefGoogle Scholar
  87. 87.
    Papin JA, Reed JL, Palsson BO (2004) Hierarchical thinking in network biology: the unbiased modularization of biochemical networks. Trends Biochem Sci 29: 641–647.PubMedCrossRefGoogle Scholar
  88. 88.
    Pržulj N, Corneil DG, Jurisica I (2004) Modeling interactome: scale-free or geometric? Bioinformatics 20:3508–3515.PubMedCrossRefGoogle Scholar
  89. 89.
    Quinn NR, Breuer MA (1979) A force directed component placement procedure for printed circuit boards. IEEE Trans Circuits Syst CAS 26:377–388.CrossRefGoogle Scholar
  90. 90.
    Rahman SA, Schomburg D (2006) Observing local and global properties of metabolic pathways: “load points” and “choke points” in the metabolic networks. Bioinformatics 22: 1767–1774.PubMedCrossRefGoogle Scholar
  91. 91.
    Ravasz E, Somera AL, Mongru DA, Oltvai ZN, Barabási AL (2002) Hierarchical organization of modularity in metabolic networks. Science 297:1551–1555.PubMedCrossRefGoogle Scholar
  92. 92.
    Rives AW, Galitski T (2003) Modular organization of cellular networks. Proc Natl Acad Sci USA 100:1128–1133.PubMedCrossRefGoogle Scholar
  93. 93.
    Roessner U, Luedemann A, Brust D, Fiehn O, Linke T, Willmitzer L, Fernie A (2001) Metabolic profiling allows comprehensive phenotyping of genetically or environmentally modified plant systems. Plant Cell 13:11–29.PubMedCrossRefGoogle Scholar
  94. 94.
    Rolletschek H, Radchuk S, Klukas C, Schreiber F, Borisjuk L (2005) Regulation of lipid biosynthesis in soybean seeds: evidence for a key role of photosynthetic oxygen release. New Phytologist 167:777–786.PubMedCrossRefGoogle Scholar
  95. 95.
    Rost U, Kummer U (2004) Visualisation of biochemical network simulations with SimWiz. In: Iyengar R, Wolkenhauer O, Kolch W, Kwang-hyun Cho, Klingmuller U (eds) Systems Biology, IEE Proc. Vol. 1, pp. 184–189.Google Scholar
  96. 96.
    Schomburg I, Chang A, Ebeling C, Gremse M, Heldt C, Huhn G, Schomburg D (2004) BRENDA, the enzyme database: updates and major new developments. Nucleic Acids Research, Database issue 32:D431–D433.CrossRefGoogle Scholar
  97. 97.
    Schreiber F (2002) High quality visualization of biochemical pathways in BioPath. In Silico Biol 2:59–73.PubMedGoogle Scholar
  98. 98.
    Schreiber F, Schwöbbermeyer H (2005) MAVisto: a tool for the exploration of network motifs. Bioinformatics 21:3572–3574.PubMedCrossRefGoogle Scholar
  99. 99.
    Schuster S, Pfeifer T, Moldenhauer F, Koch I, Dandekar T (2002) Exploring the pathway structure of metabolism: decomposition into subnetworks and application to Mycoplasma pneumoniae. Bioinformatics 18:351–361.PubMedCrossRefGoogle Scholar
  100. 100.
  101. 101.
    Shannon P, Markiel A, Ozier O, Baliga NS, Wang JT, Ramage D, Amin N, Schwikowski B, Ideker T (2003) Cytoscape: a software environment for integrated models of biomolecular interaction networks. Genome Res 13:2498–2504.PubMedCrossRefGoogle Scholar
  102. 102.
    Shen-Orr S, Milo R, Mangan S, Alon U (2002) Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genetics 31:64–68.PubMedCrossRefGoogle Scholar
  103. 103.
    Snel B, Bork P, Huynen MA (2002) The identification of functional modules from the genomic association of genes. Proc Natl Acad Sci USA 99:5890–5895.PubMedCrossRefGoogle Scholar
  104. 104.
    Sokal RR, Michener CD (1958) A statistical method for evaluating systematic relationships. Univ Kansas Sci Bull 38:1409–1438.Google Scholar
  105. 105.
    Spirin V, Mirny LA (2003) Protein complexes and functional modules in molecular networks. Proc Natl Acad Sci USA 100:12123–12128.PubMedCrossRefGoogle Scholar
  106. 106.
    Sturn A, Quackenbush J, Trajanoski Z (2002) Genesis: cluster analysis of microarray data. Bioinformatics 18:207–208.PubMedCrossRefGoogle Scholar
  107. 107.
    Sugiyama K, Tagawa S, Toda M (1981) Methods for visual understanding of hierarchical systems. IEEE Trans Syst Man Cybern 11:109–125.CrossRefGoogle Scholar
  108. 108.
    Thimm O, Bläsing O, Gibon Y, Nagel A, Meyer S, Krüger P, Selbig J, Müller LA, Rhee SY, Stitt M (2004) MAPMAN: a user-driven tool to display genomics data sets onto diagrams of metabolic pathways and other biological processes. Plant J 37: 914–939.PubMedCrossRefGoogle Scholar
  109. 109.
    Tokimatsu T, Sakurai N, Suzuki H, Ohta H, Nishitani K, Koyama T, Umezawa T, Misawa N, Saito K, Shibatanenell D (2005) KaPPA-View. A web-based analysis tool for integration of transcript and metabolite data on plant metabolic pathway maps. Plant Physiol 138: 1289–1300.PubMedCrossRefGoogle Scholar
  110. 110.
    Usadel B, Nagel A, Thimm O, Redestig H, Blaesing OE, Palacios-Rojas N, Selbig J, Hannemann J, Piques MC, Steinhauser D, Scheible WR, Gibon Y, Morcuende R, Weicht D, Meyer S, Stitt M (2005) Extension of the visualization tool MapMan to allow statistical analysis of arrays, display of corresponding genes, and comparison with known responses. Plant Physiol 138:1195–1204.PubMedCrossRefGoogle Scholar
  111. 111.
    Wagner A, Fell DA (2001) The small world inside large metabolic networks. Proc Royal Society London B 268:1803–1810.CrossRefGoogle Scholar
  112. 112.
    Wall ME, Dunlop MJ, Hlavacek WS (2005) Multiple functions of a feed-forward-loop gene circuit. J Mol Biol 349:501–514.PubMedCrossRefGoogle Scholar
  113. 113.
    Wegner K, Kummer U (2005) A new dynamical layout algorithm for complex biochemical reaction networks. BMC Bioinformatics 6:212.PubMedCrossRefGoogle Scholar
  114. 114.
    Wernicke S, Rasche F (2006) FANMOD: a tool for fast network motif detection. Bioinformatics 22:1152–1153.PubMedCrossRefGoogle Scholar
  115. 115.
    Wiese R, Eiglsperger M, Kaufmann M (2001) Visualization and automatic layout of graphs. In: Mutzel P, Jünger M, Leipert S (eds) Proc. 9th International Symposium on Graph Drawing (GD 2001). Springer, Berlin/Heidelberg, pp. 453–462.Google Scholar
  116. 116.
    Wolf G (2000) Visualising gene expression in its metabolic context. Briefings in Bioinformatics 1:297–304.PubMedCrossRefGoogle Scholar
  117. 117.
    Wuchty S, Oltvai ZN, Barabási AL (2003) Evolutionary conservation of motif constituents in the yeast protein interaction network. Nature Genet 35:176–179.PubMedCrossRefGoogle Scholar
  118. 118.
    Wuchty S, Stadler PF (2003) Centers of complex networks. J Theor Biol 223: 45–53.PubMedCrossRefGoogle Scholar
  119. 119.
    Zamora Lopez G, Steuer R (2008) Global network properties. In: BH Junker, Schreiber F (eds.) Analysis of Biological Networks. John Wiley & Sons, Hoboken, NJ, pp. 31–63.Google Scholar
  120. 120.
    Zhang LV, King OD, Wong SL, Goldberg DS, Tong AHY, Lesage G, Andrews B, Bussey H, Boone C, Rot FP (2005) Motifs, themes and thematic maps of an integrated Saccharomyces cerevisiae interaction network. J Biol 4:6.PubMedCrossRefGoogle Scholar
  121. 121.
    Zhao J, Yu H, Luo JH, Cao ZW, Li YX (2006) Hierarchical modularity of nested bow-ties in metabolic networks. BMC Bioinformatics 7:386.PubMedCrossRefGoogle Scholar
  122. 122.
    Zhu D, Qin ZS (2005) Structural comparison of metabolic networks in selected single cell organisms. BMC Bioinformatics 6:851.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Eva Grafahrend-Belau
    • 1
  • Björn H. Junker
    • 1
  • Christian Klukas
    • 1
  • Dirk Koschützki
    • 1
  • Falk Schreiber
    • 2
  • Henning Schwöbbermeyer
    • 1
  1. 1.Department of Molecular GeneticsLeibniz Institute of Plant Genetics and Crop Plant Research (IPK)Germany
  2. 2.Leibniz Institute of Plant Genetics and Crop Plant Research (IPK) GaterslebenGermany

Personalised recommendations