Skip to main content
SpringerLink
Log in

Topological Analysis of Metabolic and Regulatory Networks

  • Chapter
Modeling in Systems Biology

Part of the book series: Computational Biology ((COBO,volume 16))

  • 2069 Accesses

Abstract

The theoretical apparatus of Petri nets has been widely used for visualizing metabolic and regulatory networks and for describing their properties and behavior in a quantitative way. In this chapter, the theoretical basis, algorithmic issues and biological applications of using Petri nets in that field are reviewed, in particular, in view of topological (structural) analyses. Several useful notions such as T-invariants, P-invariants, and Maximal common transition sets are explained. The correspondence between several of these concepts and similar concepts in traditional biochemical modeling, such as between minimal T-invariants and elementary flux modes, is discussed. The presentation is illustrated by several hypothetical and biochemical examples. A larger running example is taken from sucrose metabolism in plants. For this, an important difference in functioning between monocotyledon and dicotyledon plants is explained. Algorithms and software tools for determining structural properties of Petri nets are briefly reviewed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Behre, J., Schuster, S.: Modelling signal transduction in enzyme cascades with the concept of elementary flux modes. J. Comput. Biol. 16(6), 829–844 (2009)

    Article  Google Scholar 

  2. Behre, J., Wilhelm, T., von Kamp, A., Ruppin, E., Schuster, S.: Structural robustness of metabolic networks with respect to multiple knockouts. J. Theor. Biol. 252, 433–441 (2008)

    Article  Google Scholar 

  3. Bortfeldt, R., Schuster, S., Koch, I.: Exhaustive analysis of the modular structure of the spliceosomal assembly network—a Petri net approach. In Silico Biol. 10, 0007 (2010)

    Google Scholar 

  4. Burgard, A.P., Nikolaev, E.V., Schilling, C.H., Maranas, C.D.: Flux coupling analysis of genome-scale metabolic network reconstructions. Genome Res. 14(2), 301–312 (2004)

    Article  Google Scholar 

  5. Chaouiya, C.: Petri net modelling of biological networks. Brief. Bioinform. 8(4), 210–219 (2007)

    Article  Google Scholar 

  6. Clarke, B.L.: Complete set of steady states for the general stoichiometric dynamical system. J. Chem. Phys. 75, 4970–4979 (1981)

    Article  MathSciNet  Google Scholar 

  7. Colom, J.M., Silva, M.: Convex geometry and semiflows in P/T nets. A comparative study of algorithms for computation of minimal P-semiflows. In: Rozenberg, G. (ed.) Advances in Petri Nets, pp. 79–112. Springer, Berlin (1990)

    Google Scholar 

  8. Comparot-Moss, S., Denyer, K.: The evolution of the starch biosynthetic pathway in cereals and other grasses. J. Exp. Bot. 60, 2481–2492 (2009)

    Article  Google Scholar 

  9. de Figueiredo, L.F., Schuster, S., Kaleta, C., Fell, D.A.: Can sugars be produced from fatty acids? A test case for pathway analysis tools. Bioinformatics 25, 152–158 (2009)

    Article  Google Scholar 

  10. Diniz, S.C., Voss, I., Steinbüchel, A.: Optimization of cyanophycin production in recombinant strains of Pseudomonas putida and Ralstonia eutropha employing elementary mode analysis and statistical experimental design. Biotechnol. Bioeng. 93, 698–717 (2006)

    Article  Google Scholar 

  11. Dittrich, P., di Fenizio, P.S.: Chemical organisation theory. Bull. Math. Biol. 69, 1199–1231 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Érdi, P., Tóth, J.: Mathematical Models of Chemical Reactions. Manchester University Press, Manchester (1989)

    MATH  Google Scholar 

  13. Fowler, J.H., Dawes, C.T., Christakis, N.A.: Model of genetic variation in human social networks. Proc. Natl. Acad. Sci. USA 106(6), 1720–1724 (2009)

    Article  Google Scholar 

  14. Gevorgyan, A., Poolman, M.G., Fell, D.A.: Detection of stoichiometric inconsistencies in biomolecular models. Bioinformatics 24, 2245–2251 (2008)

    Article  Google Scholar 

  15. Grafahrend-Belau, E.: Classification of t-Invariants in biochemical Petri nets on the basis of various cluster analysis methods. Master’s thesis, Technical University of Applied Sciences (TFH). Berlin (2006) (in German)

    Google Scholar 

  16. Grafahrend-Belau, E., Schreiber, F., Heiner, M., Sackmann, A., Junker, B.H., Grunwald, S., Speer, A., Winder, K., Koch, I.: Modularization of biochemical networks based on classification of Petri net t-Invariants. BMC Bioinform. 9, 90 (2008)

    Article  Google Scholar 

  17. Grunwald, S., Speer, A., Ackermann, J., Koch, I.: Petri net modelling of gene regulation of the Duchenne muscular dystrophy. Biosystems 92(2), 189–205 (2008)

    Article  Google Scholar 

  18. Heiner, M., Koch, I., Will, J.: Model validation of biological pathways using Petri nets—demonstrated for apoptosis. Biosystems 75(1), 15–28 (2004)

    Article  Google Scholar 

  19. Heinrich, R., Schuster, S.: The Regulation of Cellular Systems. Chapman and Hall, London (1996)

    Book  MATH  Google Scholar 

  20. Heinrich, R., Neel, B.G., Rapoport, T.A.: Mathematical models of protein kinase signal transduction. Mol. Cell 9, 957–970 (2002)

    Article  Google Scholar 

  21. Hofestädt, R.: A petri net application to model metabolic processes. Syst. Anal. Mod. Simul. 16(2), 113–122 (1994)

    MATH  Google Scholar 

  22. Jeong, H., Tombor, B., Albert, R., Oltvai, Z.N., Barabási, A.L.: The large-scale organization of metabolic networks. Nature 407, 651–654 (2000)

    Article  Google Scholar 

  23. Jurica, M.S., Moore, M.J.: Pre-mRNA splicing: awash in a sea of proteins. Mol. Cell 12, 5–14 (2003)

    Article  Google Scholar 

  24. Kielbassa, J., Bortfeldt, R., Schuster, S., Koch, I.: Modeling of the U1 snRNP assembly pathway in alternative splicing in human cells using Petri nets. Comput. Biol. Chem. 33(1), 46–61 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Klamt, S., Saez-Rodriguez, J., Lindquist, J.A., Simeoni, L., Gilles, E.D.: A methodology for the structural and functional analysis of signaling and regulatory networks. BMC Bioinform. 7, 56 (2006)

    Article  Google Scholar 

  26. Klamt, S., Gagneur, J., von Kamp, A.: Algorithmic approaches for computing elementary modes in large biochemical reaction networks. IEE Proc. Syst. Biol. 152, 249–255 (2005)

    Article  Google Scholar 

  27. Klamt, S., Saez-Rodriguez, J., Gilles, E.D.: Structural and functional analysis of cellular networks with CellNetAnalyzer. BMC Syst. Biol. 1, 2 (2007)

    Article  Google Scholar 

  28. Klamt, S., Haus, U.U., Theis, F.: Hypergraphs and cellular networks. PLoS Comput. Biol. 5, e1000385 (2009)

    Article  MathSciNet  Google Scholar 

  29. Klipp, E., Liebermeister, W., Wierling, C., Kowald, A.: Systems Biology: A Textbook. Wiley VCH, Weinheim (2009)

    Google Scholar 

  30. Koch, I., Heiner, M.: Petri nets. In: Junker, B.H., Schreiber, F. (eds.) Biological Network Analysis, Wiley Book Series on Bioinformatics, pp. 139–180. Wiley, New York (2008). Chapter 7

    Chapter  Google Scholar 

  31. Koch, I., Junker, B.H., Heiner, M.: Application of Petri net theory for modelling and validation of the sucrose breakdown pathway in the potato tuber. Bioinformatics 21(7), 1219–1226 (2005)

    Article  Google Scholar 

  32. Lautenbach, K.: Exact liveness conditions of a Petri net class. GMD Report 82, German National Research Center for Information Technology, Sankt Augustin, Germany (1973) (in German)

    Google Scholar 

  33. Mertens, E.: Pyrophosphate-dependent phosphofructokinase, an anaerobic glycolytic enzyme? FEBS Lett. 285, 1–5 (1991)

    Article  Google Scholar 

  34. Nuño, J.C., Sánchez-Valdenebro, I., Pérez-Iratxeta, C., Meléndez-Hevia, E., Montero, F.: Network organization of cell metabolism: monosaccharide interconversion. Biochem. J. 324, 103–111 (1997)

    Google Scholar 

  35. Palsson, B.Ø.: Systems Biology: Properties of Reconstructed Networks. Cambridge University Press, Cambridge (2006)

    Book  Google Scholar 

  36. Papin, J.A., Stelling, J., Price, N.D., Klamt, S., Schuster, S., Palsson, B.Ø.: Comparison of network-based pathway analysis methods. Trends Biotechnol. 22(8), 400–405 (2004)

    Article  Google Scholar 

  37. Pérès, S.: Analysis of the structure of metabolic networks: Application to mitochondrial energy metabolism. Ph.D. thesis, Université de Bordeaux 2 (2005) (in French)

    Google Scholar 

  38. Pérès, S., Beurton-Aimar, M., Mazat, J.P.: Pathway classification of TCA cycle. IEE Proc. Syst. Biology 153(5), 369–371 (2006)

    Article  Google Scholar 

  39. Pfeiffer, T., Sánchez-Valenebro, I., Nuño, J.C., Montero, F., Schuster, S.: METATOOL: for studying metabolic networks. Bioinformatics 15(3), 251–257 (1999)

    Article  Google Scholar 

  40. Planes, F.J., Beasley, J.E.: A critical examination of stoichiometric and pathfinding approaches to metabolic pathways. Brief. Bioinform. 9, 422–436 (2008)

    Article  Google Scholar 

  41. Reddy, V.N., Liebmann, M.N., Mavrovouniotis, M.L.: Qualitative analysis of biochemical reaction systems. Comput. Biol. Med. 26(1), 9–24 (1996)

    Article  Google Scholar 

  42. Reder, C.: Metabolic control theory: a structural approach. J. Theor. Biol. 135, 175–201 (1988)

    Article  MathSciNet  Google Scholar 

  43. Reed, J.L., Palsson, B.O.: Genome-scale in silico models of E-coli have multiple equivalent phenotypic states: assessment of correlated reaction subsets that comprise network states. Genome Res. 14, 1797–1805 (2004)

    Article  Google Scholar 

  44. Reisig, W.: Petri nets: an introduction. In: Brauer, W., et al. (eds.) EATCS Monographs on Theoretical Computer Science. Springer, Berlin (1985)

    Google Scholar 

  45. Rino, J., Carvalho, T., Braga, J., Desterro, J.M.P., Lührmann, R., Carmo-Fonseca, M.: A stochastic view of spliceosome assembly and recycling in the nucleus. PLoS Comput. Biol. 3, 2019–2031 (2007)

    Article  Google Scholar 

  46. Rohwer, J.M., Botha, F.C.: Analysis of sucrose accumulation in the sugar cane culm on the basis of in vitro kinetic data. Biochem. J. 358, 437–445 (2001)

    Article  Google Scholar 

  47. Sackmann, A., Heiner, M., Koch, I.: Application of Petri net based analysis techniques to signal transduction pathways. BMC Bioinform. 7(1), 482 (2006)

    Article  Google Scholar 

  48. Sackmann, A., Formanowicz, D., Formanowicz, P., Koch, I., Blazewicz, J.: An analysis of the Petri net based model of the human body iron homeostasis process. Comput. Biol. Chem. 31, 1–10 (2007)

    Article  MATH  Google Scholar 

  49. Schuster, S., Höfer, T.: Determining all extreme semi-positive conservation relations in chemical reaction systems. A test criterion for conservativity. J. Chem. Soc. Faraday Trans. 87, 2561–2566 (1991)

    Article  Google Scholar 

  50. Schuster, S., Hilgetag, C.: On elementary flux modes in biochemical reaction systems at steady state. J. Biol. Syst. 2, 165–182 (1994)

    Article  Google Scholar 

  51. Schuster, S., Hilgetag, C.: What information about the conserved-moiety structure of chemical reaction systems can be derived from their stoichiometry? J. Phys. Chem. 99, 8017–8023 (1995)

    Article  Google Scholar 

  52. Schuster, S., Dandekar, T., Fell, D.A.: Detection of elementary flux modes in biochemical networks: A promising tool for pathway analysis and metabolic engineering. Trends. Biotechnol. 17, 53–60 (1999)

    Article  Google Scholar 

  53. Schuster, S., Fell, D., Dandekar, T.: A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nat. Biotechnol. 18(3), 326–332 (2000)

    Article  Google Scholar 

  54. Schuster, S., Hilgetag, C., Woods, J.H., Fell, D.A.: Reaction routes in biochemical reaction systems: algebraic properties, validated calculation procedure and example from nucleotide metabolism. J. Math. Biol. 45, 153–181 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  55. Schuster, S., Klamt, S., Weckwerth, W., Moldenhauer, F., Pfeiffer, T.: Use of network analysis of metabolic systems in bioengineering. Bioproc. Biosyst. Eng. 24, 363–372 (2002)

    Article  Google Scholar 

  56. Schuster, S., Pfeiffer, T., Moldenhauer, F., Koch, I., Dandekar, T.: Exploring the pathway structure of metabolism: decomposition into subnetworks and application to Mycoplasma pneumoniae. Bioinformatics 18, 351–361 (2002)

    Article  Google Scholar 

  57. Schuster, S., von Kamp, A., Pachkov, M.: Understanding the roadmap of metabolism by pathway analysis. In: Weckwerth, W. (ed.) Metabolomics, Methods and Protocols, pp. 199–226. Humana Press, Totowa (2007)

    Google Scholar 

  58. Schwender, J., Goffman, F., Ohlrogge, J.B., Shachar-Hill, Y.: Rubisco without the Calvin cycle improves the carbon efficiency of developing green seeds. Nature 432, 779–782 (2004)

    Article  Google Scholar 

  59. Simão, E., Remy, E., Thieffry, D., Chaouiya, C.: Qualitative modelling of regulated metabolic pathways: application to the tryptophan biosynthesis in E. Coli. Bioinformatics 21(2), ii190–ii196 (2005)

    Article  Google Scholar 

  60. Starke, P.H.: Analysis of Petri Net Models. Teubner-Verlag, Stuttgart (1990) (in German)

    Book  MATH  Google Scholar 

  61. Starke, P.: INA—Integrated Net Analyzer. Manual. Humboldt University Berlin, Dept. Computer Science (1998)

    Google Scholar 

  62. Stelling, J., Klamt, S., Bettenbrock, K., Schuster, S., Gilles, E.D.: Metabolic network structure determines key aspects of functionality and regulation. Nature 420, 190–193 (2002)

    Article  Google Scholar 

  63. Berg, J.M., Tymoczko, J.L., Stryer, L.: Biochemistry, 6th edn. Freeman, New York (2006)

    Google Scholar 

  64. Terzer, M., Stelling, J.: Large-scale computation of elementary flux modes with bit pattern trees. Bioinformatics 24, 2229–2235 (2008)

    Article  Google Scholar 

  65. Tolba, C., Lefebvre, D., Thomas, P., El Moudni, A.: Continuous and timed Petri nets for the macroscopic and microscopic traffic flow modelling. Simul. Modell. Pract. Theory 13, 407–436 (2005)

    Article  Google Scholar 

  66. Trinh, C.T., Wlaschin, A., Srienc, F.: Elementary mode analysis: a useful metabolic pathway analysis tool for characterizing cellular metabolism. Appl. Microbiol. Biotechnol. 81(5), 813–826 (2009)

    Article  Google Scholar 

  67. Urbanczik, R., Wagner, C.: An improved algorithm for stoichiometric network analysis: theory and applications. Bioinformatics 21, 1203–1210 (2005)

    Article  Google Scholar 

  68. van Dien, S.J., Lidstrom, M.E.: Stoichiometric model for evaluating the metabolic capabilities of the facultative methylotroph Methylobacterium extorquens AM1, with application to reconstruction of C3 and C4 metabolism. Biotechnol. Bioeng. 78, 296–312 (2002)

    Article  Google Scholar 

  69. von Kamp, A., Schuster, S.: Metatool 5.0: fast and flexible elementary modes analysis. Bioinformatics 22, 1930–1931 (2006)

    Article  Google Scholar 

  70. Voss, K., Heiner, M., Koch, I.: Steady state analysis of metabolic pathways using Petri nets. In Silico Biol. 3, 367–387 (2003)

    Google Scholar 

  71. Weinman, E.O., Strisower, E.H., Chaikoff, I.L.: Conversion of fatty acids to carbohydrate: application of isotopes to this problem and role of the Krebs cycle as a synthetic pathway. Physiol. Rev. 37, 252–272 (1957)

    Google Scholar 

  72. Westerhoff, H.V., van Dam, K.: Thermodynamics and Control of Biological Free-Energy Transduction. Elsevier, Amsterdam (1987)

    Google Scholar 

  73. Yook, S.H., Jeong, H., Barabasi, A.L.: Modeling the Internet’s large-scale topology. Proc. Natl. Acad. Sci. USA 99, 13382–13386 (2002)

    Article  Google Scholar 

  74. Zeigarnik, A.V., Temkin, O.N.: A graph-theoretical model of complex reaction mechanisms: bipartite graphs and the stoichiometry of complex reactions. Kinet. Catal. 35, 647–655 (1994)

    Google Scholar 

  75. Zevedei-Oancea, I., Schuster, S.: Topological analysis of metabolic networks based on Petri net theory. In Silico Biol. 3(3), 323–345 (2003)

    Google Scholar 

  76. Zevedei-Oancea, I., Schuster, S.: A theoretical framework for detecting signal transfer routes in signalling networks. Comput. Chem. Eng. 29, 597–617 (2005)

    Article  Google Scholar 

Download references

Acknowledgement

The authors would like to thank Monika Heiner, Steffen Klamt, Ina Koch, Sabine Pérès, and Andrea Sackmann for very helpful discussions.

Author information

Authors and Affiliations

    Authors
    1. Stefan Schuster
      View author publications

      You can also search for this author in PubMed Google Scholar

    2. Björn H. Junker
      View author publications

      You can also search for this author in PubMed Google Scholar

    Corresponding author

    Correspondence to Stefan Schuster .

    Editor information

    Editors and Affiliations

    1. Institute for Computer Science, J.W. Goethe University Frankfurt, Robert-Mayer-Straße 11-15, Frankfurt am Main, 60325, Germany

      Ina Koch

    2. Department of Computer Science, Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

      Wolfgang Reisig

    3. Institute of Computer Science, Martin Luther Univ. Halle-Wittenberg, Von Seckendorff Platz 1, Halle, 06120, Germany

      Falk Schreiber

    Rights and permissions

    Reprints and permissions

    Copyright information

    © 2011 Springer-Verlag London Limited

    About this chapter

    Cite this chapter

    Schuster, S., Junker, B.H. (2011). Topological Analysis of Metabolic and Regulatory Networks. In: Koch, I., Reisig, W., Schreiber, F. (eds) Modeling in Systems Biology. Computational Biology, vol 16. Springer, London. https://doi.org/10.1007/978-1-84996-474-6_10

    Download citation

    • DOI: https://doi.org/10.1007/978-1-84996-474-6_10

    • Publisher Name: Springer, London

    • Print ISBN: 978-1-84996-473-9

    • Online ISBN: 978-1-84996-474-6

    • eBook Packages: Computer ScienceComputer Science (R0)

    Publish with us

    Policies and ethics

    Search

    Navigation