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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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)
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)
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)
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)
Chaouiya, C.: Petri net modelling of biological networks. Brief. Bioinform. 8(4), 210–219 (2007)
Clarke, B.L.: Complete set of steady states for the general stoichiometric dynamical system. J. Chem. Phys. 75, 4970–4979 (1981)
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)
Comparot-Moss, S., Denyer, K.: The evolution of the starch biosynthetic pathway in cereals and other grasses. J. Exp. Bot. 60, 2481–2492 (2009)
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)
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)
Dittrich, P., di Fenizio, P.S.: Chemical organisation theory. Bull. Math. Biol. 69, 1199–1231 (2007)
Érdi, P., Tóth, J.: Mathematical Models of Chemical Reactions. Manchester University Press, Manchester (1989)
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)
Gevorgyan, A., Poolman, M.G., Fell, D.A.: Detection of stoichiometric inconsistencies in biomolecular models. Bioinformatics 24, 2245–2251 (2008)
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)
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)
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)
Heiner, M., Koch, I., Will, J.: Model validation of biological pathways using Petri nets—demonstrated for apoptosis. Biosystems 75(1), 15–28 (2004)
Heinrich, R., Schuster, S.: The Regulation of Cellular Systems. Chapman and Hall, London (1996)
Heinrich, R., Neel, B.G., Rapoport, T.A.: Mathematical models of protein kinase signal transduction. Mol. Cell 9, 957–970 (2002)
Hofestädt, R.: A petri net application to model metabolic processes. Syst. Anal. Mod. Simul. 16(2), 113–122 (1994)
Jeong, H., Tombor, B., Albert, R., Oltvai, Z.N., Barabási, A.L.: The large-scale organization of metabolic networks. Nature 407, 651–654 (2000)
Jurica, M.S., Moore, M.J.: Pre-mRNA splicing: awash in a sea of proteins. Mol. Cell 12, 5–14 (2003)
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)
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)
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)
Klamt, S., Saez-Rodriguez, J., Gilles, E.D.: Structural and functional analysis of cellular networks with CellNetAnalyzer. BMC Syst. Biol. 1, 2 (2007)
Klamt, S., Haus, U.U., Theis, F.: Hypergraphs and cellular networks. PLoS Comput. Biol. 5, e1000385 (2009)
Klipp, E., Liebermeister, W., Wierling, C., Kowald, A.: Systems Biology: A Textbook. Wiley VCH, Weinheim (2009)
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
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)
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)
Mertens, E.: Pyrophosphate-dependent phosphofructokinase, an anaerobic glycolytic enzyme? FEBS Lett. 285, 1–5 (1991)
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)
Palsson, B.Ø.: Systems Biology: Properties of Reconstructed Networks. Cambridge University Press, Cambridge (2006)
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)
Pérès, S.: Analysis of the structure of metabolic networks: Application to mitochondrial energy metabolism. Ph.D. thesis, Université de Bordeaux 2 (2005) (in French)
Pérès, S., Beurton-Aimar, M., Mazat, J.P.: Pathway classification of TCA cycle. IEE Proc. Syst. Biology 153(5), 369–371 (2006)
Pfeiffer, T., Sánchez-Valenebro, I., Nuño, J.C., Montero, F., Schuster, S.: METATOOL: for studying metabolic networks. Bioinformatics 15(3), 251–257 (1999)
Planes, F.J., Beasley, J.E.: A critical examination of stoichiometric and pathfinding approaches to metabolic pathways. Brief. Bioinform. 9, 422–436 (2008)
Reddy, V.N., Liebmann, M.N., Mavrovouniotis, M.L.: Qualitative analysis of biochemical reaction systems. Comput. Biol. Med. 26(1), 9–24 (1996)
Reder, C.: Metabolic control theory: a structural approach. J. Theor. Biol. 135, 175–201 (1988)
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)
Reisig, W.: Petri nets: an introduction. In: Brauer, W., et al. (eds.) EATCS Monographs on Theoretical Computer Science. Springer, Berlin (1985)
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)
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)
Sackmann, A., Heiner, M., Koch, I.: Application of Petri net based analysis techniques to signal transduction pathways. BMC Bioinform. 7(1), 482 (2006)
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)
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)
Schuster, S., Hilgetag, C.: On elementary flux modes in biochemical reaction systems at steady state. J. Biol. Syst. 2, 165–182 (1994)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Starke, P.H.: Analysis of Petri Net Models. Teubner-Verlag, Stuttgart (1990) (in German)
Starke, P.: INA—Integrated Net Analyzer. Manual. Humboldt University Berlin, Dept. Computer Science (1998)
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)
Berg, J.M., Tymoczko, J.L., Stryer, L.: Biochemistry, 6th edn. Freeman, New York (2006)
Terzer, M., Stelling, J.: Large-scale computation of elementary flux modes with bit pattern trees. Bioinformatics 24, 2229–2235 (2008)
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)
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)
Urbanczik, R., Wagner, C.: An improved algorithm for stoichiometric network analysis: theory and applications. Bioinformatics 21, 1203–1210 (2005)
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)
von Kamp, A., Schuster, S.: Metatool 5.0: fast and flexible elementary modes analysis. Bioinformatics 22, 1930–1931 (2006)
Voss, K., Heiner, M., Koch, I.: Steady state analysis of metabolic pathways using Petri nets. In Silico Biol. 3, 367–387 (2003)
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)
Westerhoff, H.V., van Dam, K.: Thermodynamics and Control of Biological Free-Energy Transduction. Elsevier, Amsterdam (1987)
Yook, S.H., Jeong, H., Barabasi, A.L.: Modeling the Internet’s large-scale topology. Proc. Natl. Acad. Sci. USA 99, 13382–13386 (2002)
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)
Zevedei-Oancea, I., Schuster, S.: Topological analysis of metabolic networks based on Petri net theory. In Silico Biol. 3(3), 323–345 (2003)
Zevedei-Oancea, I., Schuster, S.: A theoretical framework for detecting signal transfer routes in signalling networks. Comput. Chem. Eng. 29, 597–617 (2005)
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
Corresponding author
Editor information
Editors and Affiliations
Rights 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)