Abstract
Petri nets are used in many areas. This article discusses the application of Petri nets in systems biology. Using an example from biochemistry, concepts for the automatic decomposition of biochemical systems are introduced. The article focuses on those concepts that fulfill steady-state conditions. Interestingly, all the concepts are based on minimal, semi-positive transition invariants. The article describes, which new definitions for network decomposition can be derived and how they can be interpreted in the context of biology. This is illustrated with the example of the citric acid cycle, for which a new metabolic pathway could be predicted with the help of such an analysis.
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References
Ackermann, J., Koch, I.: Quantitative analysis. In: Koch, I., Reisig, W., Schreiber, F. (eds.) Modeling in Systems Biology: The Petri Net Approach, pp. 153–178. Springer, Berlin (2011) (Comp. Biol.)
Ackermann, J., et al.: Reduction techniques for network validation in systems biology. J. Theor. Biol. 315, 71–80 (2012)
Backhaus, K., et al.: Multivariate Analysis Methods. An Application-Oriented Introduction, 10th edn. Springer, Berlin (2003) (in German)
Bahi-Jaber, N., Pontier, D.: Modeling transmission of directly transmitted infectious diseases using colored stochastic Petri nets. Math. Biosci. 185, 1–13 (2003)
Berg, J.M., Tymoczko, J.L., Stryer, L.: Biochemistry, 5th edn. W.H. Freeman, New York (2002)
Bortfeldt, R.H., Schuster, S., Koch, I.: Exhaustive analysis of the modular structure of the spliceosomal assembly network: a Petri net approach. In Silico Biol. 10, 89–123 (2010). doi:10.3233/ISB-2010-0419
Chaouiya, C.: Petri net modelling of biochemical systems. 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 (1981)
Clarke, B.L.: Stoichiometric network analysis. Cell Biophys. 12, 237–253 (1988)
Doi, A., et al.: Simulation based validation of the p53 transcriptional activity with hybrid functional Petri net. In Silico Biol. 6.1–2, 1–13 (2006)
Einloft, J., et al.: MonaLisa—visualization and analysis of functional modules in biochemical networks. Bioinformatics 29, 1469–1470 (2013)
Esparza, J.: Decidability and complexity of Petri net problems—an introduction. LNCS 1491, 374–428 (1998)
Fieber, M.: Design and Implementation of a Generic and Adaptive Tool for Graph Manipulation. Master’s Thesis. Brandenburg University of Technology at Cottbus (2004) (in German)
Finney, A., Hucka, M.: Systems biology markup language: level 2 and beyond. Biochem. Soc. Trans. 31, 1472–1473 (2003)
Fischer, E., Sauer, U.: A novel metabolic cycle catalyzes glucose oxidation and anaplerosis in hungry Escherichia coli. J. Biol. Chem. 278.47, 46446–46451 (2003)
Förster, J., et al.: Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network. Genome Res. 13, 244–253 (2003)
Genrich, H., Küffner, R., Voss, K.: Executable Petri net models for the analysis of metabolic pathways. J. Softw. Tools Technol. Transf. 3.4, 394–404 (2001)
Grafahrend-Belau, E.: Classification of T-Invariants in Biochemical Petri Nets Based on Different Cluster Analysis Techniques. Master’s Thesis. Technical University of Applied Sciences Berlin (2006) (in German)
Grafahrend-Belau, E., et al.: Modularisation of biochemical networks through hierarchical cluster analysis of T-invariants of biochemical Petri nets. BMC Bioinform. 9, 90 (2008)
Grunwald, S., et al.: Petri net modelling of gene regulation of the Duchenne muscular dystrophy. Biosystems 92, 189–205 (2008)
Heinrich, R., Rapoport, T.A.: A linear steady-state treatment of enzymatic chains. General properties, control and effector strength. Eur. J. Biochem. 42, 89–95 (1974)
Hoops, S., et al.: COPASI—a COmplex PAthway SImulator. Bioinformatics 22.24, 3067–3074 (2006)
Kielbassa, J., et al.: Modeling of the U1 snRNP assembly pathway in alternative splicing in human cells using Petri nets. Comput. Biol. Chem. 33, 46–61 (2009)
Klamt, S., Gilles, E.D.: Minimal cut sets in biochemical reaction networks. Bioinformatics 20.2, 226–234 (2004)
Koch, I.: Petri Nets and GRN models. In: Das, S., et al. (eds.) Handbook of Research on Computational Methodologies in Gene Regulatory Networks, pp. 604–637. IGI Global, Hershey, NY (2010)
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, 1219–1226 (2005)
Koch, I., Reisig, W., Schreiber, F.: Modeling in Systems Biology: The Petri Net Approach. Springer, Berlin (2011). (Comp. Biol.)
Larhlimi, A., Bockmayr, A.: A new constraint-based description of the steady-state flux cone of metabolic networks. Disc. Appl. Math. 157, 2257–2266 (2009)
Lautenbach, K.: Exact conditions of liveness for a class of Petri nets. Berichte der GMD 82. Sankt Augustin: Gesellschaft für Mathematik und Datenverarbeitung (1973) (in German)
Liao, J., Hou, S.-Y., Chao, Y.-P.: Pathway analysis, engineering, and physiological considerations for redirecting central metabolism. Biotechnol. Bioeng. 52, 129–140 (1996)
Matsuno, H., et al.: Hybrid Petri net representation of gene regulatory network. Proc. Pac. Symp. Biocomput. 5, 338–349 (2000)
MTZ-Stiftung. Definition of systems biology (2012). http://www.mtzstiftung.de/die_mtz_awards_projekte/mtz_bioquant_award/definition_systembiologie/. (in German)
Mura, I.: Stochastic modeling. In: Koch, I., Reisig, W., Schreiber, F. (eds.) Modeling in Systems Biology: The Petri Net Approach, pp. 121–152. Springer, Berlin (2011) (Comp. Biol)
Nagasaki, N., et al.: Cell illustrator 4.0: a computational platform for systems biology. Stud. Health Technol. Inform. 162, 160–181 (2011)
Orth, J.D.: A comprehensive genome-scale reconstruction of Escherichia coli metabolism. Mol. Syst. Biol. 7, 535 (2011). doi:10.1038/msb.65
Peleg, M., Rubin, D., Altman, R.B.: Using Petri net tools to study properties and dynamics of biological systems. J. Am. Med. Inf. Assoc. 12.2, 369–371 (2005)
Pèrés, S., et al.: ACoM: a classification method for elementary flux modes based on motif finding. Biosystems 103(3), 410–419 (2011)
Pfeiffer, T., et al.: METATOOL: for studying metabolic networks. Bioinformatics 15.3, 251–257 (1999)
Popova-Zeugmann, L., Heiner, M., Koch, I.: Time Petri nets for modeling and analysis of biochemical networks. Fundam. Inform. 67, 149–162 (2005)
Priami, C., et al.: Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Inf. Proc. Lett. 80, 25–31 (2001)
Reddy, V.N.: Modeling Biological Pathways: A Discrete Event Systems Approach. Master’s Thesis. University of Maryland, USA (1994)
Reddy, V.N., Liebman, M.N., Mavrovouniotis, M.L.: Qualitative analysis of biochemical reaction systems. Comput. Biol. Med. 26.2, 9–24 (1996)
Reddy, V.N., Mavrovouniotis, M.L., Liebman, M.N.: Petri net representations in metabolic pathways. In: Hunter, L., Searls, D., Shavlik, J. (eds.) Proceedings of the First International Conference on Intelligent Systems for Molecular Biology, vol. 1, pp. 328–336. AAAI Press, Menlo Park, CA, USA (1993)
Regev, A., Silverman, W., Shapiro, E.: Representation and simulation of biochemical processes using the pi-calculus process algebra. Proc. Pac. Symp. Biocomput. 6, 459–470 (2001)
Sackmann, A.: Modelling and Simulation of Signaltransduction Pathways of Saccharomyces cerevisiae Based on Petri Net Theory. Diploma Thesis. Ernst Moritz Arndt-University, Greifswald (2005) (in German)
Sackmann, A., Heiner, M., Koch, I.: Application of Petri net based analysis techniques to signal transduction pathways. BMC Bioinform. 7, 482 (2006)
Sackmann, A., et al.: An analysis of the Petri net based model of the human body iron homeostasis process. Comput. Biol. Chem. 31, 1–10 (2007)
Schrijver, A.: Theory of Linear and Integer Programming. Wiley-VCH, Weinheim (1998)
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. 17.2, 53–60 (1999)
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., Schuster, R.: Determining elementary modes of functioning in biochemical reaction networks at steady state. In: Ghista, D.N. (eds.) Biomed. and Life Phys. Vieweg Wiesbaden, pp. 101–114 (1996)
Schuster, S., et al.: Exploring the pathway structure of metabolism: decomposition into subnetworks and application to Mycoplasma pneumoniae. Bioinformatics 18, 352–361 (2002)
Srivastava, R., Peterson, M.S., Nentley, W.E.: Stochastic kinetic analysis of the Escherichia coli stress circuit using \(\sigma \)-32 targeted antisense. Biotechol. Bioeng. 231.1, 120–129 (2001)
Steinhausen, D., Langer, K.: Cluster Analysis. An Introduction to Methods for Automatic Classification. de Gruyter, Berlin (1977) (in German)
Voss, K., Heiner, M., Koch, I.: Steady state analysis of metabolic pathways using Petri nets. In Silico Biol. 3.3, 367–387 (2003)
Wang, L., Li, P.: Microfluidic DNA microarray analysis: a review. Anal. Chim. Acta 687.1, 12–27 (2011)
Wick, L.M., Quadroni, M., Egli, T.: Short- and long-term changes in proteome composition and kinetic properties in a culture of Escherichia coli during transition from glucose-excess to glucose limited growth conditions in continuous culture and vice versa. Environ. Microbiol. 3, 588–599 (2001)
Windhager, L., Erhard, F., Zimmer, R.: Fuzzy Modeling. In: Koch, I., Reisig, W., Schreiber, F. (eds.) Modeling in Systems Biology: The Petri Net Approach. Comp. Biol., pp. 179–205. Springer, Berlin (2011)
Acknowledgments
In particular, I would like to thank the initiators of this special edition, Wolfgang Reisig and Jörg Desel, for their invitation to this contribution. My special thanks goes to Stefan Schuster for introducing me to the works of Reddy in 1997 and for many inspiring discussions. I also would like to thank Jörg Ackermann, Falk Schreiber, Björn Junker, Andrea Sackmann, Eva Grafahrend-Belau, Astrid Speer and Stefanie Grunwald for fruitful collaboration. Additionally, many thanks to Michael Rücker for the professional translation and careful reading of this article.
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Communicated by Dr. Wolfgang Reisig.
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Koch, I. Petri nets in systems biology. Softw Syst Model 14, 703–710 (2015). https://doi.org/10.1007/s10270-014-0421-5
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DOI: https://doi.org/10.1007/s10270-014-0421-5