Journal of Mathematical Biology

, Volume 66, Issue 1–2, pp 203–223 | Cite as

Reconstruction of extended Petri nets from time-series data by using logical control functions

  • Markus Durzinsky
  • Wolfgang Marwan
  • Annegret WaglerEmail author


The aim of this work is to extend a previously presented algorithm (Durzinsky et al. 2008b in Computational methods in systems biology, LNCS, vol 5307. Springer, Heidelberg, pp 328–346; Marwan et al. 2008 in Math Methods Oper Res 67:117–132) for the reconstruction of standard place/transition Petri nets from time-series of experimental data sets. This previously reported method finds provably all networks capable to reproduce the experimental observations. In this paper we enhance this approach to generate extended Petri nets involving mechanisms formally corresponding to catalytic or inhibitory dependencies that mediate the involved reactions. The new algorithm delivers the set of all extended Petri nets being consistent with the time-series data used for reconstruction. It is illustrated using the phosphate regulatory network of enterobacteria as a case study.


Reverse engineering Petri nets Read arcs and inhibitory arcs Phosphate regulatory network 

Mathematics Subject Classification (2000)

68R05 92C42 


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  1. Durzinsky M, Marwan W, Wagler A, Weismantel R (2008a) Automatic reconstruction of molecular and genetic networks from experimental time series data. BioSystems 93: 181–190CrossRefGoogle Scholar
  2. Durzinsky M, Wagler A, Weismantel R (2008b) A combinatorial approach to reconstruct Petri nets from experimental data. In: Computational methods in systems biology, LNCS, vol 5307. Springer, Heidelberg, pp 328–346Google Scholar
  3. Durzinsky M, Marwan W, Wagler A (2011a) Reconstruction of extended Petri nets from time series data and its application to signal transduction and to gene regulatory networks. BMC Syst Biol 5:113. doi: 10.1186/1752-0509-5-113
  4. Durzinsky M, Wagler A, Weismantel R (2011b) An algorithmic framework for network reconstruction. J Theor Comput Sci 412(26): 2800–2815MathSciNetzbMATHCrossRefGoogle Scholar
  5. Heiner M, Koch I (2004) Petri net based model validation in systems biology. In: 25th International conference on application and theory of Petri nets. Springer, Heidelberg, pp 216–237Google Scholar
  6. Hsieh YJ, Wanner BL (2010) Global regulation by the seven-component pi signaling system. Curr Opin Microbiol 13: 198–203CrossRefGoogle Scholar
  7. Kholodenko BN, Kiyatkin A, Bruggeman FJ, Sontag E, Westerhoff HV, Hoek JB (2002) Untangling the wires: a strategy to trace functional interactions in signaling and gene networks. Proc Natl Acad Sci USA 99(20): 12841–12846CrossRefGoogle Scholar
  8. Koch I, Heiner M (2008) Petri nets in biological network analysis. In: Junker BH, Schreiber F (eds) Analysis of biological networks. Wiley Book Series on Bioinformatics. Wiley, New York, pp 139–179Google Scholar
  9. Krishna R, Guo S (2008) A partial granger causality approach to explode causal networks derived from multi-parameter data. In: Computational methods in systems biology, LNCS, vol 5307. Springer, Heidelberg, pp 9–27Google Scholar
  10. Laubenbacher R, Stigler B (2005) A computational algebra approach to reverse engineering of gene regulatory networks. J Theor Biol 229: 523–537MathSciNetCrossRefGoogle Scholar
  11. Marbach D, Prill RJ, Schaffter T, Mattiussi C, Floreano D, Stolovitzky G (2010) Revealing strengths and weaknesses of methods for gene network inference. Proc Natl Acad Sci 107(14): 6286–6291CrossRefGoogle Scholar
  12. Marwan W, Wagler A, Weismantel R (2008) A mathematical approach to solve the network reconstruction problem. Math Methods Oper Res 67: 117–132MathSciNetzbMATHCrossRefGoogle Scholar
  13. Marwan W, Rohr C, Heiner M (2010) Petri nets in Snoopy: a unifying framework for the graphical display, computational modelling, simulation, and bioinformatic annotation of bacterial regulatory network. In: Helden Jv, Toussaint A, Thieffry D (eds) Bacterial molecular networks, methods in molecular biology. Humana Press, USA (in press)Google Scholar
  14. Marwan W, Wagler A, Weismantel R (2011) Petri nets as a framework for the reconstruction and analysis of signaling transduction pathways and regulatory networks. Nat Comput 10(2): 639–654MathSciNetzbMATHCrossRefGoogle Scholar
  15. Matsuno H, Tanaka Y, Aoshima H, Doi A, Matsui M, Miyano S (2003) Biopathways representation and simulation on hybrid functional Petri net. In Silico Biol 3: 389–404Google Scholar
  16. McCluskey EJ (1956) Minimization of boolean functions. Bell Syst Tech J 35: 1417–1444MathSciNetGoogle Scholar
  17. Neidhardt FC, Ingraham JL, Schaechter M (1990) Physiology of the bacterial cell. A molecular approach. Sinauer Associates, SunderlandGoogle Scholar
  18. Pinney JW, Westhead RD, McConkey GA (2003) Petri net representations in systems biology. Biochem Soc Trans 31: 1513–1515CrossRefGoogle Scholar
  19. Umans C (1998) The minimum equivalent DNF problem and shortest implicants. In: FOCS’98, pp 556–563Google Scholar
  20. Wagler A, Weismantel R (2011) The combinatorics of modeling and analysing biological systems. Nat Comput 10(2): 655–681MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Markus Durzinsky
    • 1
  • Wolfgang Marwan
    • 1
  • Annegret Wagler
    • 2
    Email author
  1. 1.Magdeburg Centre for Systems Biology (MaCS)Otto-von-Guericke Universität MagdeburgMagdeburgGermany
  2. 2.Faculty of Sciences/LIMOSUniversité Blaise Pascal (Clermont-Ferrand II)AubièreFrance

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