Natural Computing

, Volume 10, Issue 3, pp 993–1015 | Cite as

A discrete Petri net model for cephalostatin-induced apoptosis in leukemic cells

  • Eva M. Rodriguez
  • Anita Rudy
  • Ricardo C. H. del Rosario
  • Angelika M. Vollmar
  • Eduardo R. Mendoza
Article

Abstract

Understanding the mechanisms involved in apoptosis has been an area of extensive study due to its critical role in the development and homeostasis of multi-cellular organisms. Our special interest lies in understanding the apoptosis of tumor cells which is mediated by novel potential drugs. Cephalostatin 1 is a marine compound that can induce apoptosis in leukemic cells in a dose- and time-dependent manner even at nano-molar concentrations using a recently discovered pathway that excludes the receptor-mediated pathway and which includes both the mitochondrial and endoplasmic reticulum pathways (Dirsch et al., Cancer Res 63:8869–8876, 2003; López-Antón et al., J Biol Chem 28:33078–33086, 2006). In this paper, the methods and tools of Petri net theory are used to construct, analyze, and validate a discrete Petri net model for cephalostatin 1-induced apoptosis. Based on experimental results and literature search, we constructed a discrete Petri net consisting of 43 places and 59 transitions. Standard Petri net analysis techniques such as structural and invariant analyses and a recently developed modularity analysis technique using maximal abstract dependent transition sets (ADT sets) were employed. Results of these analyses revealed model consistency with known biological behavior. The sub-modules represented by the ADT sets were compared with the functional modules of apoptosis identified by Alberghina and Colangelo (BMC Neurosci 7(Suppl 1):S2, 2006).

Keywords

Apoptosis Cephalostatin 1 Discrete Petri net Invariant analysis Maximal abstract dependent transition sets (ADT sets) Modularity analysis Structural analysis 

Supplementary material

11047_2009_9153_MOESM1_ESM.doc (118 kb)
Supplementary material 1 (DOC 118 kb)

References

  1. Albeck JG, Murke JM, Aldridge BB et al (2008) Quantitative analysis of pathways controlling extrinsic apoptosis in single cells. Mol Cell 30:11–25CrossRefGoogle Scholar
  2. Alberghina L, Colangelo AM (2006) The modular systems biology approach to investigate the control of apoptosis in Alzheimer’s disease neurodegeneration. BMC Neurosci 7(Suppl 1):S2CrossRefGoogle Scholar
  3. Bagci EZ, Vodovotz Y, Billiar TR et al (2006) Bistability in apoptosis: roles of Bax, Bcl-2, and mitchondrial permeability transition pores. Biophys J 90:1546–1559CrossRefGoogle Scholar
  4. Bentele M, Lavrik I, Ulrich M et al (2004) Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis. J Cell Biol 166:839–851CrossRefGoogle Scholar
  5. Chaouiya C (2007) Petri net modeling of biological networks. Brief Bioinform 8(4):210–219CrossRefGoogle Scholar
  6. Dirsch VM, Müller IM, Eichhorst ST et al (2003) Cephalostatin 1 selectively triggers the release of Smac/Diablo and subsequent apoptosis that is characterized by an increased density of the mitochondrial matrix. Cancer Res 63:8869–8876Google Scholar
  7. Eissing T, Conzelmann H, Gilles ED et al (2004) Bistability analyses of a caspase activation model for receptor-induced apoptosis. J Biol Chem 279:36892–36897CrossRefGoogle Scholar
  8. Fussenegger M, Bailey J, Varner J (2000) A mathematical model of caspase function in apoptosis. Nat Biotechnol 18:768–774CrossRefGoogle Scholar
  9. Heiner M (2009) Understanding network behavior by structured representations of transition invariants—a petri net perspective on systems and synthetic biology. In: Condon A et al (eds) Algorithmic bioprocesses. Springer, Natural Computing Series, BerlinGoogle Scholar
  10. Heiner M, Koch I (2004) Petri net based system validation in systems biology. In: Proc. ICATPN. Bologna, Springer, LNCS 3099, pp 216–237Google Scholar
  11. Heiner M, Koch I, Will J (2004) Model validation of biological pathways using petri nets—demonstrated for apoptosis. BioSystems 75:15–28CrossRefGoogle Scholar
  12. Hua F, Cornejo MG, Cardone et al (2005) Effects of Bcl-2 levels on Fas signaling-induced caspase-3 activation: molecular genetic tests of computational model predictions. J Immunol 175:987–995Google Scholar
  13. Ishii H, Suzuki Y, Kuboki M et al (1992) Activation of clapain 1 in thrombin-stimulated platelets is regulated by the initial elevation of the cytosolic Ca2+ concentration. Biochem J 284:755–760Google Scholar
  14. Koch I, Heiner M (2008) Petri nets. In: Junker B, Schreiber F (eds) Biological network analysis. Wiley Book Series on Bioinformatics (Chapter 7). New JerseyGoogle Scholar
  15. Koch I, Junker BH, Heiner M (2005) Application of Petri net theory for modeling and validation of the sucrose breakdown pathway in the potato tuber. Bioinformatics 21:1219–1226CrossRefGoogle Scholar
  16. Legewie S, Blüthgen N, Herzel H (2006) Mathematical modeling identifies inhibitors of apoptosis as mediators of positive feedback and bistability. PLoS Comput Biol 2(9):e120CrossRefGoogle Scholar
  17. Li C, Ge QW, Nakata M et al (2007) Modelling and simulation of signal transductions in an apoptosis pathway by using timed Petri nets. J Biosci 32(1):113–127CrossRefGoogle Scholar
  18. López-Antón N, Rudy A, Barth N et al (2006) The marine product cephalostatin 1 activates an ER stress-specific and apoptosome-independent apoptotic signaling pathway. J Biol Chem 28:33078–33086CrossRefGoogle Scholar
  19. Mandic A, Viktorsson K et al (2002) Calpain-mediated bid cleavage and calpain-independent Bak modulation: two separate pathways in cisplatin-induced apoptosis. Mol Cell Biol 22:3003–3013CrossRefGoogle Scholar
  20. Matsuno H, Tanaka Y, Aoshima H et al (2003) Biopathways representation and simulation on hybrid functional Petri net. In Silico Biol 3:0032Google Scholar
  21. Müller IM, Dirsch VM, Rudy A et al (2005) Cephalostatin 1 inactivates Bcl-2 by hyperphosphorylation independent of M-phase arrest and DNA damage. Mol Pharmacol 67:1684–1689CrossRefGoogle Scholar
  22. Nakagawa T, Yuan J (2000) Cross-talk between two cysteine protease families: activation of caspase 12 by calpain in apoptosis. J Cell Biol 4:887–894CrossRefGoogle Scholar
  23. Nijhawan D, Honarpour N, Wang X (2000) Apoptosis in neural development and disease. Annu Rev Neurosci 23:73–87CrossRefGoogle Scholar
  24. Penney J, Westhead D, MocConkey G (2003) Petri net representations in systems biology. Biochem Soc Trans 3:1513–1515CrossRefGoogle Scholar
  25. Reddy VN, Liebman MN, Mavrovouniotis ML (1996) Qualitative analysis of biochemical reaction systems. Comput Biol Med 26:9–24CrossRefGoogle Scholar
  26. Rehm M, Huber HJ, Düssmann H et al (2006) Systems analysis of effector caspase activation and its control by X-linked inhibitor of apoptosis protein. EMBO J 25:4338–4349CrossRefGoogle Scholar
  27. Rizzuto R, Pinton P, Ferrari D et al (2003) Calcium and apoptosis: facts and hypotheses. Oncogene 22:8619–8627CrossRefGoogle Scholar
  28. Rudy A, Lopez-Anton N, Dirsch VM, Vollmar A (2008a) The cephalostatin way of apoptosis. J Nat Prod 71:482–486CrossRefGoogle Scholar
  29. Rudy A, Lopez-Anton N, Barth N et al (2008b) Role of Smac in cephalostatin-induced cell death. Cell Death Differ 15:1930–1940CrossRefGoogle Scholar
  30. Szegedzdi E, Logue S, Gorman A et al (2006) Mediators of endoplasmic reticulum stress-induced apoptosis. EMBO Reports 7(9):880–885CrossRefGoogle Scholar
  31. Tinel A, Tschopp J (2004) The PIDDosome, a protein implicated in activation of caspase-2 in response to genotoxic stress. Science 304:843–846CrossRefGoogle Scholar
  32. Yap R (2006) Modeling the receptor-mediated pathway using hybrid Petri nets. Thesis, College of Science, University of the PhilippinesGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Eva M. Rodriguez
    • 1
    • 3
  • Anita Rudy
    • 2
  • Ricardo C. H. del Rosario
    • 3
    • 4
  • Angelika M. Vollmar
    • 2
  • Eduardo R. Mendoza
    • 5
    • 6
  1. 1.Department of MathematicsUniversity of Asia and the PacificPasig CityPhilippines
  2. 2.Department of Pharmacy, Center for Drug ResearchLudwig-Maximilians UniversityMunichGermany
  3. 3.Institute of MathematicsUniversity of the Philippines DilimanQuezon CityPhilippines
  4. 4.Department of Membrane BiochemistryMax-Planck Institute of BiochemistryMunichGermany
  5. 5.Department of Computer ScienceUniversity of the Philippines DilimanQuezon CityPhilippines
  6. 6.Physics Department and Center for NanoScienceLudwig-Maximilians UniversityMunichGermany

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