Skip to main content
Springer Nature Link
Log in

CSL Model Checking of Biochemical Networks with Interval Decision Diagrams

  • Conference paper
Computational Methods in Systems Biology (CMSB 2009)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 5688))

Included in the following conference series:

Abstract

This paper presents an Interval Decision Diagram based approach to symbolic CSL model checking of Continuous Time Markov Chains which are derived from stochastic Petri nets. Matrix-vector and vector-matrix multiplication are the major tasks of exact analysis. We introduce a simple, but powerful algorithm which uses explicitly the Petri net structure and allows for parallelisation. We present results demonstrating the efficiency of our first prototype implementation when applied to biochemical network models, specifically with increasing token numbers. Our tool currently supports CSL model checking of time-bounded operators and the Next operator for ordinary stochastic Petri nets.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model checking continuous time Markov chains. ACM Trans. on Computational Logic 1(1) (2000)

    Google Scholar 

  2. Baier, C., Haverkort, B., Hermanns, H., Katoen, J.-P.: Model checking Contiuous-Time Markov Chains by transient Analysis. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 358–372. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  3. Barkai, N., Leibler, S.: Biological rhythms: Circadian clocks limited by noise. Nature 403, 267–268 (2000)

    CAS  PubMed  Google Scholar 

  4. Cerotti, D., D’Aprile, D., Donatelli, S., Sproston, J.: Verifying stochastic well-formed nets with CSL model checking tools. In: Proc. ACSD 2006, pp. 143–152. IEEE Computer Society, Los Alamitos (2006)

    Google Scholar 

  5. Ciardo, G., Jones III, R.L., Miner, A.S., Siminiceanu, R.I.: Logic and stochastic modeling with smart. Perform. Eval. 63(6), 578–608 (2006)

    Article  Google Scholar 

  6. Cho, K.-H., Shin, S.-Y., Kim, H.-W., Wolkenhauer, O., McFerran, B., Kolch, W.: Mathematical modeling of the influence of RKIP on the ERK signaling pathway. In: Priami, C. (ed.) CMSB 2003. LNCS, vol. 2602, pp. 127–141. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Calder, M., Vyshemirsky, V., Orton, R., Gilbert, D.: Analysis of Signalling Pathways using the PRISM model checker. In: Proc. CMSB 2005, pp. 179–190. LFCS, Univ. of Edinburgh (2005)

    Google Scholar 

  8. Gilbert, D., Heiner, M.: From Petri nets to differential equations - an integrative approach for biochemical network analysis. In: Donatelli, S., Thiagarajan, P.S. (eds.) ICATPN 2006. LNCS, vol. 4024, pp. 181–200. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Gilbert, D., Heiner, M., Lehrack, S.: A unifying framework for modelling and analysing biochemical pathways using Petri nets. In: Calder, M., Gilmore, S. (eds.) CMSB 2007. LNCS (LNBI), vol. 4695, pp. 200–216. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  10. Heiner, M., Donaldson, R., Gilbert, D.: Petri Nets for Systems Biology. In: Iyengar, M.S. (ed.) Symbolic Systems Biology: Theory and Methods, Jones and Bartlett Publishers, Inc. (in press, 2010)

    Google Scholar 

  11. Heiner, M., Gilbert, D., Donaldson, R.: Petri nets for systems and synthetic biology. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 215–264. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  12. Heiner, M., Richter, R., Schwarick, M.: Snoopy - a tool to design and animate/simulate graph-based formalisms. In: Proc. PNTAP 2008, associated to SIMUTools 2008. ACM digital library, New York (2008)

    Google Scholar 

  13. Heiner, M., Schwarick, M., Tovchigrechko, A.: DSSZ-MC - A Tool for Symbolic Analysis of Extended Petri Nets. In: Franceschinis, G., Wolf, K. (eds.) Petri Nets 2009. LNCS, vol. 5606, pp. 323–332. Springer, Heidelberg (2009)

    Google Scholar 

  14. Jansen, D.N., Katoen, J.-P., Oldenkamp, M., Stoelinga, M., Zapreev, I.: How fast and fat is your probabilistic model checker? In: Yorav, K. (ed.) HVC 2007. LNCS, vol. 4899, pp. 69–85. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  15. Kwiatkowska, M., Norman, G., Parker, D.: Using probabilistic model checking in systems biology. ACM SIGMETRICS Performance Evaluation Review 35(4), 14–21 (2008)

    Article  Google Scholar 

  16. Levchenko, A., Bruck, J., Sternberg, P.W.: Scaffold proteins may biphasically affect the levels of mitogen-activated protein kinase signaling and reduce its threshold properties. Proc. Natl. Acad. Sci. USA 97(11), 5818–5823 (2000)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Miner, A.S., Ciardo, G.: Efficient Reachability Set Generation and Storage Using Decision Diagrams. In: Donatelli, S., Kleijn, J. (eds.) ICATPN 1999. LNCS, vol. 1639, pp. 6–25. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  18. Noack, A.: A ZBDD Package for Efficient Model Checking of Petri Nets (in German). Technical report, BTU Cottbus, Dep. of CS (1999)

    Google Scholar 

  19. Parker, D.: Implementation of Symbolic Model Checking for Probabilistic Systems. PhD thesis, University of Birmingham (2002)

    Google Scholar 

  20. Peccoud, J., Courtney, T., Sanders, W.H.: Möbius: an integrated discrete-event modeling environment. Bioinformatics 23(24), 3412–3414 (2007)

    Article  CAS  PubMed  Google Scholar 

  21. Parker, D., Norman, G., Kwiatkowska, M.: PRISM 3.0.beta1 Users’ Guide (2006)

    Google Scholar 

  22. Snoopy Website. A Tool to Design and Animate/Simulate Graphs. BTU Cottbus (2008), http://www-dssz.informatik.tu-cottbus.de/software/snoopy.html

  23. Stewart, W.J.: Introduction to the Numerical Solution of Markov Chains. Princeton Univ. Press, Princeton (1994)

    Google Scholar 

  24. Tovchigrechko, A.: Model Checking Using Interval Decision Diagrams. PhD thesis, BTU Cottbus, Dep. of CS (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Brandenburg University of Technology, Postbox 10 13 44, 03013, Cottbus, Germany

    Martin Schwarick & Monika Heiner

Authors
  1. Martin Schwarick
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Monika Heiner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Largo Bruno Pontecorvo, 3, 56127, Pisa, Italy

    Pierpaolo Degano

  2. Dipartimento di Scienze dell’Informazione, Università degli Studi di Bologna, Mura Anteo Zamboni 7, 40127, Bologna, Italy

    Roberto Gorrieri

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Schwarick, M., Heiner, M. (2009). CSL Model Checking of Biochemical Networks with Interval Decision Diagrams. In: Degano, P., Gorrieri, R. (eds) Computational Methods in Systems Biology. CMSB 2009. Lecture Notes in Computer Science(), vol 5688. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03845-7_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03845-7_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03844-0

  • Online ISBN: 978-3-642-03845-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics