Natural Computing

, Volume 14, Issue 4, pp 535–544 | Cite as

Computing maximal and minimal trap spaces of Boolean networks

  • Hannes KlarnerEmail author
  • Alexander Bockmayr
  • Heike Siebert


Asymptotic behaviors are often of particular interest when analyzing Boolean networks that represent biological systems such as signal transduction or gene regulatory networks. Methods based on a generalization of the steady state notion, the so-called trap spaces, can be exploited to investigate attractor properties as well as for model reduction techniques. In this paper, we propose a novel optimization-based method for computing all minimal and maximal trap spaces and motivate their use. In particular, we add a new result yielding a lower bound for the number of cyclic attractors and illustrate the methods with a study of a MAPK pathway model. To test the efficiency and scalability of the method, we compare the performance of the ILP solver gurobi with the ASP solver potassco in a benchmark of random networks.


Boolean networks Attractors Signal transduction  Gene regulation Answer set programming Integer linear programming 

Mathematics Subject Classification

94C10 92B05 



We thank S. Videla, M. Ostrowski and T. Schaub of University of Potsdam for their help with the ASP formulation.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Hannes Klarner
    • 1
    Email author
  • Alexander Bockmayr
    • 1
  • Heike Siebert
    • 1
  1. 1.Freie Universität BerlinBerlinGermany

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