Skip to main content
SpringerLink
Log in

Computing maximal and minimal trap spaces of Boolean networks

  • Published:
Natural Computing Aims and scope Submit manuscript

An Erratum to this article was published on 10 January 2017

Abstract

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.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Crama Y, Hammer PL (2011) Boolean functions: theory, algorithms, and applications, vol 142. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Dubrova E, Teslenko M (2011) A SAT-based algorithm for finding attractors in synchronous boolean networks. IEEE/ACM Trans Comput Biol Bioinform (TCBB) 8(5):1393–1399

    Article  Google Scholar 

  • Fogelman-Soulie F (1985) Parallel and sequential computation on boolean networks. Theor comput sci 40:275–300

    Article  MathSciNet  MATH  Google Scholar 

  • Garg A, Di Cara A, Xenarios I, Mendoza L, De Micheli G (2008) Synchronous versus asynchronous modeling of gene regulatory networks. Bioinform 24(17):1917–1925

    Article  Google Scholar 

  • Gebser M, Kaminski R, Kaufmann B, Ostrowski M, Schaub T, Schneider M (2011) Potassco: the potsdam answer set solving collection. Ai Commun 24(2):107–124

    MathSciNet  MATH  Google Scholar 

  • Gershenson C (2004) Updating schemes in random boolean networks: do they really matter. In: Artificial life IX Proceedings of the 9th international conference on the simulation and synthesis of living systems, MIT Press, pp 238–243

  • Grieco L, Calzone L, Bernard-Pierrot I, Radvanyi F, Kahn-Perlès B, Thieffry D (2013) Integrative modelling of the influence of mapk network on cancer cell fate decision. PLoS comput Biol 9(10):e1003,286

    Article  Google Scholar 

  • Gurobi Optimization I (2015) Gurobi optimizer reference manual. www.gurobi.com

  • Jabbour S, Marques-Silva J, Sais L, Salhi Y (2014) Enumerating prime implicants of propositional formulae in conjunctive normal form. In: Fermé E, Leite J (eds) Logics in artificial intelligence. Springer, pp 152–165

  • Kauffman SA (1993) The origins of order: self organization and selection in evolution. Oxford University Press, USA

    Google Scholar 

  • Klarner H (2015) www.sourceforge.net/Projects/BoolNetFixpoints

  • Klarner H, Bockmayr A, Siebert H (2014) Computing symbolic steady states of boolean networks. In: Was J, Sirakoulis G, Bandini S (eds) Cellular Automata, Lecture Notes in Computer Science, vol 8751, Springer International Publishing, pp 561–570

  • Müssel C, Hopfensitz M, Kestler HA (2010) Boolnet—an R package for generation, reconstruction, and analysis of boolean networks. Bioinformatics 10:1378–1380

    Article  Google Scholar 

  • Paulevé L, Chancellor C, Folschette M, Magnin M, Roux O (2014) Analyzing large network dynamics with process hitting. Log Model Biol Syst pp 125–166. doi: 10.1002/9781119005223.ch4

  • Siebert H (2011) Analysis of discrete bioregulatory networks using symbolic steady states. Bull Math Biol 73:873–898. doi:10.1007/s11538-010-9609-1

    Article  MathSciNet  MATH  Google Scholar 

  • Wang RS, Saadatpour A, Albert R (2012) Boolean modeling in systems biology: an overview of methodology and applications. Phys Biol 9(5):055,001

    Article  Google Scholar 

  • Zañudo JG, Albert R (2013) An effective network reduction approach to find the dynamical repertoire of discrete dynamic networks. Chaos: an interdisciplinary. J Nonlinear Sci 23(2):025–111

    MATH  Google Scholar 

Download references

Acknowledgments

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

Author information

Authors and Affiliations

  1. Freie Universität Berlin, FB Mathematik und Informatik, Arnimallee 6, 14195, Berlin, Germany

    Hannes Klarner, Alexander Bockmayr & Heike Siebert

Authors
  1. Hannes Klarner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander Bockmayr
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Heike Siebert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hannes Klarner.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s11047-016-9611-0.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Klarner, H., Bockmayr, A. & Siebert, H. Computing maximal and minimal trap spaces of Boolean networks. Nat Comput 14, 535–544 (2015). https://doi.org/10.1007/s11047-015-9520-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11047-015-9520-7

Keywords

Mathematics Subject Classification

Search

Navigation