Computing Hierarchical Transition Graphs of Asynchronous Genetic Regulatory Networks

  • Marco Pedicini
  • Maria Concetta Palumbo
  • Filippo Castiglione
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 830)


In the field of theoretical biology the study of the dynamics of the so-called gene regulatory networks is useful to follow the relationship between the expression of a gene and its dynamic regulatory effect on the cell fate. To date, most of the models developed for this purpose, applies the synchronous update schedule while reality is far from being so. On the other hand, the more realistic asynchronous update requires to compute all possible updates at each single instant, thus bearing a much greater computational load.

In the present work, we describe a novel method that addresses the problem of efficiently exploring the dynamics of a gene regulatory network with the asynchronous update.


SAT solver Discrete dynamical systems Tarjan’s algorithm Gene regulatory networks Strongly connected components 


  1. [BCM+13]
    Bérenguier, D., Chaouiya, C., Monteiro, P.T., Naldi, A., Remy, E., Thieffry, D., Tichit, L.: Dynamical modeling and analysis of large cellular regulatory networks. Chaos: Interdisc. J. Nonlinear Sci. 23(2), 025114 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  2. [BFG+93]
    Bahar, R.I., Frohm, E.A., Gaona, C.M., Hachtel, G.D., Macii, E., Pardo, A., Somenzi, F.: Algebraic decision diagrams and their applications. In: 1993 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 1993, Digest of Technical Papers, pp. 188–191. IEEE (1993)Google Scholar
  3. [BGS06]
    Bloem, R., Gabow, H.N., Somenzi, F.: An algorithm for strongly connected component analysis in \(n\) log \(n\) symbolic steps. Formal Methods Syst. Des. 28(1), 37–56 (2006)CrossRefzbMATHGoogle Scholar
  4. [DJ02]
    De Jong, H.: Modeling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol. 9(1), 67–103 (2002)CrossRefGoogle Scholar
  5. [DT11]
    Dubrova, E., Teslenko, M.: A SAT-based algorithm for finding attractors in synchronous Boolean networks. IEEE/ACM Trans. Comput. Biol. Bioinform. 8(5), 1393–1399 (2011)CrossRefGoogle Scholar
  6. [Gab00]
    Gabow, H.N.: Path-based depth-first search for strong and biconnected components. Inf. Process. Lett. 74(3–4), 107–114 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. [GCBP+13]
    Grieco, L., Calzone, L., Bernard-Pierrot, I., Radvanyi, F., Kahn-Perlès, B., Thieffry, D.: Integrative modelling of the influence of mapk network on cancer cell fate decision. PLoS Comput. Biol. 9(10), e1003286 (2013)CrossRefGoogle Scholar
  8. [GMDC+09]
    Garg, A., Mohanram, K., Di Cara, A., De Micheli, G., Xenarios, I.: Modeling stochasticity and robustness in gene regulatory networks. Bioinformatics 25(12), i101–i109 (2009)CrossRefGoogle Scholar
  9. [HB97]
    Harvey, I., Bossomaier, T.: Time out of joint: attractors in asynchronous random Boolean networks. In: Proceedings of the Fourth European Conference on Artificial Life, pp. 67–75. MIT Press, Cambridge (1997)Google Scholar
  10. [HMMK13]
    Hopfensitz, M., Müssel, C., Maucher, M.: HA Kestler: attractors in Boolean networks: a tutorial. Comput. Stat. 28(1), 19–36 (2013)CrossRefzbMATHGoogle Scholar
  11. [Kau93]
    Kauffman, S.A.: The Origins of Order: Self-organization and Selection in Evolution. Oxford University Press, Oxford (1993)Google Scholar
  12. [Mun71]
    Munro, I.: Efficient determination of the transitive closure of a directed graph. Inf. Process. Lett. 1(2), 56–58 (1971)CrossRefzbMATHGoogle Scholar
  13. [PBC+10]
    Pedicini, M., Barrenäs, F., Clancy, T., Castiglione, F., Hovig, E., Kanduri, K., Santoni, D., Benson, M.: Combining network modeling and gene expression microarray analysis to explore the dynamics of Th1 and Th2 cell regulation. PLoS Comput. Biol. 6(12), e1001032 (2010)MathSciNetCrossRefGoogle Scholar
  14. [Pur70]
    Purdom, P.: A transitive closure algorithm. BIT Numer. Math. 10(1), 76–94 (1970)CrossRefzbMATHGoogle Scholar
  15. [Tar72]
    Tarjan, R.: Depth-first search and linear graph algorithms. SIAM J. Comput. 1(2), 146–160 (1972)MathSciNetCrossRefzbMATHGoogle Scholar
  16. [VCL12]
    Veliz-Cuba, A., Laubenbacher, R.: On the computation of fixed points in Boolean networks. J. Appl. Math. Comput. 39(1–2), 145–153 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  17. [ZYL+13]
    Zheng, D., Yang, G., Li, X., Wang, Z., Liu, F., He, L.: An efficient algorithm for computing attractors of synchronous and asynchronous Boolean networks. PLoS ONE 8(4), e60593 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and PhysicsRoma Tre UniversityRomeItaly
  2. 2.CNR - Institute for Applied Computing “M. Picone”RomeItaly

Personalised recommendations