Algorithms for Inference, Analysis and Control of Boolean Networks

  • Tatsuya Akutsu
  • Morihiro Hayashida
  • Takeyuki Tamura
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5147)


Boolean networks (BNs) are known as a mathematical model of genetic networks. In this paper, we overview algorithmic aspects of inference, analysis and control of BNs while focusing on the authors’ works. For inference of BN, we review results on the sample complexity required to uniquely identify a BN. For analysis of BN, we review efficient algorithms for identifying singleton attractors. For control of BN, we review NP-hardness results and dynamic programming algorithms for general and special cases.


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  1. 1.
    Akutsu, T., Miyano, S., Kuhara, S.: Identification of genetic networks from a small number of gene expression patterns under the Boolean network model. In: Proc. Pacific Symposium on Biocomputing 1999, pp. 17–28 (1999)Google Scholar
  2. 2.
    Akutsu, T., Miyano, S., Kuhara, S.: Algorithms for identifying Boolean networks and related biological networks based on matrix multiplication and fingerprint function. Journal of Computational Biology 7, 331–343 (2000)CrossRefGoogle Scholar
  3. 3.
    Akutsu, T., Miyano, S., Kuhara, S.: Inferring qualitative relations in genetic networks and metabolic pathways. Bioinformatics 16, 727–734 (2000)CrossRefGoogle Scholar
  4. 4.
    Akutsu, T., Kuhara, S., Maruyama, O., Miyano, S.: Identification of genetic networks by strategic gene disruptions and gene overexpressions under a boolean model. Theoretical Computer Science 298, 235–251 (2003)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Akutsu, T., Hayashida, M., Ching, W.-K., Ng, M.K.: Control of Boolean networks: Hardness results and algorithms for tree-structured networks. Journal of Theoretical Biology 244, 670–679 (2007)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Arpe, J., Reischuk, R.: When does greedy learning of relevant attributes succeed? In: Lin, G. (ed.) COCOON. LNCS, vol. 4598, pp. 296–306. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Bilke, S., Sjunnesson, F.: Number of attractors in random Boolean networks. Physical Review E 72, 016110 (2005)CrossRefGoogle Scholar
  8. 8.
    Datta, A., Choudhary, A., Bittner, M.L., Dougherty, E.R.: External control in Markovian genetic regulatory networks. Machine Learning 52, 169–191 (2003)MATHCrossRefGoogle Scholar
  9. 9.
    Devloo, V., Hansen, P., Labbé, M.: Identification of all steady states in large networks by logical analysis. Bulletin of Mathematical Biology 65, 1025–1051 (2003)CrossRefGoogle Scholar
  10. 10.
    Drossel, B., Mihaljev, T., Greil, F.: Number and length of attractors in a critical Kauffman model with connectivity one. Physical Review Letters 94, 088701 (2005)CrossRefGoogle Scholar
  11. 11.
    Faryabi, B., Datta, A., Dougherty, E.R.: On approximate stochastic control in genetic regulatory networks. IET Systems Biology 1, 361–368 (2007)CrossRefGoogle Scholar
  12. 12.
    Fukagawa, D., Akutsu, T.: Performance analysis of a greedy algorithm for inferring Boolean functions. Information Processing Letters 93, 7–12 (2005)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Garg, A., Xenarios, I., Mendoza, L., DeMicheli, G.: An efficient method for dynamic analysis of gene regulatory networks and in silico gene perturbation experiments. In: Speed, T., Huang, H. (eds.) RECOMB 2007. LNCS (LNBI), vol. 4453, pp. 62–76. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Co., New York (1979)MATHGoogle Scholar
  15. 15.
    Irons, D.J.: Improving the efficiency of attractor cycle identification in Boolean networks. Physica D 217, 7–21 (2006)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Kauffman, S.A.: The Origins of Order: Self-organization and Selection in Evolution. Oxford Univ. Press, New York (1993)Google Scholar
  17. 17.
    Kitano, H.: Computational systems biology. Nature 420, 206–210 (2002)CrossRefGoogle Scholar
  18. 18.
    Kitano, H.: Cancer as a robust system: implications for anticancer therapy. Nature Reviews Cancer 4, 227–235 (2004)CrossRefGoogle Scholar
  19. 19.
    Langmead, C.J., Jha, S.K.: Symbolic approaches for finding control strategies in Boolean networks. In: Proc. 6th Asia-Pacific Bioinformatics Conference, pp. 307–319. Imperial College Press, London (2008)Google Scholar
  20. 20.
    Liang, S., Fuhrman, S., Somogyi, R.: REVEAL, a general reverse engineering algorithm for inference of genetic network architectures. In: Proc. Pacific Symposium on Biocomputing 1998, pp. 18–29 (1998)Google Scholar
  21. 21.
    Milano, M., Roli, A.: Solving the safistiability problem through Boolean networks. In: Lamma, E., Mello, P. (eds.) AI*IA 1999. LNCS (LNAI), vol. 1792, pp. 72–93. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  22. 22.
    Mochizuki, A.: An analytical study of the number of steady states in gene regulatory networks. Journal of Theoretical Biology 236, 291–310 (2005)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Mossel, E., O’Donnell, R., Servedio, R.A.: Learning functions of k relevant variables. Journal of Computer and System Sciences 69, 421–434 (2004)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Ng, M.K., Zhang, S.-Q., Ching, W.-K., Akutsu, T.: A control model for Markovian genetic regulatory network. Transactions on Computational Systems Biology V, 36–48 (2006)Google Scholar
  25. 25.
    Pal, R., Datta, A., Bittner, M.L., Dougherty, E.R.: Intervention in context-sensitive probabilistic Boolean networks. Bioinformatics 21, 1211–1218 (2005)CrossRefGoogle Scholar
  26. 26.
    Pal, R., Datta, A., Bittner, M.L., Dougherty, E.R.: Optimal infinite-horizon control for probabilistic Boolean networks. IEEE Transactions on Signal Processing 54, 2375–2387 (2006)CrossRefGoogle Scholar
  27. 27.
    Samuelsson, B., Troein, C.: Superpolynomial growth in the number of attractors in kauffman networks. Physical Review Letters 90, 098701(2003)CrossRefMathSciNetGoogle Scholar
  28. 28.
    Shmulevich, I., Dougherty, E.R., Kim, S., Zhang, W.: Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 18, 261–274 (2002)CrossRefGoogle Scholar
  29. 29.
    Tamura, T., Akutsu, T.: An improved algorithm for detecting a singleton attractor in a Boolean network consisting of AND/OR nodes. In: Proceedings of the 3rd International Conference on Algebraic Biology (to appear)Google Scholar
  30. 30.
    Zhang, S.-Q., Hayashida, M., Akutsu, T., Ching, W.-K., Ng, M.K.: Algorithms for finding small attractors in Boolean networks. EURASIP Journal on Bioinformatics and Systems Biology 2007, 20180 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Tatsuya Akutsu
    • 1
  • Morihiro Hayashida
    • 1
  • Takeyuki Tamura
    • 1
  1. 1.Bioinformatics Center, Institute for Chemical ResearchKyoto UniversityKyotoJapan

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