Determining a singleton attractor of a Boolean network with nested canalyzing functions

Journal of Computational Biology

Volumn 18, Issue 10, 2011, Pages 1275-1290

  Akutsu, Tatsuya ^a   Melkman, Avraham A ^b   Tamura, Takeyuki ^a   Yamamoto, Masaki ^c  

^a KYOTO UNIVERSITY   (Japan)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^c KWANSEI GAKUIN UNIVERSITY   (Japan)

Author keywords

Boolean network; nested canalyzing function; SAT; singleton attractor

Indexed keywords

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; BIOLOGY; COMPUTER SIMULATION; GENE EXPRESSION REGULATION; KINETICS; NONLINEAR SYSTEM; SYSTEMS BIOLOGY;

ALGORITHMS; COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; GENE EXPRESSION REGULATION; KINETICS; MODELS, GENETIC; NONLINEAR DYNAMICS; SYSTEMS BIOLOGY;

EID: 80053121012     PISSN: 10665277     EISSN: None     Source Type: Journal    
DOI: 10.1089/cmb.2010.0281     Document Type: Article

References (23)

1. Dantsin, E., Goerdt, A., Hirsch, E.A., et al. 2002. A deterministic (2-2/(k+1))n algorithm for k-SAT based on local search. Theor. Comput. Sci. 289, 69-83.
2. Devloo, V., Hansen, P., and Labbé, M. 2003. Identification of all steady states in large networks by logical analysis. Bull. Math.Biol. 65, 1025-1051. (Pubitemid 37446843)
3. Drossel, B., Mihaljev, T., and Greil, F. 2005. Number and length of attractors in a critical Kauffman model with connectivity one. Phys. Rev. Lett. 94, 088701.
4. Garg, A., DiCara, A., Xenarios, I., et al. 2008. Synchronous versus asynchronous modeling of gene regulatory networks. Bioinformatics 24, 1917-1925.
5. Gat-Viks, I., and Shamir, R. 2003. Chain functions and scoring functions in genetic networks. Bioinformatics 19, i109-i117.
6. Goles, E., and Salinas, L. 2010. Sequential operator for filtering cycles in Boolean networks. Adv. Appl. Math. 45, 346-358.
7. Harris, S.E., Sawhill, B.K., Wuensche, A., et al. 2002. A model of transcriptional regulatory networks based on biases in the observed regulation rules. Complexity 7, 23-40. (Pubitemid 34961265)
8. Hirsch, E.A. 2000. New worst-case upper bounds for SAT. J. Autom. Reasoning 24, 397-420.
9. Irons, D.J. 2006. Improving the efficiency of attractor cycle identification in Boolean networks. Physica D 217, 7-21. (Pubitemid 44287871)
10. Jarrah, A.S., Raposa, B., and Laubenbacher, R. 2007. Nested canalyzing, unate cascade, and polynomial functions. Physica D 233, 167-174. (Pubitemid 47284480)
11. Kauffman, S.A. 1993. The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press, New York.
12. Kauffman, S.A., Peterson, C., Samuelsson, B., et al. 2003. Random Boolean network models and the yeast transcriptional network. Proc. Natl. Acad. Sci. USA 100, 14796-14799. (Pubitemid 37517970)
13. Kauffman, S.A., Peterson, C., Samuelsson, B., et al. 2004. Genetic networks with canalyzing Boolean rules are always stable. Proc. Natl. Acad. Sci. USA 101, 17102-17107. (Pubitemid 39627781)
14. Leone, M., Pagnani, A., Parisi, G., et al. 2006. Finite size corrections to random Boolean networks. Journal of Stat. Mech. 2006, P12012.
15. Melkman, A., Tamura, T., and Akutsu, T. 2010. Determining a singleton attractor of an AND/OR Boolean network in O(1.587n) time. Inform. Process. Lett. 110, 565-569.
16. Samuelsson, B., and Troein, C. 2003. Superpolynomial growth in the number of attractors in kauffman networks. Phys. Rev. Lett. 90, 098701.
17. Szallasi, Z., and Liang, S. 1998. Modeling the normal and neoplastic cell cycle with realistic Boolean genetic networks: Their application for understanding carcinogenesis and assessing therapeutic strategies. Proc. Pac. Symp. Biocomput. 1998 66-76.
18. Tamura, T., and Akutsu, T. 2009. Detecting a singleton attractor in a Boolean network utilizing SAT algorithms. IEICE Trans. Fund. Electronics Commun. Comput. Sci. E92-A, 493-501.
19. Tamura, T., and Akutsu, T. 2009. Algorithms for singleton attractor detection in planar and nonplanar AND/OR Boolean networks. Math. Comput. Sci. 2, 401-420.
20. Tovey, C. A. 1984. A simplified NP-complete satisfiability problem. Discrete Appl. Math. 8, 85-89.
21. Yamamoto, M. 2005. An improved Õ (1.234m)-time deterministic algorithm for SAT. Proc. 16th Int. Symp. Algorithms Comput. 644-653. (Pubitemid 43856291)
22. Yamamoto, M. 2009. An Õ(1.732n) time algorithm for singleton attractor detection in AND/OR Boolean networks [Technical Report].
23. Zhang, S.-Q., Hayashida, M., Akutsu, T., et al. 2007. Algorithms for finding small attractors in Boolean networks. EURASIP J. Bioinformatics Syst. Biol. 2007, 20180.