Nested Canalyzing Depth and Network Stability

Bulletin of Mathematical Biology

Volumn 74, Issue 2, 2012, Pages 422-433

  Layne, Lori ^a   Dimitrova, Elena ^a   Macauley, Matthew ^a  

^a CLEMSON UNIVERSITY   (United States)

Author keywords

Boolean networks; Canalyzation; Gene networks; Stability

Indexed keywords

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; GENE EXPRESSION REGULATION; GENE REGULATORY NETWORK;

ALGORITHMS; GENE EXPRESSION REGULATION; GENE REGULATORY NETWORKS; MODELS, GENETIC;

EID: 84856285286     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-011-9692-y     Document Type: Article

References (20)

1. Albert, R., & Othmer, H. (2003). The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. J. Theor. Biol., 223, 1-18.
2. Balleza, E., Alvarez-Buylla, E., Chaos, A., Kauffman, S. A., Shmulevich, I., & Aldana, M. (2008). Critical dynamics in genetic regulatory networks: Examples from four kingdoms. PLoS ONE, 3(6), e2456.
3. Derrida, B., & Pomeau, Y. (1986). Random networks of automata: a simple annealed approximation. Europhys. Lett., 1, 45-49.
4. Drossel, B. (2009). Random Boolean networks, Chap. 3, pp. 69-110. Weinheim: Wiley-VCH Verlag GmbH & Co.
5. Gambin, A., Lasota, S., & Rutkowski, M. (2006). Analyzing stationary states of gene regulatory network using petri nets. Silico Biol., 6, 93-109.
6. Jarrah, A. S., Raposa, B., & Laubenbacher, R. (2007). Nested canalyzing, unate cascade, and polynomial functions. Physica D, 233, 167-174.
7. Karlssona, F., & Hörnquist, M. (2007). Order or chaos in Boolean gene networks depends on the mean fraction of canalyzing functions. Physica A, 384, 747-757.
8. Kauffman, S. A. (1969). Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol., 22(3), 437-467.
9. Kauffman, S. A. (1993). The origins of order: self-organization and selection in evolution. London: Oxford University Press.
10. Kauffman, S. A., Peterson, C., Samuelsson, B., & Troein, C. (2003). Random Boolean network models and the yeast transcriptional network. Proc. Natl. Acad. Sci., 100(25), 14796-14799.
11. Kauffman, S. A., Peterson, C., Samuelsson, B., & Troein, C. (2004). Genetic networks with canalyzing Boolean rules are always stable. Proc. Natl. Acad. Sci., 101(49), 17102-17107.
12. Li, F., Long, T., Lu, Y., Ouyang, Q., & Tang, C. (2004). The yeast cell-cycle network is robustly designed. Proc. Natl. Acad. Sci., 11, 4781-4786.
13. Nikolajewa, S., Friedel, M., & Wilhelm, T. (2006). Boolean networks with biologically relevant rules show ordered behavior. Biosystems, 90(1), 40-47.
14. Nykter, M., Price, N. D., Aldana, M., Ramsey, S. A., Kauffman, S. A., Hood, L. E., Yli-Harja, O., & Shmulevich, I. (2008a). Gene expression dynamics in the macrophage exhibit criticality. Proc. Natl. Acad. Sci., 105, 1897-1900.
15. Nykter, M., Price, N. D., Larjo, A., Aho, T., Kauffman, S. A., Yli-Harja, O., & Shmulevich, I. (2008b). Critical networks exhibit maximal information diversity in structure-dynamics relationships. Phys. Rev. Lett., 100, 058702.
16. Peixoto, T. P. (2010). The phase diagram of random Boolean networks with nested canalizing functions. Eur. Phys. J. B, 78(2), 187-192.
17. Saez-Rodriguez, J., Simeoni, L., Lindquist, J., Hemenway, R., Bommhardt, U., Arndt, B., Haus, U., Weismantel, R., Gilles, E., Klamt, S., & Schraven, B. (2007). A logical model provides insights into T cell receptor signaling. PLoS Comput. Biol., 3, e163.
18. Shmulevich, I., & Kauffman, S. A. (2004). Activities and sensitivities in Boolean network models. Phys. Rev. Lett., 93(4), 048701.
19. Shmulevich, I., Kauffman, S. A., & Aldana, M. (2005). Eukaryotic cells are dynamically ordered or critical but not chaotic. Proc. Natl. Acad. Sci., 102, 13439-13444.
20. Waddington, C. H. (1942). Canalisation of development and the inheritance of acquired characters. Nature, 150, 563-564.