Intrinsic properties of Boolean dynamics in complex networks

Journal of Theoretical Biology

Volumn 256, Issue 3, 2009, Pages 351-369

  Kinoshita, Shu ichi ^a   Iguchi, Kazumoto ^b   Yamada, Hiroaki S ^c  

^a NIIGATA UNIVERSITY   (Japan)

^b KazumotoIguchi Research Laboratory   (Japan)

^c Yamada Physics Research Laboratory   (Japan)

Author keywords

Attractor; Boolean dynamics; Frozen nodes; Intrinsic property; Robustness; Scale free network

Indexed keywords

COMPLEXITY; NUMERICAL MODEL; TOPOLOGY;

ARTICLE; ENTROPY; INFORMATION SCIENCE; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; PRIORITY JOURNAL;

ANIMALS; COMPUTER SIMULATION; GENE EXPRESSION REGULATION; GENE REGULATORY NETWORKS; HUMANS; MODELS, GENETIC; NONLINEAR DYNAMICS;

EID: 58149112220     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2008.10.014     Document Type: Article

References (80)

1. Akashi S. Entropy Analysis and its Applications (1999), Makino-Shoten, Tokyo (in Japanese)
2. Albert R. Scale-free networks in cell biology. J. Cell Sci. 118 (2006) 4947-4957
3. Albert R., and Barabási A.-L. Dynamics of complex systems: scaling laws for the period of boolean networks. Phys. Rev. Lett. 84 (2000) 5660
4. Albert R., and Barabási A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74 (2002) 47-97 and references therein
5. Aldana M. Boolean dynamics of networks with scale-free topology. Physica D 185 (2003) 45-66
6. Aldana M., and Cluzel P. A natural class of robust networks. Proc. Natl. Acad. Sci. 100 (2003) 8710-8714
7. Aldana M., Coppersmith S., and Kadanoff L.P. Boolean dynamics with random couplings. In: Kaplan E., Marsden J.E., and Screenivasan K.R. (Eds). Perspectives and Problems in Nonlinear Science (2003), Springer, NY 23-90
8. Aldana M., Balleza E., Kauffman S., and Resendiz O. Robustness and evolvability in genetic regulatory networks. J. Theor. Biol. 245 (2007) 433-448
9. Anderson P.E., and Jensen H.J. Network properties, species abundance and evolution in a model of evolutionary ecology. J. Theor. Biol. 232 (2005) 551-558
10. Andrade R.F.S., Miranda J.G.V., and Lobao T.P. Neighborhood properties of complex networks. Phys. Rev. E 73 (2006) 046101
11. Bar-Yam Y., and Epstein I.R. Response of complex networks to stimuli. Proc. Natl. Acad. Sci. 101 (2004) 4341-4345
12. Barabási A.-L., and Oltvai Z.N. Network biology: understanding the cell's functional organization. Nat. Rev. 5 (2004) 101-113
13. Barabási A.-L., Albert R., and Jeong H. Mean-field theory for scale-free random networks. Physica A 272 (1999) 173-187
14. Bastolla U., and Parisi G. The critical line of Kauffman networks. J. Theor. Biol. 187 (1997) 117-133
15. Bianconi G., and Marsili M. Effect of degree correlations on the loop structure of scale-free networks. Phys. Rev. E 73 (2006) 066127
16. Bianconi G., Gulbahce N., and Motter A.E. Local structure of directed networks. Phys. Rev. Lett. 100 (2008) 118701
17. Bilke S., and Sjunnesson F. Stability of the Kauffman model. Phys. Rev. E 65 (2001) 01629
18. Billingsley P. Ergodic Theory and Information (1960), Wiley, New York
19. Boccaletti S., et al. Complex networks: structure and function. Phys. Rep. 424 (2006) 175
20. Bornholdt S., and Sneppen K. Robustness as an evolutionary principle. Proc. R. Soc. London B 267 (2000) 2281-2286
21. Braunewell S., and Bornholdt S. Superstability of the yeast cell-cycle dynamics: ensuring causality in the presence of biochemical stochasticity. J. Theor. Biol. 245 (2007) 638
22. Castro e Silva A., Kamphorst Leal da Silva J., and Mendes J.F.F. A scale-free network with Boolean dynamics as a function of connectivity. Phys. Rev. E 70 (2004) 066140 cond-mat/0410469
23. Ciliberti S., Martin O.C., and Wagner A. Robustness can evolve gradually in complex regulatory gene networks with varying topology. PLoS Comput. Biol. 3 (2007) 0164-0173
24. Drossel, B., 2008, Random Boolean networks. In: H.G. Schuster (Ed.), Reviews of Nonlinear Dynamics and Complexity, vol. 1. Wiley, NY; arXiv:0706.3351v2.
25. Fox J.J., and Hill C.C. From topology to dynamics in biochemical networks. Chaos 11 (2001) 809-815
26. Fretter C., and Drossel B. Response of Boolean networks to perturbations. Eur. Phys. J. B 62 (2008) 365-371
27. Gardenes J.G.-., Moreno Y., and Floria L.M. Scale-free topologies and activatory-inhibitory interactions. Chaos 16 (2006) 015114
28. Gecow, A., 2007. Emergence of growth, complexity threshold and structural tendencies during adaptive evolution of system. EPNACS in ECCS'07 Dresden, preprint.
29. Goh K.-I., Kahng B., and Kim D. Universal behavior of load distribution in scale-free networks. Phys. Rev. Lett. 87 (2001) 278701-1-4
30. Greil F., and Drossel B. Kauffman networks with threshold functions. Eur. Phys. J. B 57 (2007) 109-113
31. Handrey C., Ferraz A., and Herrmann H.J. The Kauffman model on small-world topology. Physica A 373 (2007) 770-776
32. Haydon D.T. Maximally stable model ecosystems can be highly connected. Ecology 81 (2000) 2631-2636
33. Holme P., and Ghoshal G. Dynamics of networking agents competing for high centrality and low degree. Phys. Rev. Lett. 96 (2006) 098701
34. Iguchi K., Kinoshita S., and Yamada H.S. Rugged fitness landscapes of Kauffman models with a scale-free network. Phys. Rev. E 72 (2005) 061901
35. Iguchi K., Kinoshita S., and Yamada H.S. Boolean dynamics of Kauffman model with a scale-free network. J. Theor. Biol. 247 (2007) 138-151
36. Jansen V.A.A., and Kokkoris G.D. Complexity and stability revisited. Ecol. Lett. 6 (2003) 498-502
37. Justa W., Shmulevichb I., and Konvalinac J. The number and probability of canalizing functions. Physica D 197 (2004) 211-221
38. Kauffman S.A. Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22 (1969) 437-467
39. Kauffman S.A. Origins of Order: Self-Organization and Selection in Evolution (1993), Oxford University Press, Oxford
40. Kauffman, S.A., 2003. Complexity and genetic networks, Existence Project News 2003.
41. Kauffman S.A. The ensemble approach to understand genetic regulatory networks. Physica A 340 (2004) 733-740
42. Kauffman S.A. A proposal for using the ensemble approach to understand genetic regulatory networks. J. Theor. Biol. 230 (2004) 581-590
43. Kauffman S.A., Peterson C., Samelsson B., and Troein C. Random Boolean network models and the yeast transcriptional network. Proc. Natl. Acad. Sci. USA 100 (2003) 14796-14799
44. Kinoshita S., Iguchi K., and Yamada H.S. Attractor states of Boolean dynamics in complex networks. AIP Conf. Proc. 982 (2008) 768-771
45. Kinoshita S., Iguchi K., and Yamada H.S. Prog. Theor. Phys. Suppl. 173 (2008) 342-350
46. Kinoshita, S., Iguchi, K., Yamada, H.S., 2008c. in preparation.
47. Klemm K., and Bornhaldt S. Topology of biological networks and reliability of information processing. Proc. Natl. Acad. Sci. 102 (2005) 18414-18419
48. Kohane I.S., Kho A.T., and Butte A.J. Microarrays for an Integrative Genomics (2002), MIT Press, NY
49. Kondoh M. Foraging adaptation and the relationship between food-web complexity and stability. Science 299 (2003) 1388-1391
50. Krawitz P., and Shmulevich I. Basin entropy in Boolean network ensembles. Phys. Rev. Lett. 98 (2007) 158701
51. Krawitz P., and Shmulevich I. Basin entropy in Boolean network ensembles. Phys. Rev. Lett. 76 (2007) 036115
52. Lee T.I., et al. Transcriptional regulatory networks in Saccharomyces cerevisiae. Science 298 (2002) 799-804
53. Levin S.A. Fragile Dominion: Complexity and the Commons (2000), Perseus Publishing, Cambridge
54. Li F., et al. The yeast cell-cycle network is robustly designed. Proc. Natl. Acad. Sci. 101 (2004) 4781
55. Liu M., and Bassler K.E. Emergent criticality from co-evolution in random Boolean networks. Phys. Rev. E 74 (2006) 041910 cond-mat/0605020
56. May R. Unanswered questions in ecology. Philos. Trans. R. Soc. London B 354 (1999) 1951-1959
57. Maynard Smith J., and Szathmary E. The Major Transitions in Evolution (1995), Spektrum Akademischer Verlag
58. Maynard Smith J., and Szathmary E. The Origins of Life: From the Birth of Life to the Origin of Language (1999), Oxford University Press, Oxford
59. Monte, J.M., Liu, M.M., Sheya, A.A., Kitami, T., 2005. Definitions, measures, and models of robustness in gene regulatory networks. Report of Research Work for CSSS05, July 2005.
60. Mount D.W. Bioinformatics: Sequence and Genome Analysis. second ed (2004), Cold Spring Harbor Laboratory Press
61. Newman M.E.J. Assortative mixing in networks. Phys. Rev. Lett. 89 (2002) 208701
62. Nykter M., et al. Critical networks exhibit maximal information diversity in structure-dynamics relationships. Phys. Rev. Lett. 100 (2008) 058702
63. Oikonomou P., and Cluzel P. Effects of topology on network evolution. Nature Physics 2 (2006) 532-536
64. Oosawa C., and Savageau A. Effects of alternative connectivity on behavior of randomly constructed Boolean networks. Physica D 170 (2002) 143-161
65. Paczuski M., Bassler K.E., and Corral1 A. Self-organized networks of competing Boolean agents. Phys. Rev. Lett. 84 (2000) 3185-3188
66. Rohlf T., Gulbahce N., and Teuscher C. Damage spreading and criticality in finite random dynamical networks. Phys. Rev. Lett. 99 (2007) 248701
67. Sawhill, B.K., Kauffman, S.A., 1997. Phase transitions in logic networks. Working paper, Sana Fe Institute.
68. Sen P., et al. Small-world properties of the Indian railway network. Phys. Rev. E 67 (2003) 036106
69. Serra, R., Villani, M., Agostini, L., 2003. On the dynamics of scale-free Boolean networks. WIRN VIETRI 2003. Lecture Notes in Computer Science, vol. 2859, Springer, Berlin, pp. 43-49.
70. Shen-Orr S.S., et al. Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genetics 31 (2002) 64-68
71. Skarja M., Remic B., and Jerman I. Boolean networks with variable number of inputs (K). Chaos 14 (2004) 205-216
72. Socolar J.E.S., and Kauffman S.A. Scaling in ordered and critical random Boolean networks. Phys. Rev. Lett. 90 (2003) 068702
73. Szejka A., and Drossel B. Evolution of canalizing Boolean networks. Eur. Phys. J. B 56 (2007) 373-380
74. Ueda H.R., et al. Universality and flexibility in gene expression from bacteria to human. Proc. Natl. Acad. Sci. 101 (2004) 3765-3769
75. Wagner A. Robustness and Evolvability in Living Systems (2005), Princeton University Press, NY
76. Wang S.-J., Wu A.-C., Wu Z.-X., Xu X.-J., and Wang Y.-H. Response of degree-correlated scale-free networks to stimuli. Phys. Rev. E 75 (2007) 046113 arXiv:0704.1849v1 [cond-mat.dis-nn]
77. Wang X.F., and Chen G.-R. Synchronization in scale-free dynamical networks: robustness and fragility. IEEE Trans. Circuits Sys. 49 (2002) 54-61
78. Watts D.J., and Strogatz S.H. Collective dynamics of 'small-world' networks. Nature 393 (1998) 440-442
79. White D.R., Kejžar N., Tsallis C., Farmer D., and White S. A generative model for feedback networks. Phys. Rev. E 73 (2006) 016119-1-8 cond-mat/0508028
80. Zhang S.Q., Hayashida M., Akutsu T., Ching W.-K., and Ng M.K. EURASIP J. Bioinform. Syst. Biol. 2007 (2007) 20180