Boolean versus continuous dynamics on simple two-gene modules

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 82, Issue 4, 2010, Pages

  Gehrmann, Eva ^a   Drossel, Barbara ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN MODEL; CONTINUOUS DYNAMICS; CONTINUOUS MODELS; COOPERATIVITY; DYNAMICAL BEHAVIORS; GENE ACTIVITIES; GENERALIZED METHOD; LOGICAL STRUCTURE; PROTEIN CONCENTRATIONS; REGULATORY FUNCTIONS; STABLE OSCILLATIONS; TIME-SCALES;

GENES;

EID: 78651305710     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.046120     Document Type: Article

References (36)

1. F. Jacob and J. Monod, J. Mol. Biol. 3, 318 (1961). 10.1016/S0022- 2836(61)80072-7
2. J. Monod, J.-P. Changeaux, and F. Jacob, J. Mol. Biol. 6, 306 (1963). 10.1016/S0022-2836(63)80091-1
3. M. B. Elowitz and S. Leibler, Nature (London) 403, 335 (2000). 10.1038/35002125
4. S. A. Kauffman, J. Theor. Biol. 22, 437 (1969). 10.1016/0022-5193(69) 90015-0
5. R. Thomas, J. Theor. Biol. 42, 563 (1973). 10.1016/0022-5193(73)90247-6
6. S. Bornholdt, Science 310, 449 (2005). 10.1126/science.1119959
7. F. Li, T. Long, Y. Lu, Q. Ouyang, and C. Tang, Proc. Natl. Acad. Sci. U.S.A. 101, 4781 (2004). 10.1073/pnas.0305937101
8. H. de Jong, J. Comput. Biol. 9, 67 (2002). 10.1089/10665270252833208
9. P. Smolen, D. A. Baxter, and J. H. Byrne, Bull. Math. Biol. 62, 247 (2000). 10.1006/bulm.1999.0155
10. J. Hasty, D. McMillen, F. Isaacs, and J. J. Collins, Nat. Rev. Genet. 2, 268 (2001). 10.1038/35066056
11. L. Glass and S. A. Kauffman, J. Theor. Biol. 34, 219 (1972). 10.1016/0022-5193(72)90157-9
12. L. Glass and S. A. Kauffman, J. Theor. Biol. 39, 103 (1973). 10.1016/0022-5193(73)90208-7
13. S. Pigolotti, S. Krishna, and M. H. Jensen, Proc. Natl. Acad. Sci. U.S.A. 104, 6533 (2007). 10.1073/pnas.0610759104
14. M. Xiao and J. Cao, Math. Biosci. 215, 55 (2008). 10.1016/j.mbs.2008.05. 004
15. S. Widder, J. Schicho, and P. Schuster, J. Theor. Biol. 246, 395 (2007). 10.1016/j.jtbi.2007.01.004
16. A. Polynikis, S. J. Hogan, and M. di Bernardo, J. Theor. Biol. 261, 511 (2009). 10.1016/j.jtbi.2009.07.040
17. D. Angeli, J. E. Ferrell, Jr., and E. D. Sontag, Proc. Natl. Acad. Sci. U.S.A. 101, 1822 (2004). 10.1073/pnas.0308265100
18. C. Soule, C. R. Biol. 329, 13 (2006). 10.1016/j.crvi.2005.10.002
19. R. Guantes and J. F. Poyatos, PLOS Comput. Biol. 2, e30 (2006). 10.1371/journal.pcbi.0020030
20. D. Del Vecchio, in Proceedings of American Control Conference, New York, 2007 (IEEE, New York, 2007).
21. J. Norrell, B. Samuelsson, and J. E. S. Socolar, Phys. Rev. E 76, 046122 (2007). 10.1103/PhysRevE.76.046122
22. A. Mochizuki, J. Theor. Biol. 236, 291 (2005). 10.1016/j.jtbi.2005.03.015
23. T. Gross and U. Feudel, Phys. Rev. E 73, 016205 (2006). 10.1103/PhysRevE.73.016205
24. D. Del Vecchio and E. D. Sontag, in Proceedings of American Control Conference, New York, 2007 (IEEE, New York, 2007).
25. T. Chen, H. L. He, and G. M. Church, Pac. Symp. Biocomput 4, 29 (1999).
26. G. Yagil and E. Yagil, Biophys. J. 11, 11 (1971). 10.1016/S0006-3495(71) 86192-1
27. A. V. Hill, J. Physiol. 40, iv (1910).
28. U. Alon, An Introduction to Systems Biology (Chapman & Hall; CRC, London, 2007).
29. Y. Setty, A. E. Mayo, M. G. Surette, and U. Alon, Proc. Natl. Acad. Sci. U.S.A. 100, 7702 (2003). 10.1073/pnas.1230759100
30. D. Wittmann, J. Krumsiek, J. Saez-Rodriguez, D. A. Lauffenburger, S. Klamt, and F. Theis, BMC Syst. Biol. 3, 98 (2009). 10.1186/1752-0509-3-98
31. T. Gross and U. Feudel, Physica D 195, 292 (2004). 10.1016/j.physd.2004. 03.019
32. T. Gross, Population Dynamics: General Results from Local Analysis (Der Andere Verlag, Tönning, 2004).
33. T. Gross and U. Feudel, Ocean Dyn. 59, 417 (2009). 10.1007/s10236-008- 0165-2
34. R. Steuer, T. Gross, J. Selbig, and B. Blasius, Proc. Natl. Acad. Sci. U.S.A. 103, 11868 (2006). 10.1073/pnas.0600013103
35. R. Steuer, A. Nunes Nesi, A. R. Fernie, T. Gross, B. Blasius, and J. Selbig, Bioinformatics 23, 1378 (2007). 10.1093/bioinformatics/btm065
36. J. Norrell and J. E. S. Socolar, Phys. Rev. E 79, 061908 (2009). 10.1103/PhysRevE.79.061908