Robust dynamics in minimal hybrid models of genetic networks

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 368, Issue 1930, 2010, Pages 4961-4975

  Perkins, Theodore J ^a   Wilds, Roy ^b   Glass, Leon ^b  

^a OTTAWA HOSPITAL RESEARCH INSTITUTE   (Canada)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

Genetic networks; Nonlinear dynamics; Robustness; Symbolic dynamics; Yeast cell cycle

Indexed keywords

GENES; HYBRID SYSTEMS; REAL VARIABLES; ROBUSTNESS (CONTROL SYSTEMS); TRANSCRIPTION; TRANSCRIPTION FACTORS; YEAST;

GENETIC NETWORKS; NON-LINEAR DYNAMICS; ROBUSTNESS; SYMBOLIC DYNAMICS; YEAST CELL CYCLE;

DYNAMICS;

TRANSCRIPTION FACTOR;

ARTICLE; BIOLOGICAL MODEL; CELL CYCLE; GENE EXPRESSION REGULATION; GENETICS; NONLINEAR SYSTEM; SACCHAROMYCES CEREVISIAE;

CELL CYCLE; GENE EXPRESSION REGULATION; MODELS, GENETIC; NONLINEAR DYNAMICS; SACCHAROMYCES CEREVISIAE; TRANSCRIPTION FACTORS;

EID: 78349304245     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2010.0139     Document Type: Article

References (35)

1. Akutsu, T., Miyano, S. & Kuhara, S. 1999 Identification of genetic networks from a small number of gene expression patterns under the Boolean network model. In Proc. of the Pacific Symp. on Biocomputing, Hawaii, HI, 4-9 January 1999, pp. 17-28.
2. Albert, R. & Othmer, H. G. 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. (doi:10.1016/S0022-5193(03) 00035-3) (Pubitemid 36627542)
3. Bachmair, A., Finley, D. & Varshavsky, A. 1986 In vivo half-life of a protein is a function of its amino-terminal residue. Science 234, 179-186. (doi:10.1126/science.3018930)
4. Bagley, R. J. & Glass, L. 1996 Counting and classifying attractors in high dimensional dynamical systems. J. Theor. Biol. 183, 269-284. (doi:10.1006/jtbi.1996.0220) (Pubitemid 27007482)
5. Belle, A., Tanay, A., Bitincka, L., Shamir, R. & O'Shea, E. K. 2006 Quantification of protein half-lives in the budding yeast proteome. Proc. Natl Acad. Sci. USA 103, 13 004-13 009. (doi:10.1073/pnas.0605420103) (Pubitemid 44338907)
6. Ben-Hur, A. & Siegelmann, H. 2004 Computation in gene networks. Chaos 14, 145-151. (doi:10.1063/1.1633371) (Pubitemid 38430246)
7. De Jong, H. 2002 Modeling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol. 9, 67-103. (doi:10.1089/10665270252833208) (Pubitemid 34264287)
8. Edwards, R. & Glass, L. 2005 A calculus for relating the dynamics and structure of complex biological networks. In Adventures in chemical physics (eds R. S. Berry & J. Jortner), pp. 151-178. New York, NY: Wiley-Interscience. (doi:10.1002/0471759309.ch4)
9. Elowitz, M. B. & Leibler, S. 2000 A synthetic oscillatory network of transcriptional regulators. Nature 403, 335-338. (doi:10.1038/35002125) (Pubitemid 30062393)
10. Fauré, A. & Thieffry, D. 2009 Logical modelling of cell cycle control in eukaryotes: a comparative study. Mol. BioSyst. 5, 1569-1581. (doi:10.1039/b907562n)
11. Fauré, A., Naldi, A., Lopez, F., Chaouiya, C., Ciliberto, A. & Thieffry, D. 2009 Modular logical modelling of the budding yeast cell cycle. Mol. BioSyst. 5, 1787-1796. (doi:10.1039/b910101m)
12. Gardner, T. S., Cantor, C. R. & Collins, J. J. 2000 Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339-342. (doi:10.1038/35002131) (Pubitemid 30062394)
13. Glass, L. & Kauffman, S. A. 1973 The logical analysis of continuous, nonlinear biochemical control networks. J. Theor. Biol. 39, 103-129. (doi:10.1016/0022-5193(73)90208-7)
14. Glass, L. & Pasternack, J. 1978a Prediction of limit cycles in mathematical models of biological oscillations. Bull. Math. Biol. 40, 27-44. (Pubitemid 8292021)
15. Glass, L. & Pasternack, J. 1978b Stable oscillations in mathematical models of biological control systems. J. Math. Biol. 6, 207-223. (doi:10.1007/BF02547797) (Pubitemid 9015991)
16. Glass, L. & Young, R. 1979 Structure and dynamics of neural network oscillators. Brain Res. 179, 207. (doi:10.1016/0006-8993(79)90439-6) (Pubitemid 10160513)
17. Glass, L., Perkins, T. J., Mason, J., Siegelmann, H. T. & Edwards, R. 2005 Chaotic dynamics in an electronic model of a genetic network. J. Stat. Phys. 121, 969-994. (doi:10.1007/s10955 -005-7009-y)
18. Gouzé, J. & Sari, T. 2002 A class of piecewise linear differential equations arising in biological models. Dyn. Syst. Int. J. 17, 299-316. (doi:10.1080/1468936021000041681)
19. Ichinose, N., Yada, T., Gotoh, O. & Aihara, K. 2008 Reconstruction of transcription-translation dynamics with a model of gene networks. J. Theor. Biol. 255, 378-386. (doi:10.1016/j.jtbi. 2008.09.006)
20. Ideker, T. E., Thorsson, V. & Karp, R. M. 2000 Discovery of regulatory interactions through perturbation: inference and experimental design. In Proc. of the Pacific Symp. on Biocomputing, Oahu, HI, 4-9 January 2000, pp. 302-313.
21. Jaeger, J. et al. 2004 Dynamic control of positional information in the early Drosophila embryo. Nature 430, 368-371. (doi:10.1038/nature02678) (Pubitemid 38937746)
22. Kauffman, S. 1969 Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22, 437-467. (doi:10.1016/0022- 5193(69)90015-0)
23. Kling, U. & Székely, G. 1968 Simulation of rhythmic nervous activities. Biol. Cybern. 5, 89-103. (doi:10.1007/BF00288899)
24. Lewis, J. E. & Glass, L. 1992 Nonlinear dynamics and symbolic dynamics of neural networks. Neural Comput. 4, 621-642. (doi:10.1162/neco.1992. 4.5.621)
25. Li, F., Long, T., Lu, Y., Ouyang, Q. & Tang, C. 2004 The yeast cell-cycle network is robustly designed. Proc. Natl Acad. Sci. USA 101, 4781. (doi:10.1073/pnas.0305937101) (Pubitemid 38469154)
26. Ma, W., Lai, L., Ouyang, Q. & Tang, C. 2006 Robustness and modular design of the Drosophila segment polarity network. Mol. Syst. Bio. 2, 70. (doi:10.1038/msb4100111) (Pubitemid 46061086)
27. Mestl, T., Plahte, E. & Omholt, S. 1995 Periodic solutions in systems of piecewise-linear differential equations. Dyn. Syst. 10, 179-193. (doi:10.1080/02681119508806202)
28. Mjolsness, E., Sharp, D. H. & Reinitz, J. 1991 A connectionist model of development. J. Theor. Biol. 152, 429-453. (doi:10.1016/S0022-5193(05)80391- 1)
29. Perkins, T. J. & Hallett, M. 2010 A trade-off between sample complexity and computational complexity in learning boolean networks from time series data. IEEE Trans. Comput. Biol. Bioinform. 7, 118-125. (doi:10.1109/TCBB.2008.38)
30. Perkins, T. J., Hallett, M. & Glass, L. 2004 Inferring models of gene expression dynamics. J. Theor. Biol. 230, 289-300. (doi:10.1016/j.jtbi.2004.05. 022) (Pubitemid 39092332)
31. Perkins, T. J., Hallett, M. & Glass, L. 2006 Dynamical properties of model gene networks and implications for the inverse problem. BioSystems 84, 115-123. (doi:10.1016/j.biosystems.2005. 09.010)
32. Porreca, R., Cinquemani, E., Lygeros, J. & Ferrari-Trecate, G. 2010 Identification of genetic network dynamics with unate structure. Bioinformatics 26, 1239-1245. (doi:10.1093/bioinformatics/btq120)
33. Reinitz, J. & Sharp, D. H. 1995 Mechanism of eve stripe formation. Mech. Dev. 49, 133-158. (doi:10.1016/0925-4773(94)00310-J)
34. Von Dassow, G., Meir, E., Munro, E. M. & Odell, G. M. 2000 The segment polarity network is a robust developmental module. Nature 406, 188-192. (doi:10.1038/35018085) (Pubitemid 30469001)
35. Wilds, R. & Glass, L. 2009 An atlas of robust, stable, high-dimensional limit cycles. Int. J. Bifurcat. Chaos 19, 4055-4096. (doi:10.1142/S0218127409025225)