Abstract
We find conditions of existence of closed trajectories and describe their bifurcations for two broad classes of 3D asymmetric gene network models corresponding to two different regulation mechanisms. These results can be generalized to the case of gene networks of mixed types, where this regulation is effected either at the stages of initiation of mRNA and protein synthesis or at the stages of their degradation, and both different regulation mechanisms can appear in the same gene network. Description of the Andronov-Hopf bifurcation in these models is given as well.
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V. A. Likhoshvai, Yu. G. Matushkin, and S. I. Fadeev, Mol. Biol. 35(6), 926 (2001).
V. P. Golubyatnikov, V. A. Likhoshvai, S. I. Fadeev, et al., Proceedings of 6-th Int. Conf. Human and Computer-2003 University of Aizu, 200 (2003).
V. P. Golubyatnikov, V. A. Likhoshvai, E. P. Volokitin, et al., in Bioinformatics of Genome Regulation and Structure II, Ed. by N. A. Kolchanov, R. Hofestaedt, and L. Milanesi (Springer Science + Business Media Inc.), 405 (2006).
M. Golubitsky and I. Stewart, Bull. Amer. Math. Soc. 43(3), 305 (2006).
Y. Benenson, B. Gil, U. Ben-Dor, R. Adar, and E. Shapiro, Nature 429, 423 (2004).
V. P. Golubyatnikov, V. A. Likhoshvai, Yu. A. Gaidov, A. G. Kleshchev, and E. A. Lashina, Proceedings of 8-th International Conf. “Human and Computers-2005” University of Aizu, Japan, 7 (2005).
V. P. Golubyatnikov, A. G. Kleshchev, K. A. Kleshcheva, and A. V. Kudryavtzeva, Siberian Journal of Industrial Mathematics 9(1), 75 (2006).
S. Hastings, J. Tyson, and D. Webster, J. Diff. Equations 25, 39 (1977).
E. P. Volokitin and S. A. Treskov, Siberian Journal of Industrial Mathematics 8(1), 30 (2005).
M. Elowitz and S. Leibner, Nature 403, 335 (2000).
T. Gardner, C. R. Cantor, and J. J. Collins, Nature 403, 339 (2000).
N. Yildirim and M. C. Mackey, Biophys. J. 84, 2841 (2003).
R. N. Tchuraev, I. V. Stupak, I. S. Tropkina, and E. E. Stupak, FEBS Lett. 486(3), 200 (2000).
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Golubyatnikov, V.P., Gaidov, Y.A., Kleshchev, A.G. et al. Modeling of asymmetric gene networks functioning with different types of regulation. BIOPHYSICS 51 (Suppl 1), 61–65 (2006). https://doi.org/10.1134/S000635090607013X
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DOI: https://doi.org/10.1134/S000635090607013X