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Hopf bifurcation in a model of TGF-$\beta$ in regulation of the Th 17 phenotype
1. | School of Biological Sciences, Seoul National University, Seoul 08826, South Korea |
2. | Division of Mathematical Models, National Institute for Mathematical Sciences, Daejeon 34047, South Korea |
3. | Department of Mathematics, Konkuk University, Seoul, 05029, South Korea |
References:
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F. Gross, G. Metznerb and U. Behn, Mathematical modelling of allergy and specific immunotherapy: Th1-Th2-Treg interactions,, J. Theor. Biol., 269 (2011), 70.
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References:
[1] |
S. Al-Muhsen, S. Letuve, A. Vazquez-Tello, M. A. Pureza, H. Al-Jahdali, A. S. Bahammam, Q. Hamid and R. Halwani, Th17 cytokines induce pro-fibrotic cytokines release from human eosinophils,, Respir. Res., 14 (2013).
doi: 10.1186/1465-9921-14-34. |
[2] |
T. Alarcón, H. M. Byrne and P. K. Maini, Towards whole-organ modelling of tumour growth,, Prog. Biophys. Mol. Biol., 85 (2004), 451. Google Scholar |
[3] |
J. F. Alcorn, C. R. Crowe and J. K. Kolls, $T_H$17 cells in asthma and COPD,, Annu. Rev. Physiol., 72 (2010), 495. Google Scholar |
[4] |
O. Arino, M. L. Hbid and E. Ait Dads, Delay Differential Equations and Applications,, Springer Netherlands, (2006).
doi: 10.1007/1-4020-3647-7. |
[5] |
K. J. Baek, J. Y. Cho, P. Rosenthal, L. E. C. Alexander, V. Nizet and D. H. Broide, Hypoxia potentiates allergen induction of HIF-1$\alpha$, chemokines, airway inflammation, TGF-$\beta$1, and airway remodeling in a mouse model,, Clin. Immunol., 147 (2013), 27. Google Scholar |
[6] |
R. L. Bar-Or and L. A. Segel, On the role of a possible dialogue between cytokine and TCR-presentation mechanisms in the regulation of autoimmune disease,, J. Theor. Biol., 190 (1998), 161.
doi: 10.1006/jtbi.1997.0545. |
[7] |
U. Behn, H. Dambeck and G. Metzner, Modeling Th1-Th2 regulation, allergy, and hyposensitization,, in Dynamical Modeling in Biotechnology, (2001), 227.
doi: 10.1142/9789812813053_0011. |
[8] |
B. S. Bochner, B. J. Undem and L. M. Lichtenstein, Immunological aspects of allergic asthma,, Annu. Rev. Immunol., 12 (1994), 295.
doi: 10.1146/annurev.iy.12.040194.001455. |
[9] |
R. E. Callard and A. J. Yates, Immunology and mathematics: Crossing the divide,, Immunology, 115 (2005), 21.
doi: 10.1111/j.1365-2567.2005.02142.x. |
[10] |
J. Carneiro, J. Stewart, A. Coutinho and G. Coutinho, The ontogeny of class-regulation of CD4$^+$ T lymphocyte populations,, Int. Immunol., 7 (1995), 1265.
doi: 10.1093/intimm/7.8.1265. |
[11] |
C. Clemedson and A. Nelson, General biology: The adult organism,, in Mechanisms in Radiobiology: Multicellular Organisms (eds. M. Errera and A. Forssberg), (1960), 95.
doi: 10.1016/B978-1-4832-2829-7.50010-1. |
[12] |
L. Cosmi, F. Liotta, E. Maggi, S. Romagnani and F. Annunziato, Th17 cells: New players in asthma pathogenesis,, Allergy, 66 (2011), 989.
doi: 10.1111/j.1398-9995.2011.02576.x. |
[13] |
E. Cutz, H. Levison and D. M. Cooper, Ultrastructure of airways in children with asthma,, Histopathology, 2 (1978), 407.
doi: 10.1111/j.1365-2559.1978.tb01735.x. |
[14] |
C. Dong, Diversification of T-helper-cell lineages: Finding the family root of IL-17-producing cells,, Nat. Rev. Immunol., 6 (2006), 329.
doi: 10.1038/nri1807. |
[15] |
C. Dong, $T_H$17 cells in development: An updated view of their molecular identity and genetic programming,, Nat. Rev. Immunol., 8 (2008), 337. Google Scholar |
[16] |
S. C. Eisenbarth, D. A. Piggott, J. W. Huleatt, I. Visintin, C. A. Herrick and K. Bottomly, Lipopolysaccharide-enhanced, toll-like receptor 4-dependent T helper cell type 2 responses to inhaled antigen,, J. Exp. Med., 196 (2002), 1645.
doi: 10.1084/jem.20021340. |
[17] |
R. L. Elliott and G. C. Blobe, Role of transforming growth factor beta in human cancer,, J. Clin. Oncol., 23 (2005), 2078. Google Scholar |
[18] |
M. A. Fishman and A. S. Perelson, Th1/Th2 differentiation and cross-regulation,, Bull. Math. Biol., 61 (1999), 403.
doi: 10.1006/bulm.1998.0074. |
[19] |
J. E. Gereda, D. Y. M. Leung, A. Thatayatikom, J. E. Streib, M. R. Price, M. D. Klinnert and A. H. Liu, Relation between house-dust endotoxin exposure, type 1 T-cell development, and allergen sensitisation in infants at high risk of asthma,, Lancet, 355 (2000), 1680.
doi: 10.1016/S0140-6736(00)02239-X. |
[20] |
L. Gorelik, S. Constant and R. A. Flavell, Mechanism of transforming growth factor $\beta$-induced inhibition of T helper type 1 differentiation,, J. Exp. Med., 195 (2002), 1499. Google Scholar |
[21] |
L. Gorelik and R. A. Flavell, Abrogation of TGF$\beta$ signaling in T cells leads to spontaneous T cell differentiation and autoimmune disease,, Immunity, 12 (2000), 171. Google Scholar |
[22] |
F. Gross, G. Metznerb and U. Behn, Mathematical modelling of allergy and specific immunotherapy: Th1-Th2-Treg interactions,, J. Theor. Biol., 269 (2011), 70.
doi: 10.1016/j.jtbi.2010.10.013. |
[23] |
G. Grünig, M. Warnock, A. E. Wakil, R. Venkayya, F. Brombacher, D. M. Rennick, D. Sheppard, M. Mohrs, D. D. Donaldson, R. M. Locksley and D. B. Corry, Requirement for IL-13 independently of IL-4 in experimental asthma,, Science, 282 (1998), 2261. Google Scholar |
[24] |
J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, vol. 42 of Applied Mathematical Sciences,, 1st edition, (1983).
doi: 10.1007/978-1-4612-1140-2. |
[25] |
I. Gutcher and B. Becher, APC-derived cytokines and T cell polarization in autoimmune inflammation,, J. Clin. Invest., 117 (2007), 1119.
doi: 10.1172/JCI31720. |
[26] |
J. K. Hale, Theory of Functional Differential Equations, vol. 3 of Applied Mathematical Sciences,, Springer-Verlag New York, (1977).
|
[27] |
Q. Hamid and M. Tulic, Immunobiology of asthma,, Annu. Rev. Physiol., 71 (2009), 489.
doi: 10.1146/annurev.physiol.010908.163200. |
[28] |
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