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A Lattice model on somitogenesis of zebrafish
1. | Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan, Taiwan |
References:
[1] |
N. J. Armstrong, K. J. Painter and J. A. Sherratt, A continuum approach to modelling cell-cell adhesion, J. Theoret. Biol., 243 (2006), 98-113.
doi: 10.1016/j.jtbi.2006.05.030. |
[2] |
N. J. Armstrong, K. J. Painter and J. A. Sherratt, Adding adhesion to a chemical signaling model for somite formation, Bulletin Math. Biol., 71 (2009), 1-24. |
[3] |
R. E. Baker and S. Schnell, How can mathematics help us explore vertebrate segmentation?, HFSP J., 3 (2009), 1-5. |
[4] |
R. E. Baker, S. Schnell and P. K. Maini, A mathematical investigation of a clock and wavefornt model for somitogenesis, J. Math. Biol., 52 (2006), 458-482.
doi: 10.1007/s00285-005-0362-2. |
[5] |
M. Campanelli and T. Gedeon, Somitogenesis clock-wave initiation requires differential decay and multiple binding sites for clock protein, PLoS Comput. Biol., 6 (2010), e1000728. |
[6] |
O. Cinquin, Repressor dimerization in the zebrafish somitogenesis clock, PLoS Comput. Biol., 3 (2007), 293-303. |
[7] |
J. Cooke and E. C. Zeeman, A clock and wavefront model for control of the number of repeated structures during animal morphogenesis, J. Theoret. Biol., 58 (1976), 455-476.
doi: 10.1016/S0022-5193(76)80131-2. |
[8] |
J. Dubrulle, M. J. McGrew and O. Pourquié, FGF signaling controls somite boundary position and regulates segmentation clock control of spatiotemporal Hox gene activation, Cell, 106 (2001), 219-232.
doi: 10.1016/S0092-8674(01)00437-8. |
[9] |
J. Dubrulle and O. Pourquié, From head to tail: links between the segmentation clock and antero-posterior patterning of the embryo, Curr. Opin. Genet. Dev., 12 (2002), 519-523.
doi: 10.1016/S0959-437X(02)00335-0. |
[10] |
J. Dubrulle and O. Pourquié, fgf8 mRNA decay establishes a gradient that couples axial elongation to patterning in the vertebrate embryo, Nature, 427 (2004), 419-422.
doi: 10.1038/nature02216. |
[11] |
F. Giudicelli, E. M. Özbudak, G. J. Wright and J. Lewis, Setting the tempo in development: an investigation of the zebrafish somite clock mechanism, PLOS Biol., 5 (2007), e150, 1309-1323. |
[12] |
A. Goldbeter and O. Pourquié, Modeling the segmentation clock as a network of coupled oscillations in the Notch, Wnt and FGF signaling pathways, J. Theoret. Biol., 252 (2008), 574-585.
doi: 10.1016/j.jtbi.2008.01.006. |
[13] |
E. Hanneman and M. Westerfield, Early expression of acetyl-choline-sterase activity in functionally distinct neurons of the zebrafish, J. Comp. Neurol., 284 (1989), 350-361.
doi: 10.1002/cne.902840303. |
[14] |
S. A. Holley, The genetics and embryology of zebrafish metamerism, Dev. Dyn., 236 (2007), 1422-1449.
doi: 10.1002/dvdy.21162. |
[15] |
K. Horikawa, K. Ishimatsu, E. Yoshimoto, S. Kondo and H. Takeda, Noise-resistant and synchronized oscillation of the segmentation clock, Nature, 441 (2006), 719-723.
doi: 10.1038/nature04861. |
[16] |
Y.-J. Jiang, B. L. Aerne, L. Smithers, C. Haddon, D. Ish-Horowicz and J. Lewis, Notch signaling and the synchronization of the somite segmentation clock, Nature, 408 (2000), 475-479.
doi: 10.1038/35044091. |
[17] |
A. Kawamura, S. Koshida, H. Hijikata, T. Sakaguchi, H. Kondoh and S. Takada, Zebrafish hairy/enhancer of split protein links FGF signaling to cyclic gene expression in the periodic segmentation of somites, Genes Dev., 19 (2005), 1156-1161.
doi: 10.1101/gad.1291205. |
[18] |
J. Lewis, Autoinhibition with transcriptional delay: a simple mechanism for the zebrafish somitogenesis oscillator, Curr Biol., 13 (2003), 1398-1408.
doi: 10.1016/S0960-9822(03)00534-7. |
[19] |
K.-L. Liao, C.-W. Shih and J.-P. Tseng, Synchronized oscillations in a mathematical model of segmentation in zebrafish, Nonlinearity, 25 (2012), 869-904.
doi: 10.1088/0951-7715/25/4/869. |
[20] |
K.-L. Liao, "Analysis on Mathematical Models of Somitogenesis in Zebrafish," Ph.D thesis, National Chiao Tung University, Hsinchu, 2012. |
[21] |
A. Mara, J. Schroeder, C. Chalouni and S. A. Holley, Priming, initiation and synchronization of the segmentation clock by deltaD and deltaC, Nat. Cell. Biol., 9 (2007), 523-530. |
[22] |
L. G. Morelli, S. Ares, L. Herrgen, C. Schröter, F. Jülicher and A. C. Oates, Delayed coupling theory of vertebrate segmentation, HFSP J., 3 (2009), 55-66. |
[23] |
E. M. Özbudak and J. Lewis, Notch signalling synchronizes the zebrafish segmentation clock but is not needed to create somite boundaries, PLoS Genet., 4 (2008), e15. |
[24] |
O. Pourquié, The chick embryo: a leading model in somitogenesis studies, Mech. Dev., 121 (2004), 1069-1079.
doi: 10.1016/j.mod.2004.05.002. |
[25] |
I. H. Riedel-Kruse, C. Müller and A. C. Oates, Synchrony dynamics during initiation, failure, and rescue of the segmentation clock, Science, 317 (2007), 1911-1915.
doi: 10.1126/science.1142538. |
[26] |
J. A. Sherratt and M. J. Smith, Periodic travelling waves in cyclic populations: field studies and reaction-diffusion models, J. R. Soc. Interface, 5 (2008), 483-505. |
[27] |
C.-W. Shih and J.-P. Tseng, Convergent dynamics for multistable delayed neural networks, Nonlinearity, 21 (2008), 2361-2389.
doi: 10.1088/0951-7715/21/10/009. |
[28] |
C.-W. Shih and J.-P. Tseng, Global synchronization and asymptotic phases for a ring of identical cells with delayed coupling, SIAM J. Math. Analy., 43 (2011), 1667-1697.
doi: 10.1137/10080885X. |
[29] |
D. Sieger, B. Ackermann, C. Winkler, D. Tautz and M. Gajewski, her1 and her13.2 are jointly required for somitic border specification along the entire axis of the fish embryo, Dev. Biol., 293 (2006), 242-251.
doi: 10.1016/j.ydbio.2006.02.003. |
[30] |
K. Uriu, Y. Morishita and Y. Iwasa, Traveling wave formation in vertebrate segmentation, J. Theoret. Biol., 257 (2009), 385-396.
doi: 10.1016/j.jtbi.2009.01.003. |
[31] |
K. Uriu, Y. Morishita and Y. Iwasa, Synchronized oscillation of the segmentation clock gene in vertebrate development, J. Math. Biol., 61 (2010), 207-229.
doi: 10.1007/s00285-009-0296-1. |
[32] |
M. B. Wahl, C. Deng, M. Lewandoski and O. Pourquié, FGF signaling acts upstream of the NOTCH and WNT signaling pathways to control segmentation clock oscillations in mouse somitogenesis, Dev., 134 (2007), 4033-4041.
doi: 10.1242/dev.009167. |
[33] |
D. M. Young, "Iteration Solution of Large Linear Systems," Academic Press, New York-London, 1971. |
show all references
References:
[1] |
N. J. Armstrong, K. J. Painter and J. A. Sherratt, A continuum approach to modelling cell-cell adhesion, J. Theoret. Biol., 243 (2006), 98-113.
doi: 10.1016/j.jtbi.2006.05.030. |
[2] |
N. J. Armstrong, K. J. Painter and J. A. Sherratt, Adding adhesion to a chemical signaling model for somite formation, Bulletin Math. Biol., 71 (2009), 1-24. |
[3] |
R. E. Baker and S. Schnell, How can mathematics help us explore vertebrate segmentation?, HFSP J., 3 (2009), 1-5. |
[4] |
R. E. Baker, S. Schnell and P. K. Maini, A mathematical investigation of a clock and wavefornt model for somitogenesis, J. Math. Biol., 52 (2006), 458-482.
doi: 10.1007/s00285-005-0362-2. |
[5] |
M. Campanelli and T. Gedeon, Somitogenesis clock-wave initiation requires differential decay and multiple binding sites for clock protein, PLoS Comput. Biol., 6 (2010), e1000728. |
[6] |
O. Cinquin, Repressor dimerization in the zebrafish somitogenesis clock, PLoS Comput. Biol., 3 (2007), 293-303. |
[7] |
J. Cooke and E. C. Zeeman, A clock and wavefront model for control of the number of repeated structures during animal morphogenesis, J. Theoret. Biol., 58 (1976), 455-476.
doi: 10.1016/S0022-5193(76)80131-2. |
[8] |
J. Dubrulle, M. J. McGrew and O. Pourquié, FGF signaling controls somite boundary position and regulates segmentation clock control of spatiotemporal Hox gene activation, Cell, 106 (2001), 219-232.
doi: 10.1016/S0092-8674(01)00437-8. |
[9] |
J. Dubrulle and O. Pourquié, From head to tail: links between the segmentation clock and antero-posterior patterning of the embryo, Curr. Opin. Genet. Dev., 12 (2002), 519-523.
doi: 10.1016/S0959-437X(02)00335-0. |
[10] |
J. Dubrulle and O. Pourquié, fgf8 mRNA decay establishes a gradient that couples axial elongation to patterning in the vertebrate embryo, Nature, 427 (2004), 419-422.
doi: 10.1038/nature02216. |
[11] |
F. Giudicelli, E. M. Özbudak, G. J. Wright and J. Lewis, Setting the tempo in development: an investigation of the zebrafish somite clock mechanism, PLOS Biol., 5 (2007), e150, 1309-1323. |
[12] |
A. Goldbeter and O. Pourquié, Modeling the segmentation clock as a network of coupled oscillations in the Notch, Wnt and FGF signaling pathways, J. Theoret. Biol., 252 (2008), 574-585.
doi: 10.1016/j.jtbi.2008.01.006. |
[13] |
E. Hanneman and M. Westerfield, Early expression of acetyl-choline-sterase activity in functionally distinct neurons of the zebrafish, J. Comp. Neurol., 284 (1989), 350-361.
doi: 10.1002/cne.902840303. |
[14] |
S. A. Holley, The genetics and embryology of zebrafish metamerism, Dev. Dyn., 236 (2007), 1422-1449.
doi: 10.1002/dvdy.21162. |
[15] |
K. Horikawa, K. Ishimatsu, E. Yoshimoto, S. Kondo and H. Takeda, Noise-resistant and synchronized oscillation of the segmentation clock, Nature, 441 (2006), 719-723.
doi: 10.1038/nature04861. |
[16] |
Y.-J. Jiang, B. L. Aerne, L. Smithers, C. Haddon, D. Ish-Horowicz and J. Lewis, Notch signaling and the synchronization of the somite segmentation clock, Nature, 408 (2000), 475-479.
doi: 10.1038/35044091. |
[17] |
A. Kawamura, S. Koshida, H. Hijikata, T. Sakaguchi, H. Kondoh and S. Takada, Zebrafish hairy/enhancer of split protein links FGF signaling to cyclic gene expression in the periodic segmentation of somites, Genes Dev., 19 (2005), 1156-1161.
doi: 10.1101/gad.1291205. |
[18] |
J. Lewis, Autoinhibition with transcriptional delay: a simple mechanism for the zebrafish somitogenesis oscillator, Curr Biol., 13 (2003), 1398-1408.
doi: 10.1016/S0960-9822(03)00534-7. |
[19] |
K.-L. Liao, C.-W. Shih and J.-P. Tseng, Synchronized oscillations in a mathematical model of segmentation in zebrafish, Nonlinearity, 25 (2012), 869-904.
doi: 10.1088/0951-7715/25/4/869. |
[20] |
K.-L. Liao, "Analysis on Mathematical Models of Somitogenesis in Zebrafish," Ph.D thesis, National Chiao Tung University, Hsinchu, 2012. |
[21] |
A. Mara, J. Schroeder, C. Chalouni and S. A. Holley, Priming, initiation and synchronization of the segmentation clock by deltaD and deltaC, Nat. Cell. Biol., 9 (2007), 523-530. |
[22] |
L. G. Morelli, S. Ares, L. Herrgen, C. Schröter, F. Jülicher and A. C. Oates, Delayed coupling theory of vertebrate segmentation, HFSP J., 3 (2009), 55-66. |
[23] |
E. M. Özbudak and J. Lewis, Notch signalling synchronizes the zebrafish segmentation clock but is not needed to create somite boundaries, PLoS Genet., 4 (2008), e15. |
[24] |
O. Pourquié, The chick embryo: a leading model in somitogenesis studies, Mech. Dev., 121 (2004), 1069-1079.
doi: 10.1016/j.mod.2004.05.002. |
[25] |
I. H. Riedel-Kruse, C. Müller and A. C. Oates, Synchrony dynamics during initiation, failure, and rescue of the segmentation clock, Science, 317 (2007), 1911-1915.
doi: 10.1126/science.1142538. |
[26] |
J. A. Sherratt and M. J. Smith, Periodic travelling waves in cyclic populations: field studies and reaction-diffusion models, J. R. Soc. Interface, 5 (2008), 483-505. |
[27] |
C.-W. Shih and J.-P. Tseng, Convergent dynamics for multistable delayed neural networks, Nonlinearity, 21 (2008), 2361-2389.
doi: 10.1088/0951-7715/21/10/009. |
[28] |
C.-W. Shih and J.-P. Tseng, Global synchronization and asymptotic phases for a ring of identical cells with delayed coupling, SIAM J. Math. Analy., 43 (2011), 1667-1697.
doi: 10.1137/10080885X. |
[29] |
D. Sieger, B. Ackermann, C. Winkler, D. Tautz and M. Gajewski, her1 and her13.2 are jointly required for somitic border specification along the entire axis of the fish embryo, Dev. Biol., 293 (2006), 242-251.
doi: 10.1016/j.ydbio.2006.02.003. |
[30] |
K. Uriu, Y. Morishita and Y. Iwasa, Traveling wave formation in vertebrate segmentation, J. Theoret. Biol., 257 (2009), 385-396.
doi: 10.1016/j.jtbi.2009.01.003. |
[31] |
K. Uriu, Y. Morishita and Y. Iwasa, Synchronized oscillation of the segmentation clock gene in vertebrate development, J. Math. Biol., 61 (2010), 207-229.
doi: 10.1007/s00285-009-0296-1. |
[32] |
M. B. Wahl, C. Deng, M. Lewandoski and O. Pourquié, FGF signaling acts upstream of the NOTCH and WNT signaling pathways to control segmentation clock oscillations in mouse somitogenesis, Dev., 134 (2007), 4033-4041.
doi: 10.1242/dev.009167. |
[33] |
D. M. Young, "Iteration Solution of Large Linear Systems," Academic Press, New York-London, 1971. |
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