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Morphogen gradient with expansion-repression mechanism: Steady-state and robustness studies
1. | Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210, United States |
References:
[1] |
M. Affolter and K. Basler, The Decapentaplegic morphogen gradient: From pattern formation to growth regulation, Nature Rev. Genet., 8 (2007), 663-674.
doi: 10.1038/nrg2166. |
[2] |
D. Ben-Zvi and N. Barkai, Scaling of morphogen gradients by an expansion-repression integral feedback control, Proc. Natl. Acad. Sci. USA, 107 (2010), 6924-6929.
doi: 10.1073/pnas.0912734107. |
[3] |
D. Ben-Zvi, G. Pyrowolakis, N. Barkai and B. Z. Shilo, Expansion-repression mechanism for scaling the dpp activation gradient in drosophila wing imaginal discs, Curr Biol, 21 (2011), 1391-1396.
doi: 10.1016/j.cub.2011.07.015. |
[4] |
D. Ben-Zvi, B. Z. Shilo and N. Barkai, Scaling of morphogen gradients, Curr Opin Genet Dev, 21 (2011), 704-710.
doi: 10.1016/j.gde.2011.07.011. |
[5] |
S. Bergmann, O. Sandler, H. Sberro, S. Shnider, E. Schejter, B.-Z. Shilo and N. Barkai, Pre-steady-state decoding of the bicoid morphogen gradient, PLoS Biol, 5 (2007), e46.
doi: 10.1371/journal.pbio.0050046. |
[6] |
T. Bollenbach, K. Kruse, P. Pantazis, M. González-Gaitán and F. Jülicher, Robust formation of morphogen gradients, Phys Rev Lett., 94 (2005), 018103.
doi: 10.1103/PhysRevLett.94.018103. |
[7] |
K. Cadigan, M. Fish, E. Rulifson and R. Nusse, Wingless repression of Drosophila frizzled 2 expression shapes the wingless morphogen gradient in the wing, Cell, 93 (1998), 767-777.
doi: 10.1016/S0092-8674(00)81438-5. |
[8] |
A. Eldar, D. Rosin, B. Z. Shilo and N. Barkai, Self-enhanced ligand degradation underlies robustness of morphogen gradients, Developmental Cell, 5 (2003), 635-646.
doi: 10.1016/S1534-5807(03)00292-2. |
[9] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, New York, 1998.
doi: 10.1007/978-3-642-61798-0. |
[10] |
F. Hamaratoglu, A. M. de Lachapelle, G. Pyrowolakis, S. Bergmann and M. Affolter, Dpp signaling activity requires pentagone to scale with tissue size in the growing drosophila wing imaginal disc, PLoS Biol, 9 (2011), e1001182.
doi: 10.1371/journal.pbio.1001182. |
[11] |
H. Hardway, B. Mukhopadhyay, T. Burke, T. J. Hitchman and R. Forman, Modeling the precision and robustness of hunchback border during drosophila embryonic development, Journal of Theoretical Biology, 254 (2008), 390-399.
doi: 10.1016/j.jtbi.2008.05.021. |
[12] |
A. D. Lander, W. C. Lo, Q. Nie and F. Y. M. Wan, The measure of success: Constraints, objectives, and tradeoffs in morphogen-mediated patterning, Cold Spring Harbor Perspectives in Biology, 1 (2009), a002022. |
[13] |
A. D. Lander, Q. Nie and F. Y. M. Wan, Membrane-associated non-receptors and morphogen gradients, Bulletin of Mathematical Biology, 69 (2007), 33-54.
doi: 10.1007/s11538-006-9152-2. |
[14] |
A. Lander, Q. Nie, B. Vargas and F. Wan, Size-normalized robustness of dpp gradient in Drosophila wing imaginal disc, Journal of Mechanics of Materials and Structures, 6 (2011), 321-350. |
[15] |
A. D. Lander, Q. Nie and F. Y. M. Wan, Spatially distributed morphogen production and morphogen gradient formation, Math Biosci Eng, 2 (2005), 239-262.
doi: 10.3934/mbe.2005.2.239. |
[16] |
T. Lecuit, W. J. Brook, M. Ng, M. Calleja, H. Sun and S. M. Cohen, Two distinct mechanisms for long-range patterning by Decapentaplegic in the Drosophila wing, Nature, 381 (1996), 387-393.
doi: 10.1038/381387a0. |
[17] |
J. Lei, F. Wan, A. Lander and Q. Nie, Robustness of signaling gradient in drosophila wing imaginal disc, Discrete and Continuous Dynamical Systems, Series B, 16 (2011), 835-866.
doi: 10.3934/dcdsb.2011.16.835. |
[18] |
J. Lei, D. Wang, Y. Song, Q. Nie and F. Y. M. Wan, Robustness of morphogen gradients with "bucket brigade" transport through membrane-associated non-receptors, Discrete and Continuous Dynamical Systems, Series B, 18 (2013), 721-739.
doi: 10.3934/dcdsb.2013.18.721. |
[19] |
J. Lei and Y. Song, Mathematical model of the formation of morphogen gradients through membrane-associated non-receptors, Bull Math Biol, 72 (2010), 805-829.
doi: 10.1007/s11538-009-9470-2. |
[20] |
S. Morimura, L. Maves, Y. Chen and F. M. Hoffmann, decapentaplegic overexpression affects Drosophila wing and leg imaginal disc development and wingless expression, Dev Biol., 177 (1996), 136-151. |
[21] |
G. Reeves and S. E. Fraser, Biological systems from an engineer's point of view, PLoS Biology, 7 (2009), e1000021.
doi: 10.1371/journal.pbio.1000021. |
[22] |
W. Rudin, Real and Complex Analysis, McGraw-Hill Education, 1987. |
[23] |
D. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana University Math. J., 21 (1972), 979-1000. |
[24] |
M. Strigini and S. M. Cohen, A hedgehog activity gradient contributes to AP axial patterning of the Drosophila wing, Development, 124 (1997), 4697-4705. |
[25] |
A. A. Teleman and S. M. Cohen, Dpp gradient formation in the Drosophila wing imaginal disc, Cell, 103 (2000), 971-980.
doi: 10.1016/S0092-8674(00)00199-9. |
[26] |
L. Wolpert, Positional information and spatial pattern of cellular differentiation, Journal of Theoretical Biology, 25 (1969), 1-47.
doi: 10.1016/S0022-5193(69)80016-0. |
[27] |
L. Wolpert, Positional information and patterning revisited, Journal of Theoretical Biology, 269 (2011), 359-365.
doi: 10.1016/j.jtbi.2010.10.034. |
[28] |
M. Zecca, K. Basler and G. Struhl, Direct and long-range action of a wingless morphogen gradient, Cell, 87 (1996), 833-844.
doi: 10.1016/S0092-8674(00)81991-1. |
show all references
References:
[1] |
M. Affolter and K. Basler, The Decapentaplegic morphogen gradient: From pattern formation to growth regulation, Nature Rev. Genet., 8 (2007), 663-674.
doi: 10.1038/nrg2166. |
[2] |
D. Ben-Zvi and N. Barkai, Scaling of morphogen gradients by an expansion-repression integral feedback control, Proc. Natl. Acad. Sci. USA, 107 (2010), 6924-6929.
doi: 10.1073/pnas.0912734107. |
[3] |
D. Ben-Zvi, G. Pyrowolakis, N. Barkai and B. Z. Shilo, Expansion-repression mechanism for scaling the dpp activation gradient in drosophila wing imaginal discs, Curr Biol, 21 (2011), 1391-1396.
doi: 10.1016/j.cub.2011.07.015. |
[4] |
D. Ben-Zvi, B. Z. Shilo and N. Barkai, Scaling of morphogen gradients, Curr Opin Genet Dev, 21 (2011), 704-710.
doi: 10.1016/j.gde.2011.07.011. |
[5] |
S. Bergmann, O. Sandler, H. Sberro, S. Shnider, E. Schejter, B.-Z. Shilo and N. Barkai, Pre-steady-state decoding of the bicoid morphogen gradient, PLoS Biol, 5 (2007), e46.
doi: 10.1371/journal.pbio.0050046. |
[6] |
T. Bollenbach, K. Kruse, P. Pantazis, M. González-Gaitán and F. Jülicher, Robust formation of morphogen gradients, Phys Rev Lett., 94 (2005), 018103.
doi: 10.1103/PhysRevLett.94.018103. |
[7] |
K. Cadigan, M. Fish, E. Rulifson and R. Nusse, Wingless repression of Drosophila frizzled 2 expression shapes the wingless morphogen gradient in the wing, Cell, 93 (1998), 767-777.
doi: 10.1016/S0092-8674(00)81438-5. |
[8] |
A. Eldar, D. Rosin, B. Z. Shilo and N. Barkai, Self-enhanced ligand degradation underlies robustness of morphogen gradients, Developmental Cell, 5 (2003), 635-646.
doi: 10.1016/S1534-5807(03)00292-2. |
[9] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, New York, 1998.
doi: 10.1007/978-3-642-61798-0. |
[10] |
F. Hamaratoglu, A. M. de Lachapelle, G. Pyrowolakis, S. Bergmann and M. Affolter, Dpp signaling activity requires pentagone to scale with tissue size in the growing drosophila wing imaginal disc, PLoS Biol, 9 (2011), e1001182.
doi: 10.1371/journal.pbio.1001182. |
[11] |
H. Hardway, B. Mukhopadhyay, T. Burke, T. J. Hitchman and R. Forman, Modeling the precision and robustness of hunchback border during drosophila embryonic development, Journal of Theoretical Biology, 254 (2008), 390-399.
doi: 10.1016/j.jtbi.2008.05.021. |
[12] |
A. D. Lander, W. C. Lo, Q. Nie and F. Y. M. Wan, The measure of success: Constraints, objectives, and tradeoffs in morphogen-mediated patterning, Cold Spring Harbor Perspectives in Biology, 1 (2009), a002022. |
[13] |
A. D. Lander, Q. Nie and F. Y. M. Wan, Membrane-associated non-receptors and morphogen gradients, Bulletin of Mathematical Biology, 69 (2007), 33-54.
doi: 10.1007/s11538-006-9152-2. |
[14] |
A. Lander, Q. Nie, B. Vargas and F. Wan, Size-normalized robustness of dpp gradient in Drosophila wing imaginal disc, Journal of Mechanics of Materials and Structures, 6 (2011), 321-350. |
[15] |
A. D. Lander, Q. Nie and F. Y. M. Wan, Spatially distributed morphogen production and morphogen gradient formation, Math Biosci Eng, 2 (2005), 239-262.
doi: 10.3934/mbe.2005.2.239. |
[16] |
T. Lecuit, W. J. Brook, M. Ng, M. Calleja, H. Sun and S. M. Cohen, Two distinct mechanisms for long-range patterning by Decapentaplegic in the Drosophila wing, Nature, 381 (1996), 387-393.
doi: 10.1038/381387a0. |
[17] |
J. Lei, F. Wan, A. Lander and Q. Nie, Robustness of signaling gradient in drosophila wing imaginal disc, Discrete and Continuous Dynamical Systems, Series B, 16 (2011), 835-866.
doi: 10.3934/dcdsb.2011.16.835. |
[18] |
J. Lei, D. Wang, Y. Song, Q. Nie and F. Y. M. Wan, Robustness of morphogen gradients with "bucket brigade" transport through membrane-associated non-receptors, Discrete and Continuous Dynamical Systems, Series B, 18 (2013), 721-739.
doi: 10.3934/dcdsb.2013.18.721. |
[19] |
J. Lei and Y. Song, Mathematical model of the formation of morphogen gradients through membrane-associated non-receptors, Bull Math Biol, 72 (2010), 805-829.
doi: 10.1007/s11538-009-9470-2. |
[20] |
S. Morimura, L. Maves, Y. Chen and F. M. Hoffmann, decapentaplegic overexpression affects Drosophila wing and leg imaginal disc development and wingless expression, Dev Biol., 177 (1996), 136-151. |
[21] |
G. Reeves and S. E. Fraser, Biological systems from an engineer's point of view, PLoS Biology, 7 (2009), e1000021.
doi: 10.1371/journal.pbio.1000021. |
[22] |
W. Rudin, Real and Complex Analysis, McGraw-Hill Education, 1987. |
[23] |
D. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana University Math. J., 21 (1972), 979-1000. |
[24] |
M. Strigini and S. M. Cohen, A hedgehog activity gradient contributes to AP axial patterning of the Drosophila wing, Development, 124 (1997), 4697-4705. |
[25] |
A. A. Teleman and S. M. Cohen, Dpp gradient formation in the Drosophila wing imaginal disc, Cell, 103 (2000), 971-980.
doi: 10.1016/S0092-8674(00)00199-9. |
[26] |
L. Wolpert, Positional information and spatial pattern of cellular differentiation, Journal of Theoretical Biology, 25 (1969), 1-47.
doi: 10.1016/S0022-5193(69)80016-0. |
[27] |
L. Wolpert, Positional information and patterning revisited, Journal of Theoretical Biology, 269 (2011), 359-365.
doi: 10.1016/j.jtbi.2010.10.034. |
[28] |
M. Zecca, K. Basler and G. Struhl, Direct and long-range action of a wingless morphogen gradient, Cell, 87 (1996), 833-844.
doi: 10.1016/S0092-8674(00)81991-1. |
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