Effects of Sog on Dpp-receptor binding

SIAM Journal on Applied Mathematics

Volumn 65, Issue 5, 2005, Pages 1748-1771

  Lou, Yuan ^a   Nie, Qing ^b   Wan, Frederic Y M ^a  

^a OHIO STATE UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Mathematical modeling; Morphogen gradients; Pattern formation; Reaction diffusion

Indexed keywords

CELL SIGNALING; MORPHOGEN GRADIENTS; PATTERN FORMATION; REACTION-DIFFUSION;

COMPUTER SIMULATION; MATHEMATICAL MODELS; NUMERICAL METHODS; THEOREM PROVING; TISSUE;

BINDING ENERGY;

EID: 27844489975     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139903433219     Document Type: Article

References (25)

1. L. WOLPERT, R. BEDDINGTON, J. BROCKES, T. JESSEL, P. LAWRENCE, AND E. MEYEROWITZ, Principles of Development, 2nd ed., Oxford University Press, Oxford, UK, 2002.
2. A. A. TELEMAN, M. STRIGINI, AND S. M. COHEN, Shaping morphogen gradients, Cell, 105 (2001), pp. 559-562.
3. J. B. GURDON AND P. Y. BOURILLOT, Morphogen gradient interpretation, Nature, 413 (2001), pp. 797-803.
4. A. LANDER, Q. NIE, AND F. Y. M. WAN, Do morphogen gradients arise by diffusion?, Dev. Cell, 2 (2002), pp. 785-796.
5. E. BIER, A unity of opposites, Nature, 398 (1999), pp. 375-376.
6. H. L. ASHE AND M. LEVINE, Local inhibition and long-range enhancement of Dpp signal transduction by Sog, Nature, 398 (1999), pp. 427-431.
7. M. OELGESCHLAGER, J. LARRAIN, D. GEISSERT, AND E. M. ROBERTIS, The evolutionary conserved BMP-binding protein twisted gastrulation promotes BMP signalling, Nature, 405 (2000), pp. 757-762.
8. J. Ross, O. SHIMMI, P. VILMOS, A. PETRYK, H. KIM, K. GAUDENEZ, S. HERMANSON, A. EKKER, M. O'CONNOR, AND J. L. MARSH, Twisted gastrulation is a conserved extracellular BMP antagonist, Nature, 410 (2001), pp. 479-483.
9. Y. Lou, Q. NIE, AND F.Y.M. WAN, Nonlinear eigenvalue problems in the stability analysis of morphogen gradients, Stud. Appl. Math., 113 (2004), pp. 183-215.
10. A. LANDER, Q. NIE, B. VARGAS, AND F. Y. M. WAN, Aggregation of a distributed source in morphogen gradient formation, Stud. Appl. Math., (2005), to appear.
11. A. LANDER, Q. NIE, AND F. Y. M. WAN, Spatially distributed morphogen production and morphogen gradient formation, Math. Biosci. Eng., (2005), to appear.
12. A. LANDER, Q. NIE, AND F. Y. M. WAN, Internalization and end flux in morphogen gradient formation, J. Comput. Appl. Math., (2005), to appear.
13. A. ELDAR, R. DORFMAN, D. WEISS, H. ASHE, B. SHILO, AND N. BARKAI, Robustness of the BMP morphogen gradient in Drosophila embryonic patterning, Nature, 419 (2002), pp. 304-308.
14. A. ELDAR, R. DORFMAN, D. WEISS, H. ASHE, B. SHILO, AND N. BARKAI, Supplement -Robustness of the BMP morphogen gradient in Drosophila embryonic patterning, Nature, 419 (2002), pp. 304-308.
15. A. ELDAR, D. ROSIN, B. Z. SHILO, AND N. BARKAI, Self-enhanced ligand degradation underlies robustness of morphogen gradients, Dev. Cell, 5 (2003), pp. 635-646.
16. Z. WANG, O. MARCU, M. W. BERNS, AND J. L. MARSH, In vivo FCS measurements of ligand diffusion in intact tissues, Proc. SPIE, 5323 (2004), pp. 177-183.
17. J. KAO, Q. NIE, A. TENG, F. Y. M. WAN, A. LANDER, AND I. L. MARSH, Can morphogen activity be enhanced by its inhibitors ?, in Proceeding of the 2nd MIT Conference on Computational Mechanics, 2003, Elsevier Press, New York, Vol. 2, pp. 1729-1734.
18. C. MIZUTANI, Q. NIE, F. Y. M. WAN, Y. ZHANG, P. VILMOS, E. BIER, L. MARSH, AND A. LANDER, Origin of the BMP activity gradient in the Drosophila embryo, Devel. Cell (2005), to appear.
19. F. C. CRICK, Diffusion in embryogenesis, Nature, 225 (1970), pp. 40-42.
20. M. KERSZBERG AND L. WOLPERT, Mechanisms for positional signalling by morphogen transport: A theoretical study, J. Theoret. Biol., 191 (1998), pp. 103-114.
21. S. PICCOLO, E. AGIUSA, B. Lu, S. GOODMAN, L. DALE, AND E. DE ROBERTIS, Cleavage of chordin by Xolloid metalloprotease suggests a role for proteolytic processing in the regulation of Spemann organizer activity, Cell, 91 (1997), pp. 407-416.
22. G. MARQUES, M. MUSACCHIO, M. J. SHIMELL, K. W. STAPLETON, K. CHO, AND M. O'CONNOR, Production of a Dpp activity gradient in the early Drosophila embryo through the opposing actions of the Sog and TLD proteins, Cell, 91 (1997), pp. 417-426.
23. M. H. PROTTER AND H. F. WEINBERGER, Maximum Principle in Differential Equations, 2nd ed., Springer-Verlag, Berlin, 1984.
24. J. SMOLLER, Shock Waves and Reaction-Diffusion Equations, 2nd ed., Springer-Verlag, New York, 1994.
25. J. C. STRIKWERDA, Finite Difference Schemes and Partial Differential Equations, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1989.