Receptor-based models with diffusion-driven instability for pattern formation in hydra

Journal of Biological Systems

Volumn 11, Issue 3, 2003, Pages 293-324

  Marciniak Czochra, Anna ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

Diffusion driven instability; Hydra; Pattern formation; Receptor based model

Indexed keywords

COELENTERATA; HYDRA;

EID: 0142027556     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339003000889     Document Type: Article

References (30)

1. Bode P. M. and Bode H. R., Patterning in hydra. In Pattern Formation: A Primer in Developmental Biology, ed. by Malacinski G. M. and Bryant S. V. (MacMillan Publ. Co., New York, 1984) pp. 213-241.
2. Gantmacher F. R., Applications of the Theory of Matrices (Interscience Publishers, New York, 1959).
3. Gierer A., Berking S., Bode H., David C. N., Flick K., Hansmann G., Schaller H. and Trenkner E., Regeneration of hydra from reaggregated cells, Nat. New Biol. 239 (1972) pp. 98-101.
4. Gierer A. and Meinhardt H., A theory of biological pattern formation, Kybernetik 12 (1972) pp. 30-39.
5. Grindrod P., Patterns and Waves (Clarendon Press, Oxford, 1991).
6. Kerszberg M., Morphogen propagation and action towards molecular models, Semin. Cell. Dev. Biol. 10(3) (1999) pp. 297-302.
7. Krömker S., Model and Analysis of Heterogeneous Catalysis with Phase Transition. PhD thesis, Univ. of Heidelberg, 1997.
8. MacWilliams H. K., Hydra transplantation phenomena and the mechanism of hydra head regeneration. I. Properties of the head inhibition, Dev. Biol. 96 (1983) pp. 217-238.
9. MacWilliams H. K., Hydra transplantation phenomena and the mechanism of hydra head regeneration. II. Properties of the head activation, Dev. Biol. 96 (1983) pp. 239-257.
10. Martiel J. L. and Goldbeter A., A model based on receptor desenitization for cyclic amp signalling in Disctyostelium cells, Biophys. J. 57 (1987) pp. 807-828.
11. Meinhardt H., A model for pattern formation of hypostome, tentacles and foot in hydra: How to form structures close to each other, how to form them at a distance, Dev. Biol. 157 (1993) pp. 321-333.
12. Monk P. B. and Othmer H. G., Cyclic AMP oscillations in suspensions of Disctyostelium Discoideum, Phil. Trans. R. Soc. Lond. B323 (1989) pp. 185-224.
13. Müller W. A., Diacylglycerol-induced multihead formation in hydra, Development 105 (1989) pp. 309-316.
14. Müller W. A., Ectopic head and foot formation in hydra. Diacylglycerol induced increase in potential value and assistance of the head in foot formation, Differentiation 42 (1990) pp. 131-143.
15. Müller W. A., Pattern control in hydra: Basic experiments and concepts. In Experimental and Theoretical Advances in Biological Pattern Formation, ed. by Othmer H. G., Maini P. K. and Murray J. D. (Plenum Press, New York, 1993).
16. Müller W. A., Competition of factors and cellular resources as a principle of pattern formation in hydra, Dev. Biol. 167 (1995) pp. 175-180.
17. Müller W. A., Head formation at the basal end and mirror-image pattern duplication in hydra vulgaris, Int. J. Dev. Biol. 40 (1996) pp. 1119-1131.
18. Müller W. A., Developmental Biology (Springer-Verlag, New York, 1997).
19. Murray J. D., Mathematical Biology (Springer-Verlag, Berlin, 2nd edition, 1993).
20. Noda K., Reconstitution of dissociated cells of hydra, Zool. Mag. 80 (1971) pp. 99-101.
21. Piccolo S., Agius E., Lu B., Goodman S., Dale L. and De Robertis E. M., Cleavage of chordin by xollodin metalloproteaze in theregulation of Spemann organizers activity, Cell 91 (1997) pp. 407-416.
22. Satnoianu R. A., Menzinger M. and Maini P. K., Turing instabilities in general systems, J. Math. Biol. 41 (2000) pp. 493-512.
23. Sato M., Tashiro H., Oikawa A. and Sawada Y., Patterning of hydra cells aggregates without sorting of cells from different axial origins, Dev. Biol. 151 (1992) pp. 111-116.
24. Sherratt J. A., Maini P. K., Jäger W. and Müller W., A receptor-based model for pattern formation in hydra, Forma 10 (1995) pp. 77-95.
25. Smoller J., Shock-Waves and Reaction-Diffusion Equations Springer-Verlag, New York, 1994).
26. Tata J. R., Autoinduction of nuclear hormon receptors during metamorphosis and its significance, Insect. Biochem. Mol. Biol. 30(8-9) (2000) pp. 645-51.
27. Technau U. and Holstein T., Cell sorting during the regeneration of hydra from reaggregated cells, Dev. Biol. 151 (1992) pp. 117-127.
28. Turing A. M., The chemical basis of morphogenesis, Phil. Trans. Roy. Soc. B 237 (1952) pp. 37-72.
29. Webster G. and Wolpert L., Studies on pattern regulation in hydra. I. Regional differences in time required for hypostome determination, J. Embryol. Exp. Morph. 16 (1966) pp. 91-104.
30. Wolpert L., Positional information and the spatial pattern of cellular differentiation, J. Theor. Biol. 25 (1969) pp. 1-47.