Abstract
Mathematical modelling has become a widely accepted method for examining how and why vertebrate skin structures are laid down in an orderly and organized fashion. Although various theoretical models have been proposed for examining the morphogenetic processes responsible for the large variety of patterns observed on animal skin, these processes are still not well understood. By examining a mechanochemical tissue interaction model based on recent experimental evidence we therefore hope to contribute towards the understanding of skin morphogenesis.
Keywords
- Pattern Formation
- Epithelial Sheet
- Recent Experimental Evidence
- Homogeneous Steady State
- Appendage Formation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Chuong, C.-M., & Edelman, G. M. 1985. Expression of cell adhesion molecules in embryonic induction. I. Morphogenesis of nestling feathers. J. Cell Biol., 101, 1009–1026.
Cruywagen, G.C. & Murray, J. D. 1992. On a tissue interaction model for skin pattern formation. J. Nonlinear Sci., 2, 217–240.
Cruywagen, G. C., Maini, P. K., & Murray, J. D. 1993. Sequential pattern formation in a model for skin morphogenesis. IMA J. Maths. Appl. Med. & Biol. (In press).
Edelman, G. M. 1986. Cell adhesion molecules in the regulation of animal form and tissue pattern. Annu. Rev. Cell Biol., 2, 81–116.
Gallin, W. J., Chuong, C.-M., Finkel, L. H., & Edelman, G. M. 1986. Antibodies to liver cell adhesion molecules perturb inductive interactions and alter feather pattern and structure. Proc. Natl. Acad. Sci. USA, 83, 8235–8239.
Grumet, M., & Edelman, G. M. 1988. Neuron-glia cell adhesion molecules interact with neurons and astroglia via different binding mechanisms. J. Cell Biol., 106, 487–503.
Landau, L. D., & Lifshitz, E. M. 1970. Theory of Elasticity. 2nd edn. New York: Pergamon.
Murray, J. D. 1989. Mathematical Biology. New York: Springer-Verlag.
Murray, J. D., & Oster, G. F. 1984. Generation of biological pattern and form. IMA J. Maths Appl. Med. & Biol, 1, 51–75.
Murray, J. D., Deeming, D. C., & Ferguson, M. W. J. 1990. Size dependent pigmentation pattern formation in embryos of Alligator Mississipiensis: time of initiation of pattern generation mechanism. Proc. Roy. Soc, B239, 279–293.
Murray, J. D., Cruywagen, G.C., & Maini, P. K. 1993. Pattern formation in tissue interaction systems. Heidelberg: Springer-Verlag. (In press) Lect. Notes in Biomathematics 100.
Nagorcka, B. N. 1986. The role of a reaction-diffusion system in the initiation of skin organ primordia. I. The first wave of initiation. J. Theor. Biol., 121, 449–475.
Oster, G. F., & Murray, J. D. 1989. Pattern formation models and developmental constraints. J. exp. Zool., 251, 186–202.
Shaw, L. J., & Murray, J. D. 1990. Analysis of a model for complex skin patterns. SIAM J. Appl. Math., 50(2), 628–648.
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© 1993 Springer Science+Business Media New York
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Cruywagen, G.C., Maini, P.K., Murray, J.D. (1993). Sequential and Synchronous Skin Pattern Formation. In: Othmer, H.G., Maini, P.K., Murray, J.D. (eds) Experimental and Theoretical Advances in Biological Pattern Formation. NATO ASI Series, vol 259. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2433-5_8
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DOI: https://doi.org/10.1007/978-1-4615-2433-5_8
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