Advertisement

Sequential and Synchronous Skin Pattern Formation

  • Gerhard C. Cruywagen
  • P. K. Maini
  • J. D. Murray
Part of the NATO ASI Series book series (NSSA, volume 259)

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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.PubMedCrossRefGoogle Scholar
  2. Cruywagen, G.C. & Murray, J. D. 1992. On a tissue interaction model for skin pattern formation. J. Nonlinear Sci., 2, 217–240.CrossRefGoogle Scholar
  3. 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).Google Scholar
  4. Edelman, G. M. 1986. Cell adhesion molecules in the regulation of animal form and tissue pattern. Annu. Rev. Cell Biol., 2, 81–116.PubMedCrossRefGoogle Scholar
  5. 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.PubMedCrossRefGoogle Scholar
  6. 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.CrossRefGoogle Scholar
  7. Landau, L. D., & Lifshitz, E. M. 1970. Theory of Elasticity. 2nd edn. New York: Pergamon.Google Scholar
  8. Murray, J. D. 1989. Mathematical Biology. New York: Springer-Verlag.Google Scholar
  9. Murray, J. D., & Oster, G. F. 1984. Generation of biological pattern and form. IMA J. Maths Appl. Med. & Biol, 1, 51–75.CrossRefGoogle Scholar
  10. 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.Google Scholar
  11. 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.Google Scholar
  12. 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.CrossRefGoogle Scholar
  13. Oster, G. F., & Murray, J. D. 1989. Pattern formation models and developmental constraints. J. exp. Zool., 251, 186–202.PubMedCrossRefGoogle Scholar
  14. Shaw, L. J., & Murray, J. D. 1990. Analysis of a model for complex skin patterns. SIAM J. Appl. Math., 50(2), 628–648.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Gerhard C. Cruywagen
    • 1
  • P. K. Maini
    • 2
  • J. D. Murray
    • 1
  1. 1.Department of Applied Mathematics FS-20University of WashingtonSeattleUSA
  2. 2.Centre for Mathematical BiologyMathematical InstituteOxfordUK

Personalised recommendations