Chemotactic Cell Motion and Biological Pattern Formation

  • Peter A. Markowich
  • Dietmar Ölz

Keywords

Turing Instability Chemotaxis Model Biological Pattern Formation Slime Mold Dictyostelium Discoideum Chemotactic Sensitivity 
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

  1. [1]
    B. Perthame, F. Chalub, P.A. Markowich and C. Schmeiser, Kinetic models for chemotaxis and their drift-diffusion limits, Monatsh. Math., 142(1–2), pp. 123–141, 2004MATHGoogle Scholar
  2. [2]
    Y. Dolak and C. Schmeiser, The Keller-Segel model with logistic sensitivity function and small diffusivity, to appear in SIAM J. Appl. Math., 2005Google Scholar
  3. [3]
    P.A. Markowich, D. Oelz, C. Schmeiser, F. Chalub, Y. Dolak-Struss and A. Soreff, Model hierarchies for cell aggregation by chemotaxis, to appear in M3AS, 2006Google Scholar
  4. [4]
    E. Keller and L.A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theoret. Biol., 26, pp. 399–415, 1970CrossRefGoogle Scholar
  5. [5]
    J.D. Murray, Mathematical Biology, Volume 19 of Biomathematics, second edition, Springer, 1993Google Scholar
  6. [6]
    K.J. Painter, Chemotaxis as a mechanism for Morphogenesis, PhD thesis, University of Oxford, 1997Google Scholar
  7. [7]
    C.S. Patlak, Random walk with persistence and external bias, Bull. Math. Biophys., 15, pp. 311–338, 1953CrossRefGoogle Scholar
  8. [8]
    A. Stevens, The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems, SIAM of Appl. Math, 61(1), pp. 183–212, 2000MATHCrossRefGoogle Scholar
  9. [9]
    A.M. Turing, The chemical basis of morphogenesis, Philosophical Transactions of the Royal Society (B), 237, pp. 37–72, 1952CrossRefGoogle Scholar
  10. [10]
    L. Wolpert, Positional information and the spatial pattern of cellular differentiation, J. theor. Biol., 25, pp. 1–47, 1969CrossRefGoogle Scholar
  11. [11]
    M. Walter, Integration of Complex Shapes and natural Patterns, Ph.D. thesis, Department of Computer Science, University of British Columbia, Canada, 1998Google Scholar
  12. [12]
    C.P. Gravan and R. Lahoz-Beltra, Evolving Morphogenetic Fields in the Zebra Skin Pattern Based on Turing’s Morphogen Hypothesis, Int. J. Appl. Math. Comput. Sci., Vol. 14, No. 3, pp. 351–361, 2004MATHGoogle Scholar
  13. [13]
    L. Alibardi, Immunocytochemistry and Keratinization in the Epidermis of Crocodilians, Zoological Studies 42(2), pp. 346–356, 2003Google Scholar
  14. [14]
    J. Cebra-Thomas et al., How the Turtle Forms its Shell: A Paracrine Hypothesis of Carapace Formation, Journal of Experimental Zoology (Mod Dev Evol), 304B, pp. 558–569, 2005CrossRefGoogle Scholar
  15. [15]
    A. Gierer and H. Meinhardt, A theory of biological pattern formation, Kybernetik 12, pp. 30–39, 1972CrossRefGoogle Scholar
  16. [16]
    D. Thomas, Artificial enzyme membranes, transport, memory, and oscillatory phenomena, in: D. Thomas and J.-P. Kernevez (eds.): Analysis and Control of Immobilized Enzyme Systems, Berlin Heidelberg New York: Springer, pp. 115–150, 1975Google Scholar

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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Peter A. Markowich
  • Dietmar Ölz

There are no affiliations available

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