4 Chemotactic Cell Motion and Biological Pattern Formation
70
A study on the formation of crocodile skin, discussing the origin of the
pigmentation pattern, can be found in [13].
Is has been conjectured in the biological literature that the formation of
tortoise shells is based on a chemotactic process, responsible for the lateral
growth of the ribs, which then undergo ossification. We refer to [14].
The Images 4.1–4.5 were shot in South Africa and Namibia, 4.6 in the Mex-
ican province Chiapas, 4.7 in northern Queensland (Australia) and 4.8 on the
Galapagos Islands (Ecuador).
References
[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, 2004
[2] Y. Dolak and C. Schmeiser, The Keller–Segel model with logistic sensitivity
function and small diffusivity, to appear in SIAM J. Appl. Math., 2005
[3] P.A. Markowich, D. Oelz, C. Schmeiser, F. Chalub, Y. Dolak-Struss and
A. Soreff, Model hierarchies for cell aggregation by chemotaxis,toappear
in M3AS, 2006
[4] E. Keller and L.A. Segel, Initiationofslimemoldaggregationviewedasan
instability, J. Theoret. Biol., 26, pp. 399–415, 1970
[5] J.D. Murray, Mathematical Biology,Volume19ofBiomathematics,second
edition, Springer, 1993
[6] K.J. Painter, Chemotaxis as a mechanism for Morphogenesis, PhD thesis,
University of Oxford, 1997
[7] C.S. Patlak, Random walk with persistence and external bias, Bull. Math.
Biophys., 15, pp. 311–338, 1953
[8] A. Stevens, Thederivationofchemotaxisequationsaslimitdynamicsof
moderately interacting stochastic many-particle systems,SIAMofAppl.
Math, 61(1), pp. 183–212, 2000
[9] A.M. Turing, The chemical basis of morphogenesis, Philosophical Transac-
tions of the Royal Society (B), 237, pp. 37–72, 1952
[10] L. Wolpert, Positional information and the spatial pattern of cellular differ-
entiation, J. theor. Biol., 25, pp. 1–47, 1969
[11] M. Walter, Integration of Complex Shapes and natural Patterns,Ph. D. thesis,
Department of Computer Science, University of British Columbia, Canada,
1998
[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, 2004
[13] L. Alibardi, Immunocytochemistry and Keratinization in the Epidermis of
Crocodilians, Zoological Studies 42 (2), pp. 346–356, 2003