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Adhesive Cell Interaction

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Cellular Automaton Modeling of Biological Pattern Formation

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Abstract

The diffusive LGCA which we encountered in ch. 5 may serve as a model for random biological motion “without interaction.” It is important to note that diffusive automata are not able to generate any patterns as we demonstrated by Fourier analysis of the dominant modes which never become unstable. However, coupling of diffusion with an appropriate “reaction” may generate patterns – we presented an example of (diffusion-limited) growth patterns generated as the result of an interplay of diffusion and “sticking” (see sec. 5.5). Historically, the discovery of diffusion-driven instabilities as a pattern forming mechanism is due to Alan Turing  (1952). To what extent Turing instabilities account for biological pattern formation is not clear but it has been shown that they might influence the development of intracellular prepatterns (Kondo and Miura 2010, Meinhardt and de Boer 2001). An example of a “Turing LGCA” is introduced in ch. 13.

The questions which we shall pursue, then, are these: “What may be the forces which unite cells into tissues,” and “By what mechanism may cells exert preferences in their associations with other cells”?

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Notes

  1. 1.

    Steinberg (1958)

  2. 2.

    Indices and superscripts are taken modulo b.

  3. 3.

    That is, ω i n = −ω i 1, ω 3 1 = −ω 1 1 and ω 4 1 = ω 2 1

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Authors and Affiliations

  1. Centre for Information Services and High Performance Computing, Technische Universität Dresden, Dresden, Germany

    Andreas Deutsch

  2. FB Mathematik/Informatik, Universität Osnabrück, Osnabrück, Germany

    Sabine Dormann

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  1. Andreas Deutsch
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  2. Sabine Dormann
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Deutsch, A., Dormann, S. (2017). Adhesive Cell Interaction. In: Cellular Automaton Modeling of Biological Pattern Formation. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-7980-3_7

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