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Pattern regulation in reaction-diffusion systems-the problem of size invariance

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Abstract

Ordinary reaction-diffusion mechanisms do not account for size invariance properties of morphogenetic fields. We show that such a failure results from ignoring cell individuality. By considering purely topological factors, such as the number of intercellular contacts or the extent of the cell surface in contact with neighbouring cells, size invariance exists in reaction-diffusion systems. Our results are general, model independent and may be applied to any multi-unit ensemble exhibiting coherent behaviour.

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Authors and Affiliations

  1. Chimie-Physique 2, Faculté des Sciences, Université Libre de Bruxelles, 1050, Brussels, Belgium

    A. Babloyantz

  2. Department of Physics, Université Libre de Bruxelles, CP 223, 1050, Brussels, Belgium

    A. Bellemans

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  1. A. Babloyantz
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  2. A. Bellemans
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Babloyantz, A., Bellemans, A. Pattern regulation in reaction-diffusion systems-the problem of size invariance. Bltn Mathcal Biology 47, 475–487 (1985). https://doi.org/10.1007/BF02460007

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  • DOI: https://doi.org/10.1007/BF02460007

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