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Topological determination of early morphogenesis in Metazoa

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Abstract

This paper presents a topological interpretation of some developmental events through the use of well-known concepts and theorems of combinatorial geometry. The organization of early embryo using a simulation of cleavage considering only blastomere contacts is examined. Each blastomere is modeled as a topological cell and whole embryo—as cell packing. The egg cleavage results in a pattern of cellular contacts on the surface of each blastomere and whole embryo, a discrete morphogenetic field. We find topological distinctions between different types of early egg cleavage and suggest a topological classification of cleavage. Blastulation and gastrulation may be related to an inevitable emergence of discrete curvature that directs development in three-dimensional space. The relationship between local and global orders in metazoan development, i.e., between local morphogenetic processes and integral developmental patterns, is established. Thus, this methodology reveals a topological imperative: a certain set of topological rules that constrains and directs biological morphogenesis.

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Authors and Affiliations

  1. The Volcani Center, 85280, Gilat, Israel

    Eugene Presnov

  2. A.N. Severtsov Institute of Ecology and Evolution of the Russian Academy of Science, Moscow, Russia, 119071

    Valeria Isaeva

  3. A.V. Zhirmunsky Institute of Marine Biology, Far East Branch of Russian Academy of Sciences, Vladivostok, Russia, 690041

    Valeria Isaeva

  4. Institute of Theory of Architecture and Town Planning, Moscow, Russia

    Nikolay Kasyanov

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  1. Eugene Presnov
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  2. Valeria Isaeva
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Correspondence to Eugene Presnov.

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Presnov, E., Isaeva, V. & Kasyanov, N. Topological determination of early morphogenesis in Metazoa. Theory Biosci. 129, 259–270 (2010). https://doi.org/10.1007/s12064-010-0103-y

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