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Presnov, E., The Volcani Center, 85280 Beit Dagan, Israel
Isaeva, V., Institute of Ecology and Evolution, Moscow, 119071, Russian Federation, Institute of Marine Biology, Vladivostok, 690041, Russian Federation
Kasyanov, N., Institute of Theory and History of Architecture and Town Planning, Moscow, 105264, Russian Federation
A topological inevitability of early developmental events through the use of classical topological concepts is discussed. Topological dynamics of forms and maps in embryo development are presented. Forms of a developing organism such as cell sets and closed surfaces are topological objects. Maps (or mathematical functions) are additional topological constructions in these objects and include polarization, singularities and curvature. Topological visualization allows us to analyze relationships that link local morphogenetic processes and integral developmental structures and also to find stable spatio-temporal topological characteristics that are invariant for a taxonomic group. The application of topological principles reveals a topological imperative: certain topological rules define and direct embryogenesis. A topological stability of embryonic morphogenesis is proposed and a topological scenario of developmental and evolutionary transformations is presented. © 2013 The Author(s).
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Topological Invariance of Biological Development
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Presnov, E., The Volcani Center, 85280 Beit Dagan, Israel
Isaeva, V., Institute of Ecology and Evolution, Moscow, 119071, Russian Federation, Institute of Marine Biology, Vladivostok, 690041, Russian Federation
Kasyanov, N., Institute of Theory and History of Architecture and Town Planning, Moscow, 105264, Russian Federation
Topological Invariance of Biological Development
A topological inevitability of early developmental events through the use of classical topological concepts is discussed. Topological dynamics of forms and maps in embryo development are presented. Forms of a developing organism such as cell sets and closed surfaces are topological objects. Maps (or mathematical functions) are additional topological constructions in these objects and include polarization, singularities and curvature. Topological visualization allows us to analyze relationships that link local morphogenetic processes and integral developmental structures and also to find stable spatio-temporal topological characteristics that are invariant for a taxonomic group. The application of topological principles reveals a topological imperative: certain topological rules define and direct embryogenesis. A topological stability of embryonic morphogenesis is proposed and a topological scenario of developmental and evolutionary transformations is presented. © 2013 The Author(s).
Scientific Publication
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