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פותח על ידי קלירמאש פתרונות בע"מ -
Analysis Situs of spatial-temporal architecture in biological morphogenesis
Year:
2008
Authors :
פרסנוב, יבגני
;
.
Volume :
Co-Authors:
Isaeva, V.V., Institute of Marine Biology, Far East Branch of Russian Academy of Sciences, Vladivostok, 690041, Russian Federation
Kasyanov, N.V., Institute of Theory of Architecture and Town Planning, Moscow, Russian Federation
Presnov, E.V., The Volcani Center, 85280, Gilat, Israel
Facilitators :
From page:
141
To page:
189
(
Total pages:
49
)
Abstract:
A topological approach is used for the description and analysis of biological morphogenesis, and a topological interpretation of some morphogenetic events through the use of well known mathematical concepts and theorems is presented. We model the biological shape as a set of smooth, closed, oriented surfaces - membrane or epithelial layers. The spatial organization of membrane systems of eukaryotic cells may be represented topologically as a number of inner membrane surfaces embedded inside the outer cell membrane. During embryonic development and evolution process, the surface of an organism in most Metazoa undergoes spherical surgery (-ies), which change the topological genus of the surface. In some animal taxa topologically complicated fractal-like systems increases the genus of the surface; the body surface becomes topologically homeomorphic to a high-order torus. Fractal-like biological structures are partially chaotic. To evaluate the relationship between order and chaos in the structure of epithelial branching fractal-like channels of the gastro-vascular system in the jellyfish Aurelia aurita and the larval tracheal gills of the mayflies Siphlonurus immanis and Parameletus chelifer we compared these patterns in symmetrical parts of the organisms with deterministic fractal trees. The transition from order to chaos during morphogenesis of the dichotomously branching canals occurs as a cascade of bifurcations. We have shown that fractal dimension value may serve as a quantifier of neuronal spatial complexity correlating with cell morphology in several classes of encephalic neurons in the fishes Pholidapus dybowskii and Oncorhyhchus keta and also with morphological changes of some spinal neurons during ontogenesis of Oncorhynchus masou. Topological singularities of various fields on different levels of biological organization inevitably emerge and transform in biological morphogenesis. We studied cell morphogenetic fields and fractal self-organization in cell cultures in vitro. Two-dimensional cell direction fields with a defined set of topological singularities are shown in myogenic monolayer culture. The egg cleavage results in a pattern of cell contacts on the surface of the embryo as a discrete morphogenetic field. Membrane and epithelial surfaces are boundary layers, interfaces between a living structure and its environment, ensuring metabolism. Fractal structures as well as toroid forms of Metazoa can be considered as functionally optimized biological design and attractors in biological morphogenesis. We can say that a certain set of topological rules, a "topological imperative", constrains and directs biological morphogenesis. © 2008 by Nova Science Publishers, Inc. All rights reserved.
Note:
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DOI :
Article number:
Affiliations:
Database:
סקופוס
Publication Type:
פרק מתוך ספר
;
.
Language:
אנגלית
Editors' remarks:
ID:
24290
Last updated date:
02/03/2022 17:27
Creation date:
17/04/2018 00:06
Scientific Publication
Analysis Situs of spatial-temporal architecture in biological morphogenesis
Isaeva, V.V., Institute of Marine Biology, Far East Branch of Russian Academy of Sciences, Vladivostok, 690041, Russian Federation
Kasyanov, N.V., Institute of Theory of Architecture and Town Planning, Moscow, Russian Federation
Presnov, E.V., The Volcani Center, 85280, Gilat, Israel
Analysis Situs of spatial-temporal architecture in biological morphogenesis
A topological approach is used for the description and analysis of biological morphogenesis, and a topological interpretation of some morphogenetic events through the use of well known mathematical concepts and theorems is presented. We model the biological shape as a set of smooth, closed, oriented surfaces - membrane or epithelial layers. The spatial organization of membrane systems of eukaryotic cells may be represented topologically as a number of inner membrane surfaces embedded inside the outer cell membrane. During embryonic development and evolution process, the surface of an organism in most Metazoa undergoes spherical surgery (-ies), which change the topological genus of the surface. In some animal taxa topologically complicated fractal-like systems increases the genus of the surface; the body surface becomes topologically homeomorphic to a high-order torus. Fractal-like biological structures are partially chaotic. To evaluate the relationship between order and chaos in the structure of epithelial branching fractal-like channels of the gastro-vascular system in the jellyfish Aurelia aurita and the larval tracheal gills of the mayflies Siphlonurus immanis and Parameletus chelifer we compared these patterns in symmetrical parts of the organisms with deterministic fractal trees. The transition from order to chaos during morphogenesis of the dichotomously branching canals occurs as a cascade of bifurcations. We have shown that fractal dimension value may serve as a quantifier of neuronal spatial complexity correlating with cell morphology in several classes of encephalic neurons in the fishes Pholidapus dybowskii and Oncorhyhchus keta and also with morphological changes of some spinal neurons during ontogenesis of Oncorhynchus masou. Topological singularities of various fields on different levels of biological organization inevitably emerge and transform in biological morphogenesis. We studied cell morphogenetic fields and fractal self-organization in cell cultures in vitro. Two-dimensional cell direction fields with a defined set of topological singularities are shown in myogenic monolayer culture. The egg cleavage results in a pattern of cell contacts on the surface of the embryo as a discrete morphogenetic field. Membrane and epithelial surfaces are boundary layers, interfaces between a living structure and its environment, ensuring metabolism. Fractal structures as well as toroid forms of Metazoa can be considered as functionally optimized biological design and attractors in biological morphogenesis. We can say that a certain set of topological rules, a "topological imperative", constrains and directs biological morphogenesis. © 2008 by Nova Science Publishers, Inc. All rights reserved.
Scientific Publication
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