Biomaterial Database

Bifurcations of nonlinear reaction-diffusion systems in oblate spheroids. 1984

A Hunding

Spontaneous pattern formation may arise in biological systems as primary and secondary bifurcations to nonlinear parabolic partial differential equations describing chemical reaction-diffusion systems. Bipolarity in mitosis and cleavage planes in cytokinesis may be related to this formation of prepatterns. Three dimensional prepatterns are investigated, as they emerge in flattened spheres (i.e. oblate spheroids). Pattern sequences and selection rules are established numerically. The results confirm previously recorded results of the spherical and prolate regions, upon which a prepattern theory of mitosis and cytokinesis is based. Especially, the phenomenon of 90 degree axis tilting and the formation of a highly symmetrical saddle shaped pattern, crucial for the prepattern theory of mitosis and cytokinesis, is examined. Present results show, that these phenomena are stabilized in oblate spheroids. The bipolar "mitosis" prepattern is found as well, although the polar axis may appear with an angle toward the axis of the oblate spheroid. These results are thus further support for the prepattern theory of mitosis and cytokinesis.

UI	MeSH Term	Description	Entries
D008433	Mathematics	The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)	Mathematic
D008938	Mitosis	A type of CELL NUCLEUS division by means of which the two daughter nuclei normally receive identical complements of the number of CHROMOSOMES of the somatic cells of the species.	M Phase, Mitotic,Mitotic M Phase,M Phases, Mitotic,Mitoses,Mitotic M Phases,Phase, Mitotic M,Phases, Mitotic M
D008954	Models, Biological	Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.	Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D009024	Morphogenesis	The development of anatomical structures to create the form of a single- or multi-cell organism. Morphogenesis provides form changes of a part, parts, or the whole organism.
D002477	Cells	The fundamental, structural, and functional units or subunits of living organisms. They are composed of CYTOPLASM containing various ORGANELLES and a CELL MEMBRANE boundary.	Cell
D003593	Cytoplasm	The part of a cell that contains the CYTOSOL and small structures excluding the CELL NUCLEUS; MITOCHONDRIA; and large VACUOLES. (Glick, Glossary of Biochemistry and Molecular Biology, 1990)	Protoplasm,Cytoplasms,Protoplasms
D004058	Diffusion	The tendency of a gas or solute to pass from a point of higher pressure or concentration to a point of lower pressure or concentration and to distribute itself throughout the available space. Diffusion, especially FACILITATED DIFFUSION, is a major mechanism of BIOLOGICAL TRANSPORT.	Diffusions