ISSN:
1432-1416
Keywords:
Mitosis
;
Positional information
;
Morphogenesis
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
Abstract Spontaneous pattern formation may arise in biological systems as primary and secondary bifurcations to nonlinear parabolic partial differential equations describing chemical reaction-diffusion systems. Such Turing prepatterns have a specified geometry as long as D/R 2 (the diffusion coefficient of the morphogen D divided by the square of a characteristic length) is confined to a (usually) limited interval. As real biochemical systems like cleaving eggs or early embryos vary considerably in size, Turing prepatterns are unable to maintain a specified prepattern-geometry, unless D/R 2 is varied as well. We show, that actual biochemical control systems may vary D app/R2, where D app(k) is an apparent diffusion constant, dependent on enzyme regulated rate constants, and that such simple control systems allow Turing structures to adapt to size variations of at least a factor 103 (linearly), not only in large connected cell systems, but in single cells as well.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00280170
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