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reactiondiffusion system
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The chemical basis of morphogenesis
The chemical basis of morphogenesis,10.1016/S00928240(05)800084,Bulletin of Mathematical Biology,A. M. Turing
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The chemical basis of morphogenesis
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Citations: 1630
)
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A. M. Turing
It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reactiondiffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns onHydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in
two dimensions
gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in
two dimensions
could account for the phenomena of phyllotaxis. The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain wellknown physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in textbooks, but whose omission would make the paper difficult reading.
Journal:
Bulletin of Mathematical Biology  BULL MATH BIOL
, vol. 52, no. 12, pp. 153197, 1990
DOI:
10.1016/S00928240(05)800084
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Citation Context
(479)
...– exists which focuses on the production of patterns in gene expression, a phenomenon central to the development of multicellular organisms. A particularly wellstudied mechanism for pattern formation is diffusiondriven instability, originally proposed by Turing
...
Justin Hsia
,
et al.
A Feedback Quenched Oscillator Produces Turing Patterning with One Dif...
...combines positional information and cell migration to explain how planarians can restore AP polarity. Reactiondiffusion models
...
Daniel Lobo
,
et al.
Modeling Planarian Regeneration: A Primer for ReverseEngineering the ...
... Some of these are based on a Turing mechanism
...
William R. Holmes
,
et al.
Modelling Cell Polarization Driven by Synthetic Spatially Graded Rac A...
...Turing (
1952
) insisted that the differential equation, such as Eq...
SHUICHIROU IKE
.
A Singularity of Fertility Decline Is LotetGaronne
...The original idea about how reaction–diffusion equations can be used to create patterns was first introduced in
34
...
JyhYang Wu
,
et al.
A new intrinsic numerical method for PDE on surfaces
References
(2)
Die kinetic der invertinwirkung
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Citations: 84
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L. Michaelis
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M. L. Menten
PERMEABILITY OF NATURAL MEMBRANES
(
Citations: 118
)
J DANIELLI
Journal:
Lancet
, vol. 261, no. 6761, 1953
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Citations
(1630)
Frontotemporal dementia as a frontostriatal disorder: Neostriatal morphology as a biomarker and structural basis for an endophenotype
Jeffrey CL Looi
,
Mark Walterfang
,
Dennis Velakoulis
,
Matthew D Macfarlane
,
Leif Anders Svensson
,
LarsOlof Wahlund
Journal:
Australian and New Zealand Journal of Psychiatry  AUST N Z J PSYCHIAT
, vol. 46, no. 5, pp. 422434, 2012
A Feedback Quenched Oscillator Produces Turing Patterning with One Diffuser
Justin Hsia
,
William J. Holtz
,
Daniel C. Huang
,
Murat Arcak
,
Michel M. Maharbiz
Journal:
PLOS Computational Biology  PLOS COMPUT BIOL
, vol. 8, no. 1, 2012
Modeling Planarian Regeneration: A Primer for ReverseEngineering the Worm
Daniel Lobo
,
Wendy S. Beane
,
Michael Levin
Journal:
PLOS Computational Biology  PLOS COMPUT BIOL
, vol. 8, no. 4, 2012
Modelling Cell Polarization Driven by Synthetic Spatially Graded Rac Activation
William R. Holmes
,
Benjamin Lin
,
Andre Levchenko
,
Leah EdelsteinKeshet
Journal:
PLOS Computational Biology  PLOS COMPUT BIOL
, vol. 8, no. 6, 2012
A Singularity of Fertility Decline Is LotetGaronne
SHUICHIROU IKE
Journal:
Journal of Mathematical Sociology  J MATH SOCIOL
, vol. 36, no. 3, pp. 137155, 2012