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Pattern formation by reaction-diffusion instabilities: Application to morphogenesis in Drosophila

Authors :
Daniel Thomas
J. P. Kernevez
Gislaine Joly
Barry Bunow
Source :
Journal of Theoretical Biology. 84:629-649
Publication Year :
1980
Publisher :
Elsevier BV, 1980.

Abstract

Kauffman, Shymko & Trabert (1978) have presented a model for sequentialcompartment formation in Drosophila wing disks based upon reactiondiffusion instabilities on an elliptical model for the wing disk. Using numerical methods we have explored the properties of this model using a more accurate representation of the shape of the wing disk and other embryonic structures. The nodal lines of successive eigenfunctions on these domains differ significantly both in form and order from the compartmental lines experimentally observed on the wing disk and are very sensitive to the shape of the domain. The model of Kauffman and coworkers is linear. We present a particular non-linear reaction-diffusion model which produces different patterns. It appears to be characteristic of non-linear models that a priori prediction of the sequence of patterns resulting for given parameters is impossible. The patterns generated by these instability models are generally quite sensitive to changes in the shape of the domain and physical-chemical parameter values. This sensitivity makes it difficult to imagine how pattern form and sequence could be maintained in the face of normal biological variation. We conclude that the use of instability models in this aspect of morphogenesis is an interesting speculation, but one whose validity will be difficult to demonstrate convincingly.

Details

ISSN :
00225193
Volume :
84
Database :
OpenAIRE
Journal :
Journal of Theoretical Biology
Accession number :
edsair.doi.dedup.....015420c1ac2fbd7d4fac4a70fc45ae24
Full Text :
https://doi.org/10.1016/s0022-5193(80)80024-5