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Pattern formation by reaction-diffusion instabilities: Application to morphogenesis in Drosophila
- 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.
- Subjects :
- Statistics and Probability
Sequence
Wing
General Immunology and Microbiology
Applied Mathematics
Numerical analysis
Pattern formation
Geometry
General Medicine
Eigenfunction
Models, Biological
Instability
General Biochemistry, Genetics and Molecular Biology
Modeling and Simulation
Reaction–diffusion system
Morphogenesis
Animals
Wings, Animal
Blastoderm
Drosophila
Statistical physics
Sensitivity (control systems)
General Agricultural and Biological Sciences
Mathematics
Subjects
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