A model of phyllotaxis

Journal of Theoretical Biology

Volumn 192, Issue 4, 1998, Pages 531-544

  Cummings, F W ^a,b   Strickland, J C ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; EMBRYO PATTERN FORMATION; PLANT GROWTH; PRIORITY JOURNAL;

EID: 0032555060     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1998.0682     Document Type: Article

References (21)

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2. BARKAI, N. & LEIBLER, S. (1997). Robustness in simple biochemical networks. Nature 387, 913-917.
3. BRADY-KALNAY, S. M. & TONKS, N. K. (1995). Protein tyrosine phosphatases as adhesion receptors. Current Op. Cell Biol. 7, 650-657.
4. CUMMINGS, F. W. (1994). Aspects of growth and form. Physica D. 79, 146-163.
5. CUMMINGS, F. W. (1996). A model of growth and form based on adhesion molecules. J. theor. Biol. 178, 229-238; also CUMMINGS, F. W. (1996). "Geometrical concepts in epithelial sheets". J. theor. Biol. 179, 41-49.
6. CUMMINGS, F. W. (1996). A model of growth and form based on adhesion molecules. J. theor. Biol. 178, 229-238; also CUMMINGS, F. W. (1996). "Geometrical concepts in epithelial sheets". J. theor. Biol. 179, 41-49.
7. CUMMINGS, F. W. (1997). "Towards a model of growth and form in living systems". In: Physical Theory in Biology; Foundations and Explorations (Lumsden, C. J, Brandts, W. A. & Trainor, L. E. H., eds). London: World Scientific.
8. DOUADY, K. J. & COUDER, Y. (1992). Phyllotaxis as a physical self-organized process. In: Growth Patterns in Physical Sciences and Biology, Proc. NATO ARW, Granada, Spain, 7-11 Oct. 1991; also Phys. Rev. Lett. 68(13), 2098-2101. This very interesting work gives the major phyllotactic patterns which result from repelling oil drops in a radially symmetric magnetic field, suggesting a similar level of simplicity of the basic mechanism in plants.
9. DOUADY, K. J. & COUDER, Y. (1992). Phyllotaxis as a physical self-organized process. In: Growth Patterns in Physical Sciences and Biology, Proc. NATO ARW, Granada, Spain, 7-11 Oct. 1991; also Phys. Rev. Lett. 68(13), 2098-2101. This very interesting work gives the major phyllotactic patterns which result from repelling oil drops in a radially symmetric magnetic field, suggesting a similar level of simplicity of the basic mechanism in plants.
10. EIJGENRAAM, F. (1993). Things start getting sticky for a cell surface enzyme. Science 261, 833-834.
11. FISCHER, E. H., CHARBONNEAU, H. & TONKS, N. K. (1991). Protein tyrosine phosphatases: a diverse family of intracellular and transmembrane enzymes. Science 253, 401-406.
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13. GREEN, P. B. (1992). Pattern formation in shoots: a likely role for minimal energy configurations of the tunica. Int. J. Plant Sci. 153(3), S59-S75.
14. GREEN, P. B. & BAXTER, D. R. (1987). Phyllotactic patterns: characterization by geometrical activity at the formative region. J. theor. Biol. 128, 387-395.
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16. JEAN, R. V. (1994). Phyllotaxis. Cambridge: Cambridge University Press.
17. KAUFFMAN, S. A. (1993). The Origins of Order. Oxford: Oxford University Press. Kauffman refers to what is here called the Helmholtz equation as the equation of the "eigenvalue of the Laplacian operator".
18. KAUFFMAN, S. A., SHYMKO, R. M. & TRAYBERT, K. (1978). Control of sequential compartment formation in drosophila. Science 199, 259-270.
19. LYNDON, R. F. (1990). Plant Development; the Cellular Basis. Boston: Unwin Hyman.
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21. TONKS, N. K. & NEEL, B. G. (1996). From form to function: signalling by protein tyrosine phosphatases. Cell 87, 365-368 (a minireview).