Educación

Alan Turing's chemical theory of phyllotaxis

 

M.D. Rueda-Contreras and J.L. Aragón

 

Departamento de Nanotecnología, Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Apartado Postal 1-1010, 76000 Querétaro, México.

 

Received 20 November 2013
accepted 14 January 2014

 

Abstract

Alan Turing's seminal 1952 work on morphogenesis [1] is widely known and recognised in the field of mathematical biology. Less known is his work on the problem of phyllotaxis, which was never published at his time but is included in Turing's collected works [2]. It consists on three parts: the first is a detailed mathematical description of the arrangements of leaves on the stem of plants; the second is an application of the reaction-diffusion equation to the problem, and the third part is a solution of these equation for the case of spherical symmetry. It is the purpose of this work to present Turing's results contained in the second part in a comprehensive and detailed way. This is motivated by the fact that these researches have remained obscure and ill-understood. In particular, we focus on the morphogen equations for an assembly of cells since this discrete case may be useful in many circumstances where the continuum limit is not adequate or applicable.

Keywords: Phyllotaxis; Morphogenesis; Turing's chemical theory.

 

PACS: 82.90.+j; 87.10.+e.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Bibliografía

1. A.M. Turing, Phil. Trans. R. Soc. London B 237 (1952) 37-72.         [ Links ]

2. A.M. Turing, in Collected Works of A.M. Turing: Morphogenesis, edited by P.T. Saunders (North Holland, Amsterdam, 1992).         [ Links ]

3. S. Kondo and T. Miura, Science 329 (2010) 1616-1620.         [ Links ]

4. J. Swinton, in Alan Turing: Life and Legacy of a Great Thinker, edited by C. Teuscher (Springer, N.Y., 2005), pp. 477-498.         [ Links ]

5. I. Adler, D. Barabe, and R.V. Jean, Ann. Bot. 80 (1997) 231244.         [ Links ]

6. F. Sánchez-Garduño, Miscelánea Matemática 56 (2013) 65100.         [ Links ]

7. C.F. Schimper, Magazin für Pharmacie 29 (1830) 1-92.         [ Links ]

8. L. Bravais and A. Bravais, Annales des Sciences Naturelles Botanique 8 (1837) 11-42.         [ Links ]

9. F. Delpino, Alti della R. Universita di Genova 4 (1883) 1-345.         [ Links ]

10. J.N. Ridley, Math. Biosci. 58 (1982) 129-139.         [ Links ]

11. H. Airy, Proc. Roy. Soc. London 21 (1873) 176-179.         [ Links ]

12. W. Hofmeister, in Handbuch der Physiologischen Botanik, edited by W. Hofmeister, A. de Bary, Th. Irmisch and J. Sachs (Verlag Von Wilhem Engelmann, Lepzig, 1868), pp. 405-664.         [ Links ].

13. H. Meinhardt, in Positional controls in plant development, edited by P.W. Barlow and D.J. Carr (Cambridge University Press, Cambridge, 1984), pp. 1-32.         [ Links ]

14. F.J. Richards, Phil. Trans. R. Soc. London B 235 (1951) 509564.         [ Links ]

15. S. Douady and Y. Couder, J. Theo. Biol. 178 (1996) 295-312.         [ Links ]

16. D. Reinhardt et al., Nature 426 (2003) 255-260.         [ Links ]

17. H. Jonsson, M. Heisler, B. Shapiro, E. Meyerowitz, and E. Mjolsness, P. Natl. Acad. Sci. USA 103 (2005) 1633-1638.         [ Links ]

18. R. Smith, S. Guyomarc'h, T. Mandel, D. Reinhardt, C. Kuhlemeier, and P. Prusinkiewicz, P. Natl. Acad. Sci. USA 103 (2006) 1301-1306.         [ Links ]

19. C. Lloyd and J. Chan, Nat. Rev. Mol. Cell. Bio. 5 (2004) 13-23.         [ Links ]

20. E. Feraru, M. Feraru, J. Kleine-Vehn, A. Martiniere, G. Mouille, S. Vernhettes S. Vanneste, J. Runions, and J. Friml, Curr. Biol. 21 (2011) 338-343.         [ Links ]

21. R. Plaza, F. Sánchez-Garduño, P. Padilla, R. Barrio, and P.K. Maini, J. Dyn. Differ. Equ. 16 (2004) 1093-1121.         [ Links ]

22. S. Wyatt and N. Carpita, Trends Cell. Biol. 3 (1993) 413-417.         [ Links ]

23. J.D. Murray, Mathematical Biology. II: Spatial Models and Biomedical Applications, third edition (Springer, New York, 2003).         [ Links ]

24. A. Gierer and H. Meinhardt, Kybernetik 12 (1972) 30-39.         [ Links ]