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2016 | 85 | 4 |
Tytuł artykułu

Emergence of complex patterns in a higher-dimensional phyllotactic system

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A hypothesis commonly known as Hofmeister’s rule states that primordia appearing at the apical ring of a plant shoot in periodic time steps are formed in the position where the most space is available with respect to the space occupation of already-formed primordia. A corresponding two-dimensional dynamical model has been extensively studied by Douady and Couder, and shown to generate a variety of observable phyllotactic patterns indeed. In this study, motivated by mathematical interest in a theoretical phyllotaxis-inspired system rather than by a concrete biological problem, we generalize this model to three dimensions and present the dynamics observed in simulations, thereby illustrating the range of complex structures that phyllotactic mechanisms can give rise to. The patterns feature unexpected additional properties compared to the two-dimensional case, such as periodicity and chaotic behavior of the divergence angle.
Słowa kluczowe
EN
Wydawca
-
Rocznik
Tom
85
Numer
4
Opis fizyczny
Article 3528 [12p.], fig.,ref.
Twórcy
autor
  • McDonald Institute for Archaeological Research, University of Cambridge, Downing Street, Cambridge CB2 3ER, United Kingdom
  • Department of Mathematics, Technische Universitat Munchen, Boltzmannstrasse 3, 85748 Garching, Germany
Bibliografia
  • 1. Hofmeister W. Allgemeine Morphologie der Gewächse. In: du Bary A, Irmisch TH, Sachs J, editors. Handbuch der Physiologischen Botanik. Leipzig: Engelman; 1868. p. 405–664.
  • 2. Kirchoff BK. Shape matters: Hofmeister’s rule, primordium shape, and flower orientation. Int J Plant Sci. 2003;164:505–517. https://doi.org/10.1086/375421
  • 3. van Iterson G. Mathematische und mikroskopisch-anatomische Studien über Blattstellungen. Jena: Gustav Fisher Verlag; 1907.
  • 4. Atela P, Golé C, Hotton S. A dynamical system for plant pattern formation: rigorous analysis. Journal of Nonlinear Science. 2002;12:641–676. https://doi.org/10.1007/s00332-002-0513-1
  • 5. Douady S, Couder Y. Phyllotaxis as a physical self-organized growth process. Phys Rev Lett. 1992;68:2098. https://doi.org/10.1103/PhysRevLett.68.2098
  • 6. Kitazawa MS, Fujimoto K. A dynamical phyllotaxis model to determine floral organ number. PLoS Comput Biol. 2015;11:e1004145. https://doi.org/10.1371/journal.pcbi.1004145
  • 7. Kunz M. Some analytical results about two physical models of phyllotaxis. Communications in Mathematical Physics. 1995;169:261–295. https://doi.org/10.1007/BF02099473
  • 8. Levitov LS. Energetic approach to phyllotaxis. Europhys Lett. 1991;14:533–539. https://doi.org/10.1209/0295-5075/14/6/006
  • 9. Smith RS, Kuhlemeier C, Prusinkiewicz P. Inhibition fields for phyllotactic pattern formation: a simulation study. Can J Bot. 2006;84:1635–1649. https://doi.org/10.1139/B06-133
  • 10. Douady S, Couder Y. Phyllotaxis as a dynamical self organizing process Part I: the spiral modes resulting from time-periodic iterations. J Theor Biol. 1996;178:255–273. https://doi.org/10.1006/jtbi.1996.0024
  • 11. Schwendener S. Mechanische Theorie der Blattstellungen. Leipzig: Engelmann; 1878.
  • 12. Snow M, Snow R. A theory of the regulation of phyllotaxis based on Lupinus albus. Philos Trans R Soc Lond. 1962;244:483–513. https://doi.org/10.1098/rstb.1962.0003
  • 13. Adler I. A model of contact pressure in phyllotaxis. J Theor Biol. 1974;45:1–79. https://doi.org/10.1016/0022-5193(74)90043-5
  • 14. Adler I, Barabe D, Jean RV. A history of the study of phyllotaxis. Ann Bot. 1997;80:231–244. https://doi.org/10.1006/anbo.1997.0422
  • 15. Douady S, Yves C. Phyllotaxis as a dynamical self organizing process Part II: the spontaneous formation of a periodicity and the coexistence of spiral and whorled patterns. J Theor Biol. 1996;178:275–294. https://doi.org/10.1006/jtbi.1996.0025
  • 16. Williams RF. The shoot apex and leaf growth. Cambridge: Cambridge University Press; 1975. https://doi.org/10.1017/CBO9780511753404
  • 17. Schwabe WW. The role and importance of vertical spacing at the plant apex in determining the phyllotactic pattern. In: Jean RV, Barabé D, editors. Symmetry in plants. Singapore: World Scientific; 1998. p. 523–535. (Series in Mathematical Biology and Medicine; vol 4). https://doi.org/10.1142/9789814261074_0020
  • 18. Meicenheimer R. Relationship between shoot growth and changing phyllotaxy of Ranunculus. Am J Bot. 1995;66:557–569. https://doi.org/10.2307/2442505
  • 19. Ridley JN. Packing efficiency in sunflower heads. Math Biosci. 1983;58:129–139. https://doi.org/10.1016/0025-5564(82)90056-6
  • 20. Leigh EG. The golden section and spiral leaf-arrangement. Transactions of the Connecticut Academy of Arts and Sciences. 1972;44:163–176.
  • 21. Strang G. Introduction to linear algebra. Wellesley: Cambridge Press; 2016.
  • 22. Snow M, Snow R. Minimum areas and leaf determination. Proc R Soc Lond B Biol Sci. 1952;139:545–566. https://doi.org/10.1098/rspb.1952.0034
  • 23. Atela P, Golé C. The snow dynamical system for plant pattern formation [Preprint]. 2005 [cited 2016 Dec 15]. Available from: http://www.math.smith.edu/phyllo/Assets/pdf/snowdyn.pdf
  • 24. Douady S, Couder Y. Phyllotaxis as a dynamical self organizing process Part III: the simulation of the transient regimes of ontogeny. J Theor Biol. 1996;178:295–312. https://doi.org/10.1006/jtbi.1996.0026
Typ dokumentu
Bibliografia
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