Modelling of Plant Growth with Apical or Basal Meristem

N. Bessonov; F. Crauste; V. Volpert

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 2, page 107-132
  • ISSN: 0973-5348

Abstract

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Plant growth occurs due to cell proliferation in the meristem. We model the case of apical meristem specific for branch growth and the case of basal meristem specific for bulbous plants and grass. In the case of apical growth, our model allows us to describe the variety of plant forms and lifetimes, endogenous rhythms and apical domination. In the case of basal growth, the spatial structure, which corresponds to the appearance of leaves, results from dissipative instability of the homogeneous in space solution. We study nonlinear dynamics and wave propagation of the corresponding reaction-diffusion systems. Bifurcation of periodic at infinity waves is investigated numerically.

How to cite

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Bessonov, N., Crauste, F., and Volpert, V.. "Modelling of Plant Growth with Apical or Basal Meristem." Mathematical Modelling of Natural Phenomena 6.2 (2011): 107-132. <http://eudml.org/doc/222259>.

@article{Bessonov2011,
abstract = {Plant growth occurs due to cell proliferation in the meristem. We model the case of apical meristem specific for branch growth and the case of basal meristem specific for bulbous plants and grass. In the case of apical growth, our model allows us to describe the variety of plant forms and lifetimes, endogenous rhythms and apical domination. In the case of basal growth, the spatial structure, which corresponds to the appearance of leaves, results from dissipative instability of the homogeneous in space solution. We study nonlinear dynamics and wave propagation of the corresponding reaction-diffusion systems. Bifurcation of periodic at infinity waves is investigated numerically. },
author = {Bessonov, N., Crauste, F., Volpert, V.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {plant growth; basal meristem; dissipative structures; travelling waves},
language = {eng},
month = {3},
number = {2},
pages = {107-132},
publisher = {EDP Sciences},
title = {Modelling of Plant Growth with Apical or Basal Meristem},
url = {http://eudml.org/doc/222259},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Bessonov, N.
AU - Crauste, F.
AU - Volpert, V.
TI - Modelling of Plant Growth with Apical or Basal Meristem
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/3//
PB - EDP Sciences
VL - 6
IS - 2
SP - 107
EP - 132
AB - Plant growth occurs due to cell proliferation in the meristem. We model the case of apical meristem specific for branch growth and the case of basal meristem specific for bulbous plants and grass. In the case of apical growth, our model allows us to describe the variety of plant forms and lifetimes, endogenous rhythms and apical domination. In the case of basal growth, the spatial structure, which corresponds to the appearance of leaves, results from dissipative instability of the homogeneous in space solution. We study nonlinear dynamics and wave propagation of the corresponding reaction-diffusion systems. Bifurcation of periodic at infinity waves is investigated numerically.
LA - eng
KW - plant growth; basal meristem; dissipative structures; travelling waves
UR - http://eudml.org/doc/222259
ER -

References

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  1. B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, J.D. Watson. Biologie moléculaire de la cellule, 3th edn. Médecine-Sciences, Flammarion, 1995.  
  2. N. Bessonov, V. Volpert. On a problem of plant growth. In: Patterns and waves. A. Abramian, S. Vakulenko, V. Volpert, Eds. St. Petersburg, 2003, pp. 323–337.  
  3. N. Bessonov, V. Volpert. Dynamic models of plant growth. Publibook, Paris, 2006.  
  4. N. Bessonov, N. Morozova, V. Volpert. Modelling of branching patterns in plants. Bull. Math. Biology, 70 (2008), no. 3, 868–893.  
  5. E. Boucheron, A. Guivarch, A. Azmi, W. Dewitte, H. Van Onckelen, D. Chriqui. Competency of Nicotiana tabacum L. stem tissues to dedifferentiate is associated with differential levels of cell cycle gene expression and endogenous cytokinins. Planta, 215 (2002), 267–278.  
  6. V. Brukhin, N. Morozova. Plant growth and development - basic knowledge and current views. Math. Model. Nat. Phenom. Vol. 6, No. 2, 2011, pp. 1–53.  
  7. DArcy Thompson. On growth and forms. The complete revised edition. Dover, New York, 1992.  
  8. L. Forest, J. Demongeot. Cellular modelling of secondary radial growth in conifer trees: application to Pinus radiata (D Don). Bull. Math. Biol.68 (2006), 753–784.  
  9. K. Himanen, E. Boucheron, S. Vanneste, J. de Almeida Engler, D. Inze, T. Beeckman. Auxin mediated cell cycle activation during early lateral root initiation. Plant Cell, 14 (2002), 2339–2351.  
  10. I. Hoffmann, P.R. Clarke, M.J. Marcote, E. Karsenti, G. Draetta. Phosphorylation and activation of human cdc25-C by cdc2-cyclin B and its involvement in the self-amplification of MPF at mitosis. EMBO J.12 (1993), no. 1, 53–63.  
  11. R. V. Jean. Phyllotaxis. A systematic study in plant morphogenesis. Cambridge University Press, New York, 1994.  
  12. H. Jonsson, M.G. Heisler, B.E. Shapiro, E.M. Meyerowitz, E. Mjolsness. An auxin-driven polarized transport model for phyllotaxis. PNAS103 (2006), no. 5, 1633–1638.  
  13. N. Khiripet, R. Viruchpintu, J. Maneewattanapluk, J. Spangenberg, J. R. Jungck. Morphospace: measurement, modeling, mathematics, and meaning. Math. Model. Nat. Phenom., 6 (2011), No. 2, 54–81. 
  14. Z. Magyar, L. De Veylder, A. Atanassova, L. Bako, D. Inze, L. Bogre. The role of the Arabidopsis E2FB transcription factor in regulating auxin-dependent cell division. Plant Cell, 17 (2005) no. 9, 2527–2541.  
  15. H. Meinhardt, A.J. Koch, G. Bernasconi. Models of pattern formation applied to plant development. In: Symmetry in Plants, (D. Barabe and R. V. Jean, Eds), World Scientific Publishing, Singapore, 1998, 723–758.  
  16. H. G. Othmer, K. Painter, D. Umulis, C. Xue. The intersection of theory and application in elucidating pattern formation in developmental biology. Math. Model. Nat. Phenom., 4 (2009), No. 4, 3–82.  
  17. D. Reinhardt, E.R. Pesce, P. Stieger, T. Mandel, K. Baltensperger, M. Bennett, J. Traas, J. Friml, C. Kuhlemeier. Regulation of phyllotaxis by polar auxin transport. Nature462 (2003), 255–260.  
  18. I.V. Rudskiy, G.E. Titova, T.B. Batygina. Analysis of space-temporal symmetry in the early embryogenesis of Calla palustris L., Araceae. Math. Model. Nat. Phenom., 6 (2011), No. 2, 82–106.  
  19. F. Skoog, C.O. Miller. Chemical regulation of growth and organ formation in plant tissues cultured in vitro. Symp. Soc. Exp. Biol., 11 (1957), 118–140.  
  20. R.S. Smith, S. Guyomarch, T. Mandel, D. Reinhardt, C. Kuhlemeier, P. Prusinkiewicz. A plausible model of phyllotaxis. PNAS, 103 (2006), no. 5, 1301–1306.  
  21. R. Soni, J.P. Carmichael, Z.H. Shah, J.A. Murray. A family of cyclin D homologs from plants differentially controlled by growth regulators and containing the conserved retinoblastoma protein interaction motif. Plant Cell, 7 (1995) no. 1, 85–103.  
  22. J. Traas, I. Bohn-Courseau. Cell proliferation patterns at the shoot apical meristem. Curr. Opin. Plant Biol.8 (2005), 587–592.  
  23. B.S. Treml, S. Winderl, R. Radykewicz, M. Herz, G. Schweizer, P. Hutzler, E. Glawischnig, R.A. Ruiz. The gene ENHANCER OF PINOID controls cotyledon development in the Arabidopsis embryo. Development139 (2005), no. 18, 4063–4074.  
  24. A. Volpert, Vit. Volpert, Vl. Volpert. Traveling wave solutions of parabolic systems. Translation of Mathematical Monographs, Vol. 140, Amer. Math. Society, Providence, 1994.  
  25. M. Yamaguchi, H. Kato, S. Yoshida, S. Yamamura, H. Uchimiya, M. Umeda. Control of in vitro organogenesis by cyclin-dependent kinase activities in plants. Proc. Natl. Acad. Sci. USA, 100 (2003), no. 13, 8019–8023.  

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