Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-29T14:00:03.817Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling of Plant Growth with Apical or BasalMeristem

Published online by Cambridge University Press:  01 March 2011

N. Bessonov ,
F. Crauste  and
V. Volpert
N. Bessonov
Affiliation:
Institute of Mechanical Engineering Problems, 199178 Saint Petersburg, Russia
F. Crauste
Affiliation:
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1 69622 Villeurbanne, France
V. Volpert*
Affiliation:
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1 69622 Villeurbanne, France
*
⋆Corresponding author. E-mail: volpert@math.univ-lyon1.fr
Get access

Abstract

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

Keywords

plant growthbasal meristemdissipative structurestravelling waves
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 2: Modelling of plant growth , 2011 , pp. 107 - 132
Copyright
© EDP Sciences, 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Références

B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, J.D. Watson. Biologie moléculaire de la cellule, 3th edn. Médecine-Sciences, Flammarion, 1995.
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.
N. Bessonov, V. Volpert. Dynamic models of plant growth. Publibook, Paris, 2006.
Bessonov, N., Morozova, N., Volpert, V.. Modelling of branching patterns in plants. Bull. Math. Biology, 70 (2008), no. 3, 868–893. CrossRefGoogle Scholar
Boucheron, E., Guivarch, A., Azmi, A., Dewitte, W., Van Onckelen, H., Chriqui, D.. 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. Google ScholarPubMed
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.
DArcy Thompson. On growth and forms. The complete revised edition. Dover, New York, 1992.
Forest, L., Demongeot, J.. Cellular modelling of secondary radial growth in conifer trees: application to Pinus radiata (D Don). Bull. Math. Biol. 68 (2006), 753–784. CrossRefGoogle Scholar
Himanen, K., Boucheron, E., Vanneste, S., de Almeida Engler, J., Inze, D., Beeckman, T.. Auxin mediated cell cycle activation during early lateral root initiation. Plant Cell, 14 (2002), 2339–2351. CrossRefGoogle ScholarPubMed
Hoffmann, I., Clarke, P.R., Marcote, M.J., Karsenti, E., Draetta, G.. 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. Google Scholar
R. V. Jean. Phyllotaxis. A systematic study in plant morphogenesis. Cambridge University Press, New York, 1994.
Jonsson, H., Heisler, M.G., Shapiro, B.E., Meyerowitz, E.M., Mjolsness, E.. An auxin-driven polarized transport model for phyllotaxis. PNAS 103 (2006), no. 5, 1633–1638. CrossRefGoogle ScholarPubMed
Khiripet, N., Viruchpintu, R., Maneewattanapluk, J., Spangenberg, J., Jungck, J. R.. Morphospace: measurement, modeling, mathematics, and meaning. Math. Model. Nat. Phenom., 6 (2011), No. 2, 54–81. CrossRefGoogle Scholar
Magyar, Z., De Veylder, L., Atanassova, A., Bako, L., Inze, D., Bogre, L.. The role of the Arabidopsis E2FB transcription factor in regulating auxin-dependent cell division. Plant Cell, 17 (2005) no. 9, 2527–2541. CrossRefGoogle ScholarPubMed
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.
Othmer, H. G., Painter, K., Umulis, D., Xue, C.. The intersection of theory and application in elucidating pattern formation in developmental biology. Math. Model. Nat. Phenom., 4 (2009), No. 4, 3–82. CrossRefGoogle ScholarPubMed
Reinhardt, D., Pesce, E.R., Stieger, P., Mandel, T., Baltensperger, K., Bennett, M., Traas, J., Friml, J., Kuhlemeier, C.. Regulation of phyllotaxis by polar auxin transport. Nature 462 (2003), 255–260. CrossRefGoogle Scholar
Rudskiy, I.V., Titova, G.E., Batygina, T.B.. Analysis of space-temporal symmetry in the early embryogenesis of Calla palustris L., Araceae. Math. Model. Nat. Phenom., 6 (2011), No. 2, 82–106. CrossRefGoogle Scholar
Skoog, F., Miller, C.O.. Chemical regulation of growth and organ formation in plant tissues cultured in vitro. Symp. Soc. Exp. Biol., 11 (1957), 118–140. Google ScholarPubMed
Smith, R.S., Guyomarch, S., Mandel, T., Reinhardt, D., Kuhlemeier, C., Prusinkiewicz, P.. A plausible model of phyllotaxis. PNAS, 103 (2006), no. 5, 1301–1306. CrossRefGoogle Scholar
Soni, R., Carmichael, J.P., Shah, Z.H., Murray, J.A.. 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. CrossRefGoogle Scholar
Traas, J., Bohn-Courseau, I.. Cell proliferation patterns at the shoot apical meristem. Curr. Opin. Plant Biol. 8 (2005), 587–592. CrossRefGoogle ScholarPubMed
Treml, B.S., Winderl, S., Radykewicz, R., Herz, M., Schweizer, G., Hutzler, P., Glawischnig, E., Ruiz, R.A.. The gene ENHANCER OF PINOID controls cotyledon development in the Arabidopsis embryo. Development 139 (2005), no. 18, 4063–4074. CrossRefGoogle Scholar
A. Volpert, Vit. Volpert, Vl. Volpert. Traveling wave solutions of parabolic systems. Translation of Mathematical Monographs, Vol. 140, Amer. Math. Society, Providence, 1994.
Yamaguchi, M., Kato, H., Yoshida, S., Yamamura, S., Uchimiya, H., Umeda, M.. Control of in vitro organogenesis by cyclin-dependent kinase activities in plants. Proc. Natl. Acad. Sci. USA, 100 (2003), no. 13, 8019–8023. CrossRefGoogle ScholarPubMed