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Anisotropic and isotropic growth of the apical meristem
Yves Couder
Last modified: 2009-07-03
Abstract
Yves Couder*, Francis Corson**, Olivier Hamant***, Arezki Boudaoud**, Jan Traas***,
*Mati`ere et syst`emes complexes
Universit'e Paris 7 Denis Diderot, CNRS UMR 7057,
Batiment Condorcet, 10, rue Alice Donon et L'eonie Duquet, 75013 Paris
**Laboratoire de Physique Statistique
Ecole Normale Sup'erieure, 24, rue Lhomond, 75231 Paris Cedex 05
***Laboratoire de Reproduction et D'eveloppement des Plantes,
ENS Lyon, 46, all'ee d'Italie, 69364 Lyon Cedex 07,
The growth of vascular plants is characterized by its anisotropy, obvious at macroscopic scale in the growth of the stems and that of the roots. It is also observed at the cellular scale in the orientation of the cortical microtubules, that of the microfibril deposition in the cell walls and in the preferential directions of cell division. In a recent work(1) it was shown that the orientation of the cortical microtubules was sensitive to externally applied mechanical stresses. This suggests that in the unstressed situation the anisotropy can be self-induced, the internal mechanical stresses orienting the microtubules.
In this context it is interesting to observe the effect of the suppression of the microtubules. The effect of oryzalin, an inhibitor of microtubule polymerization, on the development of the apical meristem of Arabidopsis thaliana is revisited. While cell divisions are entirely suppressed, the growth of meristematic regions is sustained, and the cells become huge. We analyse two effects.
-Each of the existing organs now grows isotropically and tends to become spherical.
- Correlatively, the geometry of the cells becomes similar to that of the bubbles in a soap froth.
A theoretical model is presented, in which a cellular structure evolves through the plastic yielding of its walls under turgor pressure. If a cell division process is included, the appearance of the structure is that of a normal tissue. If not, a "cell froth'' very similar to that observed experimentally is obtained. In both the experimental and numerical simulations the same evolution of the vertices is observed where all angles tend towards 120^0. To meet this condition a curvature of the cell walls appear, the cells with a number of sides smaller than 6 becoming convex while those with a larger number of sides become concave. In soap froth this generates a shrinking of the former and an expansion of the latter. This coarsening process is absent in the living tissue, suggesting constraints on the mechanisms of growth regulation.
(1) O. Hamant, M. Heisler, H. J"onsson, P. Krupinski, M. Uyttewaal, P. Bokov, F. Corson, P. Sahlin, A. Boudaoud, E. Meyerowitz, Y. Couder & J. Traas, Mechanics of morphogenesis at the shoot apical meristem of Arabidopsis thaliana: an interdisciplinary view, Science, 322, 1650-1655, (2008)
*Mati`ere et syst`emes complexes
Universit'e Paris 7 Denis Diderot, CNRS UMR 7057,
Batiment Condorcet, 10, rue Alice Donon et L'eonie Duquet, 75013 Paris
**Laboratoire de Physique Statistique
Ecole Normale Sup'erieure, 24, rue Lhomond, 75231 Paris Cedex 05
***Laboratoire de Reproduction et D'eveloppement des Plantes,
ENS Lyon, 46, all'ee d'Italie, 69364 Lyon Cedex 07,
The growth of vascular plants is characterized by its anisotropy, obvious at macroscopic scale in the growth of the stems and that of the roots. It is also observed at the cellular scale in the orientation of the cortical microtubules, that of the microfibril deposition in the cell walls and in the preferential directions of cell division. In a recent work(1) it was shown that the orientation of the cortical microtubules was sensitive to externally applied mechanical stresses. This suggests that in the unstressed situation the anisotropy can be self-induced, the internal mechanical stresses orienting the microtubules.
In this context it is interesting to observe the effect of the suppression of the microtubules. The effect of oryzalin, an inhibitor of microtubule polymerization, on the development of the apical meristem of Arabidopsis thaliana is revisited. While cell divisions are entirely suppressed, the growth of meristematic regions is sustained, and the cells become huge. We analyse two effects.
-Each of the existing organs now grows isotropically and tends to become spherical.
- Correlatively, the geometry of the cells becomes similar to that of the bubbles in a soap froth.
A theoretical model is presented, in which a cellular structure evolves through the plastic yielding of its walls under turgor pressure. If a cell division process is included, the appearance of the structure is that of a normal tissue. If not, a "cell froth'' very similar to that observed experimentally is obtained. In both the experimental and numerical simulations the same evolution of the vertices is observed where all angles tend towards 120^0. To meet this condition a curvature of the cell walls appear, the cells with a number of sides smaller than 6 becoming convex while those with a larger number of sides become concave. In soap froth this generates a shrinking of the former and an expansion of the latter. This coarsening process is absent in the living tissue, suggesting constraints on the mechanisms of growth regulation.
(1) O. Hamant, M. Heisler, H. J"onsson, P. Krupinski, M. Uyttewaal, P. Bokov, F. Corson, P. Sahlin, A. Boudaoud, E. Meyerowitz, Y. Couder & J. Traas, Mechanics of morphogenesis at the shoot apical meristem of Arabidopsis thaliana: an interdisciplinary view, Science, 322, 1650-1655, (2008)