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Deformable Cell Model and its Application to Growth of Plant Meristem

Published online by Cambridge University Press:  10 July 2013

N. Bessonov ,
V. Mironova  and
V. Volpert
N. Bessonov
Affiliation:
Institute of Mechanical Engineering Problems, 199178 Saint Petersburg, Russia
V. Mironova
Affiliation:
Institute of cytology and genetics SB RAS, Novosibirsk, Russia
V. Volpert*
Affiliation:
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France Department of Mathematics, Mechanics and Computer Science Southern Federal University, Rostov-on-Don, Russia
*
⋆ Corresponding author. E-mail: volpert@math.univ-lyon1.fr
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Abstract

Deformable cell model is developed to study pattern formation and to simulate plant tissue growth. Each cell represents a polygon with a number of vertices connected by springs. Some cells in the tissue can grow and divide, other cells are differentiated and do not grow or divide but remain deformable. The model is used to investigate formation of self-similar structures which reproduce the same cell organization during their growth. In numerical experiments we observed that self-similar solutions can exist for a rather precise choice of plant structure and mechanical properties of cell walls. We test the model for simulation of apical meristems functioning which represent self-similar cell structures in plants. At the next stage of modelling, auxin distribution is introduced by means of diffusion and polar transport mechanisms. The existence of steady auxin distribution in a growing root is investigated. Single as well as multiple auxin maxima have been observed in model solutions.

Keywords

deformable cell modelself-similar solutionroot apical meristemauxin transport
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 4: Plant growth modelling , 2013 , pp. 62 - 79
Copyright
© EDP Sciences, 2013

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References

Band, L.R., Wells, D.M., Larrieu, A., Sun, J., Middleton, A.M.. Root gravitropism is regulated by a transient lateral auxin gradient controlled by a tipping-point mechanism. PNAS, 109 (2012), no. 12, 4668–4473. CrossRefGoogle ScholarPubMed
Bayer, E.M., Smith, R.S., Mandel, T., Nakayama, N., Sauer, M., Prusinkiewicz, P., Kuhlemeier, C.. Integration of transport-based models for phyllotaxis and midvein formation. Genes Dev., 23 (2009), no. 3, 373–384. CrossRefGoogle Scholar
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
Bilsborough, G.D., Runions, A., Barkoulas, M., Jenkins, H.W., Hasson, A., Galinha, C., Laufs, P., Hay, A., Prusinkiewicz, P., Tsiantis, M.. Model for the regulation of Arabidopsis thaliana leaf margin development. PNAS, 108 (2011), no. 8, 3424–3429. CrossRefGoogle ScholarPubMed
Blilou, I., Xu, J., Wildwater, M., Willemsen, V., Paponov, I., Friml, J., Heidstra, R., Aida, M., Palme, K., Scheres, B.. The PIN auxin efflux facilitator network controls growth and patterning in Arabidopsis roots. Nature, 433(7021) (2005), 39–44. CrossRefGoogle ScholarPubMed
Brukhin, V., Morozova, N.. Plant growth and development - basic knowledge and current views. Math. Model. Nat. Phenom., 6 (2011), no. 2, 1–53. CrossRefGoogle Scholar
Brunoud, G., Wells, D.M., Oliva, M., Larrieu, A., Mirabet, V., Burrow, A.H., Beeckman, T., Kepinski, S., Traas, J., Bennett, M.J., Vernoux, T.. A novel sensor to map auxin response and distribution at high spatio-temporal resolution. Nature, 482(7383) (2012), 103–106. CrossRefGoogle Scholar
De Smet, I., Tetsumura, T., De Rybel, B., Frey, N.F., Laplaze, L., Casimiro, I., Swarup, R., Naudts, M., Vanneste, S., Audenaert, D., Inze, D., Bennett, M.J., Beeckman, T.. Auxin-dependent regulation of lateral root positioning in the basal meristem of Arabidopsis. Development, 134 (2007), no. 4, 681–690. CrossRefGoogle ScholarPubMed
Dolan, L., Janmaat, K., Willemsen, V., Linstead, P., Poethig, S., Roberts, K., Scheres, B.. Cellular organisation of the Arabidopsis thaliana root. Development, 119 (1993), 71–84. Google ScholarPubMed
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
Heisler, M.G., Ohno, C., Das, P., Sieber, P., Reddy, G.V., Long, J.A., Meyerowitz, E.M.. Patterns of auxin transport and gene expression during primordium development revealed by live imaging of the Arabidopsis inflorescence meristem. Curr Biol., 2005. 15(21), 1899–1911. CrossRefGoogle ScholarPubMed
Jiang, K., Feldman, L.J.. Regulation of root apical meristem development. Ann. Rev. Cell Dev. Biol., 21 (2005), 485–509. CrossRefGoogle ScholarPubMed
Grieneisen, V.A., Xu, J., Marle, A.F., Hogeweg, P., Scheres, B.. Auxin transport is sufficient to generate a maximum and gradient guiding root growth. Nature 2007, 449(7165), 1008–1013. CrossRefGoogle ScholarPubMed
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
Kramer, E.M.. A mathematical model of pattern formation in the vascular cambium of trees. J. Theor. Biol. (2002) 216, 147–158. CrossRefGoogle Scholar
Krupinski, P., Jonsson, H.. Modeling auxin-regulated development. Cold Spring Harb Perspect Biol., 2010 0Feb. 2(2): a001560. CrossRefGoogle ScholarPubMed
Lucas, M., Laplaze, L., Bennett, M.J.. Plant systems biology: network matters. Plant Cell Environ., 34 (2011), no. 4, 535–353. CrossRefGoogle ScholarPubMed
Merks, R.M., Guravage, M., Inze, D., Beemster, G.T.. VirtualLeaf: an open-source framework for cell-based modeling of plant tissue growth and development. Plant Physiol., 155 (2011), no. 2, 656–666. CrossRefGoogle ScholarPubMed
Mironova, V.V., Omelyanchuk, N.A., Novoselova, E.S., Doroshkov, A.V., Kazantsev, F.V., Kochetov, A.V., Kolchanov, N.A., Mjolsness, E., Likhoshvai, V.A.. Combined in silico/in vivo analysis of mechanisms providing for root apical meristem self-organization and maintenance. Ann. Bot., 110 (2012), no. 2, 349–360. CrossRefGoogle Scholar
Mironova, V.V., Omelyanchuk, N.A., Yosiphon, G., Fadeev, S.I., Kolchanov, N.A., Mjolsness, E., Likhoshvai, V.A.. A plausible mechanism for auxin patterning along the developing root. BMC Syst. Biol., 2010 0Jul 21 ;4:98. CrossRefGoogle ScholarPubMed
Moreno-Risueno, M.A., Van Norman, J.M. , Moreno, A., Zhang, J., Ahnert, S.E., Benfey, P.N.. Oscillating gene expression determines competence for periodic Arabidopsis root branching. Science, 329 (2010) no. 5997, 1306–1311. CrossRefGoogle ScholarPubMed
Sauer, M., Balla, J., Luschnig, C., Wisniewska, J., Reinohl, V., Friml, J., Benkova, E.. Canalization of auxin flow by Aux/IAA-ARF-dependent feedback regulation of PIN polarity. Genes & Dev., 20 (2006), 2902–2911. CrossRefGoogle ScholarPubMed
Sahlin, P., Soderberg, B., Jonsson, H.. Regulated transport as a mechanism for pattern generation: capabilities for phyllotaxis and beyond. J. Theor. Biol., 258 (2009), no. 1, 60–70. CrossRefGoogle ScholarPubMed
Szymanowska-Pulka, J., Potocka, I., Karczewski, J., Jiang, K., Nakielski, J., Feldman, L.J.. Principal growth directions in development of the lateral root in Arabidopsis thaliana. Ann. Bot., 110 (2012), no. 2, 491–501. CrossRefGoogle ScholarPubMed
Szymanowska-Pulka, J.. Application of a changing field of growth rates to a description of root apex formation. J. Theor. Biol., 247 (2007), no. 4, 650–656. CrossRefGoogle ScholarPubMed
Vieten, A., Vanneste, S., Wisniewska, J., Benkova, E., Benjamins, R., Beeckman, T., Luschnig, C., Friml, J.. Functional redundancy of PIN proteins is accompanied by auxin dependent cross-regulation of PIN expression. Development, 132 (2005), no. 20, 4521–4531. CrossRefGoogle ScholarPubMed
Williams, L., Fletcher, J.C.. Stem cell regulation in the Arabidopsis shoot apical meristem. Curr. Opin. Plant Biol., 8 (2005), no. 6, 582–586. CrossRefGoogle ScholarPubMed