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The tensor-based model for growth and cell divisions of the root apex. II. Lateral root formation

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Abstract

In this work, the formation of the virtual lateral root (VLR) is shown. The VLR is formed using the 2D simulation model of growth and cell divisions based on the concept of growth tensor, specified for radish. Growth is generated by the field of growth rates of an unsteady type (GT field). Principal directions of growth (PDGs) are assumed to define the orientation of cell divisions. Temporal sequences of the VLR formation are a result of an application of the GT field to the polygon meshwork representing cell pattern of already initiated primordium. The computer-generated lateral root (LR) develops realistically, and its cell pattern is vivid and similar to that observed in anatomical sections. The real and virtual LRs show similar cellular organization, both originate from a small group of cells situated in two-cell layers of the pericycle and both layers are engaged in the LR development. The LR formation seems to be controlled at the tensor level and individual cells presumably detect PDGs and obey them in the course of the cell divisions. PDGs are postulated to affect the cellular organization of the LR. Using the method of computer simulations, cellular aspects of the LR morphogenesis are discussed.

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Abbreviations

GT:

Growth tensor

IL:

Inner layer

OL:

Outer layer

LR:

Lateral root

VLR:

Virtual lateral root

QC:

Quiescent center

PDGs:

Principal directions of growth

RERGl :

Relative elemental rate of linear growth

R-NCS:

Root-natural coordinate system

2D:

Two dimensional

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Acknowledgments

The authors thank Professor Lewis Feldman from Department of Plant and Microbial Biology, UC Berkeley, USA, for helpful comments on the manuscript and Jerzy Karczewski for preparing the movie (Electronic Supplementary Material Video S1). The research was supported in part by a Grant from the Polish Ministry of Science and Higher Education (Grant no. N N303 333936).

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Authors and Affiliations

  1. Department of Biophysics and Plant Morphogenesis, University of Silesia, Katowice, Poland

    Joanna Szymanowska-Pułka & Jerzy Nakielski

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  1. Joanna Szymanowska-Pułka
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  2. Jerzy Nakielski
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Correspondence to Joanna Szymanowska-Pułka.

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Appendix

Appendix

The components of V: \( V_{u} = \frac{{\rm d}u}{{\rm d}t} \) and \( V_{v} = \frac{{\rm d}v}{{\rm d}t} \) in particular zones

where \(z(t) = \left( {\frac{{\pi v}}{{v_0 (t)}}} \right)\) and c, k are constants.

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Szymanowska-Pułka, J., Nakielski, J. The tensor-based model for growth and cell divisions of the root apex. II. Lateral root formation. Planta 232, 1207–1218 (2010). https://doi.org/10.1007/s00425-010-1239-1

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