Plots of local potential, auxin concentration and cell cycle, after coupling dynamics.

<p>The normalized local potential (dashed-blue), the auxin concentration (red) and the advance of the cycle clock (dotted-black) as functions of the distance from the tip (), at time steps, corresponding to seven days.</p

Histological drawing of the <i>A. thaliana</i> root tip.

<p>Here we show the SCN and the same domains as shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003026#pcbi-1003026-g001" target="_blank">Fig. 1</a> are indicated along the root apical-basal axis, as well as an schematic representation of the processes that are included in the cellular model and their interactions.</p

Log-log plot of the maximum RAM as a function of the parameter .

<p>Numerical results are blue rhombuses, and the red line is the best fit with a function of the form with R.</p

Cell Patterns Emerge from Coupled Chemical and Physical Fields with Cell Proliferation Dynamics: The <i>Arabidopsis thaliana</i> Root as a Study System

<div><p>A central issue in developmental biology is to uncover the mechanisms by which stem cells maintain their capacity to regenerate, yet at the same time produce daughter cells that differentiate and attain their ultimate fate as a functional part of a tissue or an organ. In this paper we propose that, during development, cells within growing organs obtain positional information from a macroscopic physical field that is produced in space while cells are proliferating. This dynamical interaction triggers and responds to chemical and genetic processes that are specific to each biological system. We chose the root apical meristem of <i>Arabidopsis thaliana</i> to develop our dynamical model because this system is well studied at the molecular, genetic and cellular levels and has the key traits of multicellular stem-cell niches. We built a dynamical model that couples fundamental molecular mechanisms of the cell cycle to a tension physical field and to auxin dynamics, both of which are known to play a role in root development. We perform extensive numerical calculations that allow for quantitative comparison with experimental measurements that consider the cellular patterns at the root tip. Our model recovers, as an emergent pattern, the transition from proliferative to transition and elongation domains, characteristic of stem-cell niches in multicellular organisms. In addition, we successfully predict altered cellular patterns that are expected under various applied auxin treatments or modified physical growth conditions. Our modeling platform may be extended to explicitly consider gene regulatory networks or to treat other developmental systems.</p></div

Flow-chart diagram of the program used for the numerical simulations.

<p>We show the parameters in red and the initial conditions in blue at the top of the diagram.</p

Typical initial configuration of cells after the Voronoi tessellation of random generating points.

<p>Typical initial configuration of cells after the Voronoi tessellation of random generating points.</p

Comparisons between results obtained with the model and experimental data.

<p>(A) Cell proliferation rate as a function of the distance from the quiescent centre; calculation from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003026#pcbi-1003026-g009" target="_blank">Fig. 9</a> after six days of growth. The red line and dots are the experimental points reported in Ref. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003026#pcbi.1003026-Beemster1" target="_blank">[64]</a>. (B) Frequency distribution for cell length. Experimental data were taken from our laser microscope image of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003026#pcbi-1003026-g001" target="_blank">Fig. 1</a>. (C) Average cell length as a function of the distance from the quiescent centre; calculation from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003026#pcbi-1003026-g009" target="_blank">Fig. 9</a> after six days of growth. The red line is the experimental result reported in Ref. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003026#pcbi.1003026-Beemster1" target="_blank">[64]</a>. (D) Average cell proliferation velocity as a function of the distance from the quiescent centre; calculation from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003026#pcbi-1003026-g009" target="_blank">Fig. 9</a> after six days of growth. The red line is the experimental result reported in Ref. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003026#pcbi.1003026-Beemster1" target="_blank">[64]</a>.</p

Simplified scheme of the cell cycle.

<p>The four main phases and the expression of two key cyclins are indicated.</p

Variation of two-type cyclins concentrations and typical oscillations from the Lotka-Volterra model.

<p>Relative expression data of D-type cyclins (purple triangles) and B-type cyclins (green rhombuses) were taken from analysis of gene expression profiles using aphidicolin synchronization on Ref. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003026#pcbi.1003026-Menges2" target="_blank">[76]</a>, and are available on GENEVESTIGATOR web page. The oscillations from the Lotka-Volterra model of the inhibitor (blue dashed line) and the activator (red line) are also shown.</p

Histogram of the number of cell divisions obtained along the root when

<p><b>.</b> The potential profile is shown as red dots. Observe that there are no cell divisions beyond , meaning that the meristem has attained a stationary length.</p