A plausible mechanism for auxin patterning along the developing root

Abstract

Background: In plant roots, auxin is critical for patterning and morphogenesis. It regulates cell elongation and division, the development and maintenance of root apical meristems, and other processes. In Arabidopsis, auxin distribution along the central root axis has several maxima: in the root tip, in the basal meristem and at the shoot/root junction. The distal maximum in the root tip maintains the stem cell niche. Proximal maxima may trigger lateral or adventitious root initiation.

Results: We propose a reflected flow mechanism for the formation of the auxin maximum in the root apical meristem. The mechanism is based on auxin's known activation and inhibition of expressed PIN family auxin carriers at low and high auxin levels, respectively. Simulations showed that these regulatory interactions are sufficient for self-organization of the auxin distribution pattern along the central root axis under varying conditions. The mathematical model was extended with rules for discontinuous cell dynamics so that cell divisions were also governed by auxin, and by another morphogen Division Factor which combines the actions of cytokinin and ethylene on cell division in the root. The positional information specified by the gradients of these two morphogens is able to explain root patterning along the central root axis.

Conclusion: We present here a plausible mechanism for auxin patterning along the developing root, that may provide for self-organization of the distal auxin maximum when the reverse fountain has not yet been formed or has been disrupted. In addition, the proximal maxima are formed under the reflected flow mechanism in response to periods of increasing auxin flow from the growing shoot. These events may predetermine lateral root initiation in a rhyzotactic pattern. Another outcome of the reflected flow mechanism - the predominance of lateral or adventitious roots in different plant species - may be based on the different efficiencies with which auxin inhibits its own transport in different species, thereby distinguishing two main types of plant root architecture: taproot vs. fibrous.

Figure 1

Representation in the model the processes influencing the auxin distribution along the central root axis. a. Acropetal flow is considered in the model along the cell array on the central root axis (x axis). Arrows denote the processes that provide for auxin movements considered in the model. b. The summarized mechanism providing for regulation of PIN1 expression comprises the regulation of PIN1 protein synthesis and degradation depending on the auxin concentration.

Figure 2

The cell layouts in the 2D models of auxin distribution. a. The cell layout in the 2 D minimal model represented by two layer types - provascular (green) and epidermal (gray). b. The cell layout of the model described in [17]. c. The whole set of cell types considered in the models (a, 1 and 2) and (b, 1-5). Red unidirectional arrows in (c.) mark the directions of active auxin transport for each kind of cell. Black bidirectional arrows mark the auxin exchange by diffusion. Auxin flows in a.-b. are delineated by thick red arrows.

Figure 3

Mitotic activity in the root and its simulation. a. The scheme of root tip structure in Arabidopsis. The cells of different types marked by different colors (for details, see figure 1). b. Qualitative profile of mitotic activity in cells along the central root axis. Two maxima of mitotic activity are distinguished along the central root axis according to Dolan et al. (1993) [1] and Beemster and Baskin (2000) [27]. c. The model solution: auxin (red squares) and substance Y (blue circles) distributions regulate the rates of cell divisions in the root (gray columns). The dynamical characteristics (cell coordinates on the axis, auxin concentration, and division rates) in the model solutions reproduce root patterning, where the cells of different types are specifying around the distal auxin maximum. d. The plot of auxin-regulated Y degradation rate used in the model (Eq. (8)). (E) The plot of Y-regulated rates of cell division (first coefficient in Eq. (10)). QC is the quiescent center and RCI is the root cap initial.

Figure 4

The auxin distribution pattern reproduced by the model. a. Expression of DR5::GUS detects the auxin pattern in the root tip (adapted from Sabatini et al., 1999; [3]). b. The surface plot of DR5 activity in the root tip scanned from figure 2a by ImageJ program. The x axis corresponds to the central axis of the root; the root width extends along the y axis; and the z axis shows DR5 activity. c. The model solution (black line) agrees well with semi-quantitative data of auxin distribution along the central root axis, obtained from the surface plot at figure 2b (red line). d. The auxin distribution pattern in the stationary solution of the 2D minimal model. Blue arrowhead denotes the QC position.

Figure 5

Sensitivity of the auxin distribution pattern to parameter and initial data variations. a.-c. The 1D minimal model analysis to variations of parameters α (a.-b.) and K₀ (c.) that model changes in auxin flow from the shoot and treatment with auxin transport inhibitors, respectively. Oscillatory solutions of the model marked by dashed lines. b. When auxin flow from the shoot is too high, we observe unstable fluctuations of auxin concentration in the middle of the root. The curves correspond to unstable solutions calculated at equal time intervals. d.-f. The 1D extended model behavior under an increase in the auxin flow from the shoot when simulating the root growth. g.-j. Simulation of the experiment on QC laser ablation or root tip cut. g. Scheme of the in silico experiment on root tip cut. A qualitative correspondence of the model solutions to the auxin distribution pattern before and after the cut are shown. h.-j. Computer simulation of the changes in auxin distribution after the cut for the first seven cells. The curves are calculated for the provascular layer j = 4 and are numbered in the order the model solutions were obtained as the 2D minimal model approached the stationary state. In all plots, the x axis shows the cell number and the y axis, auxin concentration in concentration units (cu).