A recovery principle provides insight into auxin pattern control in the Arabidopsis root

Abstract

Regulated auxin patterning provides a key mechanism for controlling root growth and development. We have developed a data-driven mechanistic model using realistic root geometry and formulated a principle to theoretically investigate quantitative auxin pattern recovery following auxin transport perturbation. This principle reveals that auxin patterning is potentially controlled by multiple combinations of interlinked levels and localisation of influx and efflux carriers. We demonstrate that (1) when efflux carriers maintain polarity but change levels, maintaining the same auxin pattern requires non-uniform and polar distribution of influx carriers; (2) the emergence of the same auxin pattern, from different levels of influx carriers with the same nonpolar localisation, requires simultaneous modulation of efflux carrier level and polarity; and (3) multiple patterns of influx and efflux carriers for maintaining an auxin pattern do not have spatially proportional correlation. This reveals that auxin pattern formation requires coordination between influx and efflux carriers. We further show that the model makes various predictions that can be experimentally validated.

Figure 1. The model root with realistic cell geometry, a cytosolic space for each cell, a unique combined plasma membrane and cell wall entity for each cell, extracellular space, and auxin influx and efflux carrier localisation.

(a) A realistic root map showing the individual cells, based on confocal imaging. (b) Localisation of efflux (PIN3) and influx (AUX1) carriers at the combined plasma membrane and cell wall entity of selected cells, with extra-cellular space between the cell walls of adjacent cells. (S2 and S3: columella tier 2 and 3 cells. COL: columella, RC: root cap). The details of the data-driven mechanistic model are included in the Supplementary Methods.

Figure 2. Modelled auxin concentration patterning and relative auxin concentration trends above the initials for selected cell files.

(a) Auxin concentration colour map for the root and selected regions. (b) Relative auxin concentration trends in the first 20 cells above the initials in the epidermis, cortex, endodermis and pericycle cell files. (EZ: Elongation zone. QC: Quiescent Centre).

Figure 3. Auxin pattern recovery after 75% decrease in total wildtype PIN3,4,7 concentrations, using the recovery principle over 85 iterations.

(a) Progressive auxin percentage difference from wildtype in the whole root. Blue curve shows the maximum auxin percentage difference below wildtype in the root, at each iteration. Red curve shows the maximum auxin percentage difference above wildtype in the root, at each iteration. Green curve shows the maximum range of the percentage difference from wildtype within the root, calculated by adding the absolute values of the blue and red curves at each iteration. (b) Colour map images of the percentage difference from wildtype auxin concentrations in the root after the initial perturbation of 75% loss of PIN3,4,7, then after 2 recovery iterations, and at full recovery after 85 iterations. Symbol % is the percentage difference relative to corresponding wildtype value.

Figure 4. AUX1/LAX concentration patterning required for auxin pattern recovery after reducing total PIN3, 4 and 7 by 75%.

(a) AUX1/LAX colour map for recovery requires non-uniform and polar distribution of AUX1/LAX. (b) AUX1/LAX average cell face concentrations are ranked 1 to 4 for each cell, showing polar distribution of AUX1/LAX influx carriers. This is calculated by averaging the data in each cell face in (a) and by ranking them in terms of the average values. P: pericycle cell, V: vascular cell.

Figure 5. Comparison of auxin pattern recovery by uniform and non-uniform distribution of AUX1/LAX, for 6 different total PIN3, 4 and 7 concentrations set at 0%, 25%, 50%, 150%, 175% and 200% of wildtype.

(a) Maximum percentage difference of auxin concentration from WT after recovery by uniform (red bar, right y-axis) and non-uniform (blue bar, left y-axis) AUX1/LAX distribution, for each case. (b) Colour maps of percentage difference of auxin concentration from WT after recovery by uniform AUX1/LAX distribution, for each case. Symbol % is the percentage difference relative to corresponding wildtype value.

Figure 6. The polarity of PIN3,4,7, after wildtype auxin pattern recovery from a 50% gain in AUX1/LAX level, is different from PIN3,4,7 polarity in wildtype.

(a) Colour map of total PIN3,4,7 after recovery to wildtype auxin patterning. a1 shows an enlarged view of this map in selected epidermal and cortical cells. (b) Colour map of the ratio of PIN3,4,7 after auxin pattern recovery to wildtype PIN3,4,7. b1 shows enlarged views of this map in the epidermal and cortical cells, corresponding to the regions shown in a1. PIN3,4,7 have no polarity in the wildtype epidermal and cortical cell files (see Fig. 3 in the Supplementary Methods), however PIN3,4,7 polarity can be observed in these cells after recovery, in a1, where there is greater PIN3,4,7 concentrations at the apical cell faces. This is confirmed in b1 where the red/brown/yellow colours indicate a consistently larger percentage increase in PIN3,4,7 after recovery compared to wildtype at the apical faces of these cells. This result shows that, in these epidermal and cortical cells, the polarity of PIN3,4,7, after wildtype auxin pattern recovery from a 50% gain in AUX1/LAX level, is different from PIN3,4,7 polarity in wildtype. C: cortical cells. E: epidermal cells.

Figure 7. Recovery to the same target auxin pattern from a 15% gain in PIN3,4,7 and from a 30% gain in PIN3,4,7, shows that two very different combinations of interlinked PIN and AUX1/LAX can lead to the same auxin pattern.

(a) Auxin concentration colour map for the target auxin pattern created by a 50% loss in PIN3,4,7. (b) The percentage difference of target auxin pattern from the WT. (c) Total PIN and AUX1/LAX percentage comparison to WT for recovery from a 15% gain in PIN3,4,7, for a selected area of the root. (d) Total PIN and AUX1/LAX percentage comparison to WT for recovery from a 30% gain in PIN3,4,7, for the same selected area of the root. In (c,d), symbol % is the percentage difference relative to corresponding wildtype value.

Figure 8. The recovery principle reveals relationships between the influx and efflux carriers in establishing auxin patterning.

(a) Changes in level of the influx carriers require changes in both polarity and level of the efflux carriers and vice versa, for recovery. (b) The recovery principle makes it possible to search for influx and efflux carrier combinations that achieve a target auxin pattern.

Figure 9. Modelling predictions for the patterning of auxin biosynthesis rate.

EZ: elongation zone, TZ: transition zone, MZ: meristematic zone, QC: quiescent centre region.