Systems Biology Approach Pinpoints Minimum Requirements for Auxin Distribution during Fruit Opening

Abstract

The phytohormone auxin is implied in steering various developmental decisions during plant morphogenesis in a concentration-dependent manner. Auxin maxima have been shown to maintain meristematic activity, for example, of the root apical meristem, and position new sites of outgrowth, such as during lateral root initiation and phyllotaxis. More recently, it has been demonstrated that sites of auxin minima also provide positional information. In the developing Arabidopsis fruit, auxin minima are required for correct differentiation of the valve margin. It remains unclear, however, how this auxin minimum is generated and maintained. Here, we employ a systems biology approach to model auxin transport based on experimental observations. This allows us to determine the minimal requirements for its establishment. Our simulations reveal that two alternative processes-which we coin "flux-barrier" and "flux-passage"-are both able to generate an auxin minimum, but under different parameter settings. Both models are in principle able to yield similar auxin profiles but present qualitatively distinct patterns of auxin flux. The models were tested by tissue-specific inducible ablation, revealing that the auxin minimum in the fruit is most likely generated by a flux-passage process. Model predictions were further supported through 3D PIN localization imaging and implementing experimentally observed transporter localization. Through such an experimental-modeling cycle, we predict how the auxin minimum gradually matures during fruit development to ensure timely fruit opening and seed dispersal.

Keywords: auxin; fruit development; mathematical modeling; polar auxin transport; systems biology of patterning.

Figure 1

Modeling Auxin Transport in the Developing Arabidopsis Fruit. (A) Silique at stage 17b. (B) Dehiscence along the valve margin (VM) (stage 19). (C) Auxin-signaling minimum at the VM, shown by DR5:GFP expression. (D) Schematic transversal cross-section of the bilaterally symmetric ovary, with tissues indicated, also showing the internal septum that we do not simulate within this modeling framework. (E) Schematic of the cylindrical model layout of the external fruit tissues, visualizing the topological connectedness. (F) Zoomed-in portion of (E), displaying approximately one cell row. (G) Schematic of the model layout of the longitudinal fruit, laid out in 2D, indicating all modeled tissue types through color coding. Note that here only half of the fruit tissue is displayed, whereas simulations were always done on the full, cylindrically connected tissue. (H) Within the model, auxin transport across plasma membrane as well as diffusion in cytosol and apoplast (cell wall) at subcellular resolution are taken into account.

Figure 2

Minimal Requirements for Auxin Minimum at the VM. (A) Basic model, based on currently published transporter expression, predicts an auxin maximum, rather than minimum, in the VM; right inset shows details of minimum, by showing a magnified, one-cell-high portion of the left VM, including an outer adjacent valve cell and an inner adjacent replum cell. (B and C) Import-dependent model shows that when all tissues except the VM have augmented influx activity, the minimum does not form under reasonable auxin importer transporter rates; as seen through right inset of magnified VM (B). In contrast, the minimum is only established under very high transporter rates (background influx set at $P_{IAAH}$ = 5 μm/s; augmented influx at $P_{LAX1}$ = 100 μm/s) (C), with right inset showing corresponding VM minimum. (D) Export-dependent model reveals that the default rate of apolar efflux within the VM is sufficient to create an auxin minimum, as seen in detail in the right inset. (E) A combination of apolarly localized efflux transporters and VM-specific lack of influx transporters (combined model) strengthens the auxin minimum, as seen in detail in the right inset. (F and G) Both strengthening apolar exporters in the VM (blue line, export-dependent case) and apolar importers in the valve and replum (red line, import-dependent case) lead to a decrease in the ratio between the auxin concentration in the separation layer and in the bordering replum cell (F), as well as a decrease in the absolute auxin levels within the separation layer (G, solid lines). Auxin levels in the replum, however, increase with increasing transporter strength in the export-dependent model, but only marginally depend on the transporter strength in the import-dependent model (G, dashed lines). (H) Effect of those transporters on the total transversal fluxes crossing the VM (i.e., perpendicular to the VM). The x axes in (F–H) indicate the relative strength of either the VM-specific exporter (blue), or the augmented importer in the valve and replum (red), as a percentage of the default transport rates. (I) The fluxes crossing the VM transversally plotted against the VM minimum (as calculated in F), on a log-log scale. Details of parallel fluxes are shown in Supplemental Figure 2, and the description of average flux calculations is given in the Supplemental Information. Dashed-dotted lines indicate where the auxin level in the VM is equal to the surrounding tissue, i.e., below which an auxin minimum is formed; thin line indicates where the auxin level in the VM is 5% of the level in the surrounding tissue. Color bar indicates auxin concentrations in (A–E). Arrowheads in (A–C) indicate position of VM.

Figure 3

Detailed Analysis on Actual Transporter Localizations at Stage 17b (A)PIN3::PIN3-GFP. (B)PIN7::PIN7-GFP. (C)LAX1::LAX1-VENUS. (D)DR5::GFP. (E) Simulation using imaged transporter localization and levels at stage 17b and tissue size and layout of that stage presents minimum at VM and elevated levels in the replum, in agreement with the experimentally observed auxin-signaling pattern. (F–H) Detailed insets from (A–C), as indicated. (I and J) (I) Detailed image showing apolar PIN3 localization, with (J) showing further magnification of PIN3 localization within a VM region indicated by a white rectangle in (I). Arrowheads indicate the position of lateral PIN3-GFP in the VM. (K) Inset from (E), as indicated. (L) Magnified right portion of the VM, indicating in detail the auxin minimum in (K). See Supplemental Figure 4 for further supporting experimental images. Scale bars: 1 mm for (A–D); 200 μm for (F–H); 100 μm for (I). Color coding of auxin levels as indicated in Figure 2.

Figure 4

Interfering with the Auxin Fluxes through the VM. (A and B) Modeling predicts that if the auxin minimum is solely due to lack of augmented influx activity in the VM, then partly (A) or fully (B) ablating the VM only slightly changes the auxin levels in the valve and replum. (C and D) In contrast, if the auxin minimum were due to apolar PIN3 in the VM, then partly (C) or fully (D) ablating the VM strongly affects the auxin levels in those tissues. To better illustrate the impact, only the VMs flanking one of the repla are ablated. (E and G) DR5:GFP in control treatment (E) and after DEX-induced VM ablation (G). (F and H) Predicted auxin pattern using the full model for stage 17b (F) after VM ablation (H). Scale bar: 200 μm for (E and G). Color coding of auxin levels as indicated in Figure 2.

Figure 5

Temporal Development of the VM Minimum. (A and B) Auxin patterning as predicted by the model (A) and experimentally observed (B) during stage 17b. (C–E) (C) PIN3:PIN3-GFP (top); PIN7:PIN7-GFP (middle); LAX1:LAX1-VENUS (bottom) at stage 16, with (D and E) auxin patterns as predicted by the model (D) and experimentally observed (E). (F) Predicted auxin patterns using the full model for stage 15. (A, D, and F) illustrate the formation of the auxin minimum in the VM and build-up of auxin in the replum over time. Scale bars as indicated. Color coding of auxin levels as indicated in Figure 2.